JP2005024535A - Position estimation system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position estimation device capable of allowing precise positioning, even in the case where any of all the transmitters is affected by a multi-path, or even in the case where a problem exists on a propagation route from the transmitters to a receiver. <P>SOLUTION: This position estimation device wherein a radio wave transmitted from the plurality of transmitters 1 of which the positions are known is received in the receiver 2 of which the position is unknown, so as to estimate a receiver position is provided with a transmitter combination changer 3 for generating combinations of the transmitters of a prescribed minimum number or more out of all the receivable transmitters 1, a positioning solution calculator 6 for calculating a positioning solution, based on distances between the transmitters and the receiver provided by measuring propagation times from the transmitters 1 to the receiver 2, in every of the combinations, a predictor 8 for predicting the present position based on the position of the receiver measured in the past, and a positioning solution selector 9 for selecting the combination of the transmitters 1 by the transmitter combination changing means 3. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a position estimation apparatus, and more particularly to a position estimation apparatus used in a GPS positioning system and the like for estimating the position of a receiver position or a transmitter position using a radio wave propagation time or time difference or phase difference. It is.

  Conventionally, radio waves transmitted from multiple transmitters whose positions are known are received by a receiver whose position is unknown, and the receiver position is determined by measuring the propagation time from the transmitter to the receiver. A method has been proposed (see, for example, Non-Patent Document 1).

  As shown in Non-Patent Document 1, in this type of conventional method, a method of solving positioning equations such as the following equations (1) to (10) is common. Equation (1) is a positioning equation.

Here, δr represents a pseudorange error vector, A represents a direction cosine vector, and δu represents a receiver position error vector.
The pseudorange error vector is as shown in Equation (2).

In Equation (2), r _i (i = 1,..., N is a natural number and N ≧ 4; in the case of three-dimensional positioning) is a pseudo distance from the i-th transmitter position to the receiver position. Yes, obtained from the product of propagation time and speed of light.
In the equation (2), f _i (x ₀ , y ₀ , z ₀ , t ₀ ) (i = 1,..., N is a natural number, N ≧ 4; in the case of three-dimensional positioning) is an approximate distance. Yes, the positioning value (x ₀ , y ₀ , z ₀ ) of the previous receiver position and the receiver clock error t ₀ , the i-th transmitter position (x _i , y _i , z) that are known _i ) is calculated using equation (3). c is the speed of light.

  The direction cosine vector is as shown in Equation (4).

Each element A _{i, x} , A _{i, y} , A _{i, z} (i = 1,..., N, where N ≧ 4; in the case of three-dimensional positioning) of the direction cosine vector is It is as Formula (5), Formula (6), and Formula (7).

  The receiver position error vector is as shown in Equation (8).

  In equation (8), (x hat, y hat, z hat) is a positioning solution calculated, and t hat is a receiver clock error obtained as a secondary.

In positioning in 3D space,
If the number of transmitters that can be received is three or less, the equation (1) is indefinite and positioning is impossible.
If the number of transmitters that can be received is four, the solution of equation (1) can be obtained as in equation (9) and positioning can be performed.

  If the number of transmitters that can be received is five or more, the least squares solution of Equation (1) can be obtained as in Equation (10) and positioning can be performed.

In positioning in a two-dimensional space,
If the number of transmitters that can be received is two or less, the equation (1) becomes an indefinite solution and positioning is impossible.
If the number of transmitters that can be received is three, the solution of equation (1) can be obtained as in equation (9) and positioning can be performed.
If the number of transmitters that can be received is four or more, the least squares solution of equation (1) can be obtained as in equation (10) and positioning can be performed.

  If the number of transmitters that can be received is greater than the minimum number required for positioning (four for three-dimensional positioning, three for two-dimensional positioning), positioning is performed using the least square method shown in equation (10). As described above, the solution can be obtained. In addition to the method for obtaining the positioning solution using all the transmitters as in Non-Patent Document 1, the method for obtaining the positioning solution by appropriately selecting the transmitter. Are often used (see, for example, Patent Document 1).

In the conventional method disclosed in Patent Document 1, a positioning solution is obtained by combining any four receivable satellites from eight satellites (transmitters), and an error evaluation index for each positioning solution. Based on the integrated values of DOP and UERE, the error of each positioning solution is evaluated, and the positioning solution having the smallest integrated value is selected as the positioning result.
Here, DOP is an evaluation index of positioning accuracy depending on the arrangement of the satellites. For example, in the case of three-dimensional positioning, equation (11) is given by equation (12).

  URE is an error evaluation index corresponding to the value of SVAccuracy broadcast from the satellite as information such as the error of the internal clock of the satellite or the deviation of the orbit.

JP-A-6-59014 Edited by the Geodetic Society of Japan, “GPS-Precision Positioning System by Artificial Satellites” 3rd edition, first edition, November 15, 1989, p. 124-131

  Since the conventional method shown in the above Non-Patent Document 1 always performs positioning calculation using all transmitters, there is a transmitter that is affected by multipath in the transmitter, or on the propagation path. However, there is a problem that positioning accuracy deteriorates if there is a transmitter having a problem.

  In addition, another conventional method disclosed in Patent Document 1 obtains a positioning solution for each combination of any number of transmitters required for positioning from the number of redundantly prepared transmitters. Positioning error due to location, satellite internal clock error, orbital deviation, etc., and positioning error evaluation index caused by errors related to SVaccuracy information provided by the satellite itself is used as a transmitter selection criterion, and these errors cause problems. A combination that does not include the transmitter is selected, but there is a problem in that it is impossible to evaluate a case where the positioning accuracy is deteriorated due to the problems in the multipath and the propagation path.

  The present invention has been made to solve such a problem. One or a plurality of transmitters among all transmitters may be affected by multipath, or may be propagated from a transmitter to a receiver. An object of the present invention is to obtain a position estimation device capable of performing highly accurate positioning even when there is a problem on the route.

  This invention receives a plurality of radio waves transmitted from a plurality of transmitters whose positions are known by a receiver whose position is unknown, and is obtained by measuring a propagation time from the transmitter to the receiver. A position estimation device for estimating a receiver position based on a distance between a transmitter and a receiver, and among all receivable transmitters, a combination of a predetermined minimum number or more transmitters necessary for measuring a receiver position Based on the distance between the transmitter and the transmitter obtained by measuring the propagation time from the transmitter to the receiver for each transmitter combination by the transmitter combination changing means to be generated and the transmitter combination changing means, Positioning solution calculation means for calculating a positioning solution for the receiver position, prediction means for predicting the current receiver position from the position of the receiver measured in the past, the predicted position calculated by the prediction means, and the positioning Solution calculator In based on the prediction residual between the calculated the positioning solution, a position estimation device that includes a selection means for selecting a combination of the transmitter by the transmitter combination changing means.

  This invention receives a plurality of radio waves transmitted from a plurality of transmitters whose positions are known by a receiver whose position is unknown, and is obtained by measuring a propagation time from the transmitter to the receiver. A position estimation device for estimating a receiver position based on a distance between a transmitter and a receiver, and among all receivable transmitters, a combination of a predetermined minimum number or more transmitters necessary for measuring a receiver position Based on the distance between the transmitter and the transmitter obtained by measuring the propagation time from the transmitter to the receiver for each transmitter combination by the transmitter combination changing means to be generated and the transmitter combination changing means, A positioning solution calculating means for calculating a positioning solution of the receiver position, a predicting means for predicting a current receiver position from a position of the receiver measured in the past, a predicted position calculated by the predicting means, and the positioning Solution calculator Since the position estimation device includes a selection unit that selects a combination of the transmitters by the transmitter combination change unit based on a prediction residual with the positioning solution calculated in (1), Even when one or a plurality of transmitters are affected by multipath or when there is a problem on the propagation path from the transmitter to the receiver, it is possible to perform highly accurate positioning.

Embodiment 1 FIG.
1 is a block diagram showing a position estimation apparatus according to Embodiment 1 of the present invention. In the figure, 1 is a plurality of transmitters that emit radio waves into space, and 2 is a receiver that receives radio waves from the transmitter 1. 3 is a transmitter combination changer for changing the combination of the transmitters 1 for performing positioning, and 4 is a propagation time from the transmitter 1 to the receiver 2 combined by the combination changer 3, between the transmitters 1 and 2. 5 is a directional cosine vector calculator that calculates a direction cosine vector using position information of the transceivers 1 and 2, and 6 is a positioning solution calculated from the pseudo distance and the direction cosine vector. A least-squares positioning solution calculator 7, 7 is a positioning solution storage device that stores the positioning solution calculated by the least-squares positioning solution calculator 6, and 8 is a smoothing vector calculated by the smoother 10 that is input via the delay circuit 11. Of the receiver 2 A predictor 9 for calculating a prediction vector and a prediction error covariance matrix of the device, a prediction vector from the predictor 8 is input, a positioning solution is input from the positioning solution storage unit 7, and a positioning solution close to the predicted position is selected. A positioning solution selector 10 for calculating a smoothing vector and a smoothing error covariance matrix from the positioning solution input from the positioning solution selector 9 and the prediction vector and prediction error covariance matrix input from the predictor 8. A delay circuit 11 delays the smoothing vector and the smoothing error covariance matrix calculated by the smoothing unit 10 by one sampling time.

Next, the operation will be described.
First, the operation principle of the position estimation apparatus according to the first embodiment will be described. Here, it is assumed that a three-dimensional position is estimated.
From the propagation time between the transceivers 1 and 2 obtained by receiving the radio waves transmitted from the plurality of transmitters 1 whose positions are known by the receiver 2 whose position is unknown, the positioning equation of Equation (1) is obtained. The principle of positioning the position of the receiver 2 by solving is the same as the conventional technique described in Non-Patent Document 1 above.
A method for predicting the motion of the receiver 2 using past positioning results will be described.
A motion model of the receiver 2 is shown in Expression (13). Here, x _k under bar is a state vector representing the true values of the motion specifications of the receiver 2 at the sampling time t _k, the position vector equation (14) of the receiver 2, a velocity vector when the expression (15) The state vector of the receiver 2 is expressed by Expression (16). Here, the sampling time t _k (k = 1, 2,..., N) is a discrete time representing the timing at which positioning is performed, and is hereinafter referred to as time t _k .

Φ _k−1 is a transition matrix of the state vector from time t _k−1 to time t _k and is expressed by Expression (17). Also, _{w k} underscore is a driving noise vector at time _{t k, Γ 1 (k)} is the transformation matrix driving noise vector at time _{t k.} For example, if the truncation error term due to the assumption that the motion model of the receiver is constant-velocity linear motion is Γ ₁ (k−1) w _k−1 underbar, w _k underbar is equivalent to an acceleration vector, and Γ ₁ ( k-1) is expressed by Expression (18). T is a sampling interval, and I is a 3 × 3 unit matrix.

Further, when E is used as a symbol representing an average, w _k underbar is an average three-dimensional normal distribution white noise, which is expressed by Equation (19) and Equation (20). However, the 0 underbar is a zero vector, and Q _k is the driving noise covariance matrix at time t _k .

An observation model of the position of the receiver 2 is expressed by Equation (21). Here, u _k underscores the positioning solution selected by the positioning solution selector 9, H is the observation matrix, represented by the formula (22).
Further, v _k underscore is observed noise vector of the distance of the receiver 2 and the selected transmitter 1 at time t _k, expressed by equation (23). The observation noise vector is assumed to follow a three-dimensional normal distribution white noise with an average of 0 underbar, and is represented by Equation (24) and Equation (25). R _k is an observation error covariance matrix of the distance between the transmitter 1 and the receiver 2 at time t _k . The whole positioning solution used for tracking of the receiver 2 up to time t _k is represented by U _k and expressed by Expression (26).

Further, Γ ₂ (k) is a conversion matrix of the observed noise vector from the distance between the N transceivers 1 and 2 to the three-dimensional position, and is represented by Expression (27) and Expression (28).

Here, h _i (x _k underbar) is the distance between the i-th transmitter 1 and the receiver 2 and is represented by Expression (29). In addition, the i-th element of the matrix B is expressed by Expression (30) to Expression (32). x _k underscore (-) is the predicted vector of receiver position at time t _k, the calculation method is described in the next section.

Next, will be described a method of calculating the predicted vector when positioning solution U _k-1 to time t _k-1 is obtained. When the prediction vector of the receiver state vector x _k underbar at time t _k is (x _k underbar) hat (−) and the prediction error covariance matrix is P _k (−), the conditional average vector and conditional It is defined by a dispersion matrix and is expressed by Expression (33) and Expression (34). Here, (x _k-1 underbar) hat (+) and P _k-1 (+) are a smoothing vector and a smoothing error covariance matrix at time t _k−1 , respectively. These calculation methods will be described next.

  The method for predicting the motion of the receiver 2 using the past positioning results has been described above.

It will now be described a method of selecting a plurality of positioning solution at time t _k which is stored in the positioning solution storage unit 7. The choice of positioning solution, equation (34) represented by the current time of the receiver 2 based on historical positioning information position prediction vector u _k underscore - utilizing ().

That, m th the positioning solution _{u k} at time _{t k} which is stored in the positioning solution storage unit _{7, m} underscore (m = 1, 2, · · ·, M) When the prediction residuals in equation (36) The positioning solution u _k underbar that minimizes the d _{k, m} underbar is determined to have the highest positioning accuracy and is selected. The predicted residual d _{k, m} underbar is a residual between the predicted position of the receiver 2 and the measurement position. If one or a plurality of transmitters 1 in the combination of the transmitters 1 selected by the transmitter combination changer 3 are affected by a multipath, there is a problem on the propagation path. If there is a transmitter, the prediction residual becomes a large value. Therefore, if a combination of the transmitters 1 having the smallest prediction residual is selected, all transmitters are normal and there is no problem on the propagation path. A combination can be determined, and the position of the receiver 2 can be estimated with higher accuracy.

  The positioning solution selection method has been described above.

Next, a method for calculating a smooth vector will be described. The gain matrix K _k , the smooth vector (x _k underbar) hat (+), and the smooth error covariance matrix P _k (+) are given by Expressions (37) to (39) according to the usual Kalman filter theory. Here, R _k is an observation error covariance matrix of the distance between the transmitter 1 and the receiver 2 at time t _k represented by Expression (25). The smooth vector calculation method has been described above.

  The operation principle of the position estimation apparatus according to Embodiment 1 has been described above.

Next, a specific operation of the position estimation apparatus according to the first embodiment will be described with reference to FIG.
The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2.
The receiver 2 discriminates and receives signals from each transmitter 1. The transmitter combination changer 3 selects an appropriate combination of transmitters 1 from among all the receivable transmitters 1 by a number equal to or more than a predetermined minimum number necessary for positioning and equal to or less than the total number of transmitters. The pseudo distance calculator 4 calculates a pseudo distance r _i (i = 1, 2,..., N) from the propagation delay time of the signal of the transmitter 1 of the selected combination.

The direction cosine vector calculator 5 calculates the direction cosine vector A from preset position information of the transmitter 1 according to the equation (4). The least squares positioning solution calculator 6 substitutes the pseudo distance r _i (i = 1, 2,..., N) and the direction cosine vector A into the equation (10) to obtain the least squares positioning solution uk _{, m} underbar. Is calculated. The combination of the transmitters 1 is changed by the transmitter combination changer 3, and the above positioning calculation and distance residual calculation are repeated a predetermined M times, and the positioning solution uk _{, m} underbar (m = 1, 2,... ., M) are stored in the positioning solution storage unit 7 respectively.

In the predictor 8, the smoothing vector (x _k−1 underbar) hat (+) one sampling before and the smoothing error covariance matrix P _k−1 (+) are input via the delay circuit 11, and the equations (33) to (33) in accordance with equation (35), the predicted vector _{(x k} underscore) hat (-), the prediction error covariance matrix _{P k-1} (-), the position prediction vector _{(u k} underscore) (-) is calculated respectively. In positioning solution selector 9, the position prediction vector from the predictor 8 _{(u k} underscore) (-) type and positioning solution stored in the positioning solution storage unit 7 _{u k, m} underscore (m = 1, 2, · .., M), select the positioning solution u _k underbar of the combination of the transmitters 1 having the smallest predicted residual d _{k, m} represented by the equation (36) to obtain the final positioning solution. .

The smoother 10 uses the positioning solution u _k underbar selected by the positioning solution selector, the prediction vector (x _k underbar) hat (−) and the prediction error covariance matrix P _k (−) calculated by the predictor 8. A smooth vector (x _k underbar) hat (+) and a smooth error covariance matrix P _k (+) are calculated.

  As described above, since the position estimation apparatus according to the present embodiment selects the combination of the transmitters 1 having the smallest prediction residual, it is more reliable than the conventional method, and all transmitters are normal. It is possible to estimate the position of the receiver by selecting a combination of transmitters considered to be no problem on the propagation path.

Embodiment 2. FIG.
FIG. 2 is a block diagram showing a position estimation apparatus according to the second embodiment. In the figure, reference numerals 1 to 8, 10 and 11 that are the same as those in FIG. 1 indicate the same or corresponding parts as in the first embodiment. The description is omitted.

  12 is a prediction residual probability density calculator for inputting a smoothing error covariance matrix calculated by the smoother 10 through a delay circuit and calculates a probability density function of a prediction residual of the positioning solution; 13 is a prediction from the predictor 8; A vector, a positioning solution from the positioning solution storage unit 7, and a probability density function of the prediction residual of the positioning solution from the prediction residual probability density calculator 12 are input, and the positioning is performed from the probability density of the prediction residual of each positioning solution. A gate determiner that eliminates an unsuitable positioning solution, and 14 inputs a positioning solution that is not excluded by the gate determiner 13 and a probability density function of a prediction residual of the positioning solution calculated by the prediction residual probability density calculator 12. And a positioning solution reliability calculator that calculates the reliability of the positioning solution.

Next, the operation will be described.
First, the operation principle of the position estimation apparatus according to the second embodiment will be described. Here, it is assumed that a three-dimensional position is estimated.
By solving the positioning equation (1) from the propagation time between the transmitters and receivers obtained by receiving the radio waves transmitted from the plurality of transmitters 1 whose positions are known by the receiver 2 whose position is unknown The principle of positioning the receiver position is the same as in Non-Patent Document 1 in the prior art.

  Further, the method for predicting the movement of the positioning object using the past positioning result is the same as in the first embodiment.

  Next, a method for eliminating positioning solutions that are not suitable for positioning will be described. In the first embodiment, only the positioning solution with the smallest prediction residual is selected and the position is estimated. However, the magnitude of the prediction residual is determined by the transmitter 1 and the reception in addition to the influence of sensor failure such as multipath. It is also affected by the geometrical relationship of machine 2. There is a possibility that a higher accuracy can be obtained by using a positioning solution that has no sensor malfunction and has a large prediction residual only due to the geometrical arrangement relationship of the transceiver. Therefore, in consideration of the influence of the geometric arrangement relationship of the transceiver, only the positioning solution affected by the sensor failure is excluded.

The predicted probability distribution P [u _{k, m} underbar | U _k-1 ] of the positioning solution obtained from the past positioning information U _k-1 is represented by a conditional probability density function shown in Expression (40). That is, positioning solution of the formula (35) in given position prediction vector _{u k} underscore (-) as the average, 3-dimensional normal distribution _g 3 to covariance matrix _{S k} given by Equation (41) _{(u k ,} M underbar; u _k (−), S _k ). The second term on the right side of the probability density function equation (41) is a term that takes into account the geometrical arrangement relationship of the transceiver. Then, a positioning solution that satisfies the equation (42) is used for positioning, and positioning solutions that do not satisfy the equation (42) are excluded. Here, q is a parameter for determining the correlation range with the target, and is calculated by a χ square distribution with 3 degrees of freedom.

Next, for all positioning solutions satisfying the equation (42) (for convenience, the total number is M), the probability density r _{k, m} of the positioning solution is calculated according to the equation (43), and this is normalized. The reliability β _{k, m} of the positioning solution is calculated from (44). Then, according to equation (45), an average value uk underbar _obtained by weighting the positioning solution with this reliability is set as the estimated position of the receiver 2.

Method for calculating the smoothed vector using the average value u _k underscore weighted the positioning solution in reliability is the same as the first embodiment. Note that the position vector of the smooth vector may be the estimated position of the receiver 2.
The operation principle of the position estimation apparatus according to the second embodiment has been described above.

Next, a specific operation of the position estimation apparatus according to the second embodiment will be described with reference to FIG.
The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The receiver 2 discriminates and receives signals from each transmitter 1. The transmitter combination changer 3 selects an appropriate combination of transmitters 1 from among all the receivable transmitters 1 by a number equal to or more than a predetermined minimum number necessary for positioning and equal to or less than the total number of transmitters. The pseudo distance calculator 4 calculates a pseudo distance r _i (i = 1, 2,..., N) from the propagation delay time of the signal of the transmitter 1 of the selected combination.

The direction cosine vector calculator 5 calculates the direction cosine vector A from preset position information of the transmitter according to the equation (4). The least square positioning solution calculator 6 substitutes the pseudo distance r _i (i = 1, 2,..., N) and the direction cosine vector A into the equation (10) to obtain the least square positioning solution u _{k, m} underbar. Is calculated. The combination of the transmitters 1 is changed by the transmitter combination changer 3, and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution u _{k, m} underbar (m = 1, 2,..., M) is stored in the positioning solution storage unit 7 respectively.

In the predictor 8, the smoothing vector ((x _k−1 underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equation (33) ) (predicted according 35) vector _{((x k} underscore) to formula hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{(u k} underscore) (-) is calculated respectively.

The prediction residual probability density calculator 12 receives the prediction error covariance matrix P _k (−) from the predictor 8, and the observation error covariance matrix of the distance between the transmitter and the receiver set in advance. Then, the covariance matrix S _k of the predicted probability density function P [u _{k, m} underbar | U _k−1 ] of the positioning solution is calculated according to the equations (27) and (41). In the gate determiner 13, predictor 8 from the position prediction vector u _k underscore (-) to enter the covariance matrix S _k from the prediction residual probability density calculator 12, positioning solution stored in the positioning solution storage vessel 7 From u _{k, m} underbars (m = 1, 2,..., M), those satisfying the equation (42) are selected, and those not satisfying are excluded.

In positioning solution reliability calculator 14, predictor 8 position prediction vector is calculated in u _k underscore (-) and the covariance matrix S _k calculated by the prediction residual probability density calculator 12 via the gate determiner 13 The reliability β _{k, m} of the positioning solution u _{k and m} underbar (m = 1, 2,..., M) that are input and satisfy Equation (42) is calculated according to Equation (44), and this reliability in calculating the mean value u _k underscore weighted the positioning solution according to the equation (45).

In the smoother 10, the positioning solution u _k underbar calculated by the positioning solution reliability calculator 14, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( −) Is used to calculate a smooth vector ((x _k underbar) hat) (+) and a smooth error covariance matrix P _k (+).

  As described above, the present embodiment is affected by the positioning solution in which the positioning error is increased only by the geometrical arrangement relationship of the transceivers 1 and 2 using the predicted probability distribution of the positioning solution and the sensor failure. Since the position of the receiver 2 is estimated using all of the remaining positioning solutions excluding only the latter, the position of the receiver 2 is estimated with higher accuracy than in the second embodiment. There is a high possibility that Further, since the weighted average value of the positioning solution based on the reliability calculated using the prediction probability distribution is used as the estimation result, the adverse effect of the positioning solution with low reliability can be reduced.

Embodiment 3 FIG.
FIG. 3 is a block diagram showing a position estimation apparatus according to the third embodiment. In the figure, reference numerals 1 to 7 that are the same as those in FIG. .

  15 is a distance residual memory for storing the distance residual calculated by the least squares positioning solution calculator 6, 13 is a positioning solution input from the positioning solution storage 7, and a distance residual is input from the distance residual storage 15. A gate determination unit that eliminates a positioning solution that is not suitable for positioning from the probability density of the distance residual of each positioning solution, and 14 inputs a positioning solution that is not excluded by the gate determination unit 13 and calculates the reliability of the positioning solution. It is a positioning solution reliability calculator.

Next, the operation will be described.
First, the operation principle of the position estimation apparatus according to the third embodiment will be described. Here, it is assumed that a three-dimensional position is estimated. By solving the positioning equation (1) from the propagation time between the transmitters and receivers obtained by receiving the radio waves transmitted from the plurality of transmitters 1 whose positions are known by the receiver 2 whose position is unknown The principle of positioning the receiver position is the same as the conventional method 1 in the prior art.

  Next, a method for eliminating positioning solutions that are not suitable for positioning will be described. In the first embodiment, the accuracy of the positioning solution is determined based on the size of the predicted residual. However, when the accuracy of the positioning solution is deteriorated due to a sensor failure such as multipath, the equation (10 ), The distance residual obtained when calculating the positioning solution is also considered to be large. Therefore, in the third embodiment, a positioning solution that is not suitable for positioning is determined by using the distance residual.

That is, assuming that the probability distribution of the distance residual is a one-dimensional normal distribution with an average of 0 and a variance μ ² , the pseudo distance r _i obtained for each positioning solution represented by the equation (46) and the equation (10) A positioning solution in which the square norm ρ _m ² of the distance residual, which is a vector of the difference between the positioning solutions f _i (x hat, y hat, z hat, t hat) obtained by iterative calculation, satisfies Equation (47) is determined. The positioning solution that is not satisfied is excluded (m is the combination number of the transmitter 1). Here, w is a parameter for determining the correlation range with the target, and is calculated by a χ square distribution with 3 degrees of freedom.

Next, the probability density r ′ _{k, m} of the positioning solution is calculated according to the equation (48) and normalized for all the positioning solutions satisfying the equation (47) (for convenience, the total number is M). The reliability β ′ _{k, m} of the positioning solution is calculated from the equation (49). Then, according to the equation (50), the average value uk underbar _obtained by weighting the positioning solution with this reliability is set as the estimated position of the receiver 2.

Method for calculating the smoothed vector using the average value u _k underscore weighted the positioning solution in reliability is the same as the first embodiment.
The operation principle of the position estimation apparatus according to the third embodiment has been described above.

  Next, a specific operation of the position estimation apparatus according to the third embodiment will be described with reference to FIG. The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The receiver 2 discriminates and receives signals from each transmitter 1. The transmitter combination changer 3 selects an appropriate combination of transmitters 1 from among all the receivable transmitters 1 by a number equal to or more than a predetermined minimum number necessary for positioning and equal to or less than the total number of transmitters. The pseudo distance calculator 4 calculates the pseudo distance from the propagation delay time of the signal of the transmitter 1 of the selected combination.

The direction cosine vector calculator 5 calculates the direction cosine vector A from the preset position information of the transmitter 1 according to the equation (47). The least squares positioning solution calculator 6 substitutes the pseudo distance r _i (i = 1, 2,..., N) and the direction cosine vector A into the equation (10) to obtain the least squares positioning solution uk _{, m} underbar. Is calculated. The combination of the transmitters 1 is changed by the transmitter combination changer 3, and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution uk _{, m} underbar (m = 1, 2,..., M) is stored in the positioning solution storage unit 7 respectively.

The distance residual storage unit 15 inputs the pseudo distance r _i and the positioning solution f _i (x hat, y hat, z hat, t hat) from the least square positioning solution calculator 6, and the distance remaining according to the equation (46). The square norm ρ _m ² of the difference is calculated and stored. In the gate determination unit 13, the distance norm ρ _m ^{2 of} the distance residual input from the distance residual storage unit 15 and the variance μ ^{2 of} the preset probability distribution of the distance residual are stored in the positioning solution storage unit 7. Among the stored positioning solutions uk _{, m} underbars (m = 1, 2,..., M), those satisfying the equation (47) are selected, and those not satisfying are excluded.

The positioning solution reliability calculator 14 inputs the square norm ρ _m ² of the distance residual and the variance μ ² of the preset probability distribution of the distance residual through the gate determiner 13, and the equation (47) for all positioning solution that satisfies the reliability beta _{k, m} of the positioning solution, as well as calculated according to formula (48) to (49), receiving an average value u _k underscore weighted the positioning solution in this confidence The estimated position of the machine 2 is calculated according to the equation (50).

  As described above, the present embodiment uses the probability distribution of the distance residual of the positioning solution to determine the positioning solution affected by the malfunction, and uses all of the remaining positioning solutions excluding only the latter. Since the position of the receiver 2 is estimated, it is more reliable than the conventional method, and the receiver 1 is selected by selecting a combination of the transmitters 1 in which all the transmitters 1 are normal and considered to have no problem on the propagation path. The position of 2 can be estimated.

Embodiment 4 FIG.
In the first embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured. In this embodiment, the radio wave from the transmitter 1 whose position is unknown is received by a plurality of reception positions whose positions are known. An application example in which the present invention is applied to a method of measuring the propagation time from the transmitter 1 to the receiver 2 and measuring the position of the transmitter by receiving by the transmitter 2 will be described.

  FIG. 4 is a block diagram showing a position estimation apparatus according to the fourth embodiment. In the figure, the same reference numerals 1, 2, 4 to 11 as those in FIG. 1 denote the same or corresponding parts as those in the first embodiment. Description is omitted.

  Reference numeral 16 denotes a receiver combination changer that changes the combination of the receivers 2 for positioning.

Next, a specific operation of the position estimation apparatus according to the fourth embodiment will be described with reference to FIG. The radio waves emitted from the transmitter 1 are received by discriminating signals from the respective transmitters 1 by the plurality of receivers 2 after the propagation times of the respective propagation paths. The receiver combination changer 16 selects an appropriate combination of the receivers 2 from among all of the receivers 2 that can receive signals, by a number that is not less than a predetermined minimum number required for positioning and not more than the total number of transmitters. The pseudo distance calculator 4 calculates a pseudo distance r _i (i = 1, 2,..., N) from the propagation delay time of the signal of the receiver 2 of the selected combination.

The direction cosine vector calculator 5 calculates the direction cosine vector A from preset position information of the receiver according to the equation (4). The least square positioning solution calculator 6 substitutes the pseudo distance r _i (i = 1, 2,..., N) and the direction cosine vector A into the equation (10) to obtain the least square positioning solution u _{k, m} underbar. Is calculated. The combination of the receivers 2 is changed by the receiver combination changer 16, and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution uk _{, m} underbar (m = 1, 2,..., M) is stored in the positioning solution storage unit 7 respectively.

In the predictor 8, the smoothing vector ((x _k−1 underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equation (33) ) (predicted according 35) vector _{((x k} underscore) to formula hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{(u k} underscore) (-) is calculated respectively. In positioning solution selector 9, the position prediction vector from the predictor 8 _{(u k} underscore) (-) type and positioning solution stored in the positioning solution storage unit 7 _{u k, m} underscore (m = 1, 2, · .., M), the positioning solution u _k underbar of the combination of the receivers with the smallest prediction residual d _{k, m} represented by the equation (36) is selected as the final positioning solution.

The smoother 10, and the positioning solution u _k underscore selected in positioning solution selector, the prediction vector calculated by the predictor 8 ((x _k underscore) hat) and (- -) and the prediction error covariance matrix P _{k ()} The smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k (+) are calculated.

  As described above, the radio waves from the transmitter 1 whose position is unknown are received by the plurality of receivers 2 whose positions are known, and the propagation time from the transmitter 1 to the receiver 2 is measured and the transmitter is measured. Even if the present invention is applied to a method for measuring the position, the position of the transmitter 1 can be measured with higher accuracy as in the first embodiment.

Embodiment 5 FIG.
In the second embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured and received. Although the present invention is an application example to a method for positioning a machine position, the present invention receives radio waves from a transmitter 1 whose position is unknown by a plurality of receivers 2 whose positions are known. Since this method can also be applied to a method of measuring the propagation time to the receiver 2 and positioning the transmitter position, in this embodiment, the application example will be described.

  FIG. 5 is a block diagram showing a position estimation apparatus according to the fifth embodiment. In the figure, reference numerals 1, 2, 4 to 8, and 10 to 14, which are the same as those in FIG. 1, are the same as or equivalent to those in the second embodiment. Will not be described.

  Reference numeral 16 denotes a receiver combination changer that changes the combination of the receivers 2 for positioning.

Next, a specific operation of the position estimation apparatus according to the fifth embodiment will be described with reference to FIG. The radio waves emitted from the transmitter 1 are received by discriminating signals from the respective transmitters by the plurality of receivers 2 after the propagation times of the respective propagation paths. The receiver combination changer 16 selects an appropriate combination of the receivers 2 from among all the receivers 2 that can receive the signal, by a number that is not less than a predetermined minimum number required for positioning and not more than the total number of receivers. The pseudo distance calculator 4 calculates a pseudo distance r _i (i = 1, 2,..., N) from the propagation delay time of the signal of the transmitter 1 of the selected combination.

The direction cosine vector calculator 5 calculates the direction cosine vector A from preset position information of the transmitter according to the equation (4). The least square positioning solution calculator 6 substitutes the pseudo distance r _i (i = 1, 2,..., N) and the direction cosine vector A into the equation (10) to obtain the least square positioning solution u _{k, m} underbar. Is calculated. The combination of the receivers 2 is changed by the receiver combination changer 16, and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution uk _{, m} underbar (m = 1, 2,..., M) is stored in the positioning solution storage unit 7 respectively.

In the predictor 8, the smoothing vector ((x _k−1 underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equation (33) ) (predicted according 35) vector _{((x k} underscore) to formula hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{u k} underscore (-) is calculated respectively.

The prediction residual probability density calculator 12 receives the prediction error covariance matrix P _k (−) from the predictor 8 and the observation error covariance matrix of the distance between the transmitter 1 and the receiver 2 set in advance. Then, the covariance matrix S _k of the predicted probability density function P [u _{k, m} underbar | U _k−1 ] of the positioning solution is calculated according to the equations (27) and (41). In the gate determiner 13, predictor 8 from the position prediction vector u _k underscore (-) to enter the covariance matrix S _k from the prediction residual probability density calculator 12, positioning solution stored in the positioning solution storage vessel 7 From u _{k, m} underbars (m = 1, 2,..., M), those satisfying the equation (42) are selected, and those not satisfying are excluded.

In positioning solution reliability calculator 14, predictor 8 position prediction vector is calculated in u _k underscore (-) and the covariance matrix S _k calculated by the prediction residual probability density calculator 12 via the gate determiner 13 The reliability β _{k, m} of the positioning solution u _{k, m} underbar (m = 1, 2,..., M) that is input and satisfies equation (42) is calculated according to equation (44), and this reliability in calculating the mean value u _k underscore weighted the positioning solution according to the equation (45).

In the smoother 10, the positioning solution u _k underbar calculated by the positioning solution reliability calculator 14, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( −) Is used to calculate a smooth vector ((x _k underbar) hat) (+) and a smooth error covariance matrix P _k (+).

  As described above, the radio waves from the transmitter 1 whose position is unknown are received by the plurality of receivers 2 whose positions are known, and the propagation time from the transmitter 1 to the receiver 2 is measured and transmitted. Even if the present invention is applied to the method of positioning the machine position, the position of the transmitter 1 can be measured with higher accuracy as in the second embodiment.

Embodiment 6 FIG.
In Embodiment 3, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured and received. Although the present invention is an application example to a method for positioning a machine position, the present invention receives radio waves from a transmitter 1 whose position is unknown by a plurality of receivers 2 whose positions are known. Since this method can also be applied to a method of measuring the propagation time to the receiver 2 and positioning the transmitter position, in this embodiment, the application example will be described.

  6 is a block diagram showing a position estimation apparatus according to the sixth embodiment. In the figure, reference numerals 1, 2, 4 to 7, and 13 to 15, which are the same as those in FIG. 1, are the same as or equivalent to those in the third embodiment. Will not be described.

  Reference numeral 16 denotes a receiver combination changer that changes the combination of the receivers 2 for positioning.

Next, a specific operation of the position estimation apparatus according to the sixth embodiment will be described with reference to FIG. The radio waves emitted from the transmitter 1 are received by discriminating signals from the respective transmitters by the plurality of receivers 2 after the propagation times of the respective propagation paths. The receiver combination changer 16 selects an appropriate combination of the receivers 2 from among all the receivers 2 that can receive the signal, by a number that is not less than a predetermined minimum number required for positioning and not more than the total number of receivers. The pseudo distance calculator 4 calculates a pseudo distance r _i (i = 1, 2,..., N) from the propagation delay time of the signal of the transmitter 1 of the selected combination.

The direction cosine vector calculator 5 calculates the direction cosine vector A from the transmitter position information set in advance according to the equation (47). The least square positioning solution calculator 6 substitutes the pseudo distance r _i (i = 1, 2,..., N) and the direction cosine vector A into the equation (10) to obtain the least square positioning solution u _{k, m} underbar. Is calculated. The combination of receivers is changed by the receiver combination changer 16, and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution uk _{, m} underbar (m = 1, 2,..., M ) Are stored in the positioning solution storage unit 7 respectively.

The distance residual storage unit 15 inputs the pseudo distance r _i and the positioning solution f _i (x hat, y hat, z hat, t hat) from the least square positioning solution calculator 6, and the distance remaining according to the equation (46). The square norm ρ _m ² of the difference is calculated and stored. In the gate determination unit 13, the distance norm ρ _m ^{2 of} the distance residual input from the distance residual storage unit 15 and the variance μ ^{2 of} the preset probability distribution of the distance residual are stored in the positioning solution storage unit 7. From the stored positioning solutions uk _{, m} underbars (m = 1, 2,..., M), those satisfying the equation (47) are selected, and those not satisfying are excluded.

The positioning solution reliability calculator 14 inputs the square norm ρ _m ² of the distance residual and the variance μ ² of the preset probability distribution of the distance residual through the gate determiner 13, and the equation (47) for all positioning solution that satisfies the reliability beta _{k, m} of the positioning solution, as well as calculated according to formula (48) to (49), receiving an average value u _k underscore weighted the positioning solution in this confidence The estimated position of the aircraft is calculated according to the equation (50).

  As described above, the radio waves from the transmitter 1 whose position is unknown are received by the plurality of receivers 2 whose positions are known, and the propagation time from the transmitter 1 to the receiver 2 is measured and transmitted. Even if the present invention is applied to the method of positioning the machine position, the position of the transmitter can be measured with higher accuracy as in the third embodiment.

Embodiment 7 FIG.
In the first embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured and received. The present invention is applied to a positioning system that uses radio wave propagation time in a system for positioning the machine position. However, the present invention is different in radio wave propagation time difference or phase difference from a plurality of transmitters 1 to receivers 2. In this embodiment, the application example will be described.

  FIG. 7 is a block diagram showing a position estimation apparatus according to the seventh embodiment. In the figure, reference numerals 1 to 3 and 5 to 11 which are the same as those in FIG. 1 indicate the same or corresponding parts as those in the first embodiment. Description is omitted.

  Reference numeral 17 denotes a pseudo distance difference calculator that calculates a pseudo distance difference between the transmitter and the receiver based on a propagation time difference or a phase difference of the radio wave from the transmitter to the receiver combined by the transmitter combination changer 3.

  Next, a positioning method using propagation time differences and phase differences of radio waves from the plurality of transmitters 1 to the receiver 2 will be described. The positioning calculation uses equation (51) instead of equation (10).

  However, δu, A, and δr in Expression (51) are Expression (52), Expression (53), and Expression (54), respectively.

Δr _{i, j in} equation (53) (i, j = 1,..., N is a natural number, and N ≧ 4; in the case of three-dimensional positioning), from i-th transmitter 1 to receiver 2 This is the difference between the distance and the distance from the jth transmitter to the receiver. In the case of positioning based on the propagation time difference, it is obtained from the product of the propagation time difference and the speed of light. In the case of positioning using the phase difference of radio waves, it is obtained from the product of the phase difference and the wavelength of radio waves.

Δf _{i, j} (x ₀ , y ₀ , z ₀ ) in Expression (53) and Expression (54) is the distance from the i th transmitter position to the receiver position and from the j th transmitter position to the receiver position. And the previous positioning value (x ₀ , y ₀ , z ₀ ) obtained by iterative calculation and the known i-th transmitter position (x _i , y _i , z _i ) From the same known j-th transmitter position (x _j , y _j , z _j ), calculation is performed using equation (55).

Next, a specific operation of the position estimation apparatus according to the seventh embodiment will be described with reference to FIG. The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter to the receiver. The receiver 2 discriminates and receives signals from each transmitter. The transmitter combination changer 3 selects an appropriate transmitter combination from among all the receivable transmitters by a number equal to or greater than a predetermined minimum number necessary for positioning and equal to or less than the total number of transmitters. The pseudorange calculator 17 calculates a pseudorange difference r _{i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference between the signals of the two transmitters in the selected combination. .

The direction cosine vector calculator 5 calculates the direction cosine vector A from the transmitter position information set in advance according to the equation (54). The least square positioning solution calculator 6 substitutes the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) and the direction cosine vector A into the equation (51) to obtain the least square positioning solution. u Calculate the _{k, m} underbar. The transmitter combination is changed by the transmitter combination changer 3 and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution u _{k, m} underbar (m = 1, 2,..., M ) Are stored in the positioning solution storage unit 7 respectively.

In the predictor 8, the smoothing vector ((x _k−1 underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equation (33) ) To Expression (35), a prediction vector ((x _k underbar) hat) (−), a prediction error covariance matrix P _k (−), and a position prediction vector u _k (−) are calculated. In positioning solution selector 9, the predictor 8 from the position prediction vector _{u k} underscore (-) is input, positioning solution stored in the positioning solution storage unit 7 _{u k, m} underscore (m = 1, 2, · · · , M), the positioning solution u _k underbar of the transmitter combination having the smallest predicted residual d _{k, m} represented by the equation (36) is selected as the final positioning solution.

The smoother 10, and the positioning solution u _k underscore selected in positioning solution selector, the prediction vector calculated by the predictor 8 ((x _k underscore) hat) and (- -) and the prediction error covariance matrix P _{k ()} The smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k (+) are calculated.

  As described above, the radio wave transmitted from the plurality of transmitters 1 whose positions are known is received by the receiver 2 whose position is unknown, and the propagation time difference between the signals of each transmitter at the receiver position. Alternatively, even if the present invention is applied to a method of measuring the phase difference and measuring the receiver position, the position of the receiver 2 can be determined with higher accuracy as in the first embodiment.

Embodiment 8 FIG.
In the second embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured and received. The present invention is applied to a positioning system that uses radio wave propagation time in a system for positioning the machine position. However, the present invention is different in radio wave propagation time difference or phase difference from a plurality of transmitters 1 to receivers 2. In this embodiment, the application example will be described.

  FIG. 8 is a block diagram showing a position estimation apparatus according to the eighth embodiment. In the figure, reference numerals 1-3, 5-8, and 10-14 that are the same as those in FIG. 2 are the same as or equivalent to those in the second embodiment. Will not be described.

  Reference numeral 17 denotes a pseudo distance difference calculator that calculates a pseudo distance difference between the transmitter and the receiver based on a propagation time difference or phase difference of radio waves from the transmitter 1 to the receiver 2 combined by the transmitter combination changer 3.

  The positioning method using the propagation time difference and phase difference of radio waves from the plurality of transmitters 1 to the receiver 2 is the same as that of the seventh embodiment.

Next, a specific operation of the position estimation apparatus according to the eighth embodiment will be described with reference to FIG. The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The receiver 2 discriminates and receives signals from each transmitter 1. The transmitter combination changer 3 selects an appropriate combination of transmitters 1 from among all the receivable transmitters 1 by a number equal to or more than a predetermined minimum number necessary for positioning and equal to or less than the total number of transmitters. The pseudo-range difference calculator 17 calculates the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals of the two transmitters 1 in the selected combination. calculate.

The direction cosine vector calculator 5 calculates the direction cosine vector A from the transmitter position information set in advance according to the equation (54). The least square positioning solution calculator 6 substitutes the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) and the direction cosine vector A into the equation (51) to obtain the least square positioning solution. u Calculate the _{k, m} underbar. The combination of the transmitters 1 is changed by the transmitter combination changer 3, and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution u _{k, m} underbar (m = 1, 2,..., M) is stored in the positioning solution storage unit 7 respectively.

In the predictor 8, the smoothing vector ((x _k−1 underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equation (33) ) (predicted according 35) vector _{((x k} underscore) to formula hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{u k} underscore (-) is calculated respectively.

The prediction residual probability density calculator 12 receives the prediction error covariance matrix P _k (−) from the predictor 8 and the observation error covariance matrix of the distance between the transmitter 1 and the receiver 2 set in advance. Then, the covariance matrix S _k of the predicted probability density function P [u _{k, m} underbar | U _k−1 ] of the positioning solution is calculated according to the equations (27) and (41). In the gate determiner 13, predictor 8 from the position prediction vector u _k underscore (-) to enter the covariance matrix S _k from the prediction residual probability density calculator 12, positioning solution stored in the positioning solution storage vessel 7 From u _{k, m} underbars (m = 1, 2,..., M), those satisfying the equation (42) are selected, and those not satisfying are excluded.

In positioning solution reliability calculator 14, predictor 8 position prediction vector is calculated in u _k underscore (-) and the covariance matrix S _k calculated by the prediction residual probability density calculator 12 via the gate determiner 13 The reliability β _{k, m} of the positioning solution u _{k, m} underbar (m = 1, 2,..., M) that is input and satisfies equation (42) is calculated according to equation (44), and this reliability in calculating the mean value u _k underscore weighted the positioning solution according to the equation (45).

In the smoother 10, the positioning solution u _k underbar calculated by the positioning solution reliability calculator 14, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( −) Is used to calculate a smooth vector ((x _k underbar) hat) (+) and a smooth error covariance matrix P _k (+).

  As described above, radio waves transmitted from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and propagation between signals of each transmitter 1 at the receiver position is performed. Even if the present invention is applied to a method of measuring the time difference or phase difference and positioning the receiver position, the position of the receiver 2 can be measured with higher accuracy as in the second embodiment.

Embodiment 9 FIG.
In the third embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured and received. The present invention is applied to a positioning system that uses radio wave propagation time in a system for positioning the machine position. However, the present invention is different in radio wave propagation time difference or phase difference from a plurality of transmitters 1 to receivers 2. In this embodiment, the application example will be described.

  FIG. 9 is a block diagram showing a position estimation apparatus according to the ninth embodiment. In the figure, reference numerals 1-3, 5-7, 13, and 14 that are the same as those in FIG. 3 are the same as or equivalent to those in the third embodiment. Will not be described.

  17 is a pseudo-range difference calculator that calculates a pseudo-range difference between the transmitter and the receiver from the propagation time difference or phase difference of the radio wave from the transmitter 1 to the receiver 2 combined by the transmitter combination changer 3, and 18 is the least square positioning. This is a distance difference residual storage device that stores the distance difference residual calculated by the solution calculator 6.

  The positioning method using the propagation time difference and phase difference of radio waves from the plurality of transmitters 1 to the receiver 2 is the same as that of the seventh embodiment. Further, the square norm of the distance difference residual is expressed by Expression (56).

Next, a specific operation of the position estimation apparatus according to the ninth embodiment will be described with reference to FIG. The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The receiver 2 discriminates and receives signals from each transmitter 1. The transmitter combination changer 3 selects an appropriate combination of transmitters 1 from among all the receivable transmitters 1 by a number equal to or more than a predetermined minimum number necessary for positioning and equal to or less than the total number of transmitters. The pseudo-range difference calculator 17 calculates the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals of the two transmitters 1 in the selected combination. calculate.

The direction cosine vector calculator 5 calculates the direction cosine vector A from the transmitter position information set in advance according to the equation (54). The least square positioning solution calculator 6 substitutes the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) and the direction cosine vector A into the equation (51) to obtain the least square positioning solution. u Calculate the _{k, m} underbar. The transmitter combination is changed by the transmitter combination changer 3 and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution u _{k, m} underbar (m = 1, 2,..., M ) Are stored in the positioning solution storage unit 7 respectively.

In the distance residual storage unit 15, the pseudo-square difference r _{i, j} (i, j = 1, 2,..., N) and the positioning solution f _{i, j} (x hat, y hat, z hat) is inputted, and the square norm ρ _m ² of the distance difference residual is calculated according to the equation (56) and stored. In the gate determination unit 13, the positioning solution storage unit 7 uses the square norm ρ _m ^{2 of} the distance residual input from the distance residual storage unit 15 and the variance μ ² of the probability distribution of the distance difference residual set in advance. Are selected from the positioning solutions u _{k, m} underbars (m = 1, 2,..., M) stored in (1), and those not satisfying the expression (47) are excluded.

The positioning solution reliability calculator 14 inputs the square norm ρ _m ² of the distance difference residual and the variance μ ² of the preset probability distribution of the distance difference residual via the gate determiner 13, and the equation ( 47) For all the positioning solutions satisfying 47), the reliability β _{k, m} of the positioning solution is calculated according to the equations (48) to (49), and the average value uk underbar is _obtained by weighting the positioning solution with this reliability. As the estimated position of the receiver according to the equation (50).

  As described above, radio waves transmitted from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and propagation between signals of each transmitter 1 at the receiver position is performed. Even if the present invention is applied to a method for measuring the time difference or phase difference to determine the receiver position, the position of the receiver can be determined with higher accuracy as in the third embodiment.

Embodiment 10 FIG.
In the fourth embodiment, radio waves transmitted from a transmitter 1 whose position is unknown are received by a plurality of receivers 2 whose positions are known, and the propagation time from the transmitter 1 to the receiver 2 is measured. In this method, the present invention is applied to a positioning method that uses radio wave propagation time in the method of positioning the transmitter position.However, the present invention is not limited to the propagation time difference or phase difference of radio waves from a plurality of receivers to the transmitter. In this embodiment, the application example will be described.

  FIG. 10 is a block diagram showing a position estimation apparatus according to the tenth embodiment. In the figure, reference numerals 1, 2, 5-11, and 16, which are the same as those in FIG. 4, denote the same or corresponding parts as those in the fourth embodiment. Therefore, the description is omitted.

  Reference numeral 17 denotes a pseudo distance difference calculator that calculates a pseudo distance difference between the transmitter and the receiver based on a propagation time difference or a phase difference between the transmitter and the receiver combined by the receiver combination changer 16.

  The positioning method using the propagation time difference and phase difference of radio waves from the plurality of transmitters 1 to the receiver 2 is the same as that of the seventh embodiment.

Next, specific operations of the position estimation apparatus according to Embodiment 10 will be described with reference to FIG. The radio wave emitted from the transmitter 1 receives signals from the transmitter by the plurality of receivers 2 after the propagation time of each propagation path. The receiver combination changer 16 selects an appropriate combination of the receivers 2 from among all the receivers 2 that can receive the signal, by a number that is not less than a predetermined minimum number required for positioning and not more than the total number of receivers. The pseudo-range difference calculator 17 calculates the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals of the two transmitters 1 in the selected combination. calculate.

The direction cosine vector calculator 5 calculates the direction cosine vector A from the transmitter position information set in advance according to the equation (54). The least square positioning solution calculator 6 substitutes the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) and the direction cosine vector A into the equation (51) to obtain the least square positioning solution. u Calculate the _{k, m} underbar. The combination of receivers is changed by the receiver combination changer 16, and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution uk _{, m} underbar (m = 1, 2,..., M ) Are stored in the positioning solution storage unit 7 respectively.

In the predictor 8, the smoothing vector ((x _k−1 underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equation (33) ) (predicted according 35) vector _{((x k} underscore) to formula hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{u k} underscore (-) is calculated respectively. In positioning solution selector 9, the predictor 8 from the position prediction vector _{u k} underscore (-) is input, positioning solution stored in the positioning solution storage unit 7 _{u k, m} underscore (m = 1, 2, · · · , M), the positioning solution u _k underbar of the combination of the receivers having the smallest prediction residual d _{k, m} represented by the equation (36) is selected as the final positioning solution.

The smoother 10, and the positioning solution u _k underscore selected in positioning solution selector, the prediction vector calculated by the predictor 8 ((x _k underscore) hat) and (- -) and the prediction error covariance matrix P _{k ()} The smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k (+) are calculated.

  As described above, the radio wave transmitted from the transmitter 1 whose position is unknown is received by the plurality of receivers 2 whose positions are known, and the propagation time difference between the signals of the transmitter 1 at the receiver position. Alternatively, even if the present invention is applied to a method of measuring the phase difference and measuring the transmitter position, the position of the transmitter 1 can be determined with higher accuracy as in the fourth embodiment.

Embodiment 11 FIG.
In the fifth embodiment, radio waves transmitted from a transmitter 1 whose position is unknown are received by a plurality of receivers 2 whose positions are known, and the propagation time from the transmitter 1 to the receiver 2 is measured. In the method of positioning the transmitter position, the present invention is applied to the positioning method using the propagation time of the radio wave. The present invention is different from the propagation time difference of the radio waves from the plurality of receivers 2 to the transmitter 1. Since this embodiment can also be applied to a positioning method using a phase difference, this application example will be described in this embodiment.

  FIG. 11 is a block diagram showing a position estimation apparatus according to the eleventh embodiment. In the figure, 1, 2, 5-8, 10-14, and 16, which are the same reference numerals as those in FIG. 5, are the same as those in the fifth embodiment. Since the corresponding part is shown, the description thereof is omitted.

  Reference numeral 17 denotes a pseudo distance difference calculator that calculates a pseudo distance difference between the transmitter and the receiver based on a propagation time difference or a phase difference of the radio wave from the transmitter to the receiver combined by the transmitter combination changer 3.

  The positioning method using the propagation time difference and phase difference of radio waves from the plurality of transmitters 1 to the receiver 2 is the same as that of the seventh embodiment.

Next, specific operations of the position estimation apparatus according to the eleventh embodiment will be described with reference to FIG. The radio wave emitted from the transmitter 1 receives signals from the transmitter 1 by the plurality of receivers 2 after the propagation time of each propagation path. The receiver combination changer 16 selects an appropriate combination of the receivers 2 from among all the receivers 2 that can receive the signal, by a number that is not less than a predetermined minimum number required for positioning and not more than the total number of receivers. The pseudo-range difference calculator 17 calculates a pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals of the two transmitters in the selected combination. To do.

The direction cosine vector calculator 5 calculates a direction cosine vector A from preset receiver position information according to the equation (54). The least square positioning solution calculator 6 substitutes the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) and the direction cosine vector A into the equation (51) to obtain the least square positioning solution. u Calculate the _{k, m} underbar. The combination of the receivers 2 is changed by the receiver combination changer 16, and the above positioning calculation and distance difference residual calculation are repeated M times, and the positioning solution u _{k, m} underbar (m = 1, 2,... , M) are stored in the positioning solution storage unit 7, respectively.

In the predictor 8, the smoothing vector ((x _k−1 underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equation (33) ) (predicted according 35) vector _{((x k} underscore) to formula hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{u k} underscore (-) is calculated respectively.

The prediction residual probability density calculator 12 receives the prediction error covariance matrix P _k (−) from the predictor 8, and the observation error covariance matrix of the distance between the transmitter and the receiver set in advance. Then, the covariance matrix S _k of the predicted probability density function P [u _{k, m} underbar | U _k−1 ] of the positioning solution is calculated according to the equations (27) and (41). In the gate determiner 13, predictor 8 from the position prediction vector u _k underscore (-) to enter the covariance matrix S _k from the prediction residual probability density calculator 12, positioning solution stored in the positioning solution storage vessel 7 From u _{k, m} (m = 1, 2,..., M), those satisfying equation (42) are selected, and those not satisfying are excluded.

In positioning solution reliability calculator 14, predictor 8 position prediction vector is calculated in u _k underscore (-) and the covariance matrix S _k calculated by the prediction residual probability density calculator 12 via the gate determiner 13 The reliability β _{k, m} of the positioning solution u _{k, m} underbar (m = 1, 2,..., M) that is input and satisfies equation (42) is calculated according to equation (44), and this reliability in calculating the mean value u _k underscore weighted the positioning solution according to the equation (45).

In the smoother 10, the positioning solution u _k underbar calculated by the positioning solution reliability calculator 14, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( −) Is used to calculate a smooth vector ((x _k underbar) hat) (+) and a smooth error covariance matrix P _k (+).

  As described above, a radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or phase difference between transmitter signals at the receiver position is received. Even if the present invention is applied to a method of measuring the transmitter position by measuring the position of the transmitter, the position of the transmitter can be measured with higher accuracy as in the fifth embodiment.

Embodiment 12 FIG.
In the sixth embodiment, radio waves transmitted from a transmitter 1 whose position is unknown are received by a plurality of receivers 2 whose positions are known, and the propagation time from the transmitter 1 to the receiver 2 is measured. In this method, the present invention is applied to a positioning method that uses radio wave propagation time in the method of positioning the transmitter position.However, the present invention is not limited to the propagation time difference or phase difference of radio waves from a plurality of receivers to the transmitter. In this embodiment, the application example will be described.

  FIG. 12 is a block diagram showing a position estimation apparatus according to the twelfth embodiment. In the figure, 1, 2, 5-7, 13, 14, 16 which are the same reference numerals as those in FIG. 6 are the same as those in the sixth embodiment. Since the corresponding part is shown, the description thereof is omitted.

  Reference numeral 17 denotes a pseudo-range difference calculator that calculates a pseudo-range difference between the transmitter and the receiver based on the propagation time difference or phase difference of radio waves from the transmitter 1 to the receiver 2 combined by the receiver combination changer 16.

  The positioning method using the propagation time difference and phase difference of radio waves from the plurality of transmitters 1 to the receiver 2 is the same as that of the seventh embodiment. The square norm of the distance difference residual is the same as that in the ninth embodiment.

Next, a specific operation of the position estimation apparatus according to the twelfth embodiment will be described with reference to FIG. The radio wave emitted from the transmitter 1 receives signals from the transmitter 1 by the plurality of receivers 2 after the propagation time of each propagation path. The receiver combination changer 16 selects an appropriate combination of the receivers 2 from among all the receivers 2 that can receive the signal, by a number that is not less than a predetermined minimum number required for positioning and not more than the total number of receivers. The pseudo-range difference calculator 17 calculates the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals of the two transmitters 1 in the selected combination. calculate.

The direction cosine vector calculator 5 calculates the direction cosine vector A from the transmitter position information set in advance according to the equation (54). The least square positioning solution calculator 6 substitutes the pseudo-range difference r _{i, j} (i, j = 1, 2,..., N) and the direction cosine vector A into the equation (51) to obtain the least square positioning solution. u Calculate the _{k, m} underbar. The combination of receivers is changed by the receiver combination changer 16, and the above positioning calculation and distance residual calculation are repeated M times, and the positioning solution uk _{, m} underbar (m = 1, 2,..., M ) Are stored in the positioning solution storage unit 7 respectively.

In the distance residual storage unit 15, the pseudo-square difference r _{i, j} (i, j = 1, 2,..., N) and the positioning solution f _{i, j} (x hat, y hat, z hat) is inputted, and the square norm ρ _m ² of the distance difference residual is calculated according to the equation (56) and stored. In the gate determination unit 13, a positioning solution storage unit is obtained from the square norm ρ _m ² of the distance difference residual input from the distance residual storage unit 15 and a variance μ ^{2 of} a preset probability distribution of the distance difference residual unit. Among the positioning solutions u _{k, m} underbars (m = 1, 2,..., M) stored in 7, those satisfying the equation (47) are selected, and those not satisfying are excluded.

The positioning solution reliability calculator 14 inputs the square norm ρ _m ² of the distance difference residual and the variance μ ² of the preset probability distribution of the distance difference residual via the gate determiner 13, and the equation ( 47) For all the positioning solutions satisfying 47), the reliability β _{k, m} of the positioning solution is calculated according to the equations (48) to (49), and the average value uk underbar is _obtained by weighting the positioning solution with this reliability. As the estimated position of the receiver according to the equation (50).

  As described above, a radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or phase difference between transmitter signals at the receiver position is received. Even if the present invention is applied to a method of measuring the transmitter position by measuring the position of the transmitter, the position of the transmitter can be measured with higher accuracy as in the sixth embodiment.

Embodiment 13 FIG.
FIG. 13 is a block diagram showing a position estimation apparatus according to the thirteenth embodiment. In the figure, 1, 2, 4 to 6, 8, 10, and 11, which are the same reference numerals as those in FIG. 1, are the same as those in the first embodiment. Or, since the corresponding parts are shown, the description thereof is omitted.

  18 inputs a probability density function of the predicted distance residual output from the predicted distance residual probability density calculator 20, and selects a distance suitable for positioning from the distance between each transmitter and receiver output from the receiver 2. A transmitter selector based on a distance for selecting and selecting a transmitter, 19 is a distance converter that converts the predicted position output by the predictor 8 into a predicted distance between each transmitter and receiver, and 20 is a distance converter. 19 is a prediction distance residual probability density calculator that inputs a prediction distance between each transmitter and receiver output by 19 and calculates a probability density function of a prediction distance residual.

Next, the operation will be described.
First, the operation principle of the position estimation apparatus according to the thirteenth embodiment will be described. Here, it is assumed that a three-dimensional position is estimated.

  The method for predicting the movement of the positioning target using the past positioning result is the same as that in the first embodiment.

  Next, a method for determining the transmitter 1 suitable for positioning that is not affected by multipath or the like will be described. In the first embodiment, a plurality of positioning solutions calculated by changing the combination of the transmitters 1 by the transmitter combination changer 3 are determined and selected, but in this thirteenth embodiment, before the positioning solution is obtained. The stage, that is, the distance between the transceivers 1 and 2 output from the receiver 2 is determined and selected.

The predicted distance r _{k, i} (−) for the i-th transmitter 1 is expressed by Expression (57) from Expression (29). If a part of the transmitter 1 is affected by multipath or there is a problem on the propagation path, the prediction residual of the distance becomes a large value. Therefore, the prediction residual d ′ _{k, i,} which is the difference between the prediction distance and the pseudo-range r _{k, i} (i = 1, 2,..., N) between the i-th transmitter 1 and receiver 2 is A pseudo distance satisfying the equation (58) with respect to the parameter ξ is selected as a positioning target. As a result, it is possible to determine a combination of transmitters that are normal and have no problem on the propagation path, and estimate the position of the receiver 2 with higher accuracy by performing positioning using these pseudoranges. can do.

On the other hand, as another method for selecting a transmitter, there is a method using a probability distribution of a distance prediction residual. The distance residual prediction probability distribution P [r _{k, i} | U _k−1 ] obtained from the past positioning information U _k−1 is expressed by a conditional probability density function shown in Expression (59). That is, the distance residual is a one-dimensional normal distribution g ₁ (with a predicted distance r _{k, i} (−) given by Expression (57) as an average and S ′ _{k, i} given by Expression (60) as variance. r _{k, i} ; r _{k, i} (−), S ′ _{k, i} ). Then, the pseudo distance satisfying the equation (61) is used for positioning, and the pseudo distance not satisfying is excluded. Here, q ′ is a parameter for determining the correlation range with the target, and is calculated by a χ square distribution with one degree of freedom. H _{2, i} (((x _k underbar) hat) (−)) is a matrix for converting the error covariance of the three-dimensional orthogonal coordinates into the variance of the distance between the i-th transmitter 1 and the receiver 2. As shown in (62) and (63), the error of the three-dimensional orthogonal coordinate is obtained by linear approximation around the prediction vector ((x _k underbar) hat) (−). Formulas (30) to (32) are referred to as formulas for calculating the elements of the matrix of Formula (63).

  The method for selecting the transmitter 1 according to the distance has been described above.

  Next, the position of the receiver 2 is measured using the pseudo distance of the transmitter 1 selected by the above-described method. Since this principle is the same as that of Non-Patent Document 1 in the prior art, it will be omitted.

  Next, a smooth vector is calculated using the above positioning result. Since this principle is the same as that of the first embodiment, a description thereof will be omitted.

  The operation principle of the position estimation device according to the thirteenth embodiment has been described above.

Next, specific operations of the position estimation apparatus according to the thirteenth embodiment will be described with reference to FIG.
The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The receiver 2 discriminates and receives signals from each transmitter 1. The pseudo distance calculator 4 calculates a pseudo distance r _{k, i} (i = 1, 2,..., N) from the propagation delay time of the signal from the transmitter 1.

In the transmitter selector 18 by distance, the prediction distance r _{k, i} (−) and the variance S ′ _{k, i} of the probability density function of the distance prediction residual are input from the prediction distance residual probability density calculator 20 and simulated. From the distances r _{k, i} (i = 1, 2,..., N), those satisfying the equation (61) are selected, and those not satisfying are excluded.

The direction cosine vector calculator 5 calculates the direction cosine vector A from preset position information of the transmitter according to the equation (4). The least-squares positioning solution calculator 6 calculates the least-squares positioning solution u _k underbar by substituting the pseudo-range r _{k, i} selected by the transmitter selector 18 according to distance and the direction cosine vector A into the equation (10). To do.

In the smoother 10, the positioning solution u _k underbar calculated by the least square positioning solution calculator 6, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( −) Is used to calculate a smooth vector (x _k underbar) hat) (+) and a smooth error covariance matrix (P _k (+)).

In the predictor 8, the smoothing vector (x _k−1 underbar) hat) (+) before one sampling and the smoothing error covariance matrix P _k−1 (+) are input via the delay circuit 11, and Expression (33) prediction according to formula (35) vector _{((x k} underscore) hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{(u k} underscore) (-) is calculated respectively. The distance converter 19 converts the prediction vector ((x _k underbar) hat) (−) calculated by the predictor 8 into a distance prediction vector according to the equation (57).

The prediction distance residual probability density calculator 20 receives a prediction vector ((x _k underbar) hat) (−) and a prediction error covariance matrix P _k (−) from the predictor 8, and this is set in advance. From the observation error variance σ _{k, i} of the distance between the transmitter 1 and the receiver 2, the variance S of the probability density function P [r _{k, i} | U _k−1 ] of the distance prediction residual according to the equation (60). 'Calculate _{k and i} .

  As described above, since the present embodiment estimates the position of the receiver 2 using the pseudo-range of the transmitter 1 selected using the distance prediction residual or the probability density function of the distance prediction residual. Therefore, it is possible to prevent deterioration in positioning accuracy due to the influence of a transmitter having an abnormal operation or a problem on the propagation path. Further, unlike the first to twelfth embodiments, it is not necessary to obtain a plurality of angle measurement solutions, so the calculation load is light.

Embodiment 14 FIG.
FIG. 14 is a block diagram showing a position estimation apparatus according to the fourteenth embodiment. In FIG. The reference numerals 18 to 20 that are the same as those in FIG.

  21 is a filter switcher that switches a smoothing method according to the number of transmitters selected by the transmitter selector 18 according to distance, 22 is a distance observation matrix calculator that calculates a distance observation matrix, and 23 is based on distance. The pseudo distance output from the transmitter selector 18, the distance observation matrix output from the distance observation matrix calculator 22, the prediction vector of the pre-sampling time output from the predictor, and the prediction error covariance matrix are input and smoothed. It is a position smoother by the distance which calculates a vector.

Next, the operation will be described.
First, the operation principle of the position estimation apparatus according to the fourteenth embodiment will be described. Here, it is assumed that a three-dimensional position is estimated.

  The method for predicting the movement of the positioning target using the past positioning result is the same as that in the first embodiment.

  The method for determining and selecting the transmitter 1 suitable for positioning that is not affected by multipath or the like is the same as that of the thirteenth embodiment.

In the thirteenth embodiment, as a result of selecting the transmitter 1 suitable for positioning, positioning cannot be performed when the number is less than four, which is the minimum necessary for performing three-dimensional positioning. In this case, the smooth vector is calculated using the selected pseudo distance directly. Next, this method will be described.
The pseudo distance corresponding to the selected transmitter 1 is set to r _{k, i} (i = 1, 2,..., L), and this is expressed as a vector as shown in Expression (64). In this case, the observation model is expressed by Expression (65).

Since the distance observation model represented by Expression (65) is non-linear, a smooth vector cannot be calculated with a normal Kalman filter. Therefore, as shown in Expression (67) and Expression (68), an extended Kalman filter obtained by linearly approximating this observation model around a prediction vector ((x _k underbar) hat) (−) is used.

Based on the theory of the extended Kalman filter, the gain matrix K _k , the smooth vector ((x _k underbar) hat) (+), and the smooth error covariance matrix P _k (+) are given by Expressions (69) to (71). The smooth vector calculation method has been described above.

  Next, a process when the number of transmitters 1 selected as a result of the selection is four or more will be described. In this case, the position of the receiver 2 is measured using the pseudo distance of the transmitter 1 selected in the same manner as in Non-Patent Document 1. Since this principle is the same as that of Non-Patent Document 1 in the prior art, a description thereof will be omitted. Further, the principle of calculating a smooth vector using the positioning result is the same as that of the first embodiment, and therefore will be omitted.

  The operation principle of the position estimation device according to the fourteenth embodiment has been described above.

Next, specific operations of the position estimation apparatus according to Embodiment 14 will be described with reference to FIG.
The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The receiver 2 discriminates and receives signals from each transmitter 1. The pseudo distance calculator 4 calculates a pseudo distance r _{k, i} (i = 1, 2,..., N) from the propagation delay time of the signal from the transmitter 1.

In the transmitter selector 18 by distance, the prediction distance r _{k, i} (−) and the variance S ′ _{k, i} of the probability density function of the distance prediction residual are input from the prediction distance residual probability density calculator 20 and simulated. From the distances r _{k, i} (i = 1, 2,..., N), those satisfying the equation (61) are selected, and those not satisfying are excluded.

  In the filter switching unit 21, when the transmitter 1 is selected by the transmitter selector 18 according to the distance, the direction cosine vector calculator 5 performs processing when the number is four or more which is sufficient for positioning. If the number is less than 4, the process proceeds to the distance observation matrix calculator 22.

In the direction cosine vector calculator 5, when the number of transmitters 1 selected by the transmitter selector 18 according to distance is four or more, the direction cosine is calculated from the preset transmitter position information according to the equation (4). Vector A is calculated. The least-squares positioning solution calculator 6 calculates the least-squares positioning solution u _k underbar by substituting the pseudo-range r _{k, i} selected by the transmitter selector 18 according to distance and the direction cosine vector A into the equation (10). To do.

In the smoother 10, the positioning solution u _k underbar calculated by the least square positioning solution calculator 6, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( −) Is used to calculate a smooth vector ((x _k underbar) hat) (+) and a smooth error covariance matrix P _k (+).

In the distance observation matrix calculator 22, when the number of transmitters 1 selected by the transmitter selector 18 according to distance is less than 4, the prediction vector ((x _k underbar) hat) calculated by the predictor 8 (− ) To calculate the distance observation matrix H ₂ (((x _k underbar) hat) (−)) according to the equation (68).

In the position smoother 23 according to the distance, pseudoranges selected in the transmitter selector 18 according to distance vector r _k underscores and distance observation matrix calculator 22 distance calculated in observation matrix H _{2 (((x k} underscore) hat ) (−)) And the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k (−) calculated by the predictor 8 (smooth vector ((x _k underbar) hat)) (+) And the smoothing error covariance matrix P _k (+) are calculated.

In the predictor 8, when the number of transmitters 1 selected by the transmitter selector 18 according to distance is four or more, the input is performed via the delay circuit 11 calculated by the smoother 10, while the selected transmission is performed. When the number of the machines 1 is less than 4, the smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) calculated by the position smoother 23 according to the distance are used. ) Is input via the delay circuit 11, and the prediction vector ((x _k underbar) hat) (−), the prediction error covariance matrix P _k (−), the position prediction vector ( u _k underscore) (-) is calculated respectively. The distance converter 19 converts the prediction vector ((x _k underbar) hat) (−) calculated by the predictor 8 into a distance prediction vector according to the equation (57).

The prediction distance residual probability density calculator 20 receives a prediction vector ((x _k underbar) hat) (−) and a prediction error covariance matrix P _k (−) from the predictor 8, and this is set in advance. From the observation error variance σ _{k, i} of the distance between the transmitter 1 and the receiver 2, the variance S of the probability density function P [r _{k, i} | U _k−1 ] of the distance prediction residual according to the equation (60). 'Calculate _{k and i} .

As described above, since the present embodiment estimates the position of the receiver 2 using the pseudo-range of the transmitter 1 selected using the distance prediction residual or the probability density function of the distance prediction residual, It is possible to prevent deterioration in positioning accuracy due to the influence of a transmitter having an abnormal operation or a problem on the propagation path. Further, unlike the first to twelfth embodiments, it is not necessary to obtain a plurality of angle measurement solutions, so the calculation load is light.
Furthermore, in the above-described thirteenth embodiment, there is a problem that positioning cannot be performed when the number of transmitters selected by the transmitter selector 18 by distance is less than four. In this embodiment, the position smoother 23 by distance is used. Therefore, the position of the receiver can be estimated with high accuracy even when positioning is impossible.

Embodiment 15 FIG.
In the thirteenth embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured. In this embodiment, the radio wave from the transmitter 1 whose position is unknown is received by a plurality of reception positions whose positions are known. An application example in which the present invention is applied to a method of measuring the propagation time from the transmitter 1 to the receiver 2 and measuring the position of the transmitter by receiving by the transmitter 2 will be described.

  FIG. 15 is a block diagram showing a position estimation apparatus according to the fifteenth embodiment. In the figure, reference numerals 1, 2, 4 to 6, 8, 10, 11, 19, and 20, which are the same as those in FIG. The same or corresponding parts as those shown in FIG.

  24, a probability density function of the predicted distance residual output from the predicted distance residual probability density calculator 20 is input, and the pseudo distance between the transmitter and each receiver output from each receiver 2 is suitable for positioning. It is a receiver selector by the distance which selects distance.

Next, a specific operation of the position estimation apparatus according to the fifteenth embodiment will be described with reference to FIG. The radio wave emitted from the transmitter 1 reaches the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The pseudo distance calculator 4 calculates a pseudo distance r _{k, i} (i = 1, 2,..., N) from the propagation delay time of the signal from the transmitter 1.

In the receiver selector 24 by distance, the prediction distance r _{k, i} (−) and the variance S ′ _{k, i} of the probability density function of the prediction residual of the distance are input from the prediction distance residual probability density calculator 20 and simulated. From the distances r _{k, i} (i = 1, 2,..., N), those satisfying the equation (61) are selected, and those not satisfying are excluded.

The direction cosine vector calculator 5 calculates the direction cosine vector A from preset position information of the receiver according to the equation (4). The least-squares positioning solution calculator 6 calculates the least-squares positioning solution u _k underbar by substituting the pseudo-range r _{k, i} selected by the transmitter selector 18 according to distance and the direction cosine vector A into the equation (10). To do.

In the smoother 10, the positioning solution u _k underbar calculated by the least square positioning solution calculator 6, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( −) Is used to calculate a smooth vector ((x _k underbar) hat) (+) and a smooth error covariance matrix P _k (+).

In the predictor 8, the smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equations (33) to (33) to prediction vector in accordance with equation (35) _{((x k} underscore) hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{(u k} underscore) (-) is calculated respectively. The distance converter 19 converts the prediction vector ((x _k underbar) hat) (−) calculated by the predictor 8 into a distance prediction vector according to the equation (57).

The prediction distance residual probability density calculator 20 receives a prediction vector ((x _k underbar) hat) (−) and a prediction error covariance matrix P _k (−) from the predictor 8, and this is set in advance. From the observation error variance σ _{k, i} of the distance between the transmitter 1 and the receiver 2, the variance S of the probability density function P [r _{k, i} | U _k−1 ] of the distance prediction residual according to the equation (60). 'Calculate _{k and i} .

  As described above, the radio waves from the transmitter 1 whose position is unknown are received by the plurality of receivers 2 whose positions are known, and the propagation time from the transmitter 1 to the receiver 2 is measured and the transmitter is measured. Even if the present invention is applied to a method for measuring the position, the position of the transmitter 1 can be measured with higher accuracy as in the thirteenth embodiment.

Embodiment 16 FIG.
In the fourteenth embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured. The present invention is an application example to a method for positioning the receiver position. The present invention, however, receives a radio wave from the transmitter 1 whose position is unknown by a plurality of receivers 2 whose positions are known. Since the present invention can be applied to a method of measuring the propagation time from 1 to the receiver 2 to determine the transmitter position, this embodiment will describe the application example.

  FIG. 16 is a block diagram showing a position estimation apparatus according to the sixteenth embodiment. In the figure, reference numerals 1, 2, 4 to 6, 8, 10, 11, 19 to 23, which are the same as those in FIG. 14 are the same as or equivalent to those shown in FIG.

  24, a probability density function of the predicted distance residual output from the predicted distance residual probability density calculator 20 is input, and the pseudo distance between the transmitter and each receiver output from each receiver 2 is suitable for positioning. It is a receiver selector by the distance which selects distance.

Next, specific operations of the position estimation apparatus according to the sixteenth embodiment will be described with reference to FIG. The radio wave emitted from the transmitter 1 reaches the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The pseudo distance calculator 4 calculates a pseudo distance r _{k, i} (i = 1, 2,..., N) from the propagation delay time of the signal from the transmitter 1.

In the receiver selector 24 by distance, the prediction distance r _{k, i} (−) and the variance S ′ _{k, i} of the probability density function of the prediction residual of the distance are input from the prediction distance residual probability density calculator 20 and simulated. From the distances r _{k, i} (i = 1, 2,..., N), those satisfying the equation (61) are selected, and those not satisfying are excluded.

  In the filter switching unit 21, when the receiver 2 is selected by the distance-based receiver selector 24 and the number is four or more, which is sufficient for positioning, the direction cosine vector calculator 5 performs processing. If the number is less than 4, the process proceeds to the distance observation matrix calculator 22.

In the direction cosine vector calculator 5, when the number of the receivers 2 selected by the receiver selector 24 according to distance is four or more, the direction cosine is calculated from the preset position information of the receiver according to the equation (4). Vector A is calculated. In least squares positioning solution calculator 6, pseudorange r _k is selected by the receiver selector 24 by a _{distance, i} and direction cosine vector A into Equation (10), calculates a least squares positioning solution u _k underbar To do.

In the smoother 10, the positioning solution u _k underbar calculated by the least square positioning solution calculator 6, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( −) Is used to calculate a smooth vector ((x _k underbar) hat) (+) and a smooth error covariance matrix P _k (+).

In the distance observation matrix calculator 22, when the number of the receivers 2 selected by the receiver selector 24 according to distance is less than 4, the prediction vector ((x _k underbar) hat) calculated by the predictor 8 (− ) To calculate the distance observation matrix H ₂ (((x _k underbar) hat) (−)) according to the equation (68).

In the position smoother 23 according to the distance, the pseudo distance is selected at the receiver selector 24 according to distance vector r _k underscores and distance observation matrix calculator 22 distance calculated in observation matrix H _{2 (((x k} underscore) hat ) (−)) And the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k (−) calculated by the predictor 8 (smooth vector ((x _k underbar) hat)) (+) And the smoothing error covariance matrix P _k (+) are calculated.

In the predictor 8, when the number of receivers 2 selected by the receiver selector 24 according to distance is four or more, the input is made through the delay circuit 11 calculated by the smoother 10, while the selected reception is performed. If the number of the machines 2 is less than 4, the smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) calculated by the position smoother 23 according to the distance are used. ) Is input via the delay circuit 11, and the prediction vector ((x _k underbar) hat) (−), the prediction error covariance matrix P _k (−), and the position prediction vector u according to Expressions (33) to (35) Each _k underbar (-) is calculated. The distance converter 19 converts the prediction vector ((x _k underbar) hat) (−) calculated by the predictor 8 into a distance prediction vector according to the equation (57).

The prediction distance residual probability density calculator 20 receives a prediction vector ((x _k underbar) hat) (−) and a prediction error covariance matrix P _k (−) from the predictor 8, and this is set in advance. From the observation error variance σ _{k, i} of the distance between the transmitter 1 and the receiver 2, the variance S of the probability density function P [r _{k, i} | U _k−1 ] of the distance prediction residual according to the equation (60). 'Calculate _{k and i} .

  As described above, the radio waves from the transmitter 1 whose position is unknown are received by the plurality of receivers 2 whose positions are known, and the propagation time from the transmitter 1 to the receiver 2 is measured and the transmitter is measured. Even if the present invention is applied to a method for measuring the position, the position of the transmitter 1 can be measured with higher accuracy as in the fourteenth embodiment.

Embodiment 17. FIG.
In the thirteenth embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured. In the method of positioning the receiver position, the present invention is applied to a positioning method using the propagation time of the radio wave. The present invention is different from the propagation time difference of the radio wave from the plurality of transmitters 1 to the receiver 2. Since this embodiment can also be applied to a positioning method using a phase difference, this application example will be described in this embodiment.

  FIG. 17 is a block diagram showing a position estimation apparatus according to the seventeenth embodiment. In the figure, reference numerals 1, 2, 5, 6, 8, 10, 11, 17 which are the same as those in FIG. Since the same or corresponding parts are shown, the description thereof is omitted.

  25 is input a probability density function of the prediction distance difference residual output from the prediction distance difference residual probability density calculator 27, and is used for positioning among the pseudo-range differences between the transmitters and receivers output from the receiver 2. A transmitter selector based on a distance difference for selecting a suitable pseudo-range difference, 26 is a distance difference converter that converts the predicted position output from the predictor 8 into a predicted distance difference between each transmitter and receiver, and 27 is a distance difference converter. 26 is a prediction distance difference residual probability density calculator that inputs a prediction distance difference between each transmitter and receiver output by 26 and calculates a probability density function of the prediction distance difference residual.

  A method for determining a transmitter 1 suitable for positioning that is not affected by multipath or the like using a propagation time difference or phase difference of radio waves from a plurality of transmitters 1 to a receiver 2 will be described.

The predicted distance difference Δr _{k, i, j} (−) for the i-th transmitter 1 is the known i-th transmitter position (x _i , y _i , z _i ) and the j-th transmitter that is also known. From the position (x _j , y _j , z _j ), calculation is performed using Expression (72). If a part of the transmitter 1 is affected by multipath or there is a problem on the propagation path, the prediction residual of the distance difference becomes a large value. Therefore, a prediction residual τ _k that is a difference between the prediction distance difference and the pseudo-range difference Δr _{k, i, j} (i = 1, 2,..., N) between the i-th transmitter 1 and receiver 2. _{, I} is selected as a positioning target a pseudo-range difference that satisfies the equation (73) with respect to the parameter η. As a result, it is possible to determine a combination of transmitters that are normal and have no problem on the propagation path, and the position of the receiver 2 can be determined with higher accuracy by performing positioning using these pseudo-range differences. Can be estimated.

On the other hand, as another method for selecting a transmitter, there is a method using a probability distribution of a prediction residual of a distance difference. The prediction probability distribution P [Δr _{k, i, j} | U _k−1 ] of the distance difference residual obtained from the past positioning information U _k−1 is represented by a conditional probability density function shown in Expression (74). . That is, the distance difference residual is a one-dimensional distribution in which the predicted distance difference Δr _{k, i, j} (−) given by the equation (72) is averaged and Ω _{k, i, j} given by the equation (75) is distributed. It is assumed that the normal distribution g ₁ (Δr _{k, i, j} ; Δr _{k, i, j} (−), Ω _{k, i, j} ) is followed. Then, the pseudo distance difference satisfying the equation (76) is used for positioning, and the pseudo distance difference not satisfying is excluded. Here, κ is a parameter for determining the correlation range with the target, and is calculated by a χ square distribution with one degree of freedom. H _{3, i, j} (((x _k underbar) hat) (−)) is the error covariance of the three-dimensional orthogonal coordinates, the distance between the i th transmitter and the receiver 2, the j th transmitter and the reception. This is a matrix for converting the variance of the difference from the distance of the machine 2 and, as shown in the equations (77) and (78), the error of the three-dimensional orthogonal coordinates is converted into the prediction vector ((x _k underbar) hat) Obtained by linear approximation around.

  The method for selecting the transmitter 1 based on the distance difference has been described above.

  Note that the principle of positioning the position of the receiver 2 using the pseudo-range difference between the two transmitters selected by the above-described method and the receiver 2 is the same as that of the seventeenth embodiment, and therefore will not be described.

Next, specific operations of the position estimation apparatus according to the seventeenth embodiment will be described with reference to FIG.
The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The receiver 2 discriminates and receives signals from each transmitter 1. The pseudo-range difference calculator 17 calculates a pseudo-range difference Δr _{k, i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals from the two transmitters 1.

In the transmitter selector 25 based on the distance difference, the prediction distance difference Δr _{k, i, j} (−) and the variance Ω _{k, i, j} of the probability density function of the prediction residual of the pseudo distance difference are used as the prediction distance difference residual probability density. Input from the calculator 27, select a pseudo-range difference Δr _{k, i, j} (i, j = 1, 2,..., N) that satisfies Equation (76), and not Exclude.

The direction cosine vector calculator 5 calculates the direction cosine vector A from the transmitter position information set in advance according to the equation (54). The least square positioning solution calculator 6 substitutes the pseudo distance difference Δr _{k, i, j} selected by the transmitter selector 25 based on the distance difference and the direction cosine vector A into the equation (51) to obtain the least square positioning solution u. Calculate _k underbar.

In the smoother 10, the positioning solution u _k underbar calculated by the least square positioning solution calculator 6, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( -) Is used to calculate the smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k (+) according to the equations (37) to (39).

In the predictor 8, the smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equations (33) to (33) to prediction vector in accordance with equation (35) _{((x k} underscore) hat) (-), the prediction error covariance matrix _P k (-) positions predicted vector _{(u k} underscore) (-) is calculated respectively. The distance difference converter 26 converts the prediction vector ((x _k underbar) hat) (−) calculated by the predictor 8 into a distance difference prediction vector according to the equation (72).

The prediction distance difference residual probability density calculator 27 receives a prediction vector ((x _k underbar) hat) (−) and a prediction error covariance matrix P _k (−) from the predictor 8, and is set in advance. From the observation error variance σ ′ _{k, i, j} of the distance difference between the two transmitters and the receiver 2, the probability density function P [Δr _{k, i, j} of the prediction residual of the distance difference according to the equation (75) | U _k−1 ] variance Ω _{k, i} is calculated.

  As described above, the radio wave transmitted from the plurality of transmitters 1 whose positions are known is received by the receiver 2 whose position is unknown, and the propagation time difference between the signals of the respective transmitters at the receiver position. Alternatively, even if the present invention is applied to a method of measuring the phase difference and measuring the receiver position, the position of the receiver 2 can be determined with higher accuracy as in the thirteenth embodiment.

Embodiment 18 FIG.
In the fourteenth embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured. In the method of positioning the receiver position, the present invention is applied to a positioning method using the propagation time of the radio wave. The present invention is different from the propagation time difference of the radio wave from the plurality of transmitters 1 to the receiver 2. Since this embodiment can also be applied to a positioning method using a phase difference, this application example will be described in this embodiment.

  18 is a block diagram showing a position estimation apparatus according to the eighteenth embodiment. In the figure, reference numerals 1, 2, 5, 6, 8, 10, 11, and 17 that are the same as those in FIG. Since the same or corresponding parts are shown, the description thereof is omitted.

  25 is input a probability density function of the prediction distance difference residual output from the prediction distance difference residual probability density calculator 27, and is used for positioning among the pseudo-range differences between the transmitters and receivers output from the receiver 2. A transmitter selector based on a distance difference for selecting a suitable pseudo-range difference, 26 is a distance difference converter that converts the predicted position output from the predictor 8 into a predicted distance difference between each transmitter and receiver, and 27 is a distance difference converter. A predicted distance difference residual probability density calculator for calculating a probability density function of a predicted distance difference residual by inputting a predicted distance difference between each transmitter and receiver output by 26, and 28 calculates an observation matrix of the distance difference. A distance difference observation matrix calculator 29 is a pseudo-range difference output from the transmitter selector 25 based on the distance difference, a distance difference observation matrix output from the distance difference observation matrix calculator 28, and a pre-sampling output from the predictor 8. Enter time prediction vector and prediction error covariance matrix And a position smoother due to the distance difference calculating a smoothed vector.

  The principle of measuring the position of the receiver 2 using the selection method of the transmitter 1 based on the distance difference and the pseudo distance difference between the two selected transmitters and the receiver 2 is the same as that of the seventeenth embodiment. Therefore, it is omitted.

Next, the calculation method of the distance difference observation matrix and the operation principle of the position smoother based on the distance difference will be described.
The pseudo-range difference corresponding to the selected transmitter 1 is Δr _{k, i, j} (i, j = 1, 2,..., L), and this is expressed as a vector notation as shown in equation (79). In this case, the observation model is represented by Expression (80).

Since the observation model of the distance difference represented by Expression (80) is non-linear, a smooth vector cannot be calculated with a normal Kalman filter. Therefore, as shown in Expression (82) and Expression (83), an extended Kalman filter obtained by linearly approximating this observation model around a prediction vector ((x _k underbar) hat) (−) is used.

According to the theory of the extended Kalman filter, the gain matrix K _k , the smooth vector ((x _k underbar) hat) (+), and the smooth error covariance matrix P _k (+) are given by Expressions (84) to (86). The smooth vector calculation method has been described above.

Next, specific operations of the position estimation apparatus according to Embodiment 18 will be described with reference to FIG.
The radio waves emitted from the plurality of transmitters 1 reach the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The receiver 2 discriminates and receives signals from each transmitter 1. The pseudo-range difference calculator 17 calculates a pseudo-range difference Δr _{k, i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals from the two transmitters 1.

In the transmitter selector 25 based on the distance difference, the prediction distance difference Δr _{k, i, j} (−) and the variance Ω _{k, i, j} of the probability density function of the prediction residual of the pseudo distance difference are used as the prediction distance difference residual probability density. Input from the calculator 27, select a pseudo-range difference Δr _{k, i, j} (i, j = 1, 2,..., N) that satisfies Equation (76), and not Exclude.

  In the filter switching unit 21, the direction cosine vector calculation is performed when the pair of the transmitters 1 is selected by the transmitter selector 25 based on the distance difference and, as a result, the number of pairs is four or more that is sufficient for positioning. The processing is transferred to the device 5, and the processing is transferred to the distance difference observation matrix calculator 28 when the number is less than four.

In the direction cosine vector calculator 5, when the number of the transmitters 1 selected by the transmitter selector 25 based on the distance difference is four or more, the direction cosine vector is calculated from the preset transmitter position information according to the equation (54). A cosine vector A is calculated. The least square positioning solution calculator 6 substitutes the pseudo distance difference Δr _{k, i, j} selected by the transmitter selector 25 based on the distance difference and the direction cosine vector A into the equation (51) to obtain the least square positioning solution u. Calculate _k underbar.

In the smoother 10, the positioning solution u _k underbar calculated by the least square positioning solution calculator 6, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( -) Is used to calculate the smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k (+) according to the equations (37) to (39).

In the distance difference observation matrix calculator 28, the prediction vector ((x _k underbar) hat) calculated by the predictor 8 when the number of transmitters 1 selected by the transmitter selector 25 based on the distance difference is less than four. A distance difference observation matrix H ₄ (((x _k underbar) hat) (−)) is calculated from (−) according to the equation (83).

In the position smoother 29 according to the distance difference, the distance pseudo distance difference is selected in the transmitter selector 25 by difference vector [Delta] r _k underscores the distance difference observation matrix calculator distance difference calculated at 28 observation matrix H _{4 (((} x _k underbar) hat) (−)), the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k (−) calculated by the predictor 8, A smoothing vector ((x _k underbar) hat) (+)) and a smoothing error covariance matrix P _k (+) are calculated according to Equation (86).

In the predictor 8, when the number of the transmitters 1 selected by the transmitter selector 25 based on the distance difference is 4 or more, it is input via the delay circuit 11 calculated by the smoother 10, while the selected one is selected. When the number of the transmitters 1 is less than 4, the smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k−1 calculated by the position smoother 29 based on the distance difference are used. (+) Is input via the delay circuit 11, and the prediction vector ((x _k underbar) hat) (−), prediction error covariance matrix P _k (−), position prediction is performed according to the equations (33) to (35). vector _{u k} underscore (-) is calculated respectively. The distance difference converter 26 converts the prediction vector ((x _k underbar) hat) (−) calculated by the predictor 8 into a distance difference prediction vector according to the equation (72).

The prediction distance difference residual probability density calculator 27 receives a prediction vector ((x _k underbar) hat) (−) and a prediction error covariance matrix P _k (−) from the predictor 8, and is set in advance. From the observation error variance σ ′ _{k, i, j} of the distance difference between the two transmitters and the receiver 2, the probability density function P [Δr _{k, i, j} of the prediction residual of the distance difference according to the equation (75) | U _k−1 ] variance Ω _{k, i} is calculated.

  As described above, the radio wave transmitted from the plurality of transmitters 1 whose positions are known is received by the receiver 2 whose position is unknown, and the propagation time difference between the signals of each transmitter at the receiver position. Alternatively, even if the present invention is applied to a method of measuring the phase difference and measuring the receiver position, the position of the receiver 2 can be determined with higher accuracy as in the fourteenth embodiment.

Embodiment 19. FIG.
In the above-described seventeenth embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time difference of radio waves from the transmitter 1 to the receiver 2 is Although the application example of the present invention to the method of measuring the phase difference and measuring the position of the receiver has been shown, this embodiment conversely, the position of the radio wave from the transmitter 1 whose position is unknown is known. The present invention is applied to a method of measuring the position of the transmitter by measuring the propagation time difference or phase difference of radio waves from the transmitter 1 to the receiver 2 and from the transmitter 1 to the receiver 2. An applied application example will be described.

  FIG. 19 is a block diagram showing a position estimation apparatus according to the nineteenth embodiment. In the figure, reference numerals 1, 2, 5, 6, 8, 10, 11, 17, 26, and 27, which are the same as those in FIG. Since the same or equivalent parts as those of the seventeenth form are shown, the description thereof is omitted.

  30 is input a probability density function of the predicted distance difference residual output from the predicted distance difference residual probability calculator 27, and is used for positioning among the pseudo-range differences between the transmitter 1 and the receiver 2 output from each receiver 2. A receiver selector with distance difference to select a suitable pseudorange difference.

Next, a specific operation of the position estimation apparatus according to the nineteenth embodiment will be described with reference to FIG. The radio wave emitted from the transmitter 1 reaches the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The pseudo-range difference calculator 17 calculates a pseudo-range difference Δr _{k, i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals from the two transmitters 1.

In the receiver selector 30 based on the distance difference, the prediction distance difference Δr _{k, i, j} (−) and the variance Ω _{k, i, j} of the probability density function of the prediction residual of the pseudo distance difference are used as the prediction distance difference residual probability density. Input from the calculator 27, select a pseudo-range difference Δr _{k, i, j} (i, j = 1, 2,..., N) that satisfies Equation (76), and not Exclude.

The direction cosine vector calculator 5 calculates a direction cosine vector A from preset receiver position information according to the equation (54). The least square positioning solution calculator 6 substitutes the pseudo distance difference Δr _{k, i, j} selected by the receiver selector 30 based on the distance difference and the direction cosine vector A into the equation (51) to obtain the least square positioning solution u. Calculate _k underbar.

In the smoother 10, the positioning solution u _k underbar calculated by the least square positioning solution calculator 6, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k ( -) Is used to calculate a smoothing vector ((x _k underbar) hat) (+) and a smoothing error covariance matrix P _k (+) according to equations (37) to (39).

In the predictor 8, the smoothing vector ((x _k−1 underbar) hat) (+) and the smoothing error covariance matrix P _k−1 (+) before one sampling are input via the delay circuit 11, and the equation (33) ) (predicted vector according 35) _{((x k} underscore) to formula hat) (-), the prediction error covariance matrix _P k (-), the position prediction vector _{((u k} underscore) hat) (-) is calculated respectively . The distance difference converter 26 converts the prediction vector ((x _k underbar) hat) (−) calculated by the predictor 8 into a distance difference prediction vector according to the equation (72).

The prediction distance difference residual probability density calculator 27 receives a prediction vector ((x _k underbar) hat) (−) and a prediction error covariance matrix P _k (−) from the predictor 8, and is set in advance. From the observation error variance σ ′ _{k, i, j} of the distance difference between the two transmitters and the receiver 2, the probability density function P [Δr _{k, i, j} of the prediction residual of the distance difference according to the equation (75) | U _k−1 ] variance Ω _{k, i} is calculated.

  As described above, the radio wave transmitted from the transmitter 1 whose position is unknown is received by the plurality of receivers 2 whose positions are known, and the propagation time difference between the signals of the transmitter 1 at the receiver position. Alternatively, even if the present invention is applied to a method of measuring the phase difference and measuring the transmitter position, the position of the transmitter 1 can be determined with higher accuracy as in the seventeenth embodiment.

Embodiment 20. FIG.
In the eighteenth embodiment, radio waves from a plurality of transmitters 1 whose positions are known are received by a receiver 2 whose positions are unknown, and the propagation time from the transmitter 1 to the receiver 2 is measured. In this embodiment, on the contrary, the radio waves from the transmitter 1 whose position is unknown are received by a plurality of receivers 2 whose positions are known. Then, an application example in which the present invention is applied to a method of measuring the propagation time difference and phase difference of radio waves from the transmitter 1 to the receiver 2 and from the transmitter 1 to the receiver 2 to determine the position of the transmitter will be described.

  20 is a block diagram showing a position estimation apparatus according to the twentieth embodiment. In the figure, reference numerals 1, 2, 5, 6, 8, 10, 11, 17, 26 to 29, which are the same as those in FIG. Since this is the same as or equivalent to that of Form 18, the description thereof is omitted.

  30 is input a probability density function of the predicted distance difference residual output from the predicted distance difference residual probability density calculator 27, and positioning is determined from among the pseudo-range differences between the transmitter and each receiver output from each receiver 2. This is a receiver selector based on a distance difference that selects a pseudo-range difference suitable for.

Next, specific operations of the position estimation apparatus according to Embodiment 20 will be described with reference to FIG. The radio wave emitted from the transmitter 1 reaches the receiver 2 after a delay time based on the distance from the transmitter 1 to the receiver 2. The pseudo-range difference calculator 17 calculates a pseudo-range difference Δr _{k, i, j} (i, j = 1, 2,..., N) from the propagation time difference or phase difference of the signals from the two transmitters 1.

In the receiver selector 30 based on the distance difference, the prediction distance difference Δr _{k, i, j} (−) and the variance Ω _{k, i, j} of the probability density function of the prediction residual of the pseudo distance difference are used as the prediction distance difference residual probability density. Input from the calculator 27, select a pseudo-range difference Δr _{k, i, j} (i, j = 1, 2,..., N) that satisfies Equation (76), and not Exclude.

  In the filter switching unit 21, the direction cosine vector calculation is performed when the pair of the receivers 1 is selected by the receiver selector 30 based on the distance difference and the number of the pairs is four or more that is sufficient for positioning. The processing is transferred to the device 5, and the processing is transferred to the distance difference observation matrix calculator 28 when the number is less than four.

In the direction cosine vector calculator 5, when the number of the receivers 2 selected by the receiver selector 30 based on the distance difference is four or more, the direction cosine vector calculator 5 calculates the direction from the preset transmitter position information according to the equation (54). A cosine vector A is calculated. The least square positioning solution calculator 6 substitutes the pseudo distance difference Δr _{k, i, j} selected by the receiver selector 30 based on the distance difference and the direction cosine vector A into the equation (51) to obtain the least square positioning solution u. Calculate _k underbar.

In the smoother 10, the positioning solution calculated by the least square positioning solution calculator 6, the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k (−) calculated by the predictor 8 are used. The smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k (+) are calculated using the equations (37) to (39).

In the distance difference observation matrix calculator 28, when the number of the receivers 2 selected by the receiver selector 30 based on the distance difference is less than four, the prediction vector ((x _k underbar) hat) calculated by the predictor 8 is used. A distance difference observation matrix H ₄ (((x _k underbar) hat) (−)) is calculated from (−) according to the equation (83).

In the distance difference by the position smoother 29, the distance pseudo distance difference is selected by the receiver selector 30 by difference vector [Delta] r _k underscores the distance difference observation matrix calculator distance difference calculated at 28 observation matrix H _{4 (((} x _k underbar) hat) (−)), the prediction vector ((x _k underbar) hat) (−) and the prediction error covariance matrix P _k (−) calculated by the predictor 8, The smoothing vector ((x _k underbar) hat) (+) and the smoothing error covariance matrix P _k (+) are calculated according to the equation (86).

In the predictor 8, when the number of the receivers 2 selected by the receiver selector 30 due to the distance difference is four or more, the input is made through the delay circuit 11 calculated by the smoother 10, while the selected one is selected. When the number of receivers 2 is less than 4, the smoothing vector ((x _k-1 underbar) hat) (+) before sampling calculated by the position smoother 29 based on the distance difference and the smoothing error covariance matrix P _{k −1} (+) is input via the delay circuit 11, and a prediction vector ((x _k underbar) hat) (−), a prediction error covariance matrix P _k (−), according to Expressions (33) to (35), position prediction vector _{(u k} underscore) (-) is calculated respectively. The distance difference converter 26 converts the prediction vector ((x _k underbar) hat) (−) calculated by the predictor 8 into a distance difference prediction vector according to the equation (72).

The prediction distance difference residual probability density calculator 27 receives a prediction vector ((x _k underbar) hat) (−) and a prediction error covariance matrix P _k (−) from the predictor 8, and is set in advance. From the observation error variance σ ′ _{k, i, j} of the distance difference between the two transmitters and the receiver 2, the probability density function P [Δr _{k, i, j} of the prediction residual of the distance difference according to the equation (75) | U _k−1 ] variance Ω _{k, i} is calculated.

  As described above, the radio wave transmitted from the transmitter 1 whose position is unknown is received by the plurality of receivers 2 whose positions are known, and the propagation time difference between the signals of the transmitter 1 at the receiver position. Alternatively, even if the present invention is applied to a method of measuring the phase difference and measuring the transmitter position, the position of the transmitter 1 can be determined with higher accuracy as in the eighteenth embodiment.

It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 1 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 2 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 3 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 4 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 5 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 6 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 7 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 8 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 9 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 10 of this invention. It is the block diagram which showed the structure of the position estimation apparatus based on Embodiment 11 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 12 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 13 of this invention. It is the block diagram which showed the structure of the position estimation apparatus based on Embodiment 14 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 15 of this invention. It is the block diagram which showed the structure of the position estimation apparatus based on Embodiment 16 of this invention. It is the block diagram which showed the structure of the position estimation apparatus which concerns on Embodiment 17 of this invention. It is the block diagram which showed the structure of the position estimation apparatus based on Embodiment 18 of this invention. It is the block diagram which showed the structure of the position estimation apparatus based on Embodiment 19 of this invention. It is the block diagram which showed the structure of the position estimation apparatus based on Embodiment 20 of this invention.

Explanation of symbols

  1 transmitter, 2 receiver, 3 transmitter combination changer, 4 pseudorange calculator, 5 direction cosine vector calculator, 6 least squares positioning solution calculator, 7 positioning solution memory, 8 predictor, 9 positioning solution selection , 10 smoother, 11 delay circuit, 12 prediction residual probability density calculator, 13 gate determiner, 14 positioning solution reliability calculator, 15 distance residual storage, 16 receiver combination changer, 17 pseudorange difference Calculator, transmitter selector by 18 distance, 19 distance converter, 20 predicted distance residual probability density calculator, 21 filter switcher, 22 distance observation matrix calculator, 23 position smoother by distance, receiver by 24 distance Selector, 25 Transmitter selector by distance difference, 26 Distance difference converter, 27 Predicted distance difference residual probability density calculator, 28 Distance difference observation matrix calculator, 29 Position by distance difference Smoother, 30 receiver selector by distance difference.

Claims (36)

Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
For each combination of the transmitters by the transmitter combination changing means, a positioning solution for the receiver position is calculated based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver. Positioning solution calculation means;
A predicting means for predicting a current receiver position from a previously measured receiver position;
Selection means for selecting the transmitter combination by the transmitter combination changing means based on the prediction residual between the predicted position calculated by the prediction means and the positioning solution calculated by the positioning solution calculation means; A position estimation apparatus comprising the position estimation device. Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
For each combination of the transmitters by the transmitter combination changing means, a positioning solution for the receiver position is calculated based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver. Positioning solution calculation means;
A prediction probability distribution calculating means for calculating a prediction probability distribution of the positioning solution calculated by the positioning solution calculating means for each combination of the transmitters by the transmitter combination changing means;
A position estimation apparatus comprising: selection means for selecting a combination of the transmitters by the transmitter combination change means based on the probability density of the positioning solution in the prediction probability distribution. Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
For each combination of the transmitters by the transmitter combination changing means, a positioning solution for the receiver position is calculated based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver. Positioning solution calculation means;
Prediction probability distribution calculating means for calculating a prediction probability distribution of the positioning solution by the positioning solution calculating means for each combination of the transmitters by the transmitter combination changing means;
Reliability calculation means for calculating the reliability of the positioning solution based on the probability density of the positioning solution in the predicted probability distribution;
And a weighting means for weighting the positioning solution according to the reliability. Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
Least-squares positioning solution calculation that uses the least-squares method to calculate the positioning solution of the receiver position based on the distance between a plurality of transceivers obtained by measuring the propagation time from the transmitter to the receiver Means,
Probability distribution calculating means for calculating a probability distribution of a distance residual between the propagation distance calculated from the propagation time from the transmitter to the receiver and the positioning solution for each combination of the transmitters by the transmitter combination changing means; ,
A position estimation apparatus comprising: selection means for selecting a combination of the transmitters by the transmitter combination change means based on the probability density of the distance residual in the probability distribution. Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
Least-squares positioning solution calculation that uses the least-squares method to calculate the positioning solution of the receiver position based on the distance between a plurality of transceivers obtained by measuring the propagation time from the transmitter to the receiver Means,
Probability distribution calculating means for calculating a probability distribution of a distance residual between the propagation distance calculated from the propagation time from the transmitter to the receiver and the positioning solution for each combination of the transmitters by the transmitter combination changing means; ,
Reliability calculation means for calculating the reliability of the positioning solution based on the probability density of the distance residual in the probability distribution;
And a weighting means for weighting a positioning solution according to the reliability. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A receiver combination changing means for generating a combination of a predetermined minimum number or more of receivers necessary for measuring the transmitter position from all receivable receivers;
For each combination of the receivers by the receiver combination changing means, a positioning solution for the transmitter position is calculated based on the distance between the transmitters and receivers obtained by measuring the propagation time from the transmitter to the receiver. Positioning solution calculation means;
A prediction means for predicting the current position from the transmitter positions measured in the past;
Selection means for selecting a combination of the receivers by the receiver combination changing means based on a prediction residual between the predicted position calculated by the prediction means and the positioning solution calculated by the positioning solution calculation means; A position estimation apparatus comprising the position estimation device. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A receiver combination changing means for changing a combination of a predetermined minimum number or more of the receivers necessary for measuring the transmitter position from all the receivers capable of receiving;
For each combination of the receivers by the receiver combination changing means, a positioning solution for the transmitter position is calculated based on the distance between the transmitters and receivers obtained by measuring the propagation time from the transmitter to the receiver. Positioning solution calculation means;
Prediction probability distribution calculating means for calculating a prediction probability distribution of the positioning solution calculated by the positioning solution calculating means for each combination of the receivers by the receiver combination changing means;
A position estimation apparatus comprising: selection means for selecting a combination of the receivers by the receiver combination change means based on the probability density of the positioning solution in the prediction probability distribution. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A receiver combination changing means for generating a combination of a predetermined minimum number or more of receivers necessary for measuring the transmitter position from all receivable receivers;
For each combination of the receivers by the receiver combination changing means, a positioning solution for the transmitter position is calculated based on the distance between the transmitters and receivers obtained by measuring the propagation time from the transmitter to the receiver. Positioning solution calculation means;
Prediction probability distribution calculating means for calculating a prediction probability distribution of the positioning solution by the positioning solution calculating means for each combination of the receivers by the receiver combination changing means;
Reliability calculation means for calculating the reliability of the positioning solution based on the probability density of the positioning solution in the predicted probability distribution;
And a weighting means for weighting the positioning solution according to the reliability. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A receiver combination changing means for generating a combination of a predetermined minimum number or more of receivers necessary for measuring the transmitter position from all receivable receivers;
Based on the distance between a plurality of transmitters and receivers obtained by measuring the propagation time from the transmitter to the receiver, the least-squares positioning solution calculation that calculates the positioning solution of the transmitter position using the least square method Means,
Probability distribution calculating means for calculating a probability distribution of the distance residual between the propagation distance calculated from the propagation time from the transmitter to the receiver and the positioning solution for each combination of the receivers by the receiver combination changing means; ,
A position estimation apparatus comprising: selection means for selecting a combination of the receivers by the receiver combination change means based on the probability density of the distance residual in the probability distribution. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A receiver combination changing means for generating a combination of a predetermined minimum number or more of receivers necessary for measuring the transmitter position from all receivable receivers;
Based on the distance between a plurality of transmitters and receivers obtained by measuring the propagation time from the transmitter to the receiver, the least-squares positioning solution calculation that calculates the positioning solution of the transmitter position using the least square method Means,
Probability distribution calculating means for calculating a probability distribution of the distance residual between the propagation distance calculated from the propagation time from the transmitter to the receiver and the positioning solution for each combination of the receivers by the receiver combination changing means; ,
Reliability calculation means for calculating the reliability of the positioning solution based on the probability density of the distance residual in the probability distribution;
And a weighting means for weighting the positioning solution according to the reliability. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
For each combination of the transmitters by the transmitter combination changing means, the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured, and the reception is performed based on the propagation time difference or the phase difference. Positioning solution calculation means for calculating a positioning solution of the aircraft position;
A prediction means for predicting the current position from the position of the receiver measured in the past;
Selection means for selecting the transmitter combination by the transmitter combination changing means based on the prediction residual between the predicted position calculated by the prediction means and the positioning solution calculated by the positioning solution calculation means; A position estimation apparatus comprising the position estimation device. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
For each combination of the transmitters by the transmitter combination changing means, the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured, and the reception is performed based on the propagation time difference or the phase difference. Positioning solution calculation means for calculating a positioning solution of the aircraft position;
A prediction probability distribution calculating means for calculating a prediction probability distribution of the positioning solution calculated by the positioning solution calculating means for each combination of the transmitters by the transmitter combination changing means;
A position estimation apparatus comprising: selection means for selecting a combination of the transmitters by the transmitter combination change means based on the probability density of the positioning solution in the prediction probability distribution. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
For each combination of the transmitters by the transmitter combination changing means, the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured, and the reception is performed based on the propagation time difference or the phase difference. Positioning solution calculation means for calculating a positioning solution of the aircraft position;
Prediction probability distribution calculating means for calculating a prediction probability distribution of the positioning solution by the positioning solution calculating means for each combination of the transmitters by the transmitter combination changing means;
Reliability calculation means for calculating the reliability of the positioning solution based on the probability density of the positioning solution in the predicted probability distribution;
And a weighting means for weighting the positioning solution according to the reliability. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
Based on the propagation time difference or phase difference between signals from each transmitter at the receiver position, a least square positioning solution calculation means for calculating a positioning solution of the receiver position using a least square method;
Probability distribution calculating means for calculating a probability distribution of a distance residual between the propagation distance difference calculated from the propagation time difference or the phase difference and the positioning solution for each combination of the transmitters by the transmitter combination changing means;
A position estimation apparatus comprising: selection means for selecting a combination of the transmitters by the transmitter combination change means based on the probability density of the distance residual in the probability distribution. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
Transmitter combination changing means for generating a combination of a predetermined minimum number of transmitters or more necessary for measuring the receiver position from all receivable transmitters; and
Based on the propagation time difference or phase difference between signals from each transmitter at the receiver position, a least square positioning solution calculation means for calculating a positioning solution of the receiver position using a least square method;
Probability distribution calculating means for calculating a probability distribution of a distance residual between the propagation distance difference calculated from the propagation time difference or the phase difference and the positioning solution for each combination of the transmitters by the transmitter combination changing means;
Reliability calculation means for calculating the reliability of the positioning solution based on the probability density of the distance residual in the probability distribution;
And a weighting means for weighting a positioning solution according to the reliability. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A receiver combination changing means for generating a combination of a predetermined minimum number or more of receivers necessary for measuring the transmitter position from all receivable receivers;
For each combination of the receivers by the receiver combination changing means, the propagation time difference or phase difference between the received signals in each receiver is measured, and the positioning solution of the transmitter position is based on the propagation time difference or the phase difference. Positioning solution calculation means for calculating
A prediction means for predicting the current position from the transmitter positions measured in the past;
Selection means for selecting a combination of the receivers by the receiver combination changing means based on a prediction residual between the predicted position calculated by the prediction means and the positioning solution calculated by the positioning solution calculation means; A position estimation apparatus comprising the position estimation device. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A receiver combination changing means for changing a combination of a predetermined minimum number or more of the receivers necessary for measuring the transmitter position from all the receivers capable of receiving;
For each combination of the receivers by the receiver combination changing means, the propagation time difference or phase difference between the received signals in each receiver is measured, and the positioning solution of the transmitter position is based on the propagation time difference or the phase difference. Positioning solution calculation means for calculating
Prediction probability distribution calculating means for calculating a prediction probability distribution of the positioning solution calculated by the positioning solution calculating means for each combination of the receivers by the receiver combination changing means;
A position estimation apparatus comprising: selection means for selecting a combination of the receivers by the receiver combination change means based on the probability density of the positioning solution in the prediction probability distribution. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A receiver combination changing means for generating a combination of a predetermined minimum number or more of receivers necessary for measuring the transmitter position from all receivable receivers;
For each combination of the receivers by the receiver combination changing means, the propagation time difference or phase difference between the received signals in each receiver is measured, and the positioning solution of the transmitter position is based on the propagation time difference or the phase difference. Positioning solution calculation means for calculating
Prediction probability distribution calculating means for calculating a prediction probability distribution of the positioning solution by the positioning solution calculating means for each combination of the receivers by the receiver combination changing means;
Reliability calculation means for calculating the reliability of the positioning solution based on the probability density of the positioning solution in the predicted probability distribution;
And a weighting means for weighting the positioning solution according to the reliability. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A receiver combination changing means for generating a combination of a predetermined minimum number or more of receivers necessary for measuring the transmitter position from all receivable receivers;
Based on the propagation time difference or phase difference between the received signals at each receiver, least square positioning solution calculation means for calculating a positioning solution of the transmitter position using the least square method,
For each combination of the receivers by the receiver combination changing means, the propagation time difference or phase difference between the received signals in each receiver is measured, and the propagation distance difference calculated from the propagation time difference or the phase difference and the positioning are measured. A probability distribution calculating means for calculating a probability distribution of a distance residual with the solution;
A position estimation apparatus comprising: selection means for selecting a combination of the transmitters by the receiver combination change means based on a probability density of the distance residual in the probability distribution. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A receiver combination changing means for generating a combination of a predetermined minimum number or more of receivers necessary for measuring the transmitter position from all receivable receivers;
Based on a propagation time difference or phase difference between received signals in the receiver, a least-squares positioning solution calculation means for calculating a positioning solution of the transmitter position using a least-squares method;
For each combination of the receivers by the receiver combination changing means, the propagation time difference or phase difference between the received signals in each receiver is measured, and the propagation distance difference calculated from the propagation time difference or the phase difference and the positioning are measured. A probability distribution calculating means for calculating a probability distribution of a distance residual with the solution;
Reliability calculation means for calculating the reliability of the positioning solution based on the probability density of the distance residual in the probability distribution;
And a weighting means for weighting the positioning solution according to the reliability. Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
A prediction means for predicting the observation distance between each current transmitter and receiver from the position of the receiver measured in the past;
Selection means for selecting a transmitter based on a prediction residual between the predicted distance calculated by the prediction means and the observed distance between the transceivers;
A positioning solution that calculates a positioning solution for the receiver position based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver using the transmitter selected by the selection means. A position estimation device comprising: a calculating means. Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
A prediction means for predicting the distance between each current transmitter and receiver from the position of the receiver measured in the past;
A prediction probability distribution calculating means for calculating a probability distribution of a prediction residual between the prediction distance calculated by the prediction means and the observed distance between the transceivers;
Selection means for selecting a transmitter based on the probability density of the prediction residual in the prediction probability distribution;
A positioning solution that calculates a positioning solution for the receiver position based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver using the transmitter selected by the selection means. A position estimation device comprising: a calculating means. Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
A prediction means for predicting the distance between each current transmitter and receiver from the position of the receiver measured in the past;
Selection means for selecting a transmitter based on a prediction residual between the predicted distance calculated by the prediction means and the observed observation distance between the transceivers;
Filter switching means for switching to one of the first and second smoothing means according to the number of transmitters selected by the selection means;
A positioning solution that calculates a positioning solution for the receiver position based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver using the transmitter selected by the selection means. A calculation means;
Position estimation means based on a distance for estimating the position of the receiver based on the distance between the transmitter and receiver obtained by measuring the propagation time from the transmitter to the receiver using the transmitter selected by the selection means. And
The first smoothing means calculates a smooth distance based on the positioning solution and the predicted distance, and outputs the calculated smooth distance to the predictor.
The second smoothing unit calculates a smoothing distance before one sampling based on the pseudo distance, the predicted distance, and the observed distance, and outputs the calculated smoothed distance to the predicting unit. Between multiple transceivers obtained by receiving radio waves transmitted from multiple transmitters with known positions at a receiver with unknown positions and measuring the propagation time from the transmitter to the receiver A position estimation device for estimating a receiver position based on a distance,
A prediction means for predicting the distance between each current transmitter and receiver from the position of the receiver measured in the past;
A prediction probability distribution calculating means for calculating a probability distribution of a prediction residual between the prediction distance calculated by the prediction means and the observed distance between the transceivers;
Selection means for selecting a transmitter based on the probability density of the prediction residual in the prediction probability distribution;
Filter switching means for switching to one of the first and second smoothing means according to the number of transmitters selected by the selection means;
A positioning solution that calculates a positioning solution for the receiver position based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver using the transmitter selected by the selection means. A calculation means;
Position estimation means based on a distance for estimating the position of the receiver based on the distance between the transmitter and receiver obtained by measuring the propagation time from the transmitter to the receiver using the transmitter selected by the selection means. And
The first smoothing means calculates a smooth distance based on the positioning solution and the predicted distance, and outputs the calculated smooth distance to the predictor.
The second smoothing unit calculates a smoothing distance before one sampling based on the pseudo distance, the predicted distance, and the observed distance, and outputs the calculated smoothed distance to the predicting unit. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A predicting means for predicting the distance between each current receiver and the transmitter from the transmitter position measured in the past;
Selection means for selecting a receiver based on a prediction residual between the prediction distance calculated by the prediction means and the observed observation distance between the transceivers;
A positioning solution that calculates a positioning solution for the transmitter position based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver using the receiver selected by the selection means. A position estimation device comprising: a calculating means. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A predicting means for predicting the distance between each current transmitter and receiver from the position of the transmitter measured in the past;
A prediction probability distribution calculating means for calculating a probability distribution of a prediction residual between the prediction distance calculated by the prediction means and the observed distance between the transceivers;
Selection means for selecting a receiver based on the probability density of the prediction residual in the prediction probability distribution;
A positioning solution that calculates a positioning solution for the transmitter position based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver using the receiver selected by the selection means. A position estimation device comprising: a calculating means. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A predicting means for predicting the distance between each current receiver and the transmitter from the transmitter position measured in the past;
Selection means for selecting a receiver based on a prediction residual between the prediction distance calculated by the prediction means and the observed observation distance between the transceivers;
Filter switching means for switching to one of the first and second smoothing means according to the number of receivers selected by the selection means;
A positioning solution that calculates a positioning solution for the transmitter position based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver using the receiver selected by the selection means. A calculation means;
Position estimation means based on the distance for estimating the position of the transmitter based on the distance between the transmitter and receiver obtained by measuring the propagation time from the transmitter to the receiver using the receiver selected by the selection means. When,
With
The first smoothing means calculates a smooth distance based on the positioning solution and the predicted distance, and outputs the calculated smooth distance to the predictor.
The second smoothing unit calculates a smoothing distance before one sampling based on the pseudo distance, the predicted distance, and the observed distance, and outputs the calculated smoothed distance to the predicting unit. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and the propagation time from the transmitter to the receiver is measured. A position estimation device for estimating a transmitter position based on a distance,
A predicting means for predicting the distance between each current transmitter and receiver from the position of the transmitter measured in the past;
A prediction probability distribution calculating means for calculating a probability distribution of a prediction residual between the prediction distance calculated by the prediction means and the observed distance between the transceivers;
Selection means for selecting a receiver based on the probability density of the prediction residual in the prediction probability distribution;
Filter switching means for switching to one of the first and second smoothing means according to the number of receivers selected by the selection means;
A positioning solution that calculates a positioning solution for the transmitter position based on the distance between the transmitter and the receiver obtained by measuring the propagation time from the transmitter to the receiver using the receiver selected by the selection means. A calculation means;
Position estimation means based on the distance for estimating the position of the transmitter based on the distance between the transmitter and receiver obtained by measuring the propagation time from the transmitter to the receiver using the receiver selected by the selection means. And
The first smoothing means calculates a smooth distance based on the positioning solution and the predicted distance, and outputs the calculated smooth distance to the predictor.
The second smoothing unit calculates a smoothing distance before one sampling based on the pseudo distance, the predicted distance, and the observed distance, and outputs the calculated smoothed distance to the predicting unit. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
A prediction means for predicting a propagation time difference or a phase difference between signals from each transmitter at a current receiver position from a position of a receiver measured in the past;
Selection means for selecting a transmitter based on the prediction residual between the prediction time difference or prediction phase difference calculated by the prediction means and the observed time difference or phase difference;
Using the transmitter selected by the selection means, measure the propagation time difference or phase difference between signals from each transmitter at the receiver position, and based on the propagation time difference or phase difference, the receiver position A position estimation device comprising: a positioning solution calculating means for calculating a positioning solution. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
A prediction means for predicting a propagation time difference or a phase difference between signals from each transmitter at a current receiver position from a position of a receiver measured in the past;
A prediction probability distribution calculation means for calculating a probability distribution of a prediction residual between the prediction time difference or prediction phase difference calculated by the prediction means and the observed time difference or phase difference;
Selection means for selecting a transmitter based on the probability density of the prediction residual in the prediction probability distribution;
Using the transmitter selected by the selection means, measure the propagation time difference or phase difference between signals from each transmitter at the receiver position, and based on the propagation time difference or phase difference, the receiver position A position estimation device comprising: a positioning solution calculating means for calculating a positioning solution. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
A prediction means for predicting a propagation time difference or a phase difference between signals from each transmitter at a current receiver position from a position of a receiver measured in the past;
Selection means for selecting a transmitter based on the prediction residual between the prediction time difference or prediction phase difference calculated by the prediction means and the observed time difference or phase difference;
Filter switching means for switching to one of the first and third smoothing means according to the number of transmitters selected by the selection means;
Using the transmitter selected by the selection means, measure the propagation time difference or phase difference between signals from each transmitter at the receiver position, and based on the propagation time difference or phase difference, the receiver position Positioning solution calculation means for calculating a positioning solution of
Using the transmitter selected by the selection means, measure the propagation time difference or phase difference between the signals from each transmitter at the receiver position, and based on the propagation time difference or the phase difference, Position estimation means by time difference or phase difference for estimating position;
With
The first smoothing means calculates a smooth distance based on the positioning solution and the predicted distance, and outputs the calculated smooth distance to the predictor.
The third smoothing means calculates a smooth distance before one sampling based on the pseudo-range difference, the predicted distance, and the distance difference of the observation distance, and outputs the calculated smooth distance to the predicting means. Estimating device. Radio waves transmitted from multiple transmitters with known positions are received by receivers with unknown positions, and the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured. A position estimation device for estimating a receiver position based on the propagation time difference or the phase difference,
A prediction means for predicting a propagation time difference or a phase difference between signals from each transmitter at a current receiver position from a position of a receiver measured in the past;
A prediction probability distribution calculation means for calculating a probability distribution of a prediction residual between the prediction time difference or prediction phase difference calculated by the prediction means and the observed time difference or phase difference;
Selection means for selecting a transmitter based on the probability density of the prediction residual in the prediction probability distribution;
Filter switching means for switching to one of the first and second smoothing means according to the number of transmitters selected by the selection means;
Using the transmitter selected by the selection means, the propagation time difference or phase difference between signals from each transmitter at the receiver position is measured, and based on the propagation time difference or phase difference, the receiver A positioning solution calculating means for calculating a positioning solution;
Using the transmitter selected by the selection means, measure the propagation time difference or phase difference between the signals from each transmitter at the receiver position, and based on the propagation time difference or the phase difference, Position estimation means by time difference or phase difference for estimating position;
With
The first smoothing means calculates a smooth distance based on the positioning solution and the predicted distance, and outputs the calculated smooth distance to the predictor.
The third smoothing unit calculates a smoothing distance before one sampling based on the pseudo-range difference, the predicted distance, and the distance difference of the observation distance, and outputs the smoothed distance to the predicting unit. Estimating device. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A predicting means for predicting a propagation time difference or a phase difference between signals from each transmitter at a current receiver position from a transmitter position measured in the past;
Selection means for selecting a receiver based on the prediction residual between the prediction time difference or prediction phase difference calculated by the prediction means and the observed time difference or phase difference;
Using the receiver selected by the selection means, measure the propagation time difference or phase difference between signals from each transmitter at the receiver position, and based on the propagation time difference or phase difference, the transmitter position Positioning solution calculation means for calculating a positioning solution of
A position estimation apparatus comprising: A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A predicting means for predicting a propagation time difference or a phase difference between signals from each transmitter at a current receiver position from a transmitter position measured in the past;
A prediction probability distribution calculation means for calculating a probability distribution of a prediction residual between the prediction time difference or prediction phase difference calculated by the prediction means and the observed time difference or phase difference;
Selection means for selecting a receiver based on the probability density of the prediction residual in the prediction probability distribution;
Using the receiver selected by the selection means, measure the propagation time difference or phase difference between signals from each transmitter at the receiver position, and based on the propagation time difference or phase difference, the transmitter position Positioning solution calculation means for calculating a positioning solution of
A position estimation apparatus comprising: A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A predicting means for predicting a propagation time difference or a phase difference between signals from each transmitter at a current receiver position from a transmitter position measured in the past;
Selection means for selecting a receiver based on the prediction residual between the prediction time difference or prediction phase difference calculated by the prediction means and the observed time difference or phase difference;
Filter switching means for switching to one of the first and third smoothing means according to the number of receivers selected by the selection means;
Using the receiver selected by the selection means, measure the propagation time difference or phase difference between signals from each transmitter at the receiver position, and based on the propagation time difference or phase difference, the transmitter position Positioning solution calculation means for calculating a positioning solution of
Using the receiver selected by the selection means, measure the propagation time difference or phase difference between the signals from each transmitter at the receiver position, and based on the propagation time difference or the phase difference, A position estimation means based on a time difference or phase difference for estimating the position,
The first smoothing means calculates a smooth distance based on the positioning solution and the predicted distance, and outputs the calculated smooth distance to the predictor.
The third smoothing means calculates a smooth distance before one sampling based on the pseudo-range difference, the predicted distance, and the distance difference of the observation distance, and outputs the calculated smooth distance to the predicting means. Estimating device. A radio wave transmitted from a transmitter whose position is unknown is received by a plurality of receivers whose positions are known, and a propagation time difference or a phase difference between received signals at each receiver is measured. A position estimation device that estimates a transmitter position based on the phase difference,
A predicting means for predicting a propagation time difference or a phase difference between signals from each transmitter at a current receiver position from a transmitter position measured in the past;
A prediction probability distribution calculation means for calculating a probability distribution of a prediction residual between the prediction time difference or prediction phase difference calculated by the prediction means and the observed time difference or phase difference;
Selection means for selecting a receiver based on the probability density of the prediction residual in the prediction probability distribution;
Filter switching means for switching to one of the first and third smoothing means according to the number of receivers selected by the selection means;
Using the receiver selected by the selection means, measure the propagation time difference or phase difference between signals from each transmitter at the receiver position, and based on the propagation time difference or phase difference, the transmitter position Positioning solution calculation means for calculating a positioning solution of
Using the receiver selected by the selection means, measure the propagation time difference or phase difference between the signals from each transmitter at the receiver position, and based on the propagation time difference or the phase difference, Position estimation means by time difference or phase difference for estimating position;
With
The first smoothing means calculates a smooth distance based on the positioning solution and the predicted distance, and outputs the calculated smooth distance to the predictor.
The third smoothing means calculates a smooth distance before one sampling based on the pseudo-range difference, the predicted distance, and the distance difference of the observation distance, and outputs the calculated smooth distance to the predicting means. Estimating device.

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