JP2011145128A - Measurement apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a measurement apparatus for providing a user with information on an error generated in measurement information when the to-be-measured measurement information is estimated. <P>SOLUTION: An estimation means 13 estimates the to-be-measured measurement information such as an arrival orientation of a radio signal, a distance to a transmission source or a position of the transmission source based on the radio signal received by an observation means 12, thereby making a display means 14 display the to-be-measured measurement information. A maximum error evaluation means 11 obtains error information indicating an error included in the physical quantity estimated by the estimation means 13, thereby making the display means 14 display the error information. The maximum error evaluation means 11 obtains the maximum value of the estimation error generated in the estimation quantity due to a model error as an error of the actual observation quantity from an estimation model used for the estimation of the physical quantity by the estimation means 13, thereby making the display means 14 display the maximum value. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a measurement apparatus that measures measurement information to be measured, and more specifically, using a radio signal, at least one of the direction of the source of the radio signal, the distance to the source, and the position of the source. The present invention relates to a measuring device for measuring one.

  As a measuring device for measuring at least one of the azimuth of the transmission source of the radio signal, the distance to the transmission source, and the position of the transmission source using the radio signal, the angle measuring device described in Non-Patent Document 1, the measurement Distance devices and positioning devices are known.

  The angle measuring device receives a radio signal using a plurality of antennas arranged close to each other, and estimates the arrival direction of the radio signal from the received signal. The distance measuring device receives a radio wave signal transmitted from a transmitter or a reflected wave signal reflected by a radio wave reflector, and measures a distance from the received signal to the transmitter or the radio wave reflector. As a positioning device, the position of the radio wave transmitter is measured using a plurality of positioning means, and the position of the radio wave transmitter is measured using the difference in arrival time of the radio signal between the antennas using a plurality of antennas. What measures the position of a radio wave transmitter by combining a ranging device and a angle measuring device, and what measures the position of a radio wave transmitter by combining a plurality of angle measuring devices are known.

  In a measuring apparatus that measures the azimuth, distance, position, and the like using such a radio signal, thermal noise is superimposed on a received signal that is an observation amount, resulting in an error in the measurement result. Therefore, a measurement device that uses radio signals makes use of the fact that thermal noise follows a Gaussian distribution, performs multiple observations, and integrates the observation results to reduce errors due to thermal noise, such as orientation. Estimating means for estimating the measurement object is provided.

  For example, Patent Document 1 discloses an angle measuring device using a radio wave signal. This angle measuring device is also based on the assumption that noise according to a Gaussian distribution is superimposed on an observation signal. And estimating means for estimating the arrival direction of the radio signal.

JP 2004-361377 A

Tadao Saito and Keiji Tachikawa, “New Edition Mobile Communication Handbook”, 1st Edition, Ohm Co., Ltd., November 25, 2000, p. 507-509

  In order to configure the estimation means disclosed in the above-mentioned Patent Document 1 and the like, first, it is assumed that the statistical property of the observation amount is expressed by a certain function. This function is a random variable that expresses the statistical properties of thermal noise and at least one of the quantity to be estimated, that is, the direction of the source of the radio signal, the distance to the source, and the position of the source. To a random variable that represents the statistical properties of the observed quantity. Since this function is a function for modeling the observation environment and the observation apparatus, it is referred to as a “model function” in the following description.

  If the sample of the actually observed observables has a statistical property that is exactly expressed by the model function, observe a sufficiently large number of samples using appropriate observation means, It is known that the estimation error due to thermal noise can be reduced to a negligible level by performing the overall estimation. Based on this fact, the measuring device using the radio signal estimates the azimuth, distance, position, and the like.

  In order for the above fact to hold, the actual observation environment and the observation apparatus must exactly match the estimation model which is a model according to the model function. However, since the radio wave signal propagating in the space is reflected or diffracted by the object, the antenna cannot measure only the direct wave from the transmission source. It is also difficult to manufacture a transmitting device and a receiving device that handle high frequencies strictly without causing an error. That is, the actual observation environment and the observation apparatus have an error from the estimation model, and the observation amount includes a model error that is an error from the model function.

  In a conventional measuring apparatus using a radio signal, it is implicitly assumed that the model error is negligibly small. In this conventional measuring apparatus using radio signals, there is no problem as to how small the model error is, and how large the problem is. Also, no information is provided on how much estimation error an expected model error produces.

  It is unknown to the user of the measuring apparatus how much model error the actual observation environment and the observation apparatus have. As described above, the measurement apparatus using the conventional radio wave signal does not provide information on the model error and the estimation error caused by the model error. Therefore, the error of the estimated amount by the user of the measurement apparatus. There is a problem of not knowing.

  An object of the present invention is to provide a measuring apparatus capable of providing a user with information regarding errors occurring in measurement information when estimating measurement information to be measured.

  The measurement apparatus of the present invention includes an acquisition unit that acquires relationship information related to measurement information to be measured, an estimation unit that estimates the measurement information based on the relationship information acquired by the acquisition unit, and the estimation Error evaluation means for obtaining error information representing an error included in the measurement information estimated by the means, display for displaying the measurement information estimated by the estimation means, and the error information obtained by the error evaluation means Means.

  According to the measurement apparatus of the present invention, the relationship information related to the measurement information to be measured is acquired by the acquisition unit, and the measurement information is estimated by the estimation unit based on the acquired relationship information. Further, error information representing an error included in the estimated measurement information is obtained by the error evaluation means. The measurement information estimated by the estimation unit and the error information obtained by the error evaluation unit are displayed by the display unit. Thereby, when the measurement information is estimated by the estimation means, error information regarding an error occurring in the measurement information can be provided to the user.

It is a block diagram which shows the structure of the measuring apparatus 1 which is the 1st Embodiment of this invention. It is a figure which shows typically the structure of the ranging system 20 containing the ranging apparatus 21 which is the 4th Embodiment of this invention. 3 is a block diagram showing a configuration of observation means 12. FIG. It is a figure which shows typically the structure of the positioning system 40 containing the positioning apparatus 41 which is the 6th Embodiment of this invention. It is a figure which shows typically the structure of the positioning system 50 containing the positioning apparatus 51 which is the 9th Embodiment of this invention. It is a figure which shows typically the structure of the angle measuring device 61 which is the 12th Embodiment of this invention. It is a figure which shows typically the structure of the positioning system 70 containing the positioning apparatus 71 which is the 14th Embodiment of this invention. It is a figure which shows typically the structure of the positioning system 80 containing the positioning apparatus 81 which is a 16th Embodiment of this invention.

<First Embodiment>
FIG. 1 is a block diagram showing a configuration of a measuring apparatus 1 according to the first embodiment of the present invention. The measuring device 1 measures measurement information to be measured. The measurement information is a physical quantity such as a distance. In the present embodiment, measurement apparatus 1 uses a radio signal to measure a physical quantity related to the source of the radio signal as measurement information. In the present embodiment, measuring device 1 measures at least one of the direction of a radio wave signal transmission source, the distance to the transmission source, and the position of the transmission source. Hereinafter, the direction of the radio signal transmission source may be referred to as the radio signal arrival direction.

  The measuring apparatus 1 includes a maximum error evaluation unit 11, an observation unit 12, an estimation unit 13, a display unit 14, and a sensor 19. The maximum error evaluation unit 11 corresponds to an error evaluation unit. The observation unit 12 corresponds to an acquisition unit. The measuring device 1 is used as, for example, an angle measuring device, a distance measuring device or a positioning device. The angle measuring device, the distance measuring device, and the positioning device to which the measuring device 1 of the present embodiment is applied will be described in the embodiments described later.

  The observation unit 12 acquires relation information related to the measurement information. In the present embodiment, the observation unit 12 is realized by a reception unit that receives a radio signal, and observes the radio signal. The observation means 12 acquires related information from the received radio wave signal. In this embodiment, as the measurement information, at least one of the azimuth of the transmission source of the radio signal, the distance to the transmission source, and the position of the transmission source is measured. The arrival time from the transmission source, the phase difference between radio signals arriving from a plurality of transmission sources, and the like are acquired. The radio signal observed by the observation unit 12 is processed by the estimation unit 13.

  The estimation unit 13 estimates measurement information based on the relationship information acquired by the observation unit 12. More specifically, the estimation unit 13 estimates the measurement information using a model function that models and expresses the relationship information. A model that follows the model function is called an “estimated model”. In the present embodiment, the estimating means 13 processes the radio wave signal observed by the observing means 12 to estimate a physical quantity related to the radio signal source as measurement information. Specifically, the estimation means 13 estimates at least one of the azimuth of the radio signal transmission source, the distance to the transmission source, and the position of the transmission source as measurement information. Hereinafter, the measurement information estimated by the estimation means 13 may be referred to as “estimated amount”.

  Measurement information estimated by the estimating means 13, that is, estimated quantities such as azimuth, distance and position are displayed by the display means 14. The display unit 14 provides the user of the measuring apparatus 1 by displaying the estimation amount estimated by the estimation unit 13.

  The maximum error evaluation unit 11 obtains error information representing an error included in the estimated amount that is the measurement information estimated by the estimation unit 13 and outputs the error information to the display unit 14. In the present embodiment, the maximum error evaluation means 11 obtains the maximum value of the estimation error that may occur in the estimation amount due to the model error (hereinafter sometimes referred to as “maximum estimation error”). Here, the model error is an error from the model function included in the observation amount, which is the relationship information acquired by the observation unit 12. The estimation error is an error generated in the estimated amount due to the model error.

  Specifically, the maximum error evaluation unit 11 uses the estimation amount such as the azimuth, the distance, and the position estimated by the estimation unit 13, and uses information provided from the sensor 19 as necessary, as the error information. The maximum estimation error which is the maximum estimation error occurring in the estimation amount is quantified and output to the display means 14. Specific examples of cases where information from the sensor 19 is necessary and not required will be described later. The display unit 14 displays the error information quantified by the maximum error evaluation unit 11 in addition to the estimated amount estimated by the estimation unit 13, in this embodiment, the total estimated error in the present embodiment. Provide to users.

  The maximum error evaluation unit 11 includes a proportional coefficient calculation unit 15, an estimated model storage unit 16, a maximum error calculation unit 17, and a model error amount estimation unit 18. The estimation model storage unit 16 stores a model function that is a function for modeling an observation amount such as a radio signal observed by the observation unit 12 as an estimation model. The proportional coefficient calculation means 15 is configured to calculate a model error and an estimation error, which is an error generated in the estimation amount due to the model error, from the estimation model stored in the estimation model storage means 16 and the estimation amount estimated by the estimation means 13. The proportionality coefficient, that is, the proportionality coefficient from the model error to the estimation error is calculated.

  The model error amount estimation means 18 estimates the amount of model error (hereinafter referred to as “model error amount”). The model error amount estimation means 18 estimates the model error amount using information given from the sensor 19 as necessary. The maximum error calculation unit 17 quantifies the maximum estimation error, that is, the maximum error of the estimation amount, from the model error amount estimated by the model error amount estimation unit 18 and the proportionality coefficient calculated by the proportionality coefficient calculation unit 15. Hereinafter, the quantified amount of maximum error may be referred to as “maximum error amount”.

  Below, each component contained in the maximum error evaluation means 11 is demonstrated in detail.

  First, prior to configuring the maximum error evaluation means 11, the model error is parametrized with a vector η, that is, a parametric variable is displayed, and a set Eγ of model errors to be considered is expressed by the following equation (1). Hereinafter, the model error may be referred to as “model error η”.

  In equation (1), symbol γ represents a threshold value that determines the magnitude of the model error η. The p-norm of the vector η shown in equation (1) is defined by the following equation (2).

In Formula (1) and Formula (2), the symbol p represents an integer of 1 or 2, or infinity (∞). In Equation (2), η _i represents the i-th element of the vector η, and | η _i | means the absolute value of η _i . When η is 0, it is assumed that there is no model error.

  The estimated amount estimated by the estimating means 13 differs depending on what the measuring apparatus 1 is applied to. The estimated amount is, for example, an orientation when the measuring device 1 is used as an angle measuring device, a distance when used as a distance measuring device, and a position when used as a positioning device. Depending on the application destination of the measuring apparatus 1, when estimating these estimation quantities, the variance of noise and the intensity of radio signals may be estimated simultaneously. In addition, when estimating the azimuth, distance, and position of a plurality of transmission sources, there are cases where it is desired to quantify only the estimation error relating to some of the estimated amounts.

  Therefore, the estimated amount for which the estimation error is to be quantified, such as the azimuth, distance and position, or a part thereof, is parameterized by the vector ξ, and the estimated amount for which the estimation error is not quantified is parameterized by the vector ζ. Since how to estimate various estimation amounts depends on the measurement amount and the measurement method, it will not be described in the present embodiment, and specific parameterization will be exemplified in the following embodiments.

  The statistical property of the observation amount observed by the observation means 12 is represented by a random variable Y. Since the vector ξ and the vector ζ can be estimated from the actual observation values by the observation means 12, that is, the sample of the random variable Y, the distribution followed by the random variable Y should change depending on the vector ξ and the vector ζ. Further, since an error occurs in the estimated value due to the model error η, the distribution followed by the random variable Y should also depend on the model error η. Therefore, the probability density function of the distribution that the random variable Y follows when there is no model error η is expressed as f (y, ξ, ζ), and the probability density function of the distribution that the random variable Y follows when there is a model error η. It is expressed as f˜ (y, ξ, ζ, η). However, it is assumed that f˜ (y, ξ, ζ, 0) = f (y, ξ, ζ). “F˜” represents a symbol in which the symbol “˜” is added to the symbol “f”.

  The estimated model storage means 16 stores a probability density function f˜ as a model function that is an estimated model. The estimated model storage means 16 stores the function form of the probability density function f˜ as a predetermined value using a semiconductor memory or the like. The specific method of storing is arbitrary, and it is sufficient that the probability density function f˜ can be calculated when y, ξ, ζ, and η are given at the minimum. For example, the estimated model storage means 16 stores the probability density function f˜ in the form of a computer program that calculates the probability density function f˜ from y, ξ, ζ, η.

The proportionality coefficient calculation means 15 is expressed by the following equation (3) from the probability density function f˜ stored in the estimation model storage means 16 and the estimated values ξ _est and ζ _{est of} the vectors ξ and ζ estimated by the estimation means 13. A matrix Ξ (y) in which matrix elements 行列_i (y) to be defined are arranged side by side with respect to all the elements ξ _i of the vector ξ is formed.

Similarly, the proportional coefficient calculation means 15 constitutes a matrix Φ (y) in which matrix elements φ _i (y) defined by the following expression (4) are arranged horizontally with respect to all elements ζ _i of the vector ζ. . Further, the proportionality coefficient calculation means 15 constitutes a matrix Ψ (y) in which matrix elements ψ _i (y) defined by the following equation (5) are arranged horizontally with respect to all elements η _i of the vector η.

  In addition, the proportionality coefficient calculation means 15 calculates a matrix defined by the following equations (6) and (7). In the equations (6) and (7), E is an expected value operator. The proportionality coefficient calculation means 15 calculates the expected value assuming that the random variable Y follows an ideal distribution with no model error.

  Finally, the proportional coefficient calculation means 15 calculates a matrix Λ defined by the following equation (8). This matrix Λ becomes the output of the proportional coefficient calculation means 15.

  As described above, when the probability density function f˜ is stored in the form of a computer program in the estimation model storage unit 16, the expected value is calculated in the proportional coefficient calculation unit 15 using the Markov chain Monte Carlo method. Calculation of differentiation at each step of the Markov chain Monte Carlo method is performed using numerical differentiation. For numerical differentiation, a known method described in S. Diop, JWGrizzle, F. Chaplais “On Numerical Differentiation Algorithms for Nonlinear Estimation” Proc. Of IEEE Conf. Decision and Control, 2000. (hereinafter referred to as “Reference 1”). The method can be used. For Markov chain Monte Carlo method, Yukito Iba and five others, "Frontier of Statistical Science (Volume 12) Computational Statistics II-Markov Chain Monte Carlo method and its surroundings", 1st edition, Iwanami Shoten Co., Ltd., 2005 10 May 28, p. A known method described in 8-13 (hereinafter referred to as “Reference 2”) can be used.

  Here, assuming that an estimation error caused by a model error η of the vector ξ is dξ, the estimation error dξ satisfies the relationship of the following equation (9).

  In Expression (9), O is Landau's asymptotic notation, and indicates that the difference between each element of the estimation error dξ and each element of Λη is equal to or less than a constant multiple of the square of the 2 norm of the model error η. Therefore, if the model error η is sufficiently small, the estimation error dξ can be approximated by Λη. That is, the example Λ is a proportional coefficient from the model error η to the estimated error dξ.

As described above, the proportional coefficient calculation unit 17 uses the probability density function f˜ stored in the estimation model storage unit 16 and the estimated values ξ _est and ζ _est estimated by the estimation unit 13 from the model error η. A matrix Λ that is a proportional coefficient to the estimation error dξ (hereinafter may be referred to as “proportional coefficient Λ”) is calculated.

As described above, since the estimation error dξ satisfies the relationship of the equation (9), when the model error η is included in the model error set E _γ , the maximum value of the estimation error dξ caused by the model error η (hereinafter “maximum”). The estimation error ”may be approximately evaluated by the following equations (10) and (11). Specifically, when the code p in the equation (1) representing the model error set E _γ is 1 or 2 (p = 1 or p = 2), the maximum estimation error is approximately expressed by the following equation (10). Can be evaluated. When the sign p in equation (1) is ∞ (p = ∞), the maximum estimation error can be approximately evaluated by the following equation (11). In Formula (10) and Formula (11), the symbol q represents an integer of 1 or 2, or ∞. In Expression (11), the symbol n indicates the number of columns of the matrix Λ.

  The right sides of Equation (10) and Equation (11) can be calculated as shown in Table 1 according to p and q. In Table 1, approximate evaluation of the maximum estimation error represented by the right side of Expression (10) or Expression (11) is shown for each combination of p and q.

  In Table 1, the symbol m indicates the number of rows of the matrix Λ. Further, the 1 norm, 2 norm and infinity norm of the matrix Λ shown in Table 1 are represented by the following equations (12), (13), and (14), respectively.

In Equation (13), σ _max (Λ) means the maximum singular value of the matrix Λ. Maximum singular values, for example, by WHPress, SATeukolsky, WTVetterling, BPFlannery, Tankeikatsu City, Haruhiko Okumura, Toshiro Sato, Makoto Kobayashi, “Numerical Recipes in C [Japanese version] Recipe for numerical computation in C language”, first edition, Technical Review Co., Ltd., November 1, 2001, p. 73-85, p. 386-p. 391 (hereinafter referred to as “Reference 3”).

  Among the evaluations shown in Table 1, evaluations other than the two items of p = q = 1 and p = q = 2 are conservative evaluations.

  The model error amount estimating means 18 estimates the above-described model error amount by estimating a threshold value γ that determines the magnitude of the model error η shown in the above-described equation (1). The simplest estimation of the threshold value γ is to output a predetermined constant. In other words, the model error amount estimation means 18 estimates the threshold value γ by outputting a predetermined constant as the threshold value γ, most simply. In this case, the measuring device 1 does not require the sensor 19.

  The model error amount estimation means 18 may estimate the threshold value γ from the radio wave signal observed by the observation means 12 (hereinafter sometimes referred to as “observation signal”), or estimate the threshold value γ using the sensor 19. Also good. When the threshold value γ is estimated from the observation signal, the observation means 12 performs the same function as the sensor 19, that is, the function that measures the radio wave environment and gives it to the model error amount estimation means 18, so there is no need to provide the sensor 19. . Therefore, the measuring apparatus 1 may not include the sensor 19.

  The maximum error calculation means 17 uses one of the evaluation values described in Table 1 or the matrix Λ that is the proportionality coefficient obtained by the proportionality coefficient calculation means 15 and the threshold value γ estimated by the model error amount estimation means 18 or Calculate multiple and output as maximum estimation error.

As described above, the maximum estimation error with respect to the model error η included in the model error set E _γ can be quantified by the maximum error evaluation unit 11. As a result, the measuring apparatus 1 can provide the user of the measuring apparatus 1 with error information regarding an error that has occurred in the estimated amount that is the measurement information, when the estimation means 13 estimates the measurement information. Specifically, the measuring apparatus 1 can provide the user of the measuring apparatus 1 with information on how much estimation error has occurred in the estimated value due to the model error η. Therefore, according to the measurement apparatus 1 of the present embodiment, when the actual observation environment and the model error η possessed by the observation apparatus are unknown, for example, when measurement is performed in an environment where there are many weak interference wave signals, and Even when the observation means 12 has a manufacturing error, the maximum estimation error caused by the model error η can be quantified and the information can be provided to the user of the measuring apparatus 1.

  Moreover, the measuring apparatus 1 of this Embodiment receives a radio signal by the observation means 12, and estimates measurement information by the estimation means 13 based on the received radio signal. According to the measurement apparatus 1 of the present embodiment, when the measurement information is estimated using the radio wave signal as described above, information regarding an error occurring in the measurement information can be provided to the user of the measurement apparatus 1.

<Second Embodiment>
Next, a measuring apparatus according to a second embodiment of the present invention will be described. The measuring apparatus of the present embodiment is the same as the measuring apparatus 1 of the first embodiment described above except that the processing in the maximum error evaluation means 11 is different. Description is omitted.

In the present embodiment, the maximum error evaluation means 11 analytically solves the proportionality coefficient Λ including the estimated values ξ _est and ζ _est . In the present embodiment, the estimated model storage means 16 is composed of a semiconductor memory or the like, and stores a program for calculating the proportional coefficient Λ from the estimated values ξ _est and ζ _est . The probability density function f˜, which is an estimation model, is incorporated in a program for calculating the proportionality coefficient Λ. Therefore, storing the program for calculating the proportionality coefficient Λ by the estimation model storage unit 16 corresponds to storing the probability density function f˜.

  The proportional coefficient calculation means 15 is realized by a program execution device such as a computer, and calculates the proportional coefficient Λ using a program stored in the estimation model storage means 16. The model error amount estimating means 18 and the maximum error calculating means 17 are configured in the same manner as in the first embodiment.

As described above, in the present embodiment, the maximum error evaluation unit 11 stores the program for calculating the proportional coefficient Λ from the estimated values ξ _est and ζ _{est in} the estimation model storage unit 16. Then, the maximum error evaluation means 11 calculates the proportionality coefficient Λ by the proportionality coefficient calculation means 15 using the program stored in the estimation model storage means 16. Thereby, the calculation using the Markov chain Monte Carlo method and the numerical differentiation in the proportionality coefficient calculation means 15 of the maximum error evaluation means 11 of the first embodiment can be omitted. Therefore, it is possible to reduce the amount of calculation required for the entire measuring apparatus as compared with the first embodiment.

<Third Embodiment>
Next, a measuring apparatus according to a third embodiment of the present invention will be described. The measurement apparatus of the present embodiment is the same as the measurement apparatus 1 of the first and second embodiments described above except that the processing in the maximum error evaluation means 11 is different. Similar descriptions are omitted.

In the above-described second embodiment, even when p and q shown in Table 1 are 2 (p = q = 2), the maximum error evaluation means 11 calculates the proportionality coefficient Λ using the estimated values ξ _{est and} ζ _est. Solve it analytically in a form that includes. On the other hand, in this embodiment, when p and q are 2 (p = q = 2), the maximum error evaluation means 11 uses the estimated value ξ as a matrix represented by the following equation (15). Analytical solution including _{est and} ζ _est .

The estimation model storage means 16 is composed of a semiconductor memory or the like, and stores a program for calculating a matrix represented by the formula (15) from the estimated values ξ _{est and} ζ _est . The probability density function f˜, which is an estimation model, is incorporated into a program that calculates the matrix represented by the equation (15). Therefore, storing the program for calculating the matrix represented by the equation (15) in the estimation model storage unit 16 corresponds to storing the probability density function f˜.

The proportional coefficient calculation means 15 is realized by a program execution device such as a computer, and calculates a matrix represented by the equation (15) using a program stored in the estimation model storage means 16. The model error amount estimation means 18 is configured in the same manner as in the first embodiment. In the present embodiment, the maximum error calculation means 17 uses the fact that the maximum singular value σ _max (Λ) of the proportionality coefficient Λ is equal to the square root of the maximum eigenvalue of the equation (15), and calculates the maximum error from the equation (15). Calculate the singular value σ _max (Λ).

  The proportionality coefficient Λ is a matrix having the number of rows for the number of estimators for which the estimation error is to be evaluated and the number of columns for the dimension of the model error parameter η. Since the model error parameter η has a large dimension, the proportionality coefficient Λ becomes a large matrix in the column direction. On the other hand, since the matrix represented by Equation (15) is a square matrix having the number of columns and the number of rows equal to the number of estimators for which estimation errors are to be evaluated, it is a matrix that is significantly smaller than the proportionality coefficient Λ. is there.

  In the present embodiment, since the maximum error evaluation means 11 calculates the matrix represented by the equation (15), the maximum estimation error can be obtained without directly calculating the large matrix Λ. As a result, the amount of calculation required by the entire measurement apparatus can be further reduced as compared with the measurement apparatus of the second embodiment described above.

<Fourth embodiment>
Next, a fourth embodiment of the present invention will be described. FIG. 2 is a diagram schematically showing a configuration of a distance measuring system 20 including a distance measuring device 21 according to the fourth embodiment of the present invention. The distance measuring system 20 includes a distance measuring device 21 and a transponder 23. The distance measuring device 21 according to the present embodiment is a distance measuring device to which the measuring device 1 according to the first embodiment described above is applied. Accordingly, the distance measuring device 21 includes the maximum error evaluation means 11, the observation means 12, the estimation means 13, the display means 14, and the sensor 19 shown in FIG. The distance measuring device 21 measures the distance between two points using a radio wave signal. In the present embodiment, the distance measuring device 21 considers the influence of the weak interference wave signal 27, that is, the error caused by the interference wave signal 27 as the model error.

  In the distance measuring system 20, a plurality of transponders 23 may be provided at different positions with respect to one distance measuring device 21. In the present embodiment, the ranging system 20 including two transponders 23 will be described for ease of understanding, but three or more transponders 23 may be provided.

  The distance measuring device 21 includes a distance measuring device antenna 22. The distance measuring device antenna 22 is provided in the observation means 12 shown in FIG. Each transponder 23 includes a transponder antenna 24. The distance measuring device 21 and the transponder 23 are respectively installed at two points where the distance is desired to be measured. More specifically, the distance measuring device 21 and the transponder 23 are installed such that the distance measuring device antenna 22 and the transponder antenna 24 exactly coincide with two points where the distance is desired to be measured.

  The distance measuring system 20 operates in the following procedure. First, the distance measuring device 21 transmits a trigger signal 25 to each transponder 23 via the distance measuring device antenna 22. Each transponder 23 receives the trigger signal 25 transmitted from the distance measuring device 21 by the transponder antenna 24. Upon receiving the trigger signal 25 transmitted from the distance measuring device 21, the transponder 23 sends a response signal 26 to the distance measuring device 21 via the transponder antenna 24 immediately or after a predetermined time β has elapsed. Send. The distance measuring device 21 receives the response signal 26 transmitted from each transponder 23 via the distance measuring device antenna 22. In the present embodiment, it is assumed that the weak interference wave signal 27 is received at the same time when the distance measuring device 21 receives the response signal 26.

  The transponder 23 may be realized by a wireless device including a radio signal transmitter / receiver and an amplifier, or may be realized by a simple radio wave reflector. When the transponder 23 is realized by a wireless device, the trigger signal 25 and the response signal 26 may be different or the same. When the transponder 23 is realized by a radio wave reflector, the signal reflected by the transponder 23 whose trigger signal 25 is a radio wave reflector is the response signal 26, and the predetermined time β is zero.

In the present embodiment, the number of transponders 23 is set to N, and each transponder 23 is distinguished by the subscript n. For example, the n-th transponder 23 among the plurality of transponders 23 is referred to as an n-th transponder 23. Since the radio wave signal propagates at the speed of light c, the elapsed time from when the distance measuring device 21 transmits the trigger signal 25 to when the response signal 26 is received is the distance between the distance measuring device 21 and the nth transponder 23. as l _n, it is expressed by the following equation (16).

  Therefore, the received signal received by the distance measuring device 21 under ideal conditions without an interference wave signal, specifically, the sample z (k) obtained by detecting the response signal 26 by IQ (In Phase-Quadrant Phase) is the transponder 23. Can be expressed by the following equation (17), where w (t) is the response signal 26 transmitted by the. In Expression (17), symbol h indicates a sampling period, and x (k) indicates noise.

When the n-th transponder 23 is realized by a wireless device, α _n in Equation (17) means a complex propagation coefficient of a radio wave signal that is a response signal 26 from the n-th transponder 23 to the distance measuring device 21. When the n-th transponder 23 is realized by a radio wave reflector, α _n in the equation (17) is the square of the complex propagation coefficient of the radio wave signal that is the response signal 26 from the n-th transponder 23 to the distance measuring device 21. It means the product of the reflection coefficient of the n transponder 23 multiplied.

Here, since x (k) can be regarded as following a complex Gaussian distribution, under an ideal situation where there is no interference wave signal, the probability density function f of the distribution followed by the received signal z (k) is expressed by the following equation (18). Can be expressed as U (k) in the equation (18) is defined by the following equation (19). In the equations (18) and (19), the symbol 1 indicates the distance between the distance measuring device 21 and the transponder 23 (hereinafter sometimes simply referred to as “distance”), and the distance measuring device 21 and the nth transponder. The distance l _n between the two is expressed by a vector arranged vertically. Α represents a propagation coefficient of a radio wave signal from the transponder 23 to the distance measuring device 21 (hereinafter sometimes simply referred to as “propagation coefficient”), and the complex propagation of the radio wave signal from the nth transponder 23 to the distance measuring device 21 is indicated. It is represented by a vector in which the coefficients α _n are arranged vertically. Also, σ represents the standard deviation of noise.

  In the present embodiment, the observation means 12 receives the response signal 26 that is a radio wave signal from the transponder 23, performs IQ detection on the received response signal 26, and outputs it as a complex digital sample z. The estimation means 13 obtains at least the distance l as an estimated value among the distance l, the propagation coefficient α, and the standard deviation σ that maximize the probability density function f when the sample z is an actual received signal. As a method for obtaining the distance l, for example, a known method described in the above-mentioned Reference 1 can be used. The estimated values of the propagation coefficient α and the standard deviation σ can be obtained from the estimated value of the distance l.

  Next, consider a case where an interference wave signal v (k) exists. When the interference wave signal v (k) exists, the received signal z (k) is represented by the following equation (20).

In the distance measuring device 21 according to the present embodiment, the maximum error evaluation unit 11 described in the first embodiment is used to perform interference under the assumption that the maximum power of the interference wave signal is approximately γ ^2. The maximum estimation error due to the wave signal can be quantified.

  The probability density function f˜ of the distribution followed by the received signal z when the interference wave signal is superimposed on the received signal is expressed by the following equation (21). U (k) in the equation (21) is defined by the following equation (22).

  Here, y, ξ, ζ, and η are set as shown in the following equations (23), (24), (25), and (26).

  If y, ξ, ζ, and η are set as shown in equations (23) to (26), the probability density function f of y depending on ξ, ζ, and η is expressed by the following equation (27). The U (ξ, ζ) in the equation (27) is defined by the following equation (28).

In equations (23) to (26), z ^r , α ^r , and v ^r represent the real parts of z, α, and v, respectively, and z ⁱ , α ⁱ , and v ⁱ represent imaginary parts of z, α, and v, respectively. Represents.

In equation (24), although with all of the l _n in the formula (22) xi], only a portion of the l _n in the formula (22) and xi], may be included the rest zeta. From The a total power of the interference wave signal is gamma ^2, the norm of the model error is p = 2. After that, the maximum error evaluation means 11 is configured as in the first embodiment.

<First Modification of Fourth Embodiment>
Next, as a maximum error evaluation means 11 of the distance measuring apparatus 21, a distance measuring apparatus to which the maximum error evaluation means 11 in the second embodiment is applied instead of the maximum error evaluation means 11 in the first embodiment. explain. In order to more clearly show the effect of reducing the above-described calculation amount by using the maximum error evaluation means 11 in the second embodiment, the number of samples K is sufficiently large and the response signal w (t) is approximately steady. Consider the signal case. In this case, the proportionality coefficient Λ can be calculated by the following procedure.

  First, the derivative of the function w (t) representing the response signal 26 is d (t), and a matrix W in which all elements of the function w (t) are arranged and a matrix D in which all elements of the derivative d (t) are arranged. , Respectively, as shown in the following equations (29) and (30).

Furthermore, the autocorrelation function of the function w (t) is R _{w, w} (t), and a matrix S _{w, w in} which all elements of the autocorrelation function R _{w, w} (t) are arranged is expressed by the following equation (31). As shown.

The cross-correlation function between the differential d (t) of the function w (t) and the function w (t) is R _{d, w} (t), and the autocorrelation function of the differential d (t) is R _{d, d} (t). A matrix S _{d, w in} which all elements of the cross-correlation function R _{d, w} (t) are arranged and a matrix S in which all elements of the autocorrelation function R _{d, d} (t) of the differential d (t) are arranged _{d and d} are set in the same manner as in equation (31). At this time, _let A be a matrix in which α _n is arranged diagonally, and ^let G ^r and G ⁱ be the real and imaginary parts of the matrix represented by the following equation (32), respectively.

  Further, let F be a matrix represented by the equation (33).

  The estimation error caused by the interference wave signal v at this time is expressed by the following equation (34).

Where v ^r is a matrix in which the real part of the interference wave signal v (k) is vertically arranged from k = 0 to k = K−1, and v ⁱ is the imaginary part of the interference wave signal v (k). It is a matrix arranged vertically from 0 to k = K-1. Therefore, the proportionality coefficient Λ is expressed by the following equation (35).

  The calculation of the proportionality coefficient Λ represented by the equation (35) is much smaller in calculation amount than the calculation using the Markov chain Monte Carlo method and the numerical differentiation method in the proportionality coefficient calculation means 15 of the first embodiment. . Therefore, the maximum error evaluation unit 11 of the distance measuring device 21 is replaced with the maximum error evaluation unit 11 in the first embodiment, instead of the maximum error evaluation unit 11 in the first embodiment. Compared to the embodiment, the amount of calculation required for the entire measuring apparatus can be reduced.

<Second Modification of Fourth Embodiment>
Next, as a maximum error evaluation means 11 of the distance measuring apparatus 21, a distance measuring apparatus to which the maximum error evaluation means 11 in the third embodiment is applied instead of the maximum error evaluation means 11 in the first embodiment. explain. When p = q = 2 and the maximum error evaluation means 11 described in the third embodiment is applied to the fourth embodiment, the maximum error evaluation means 11 is expressed as a matrix represented by the equation (15): What is necessary is ^just to calculate the matrix F ⁻¹ represented by the following equation (36).

  As apparent from the form of the equation (36), the calculation amount of the equation (36) is smaller than the calculation amount of the equation (35) used in the first modified example. Therefore, by using the maximum error evaluation means 11 in the third embodiment as the maximum error evaluation means 11 of the distance measuring device 21, a first modification using the maximum error evaluation means 11 in the second embodiment. Compared with the measuring apparatus, the amount of calculation required by the entire measuring apparatus can be further reduced.

  In the fourth embodiment, the observation unit 12 receives the response signal 26 from the transponder 23. The estimation means 13 estimates the distance l, the propagation coefficient α, and the noise standard deviation σ between the distance measuring device 21 that is a receiver and the transponder 23 from the response signal 26 received by the observation means 12. Since the estimated value of the propagation coefficient α and the standard deviation σ of noise can be calculated from the estimated value of the distance l, the estimating unit 13 only needs to be able to estimate at least the distance l.

  The estimated value of the distance l is characterized as a distance l that maximizes the probability density function f, but it is not always necessary to obtain the distance l by maximizing the probability density function f. The estimation means 13 may obtain an estimated value of the distance l by using a known means for obtaining the distance l that maximizes the probability density function f or an approximate value thereof with sufficient accuracy. As a known means for obtaining the estimated value of the distance l, for example, the means described in the above-mentioned Reference 1 can be used.

The maximum error evaluation means 11 quantifies the maximum estimation error, which is the maximum error given to the estimated value by the interference wave signal having the total power γ ² or less, from at least the estimated value of the distance l estimated by the estimating means 13, and the display means 14. To give. The display unit 14 provides the user of the distance measuring device 21 by displaying the estimated value estimated by the estimating unit 13 and the maximum estimated error quantified by the maximum error evaluating unit 11 in a comprehensive manner.

  In the maximum error evaluation unit 11, the estimation model storage unit 16 stores a program for calculating the probability density function f˜. The proportional coefficient calculation means 15 calculates the proportional coefficient Λ in the same manner as the maximum error evaluation means 11 in the first embodiment by using a program for forming the probability density function f˜ stored in the estimation model storage means 16. Ask. At this time, the estimation amount for which the estimation error should be quantified may be the distance between the distance measuring device 21 and all the transponders 23, or may be the distance between the distance measuring device 21 and some of the transponders 23. .

The model error amount estimation means 18 outputs, for example, a predetermined value as the threshold γ, outputs the noise standard deviation σ estimated by the estimation means 13 as the threshold γ, or measures the radio wave environment using the sensor 19. The model error amount is estimated by estimating the total power γ ² of the interference wave signal and outputting the threshold value γ. When outputting a predetermined value as the threshold γ, the sensor 19 is not necessary. When the standard deviation σ is output as the threshold value γ, the observation means 12 and the estimation means 13 perform the same function as the sensor 19, so the sensor 19 is not necessary.

  The maximum error calculation means 17 uses the threshold value γ estimated by the model error amount estimation means 18 and the proportionality coefficient Λ calculated by the proportionality coefficient calculation means 15 as p = 2, q in Table 1 as a quantitative value of the maximum estimation error. = 1, 2, or at least one of the quantities ∞ is calculated and output.

  When the maximum error evaluation unit 11 described in the second embodiment is used as the maximum error evaluation unit 11 of the distance measuring device 21 as in the first modification, the estimation model storage unit 16 is proportional to the equation (35). A program for calculating the coefficient Λ is stored. The proportionality coefficient calculation unit 15 is configured as a program execution device such as a computer that executes a program stored in the estimation model storage unit 16.

When p = q = 2 and the maximum error evaluation unit 11 described in the third embodiment is used as the maximum error evaluation unit 11 of the distance measuring device 21 as in the second modification, the estimated model storage unit 16 is , Configured to store a program for calculating ΛΛ ^T according to equation (36). Proportionality coefficient calculation unit 15 executes the program stored in the estimation model storage unit 16 obtains the matrix Ramudaramuda ^T represented by the formula (36). The maximum error calculation means 17 calculates the maximum estimation error from the ΛΛ ^T obtained by the proportional coefficient calculation means 15.

  According to the distance measuring device 21 of the present embodiment, in an environment where various interference wave signals exist, not only the distance between two distant points is measured using a radio wave signal, but the interference wave signal The maximum estimation error given to the estimated value of the distance can be quantified, and the information can be provided to the user of the distance measuring device 21. Further, as in the first and second modifications, the maximum estimation error can be provided with a smaller calculation amount by using the maximum error evaluation unit 11 described in the second or third embodiment. Therefore, as described above, the distance measuring device 21 that can quantify the maximum estimation error and provide it to the user can be realized with a simpler configuration.

<Fifth embodiment>
Next, a distance measuring apparatus according to a fifth embodiment of the present invention will be described. The distance measuring device according to the present embodiment uses a manufacturing error of the observation means 12 instead of an error caused by the interference wave signal 27 as a model error in the distance measuring device 21 according to the fourth embodiment shown in FIG. It has a structure that takes into account. The distance measuring apparatus according to the present embodiment is the same as the distance measuring apparatus 21 according to the fourth embodiment described above except that the model error to be considered is a manufacturing error of the observation means 12, and therefore different parts will be described. Similar explanations are omitted.

  Similar to the distance measuring device 21 of the fourth embodiment, the distance measuring device of the present embodiment constitutes the distance measuring system 20 together with the transponder 23 shown in FIG. The distance measuring device according to the present embodiment is a distance measuring device to which the measuring device 1 according to the first embodiment is applied, as in the fourth embodiment. Therefore, the distance measuring apparatus of the present embodiment is configured to include the maximum error evaluation means 11, the observation means 12, the estimation means 13, the display means 14, and the sensor 19 shown in FIG.

  FIG. 3 is a block diagram showing the configuration of the observation means 12. Specifically, the observation means 12 includes a ranging device antenna 22, a first amplifier 31, an I detector 32, a second amplifier 32, and a Q detector 34. The observation means 12 receives the response signal 26 transmitted from the transponder 23 via the distance measuring device antenna 22. The received response signal 26 is supplied to the first amplifier 31 and the second amplifier 33 and amplified by the amplifiers 31 and 32. The signal amplified by the first amplifier 31 is given to the I detector 32, and I detection is performed by the I detector 32. The signal amplified by the second amplifier 33 is given to the Q detector 34, and Q detection is performed by the Q detector 34. The signal I-detected by the I-detector 32 and the signal Q-detected by the Q-detector 34 are supplied to the estimating means 13.

In the present embodiment, a case is considered in which a gain error is superimposed in a multiplicative manner on the real part and the imaginary part of the signal given to the estimation means 13 due to the manufacturing error of the observation means 12. The I detector 32 is given a gain due to the first amplifier 31, and the Q detector 34 is given a gain due to the second amplifier 33. As a result, the received signal z (k) is expressed by the following equation (37), where b ^r is the real part parameter of the gain error and b ⁱ is the imaginary part parameter.

In Formula (37), the symbol j represents an imaginary unit. α _n ^r represents the real part of the complex propagation coefficient α _n shown in Expression (17), and α _n ⁱ represents the imaginary part of the complex propagation coefficient α _n shown in Expression (17). ω, k, h, l _n , c, β, and x (k) are the same as in equation (17). As a standard at the time of manufacture, it is assumed that the gain error parameters b ^r and b ⁱ in the equation (37) satisfy the following equation (38).

  At this time, the manufacturing error η of the observation means 12 which is a model error is set as shown in the following equation (39), and the others constitute the maximum error evaluation means 11 as in the fourth embodiment described above. Thereby, the maximum estimation error caused by the manufacturing error of the observation means 12 can be quantified.

Also in the present embodiment, as described in the second or third embodiment, the calculation amount is reduced by analytically obtaining the proportionality coefficient Λ or ΛΛ ^T and configuring the maximum error evaluation means 11. can do.

  As described above, according to the distance measuring apparatus of the present embodiment, even when the observation unit 12 has a manufacturing error, the distance between two distant points is estimated using the radio signal, and the observation unit It is possible to quantify the maximum estimated error, which is the maximum error of the 12 manufacturing errors on the estimated value, and provide the information to the user of the distance measuring apparatus. Further, by using the maximum error evaluation unit 11 of the second or third embodiment as the maximum error evaluation unit 11, the estimated value and the maximum estimation error can be provided with a smaller calculation amount.

  In the present embodiment, the maximum error evaluation means 11 for the manufacturing error of the observation means 12 is shown following the maximum error evaluation means 11 for the interference wave signal shown in the fourth embodiment, but for other model errors. However, the maximum error evaluation means 11 can be configured similarly.

<Sixth Embodiment>
Next, a sixth embodiment of the present invention will be described. FIG. 4 is a diagram schematically showing a configuration of a positioning system 40 including a positioning device 41 according to the sixth embodiment of the present invention. The positioning system 40 includes a positioning device 41 and a transponder 43. The positioning device 41 of the present embodiment is a positioning device to which the measuring device 1 of the first embodiment described above is applied. Therefore, the positioning device 41 includes the maximum error evaluation means 11, the observation means 12, the estimation means 13, the display means 14, and the sensor 19 shown in FIG. The positioning device 41 measures the position of the transponder 43 using a radio wave signal. In the present embodiment, the positioning device 41 considers the influence of the weak interference wave signal 46, that is, the error caused by the interference wave signal 46 as the model error.

  The transponder 43 is installed at a point whose position is to be measured. In the positioning system 40, a plurality of transponders 43 may be installed at different positions with respect to one positioning device 41. In FIG. 4, for ease of understanding, the positioning system 40 including one transponder 43 is illustrated, but two or more transponders 43 may be provided.

  The positioning device 41 includes a plurality of positioning device antennas 42. In the present embodiment, the positioning device 41 includes three positioning device antennas 42. The plurality of positioning device antennas 42 are provided at different positions. In other words, the positioning device 41 includes positioning device antennas 42 at two or more different positions. The positioning device antenna 42 is provided in the observation means 12 shown in FIG. The plurality of positioning device antennas 42 are configured to transmit and receive radio signals to and from the transponder 43 independently, for example, by transmitting a trigger signal in a time division manner.

  The transponder 43 includes a transponder antenna 44. Similar to the transponder 23 in the fourth embodiment, the transponder 43 may be realized by a radio apparatus including a radio signal transmitter / receiver and an amplifier, or may be realized by a simple radio wave reflector. .

  The positioning system 40 operates in the same procedure as the distance measuring system 20 shown in FIG. Specifically, first, the positioning device 41 transmits a trigger signal to each transponder 43 via each positioning device antenna 42. The transponder 43 receives the trigger signal transmitted from the positioning device 41 by the transponder antenna 44. When the transponder 43 receives the trigger signal transmitted from the positioning device 41, the radio signal 45 is transmitted as a response signal via the transponder antenna 44 to the positioning device 41 immediately or after a predetermined time β has elapsed. Send. The positioning device 41 receives the radio wave signal 45 transmitted from the transponder 43 via each positioning device antenna 42.

  When the transponder 43 is realized by a wireless device, the trigger signal and the radio signal 45 that is a response signal may be different or the same. When the transponder 43 is realized by a radio wave reflector, a signal reflected by the transponder 43 whose trigger signal is a radio wave reflector is a radio signal 45 which is a response signal, and the predetermined time β is zero.

In the present embodiment, it is assumed that the interference wave signal 46 is received as the model error η via each positioning device antenna 42. Further, it is assumed that the total power of the interference wave signal 46 is the square γ ² of the threshold value γ that determines the magnitude of the model error η shown in the above equation (1).

  A set of points equidistant from a certain positioning device antenna 42 draws a circle centered on the positioning device antenna 42 on a two-dimensional plane. When the positioning device 41 includes two positioning device antennas 42, if the distances from the two positioning device antennas 42 to the transponder 43 are measured, the position of the transponder 43 is limited to two points on the plane. In this case, as the prior knowledge, if the existence range of the transponder 43 is limited, the position of the transponder 43 can be determined by the two positioning device antennas 42. When the positioning device 41 includes three positioning device antennas 42, the distances from the three positioning device antennas 42 to the transponder 43 are respectively determined if the three positioning device antennas 42 are not in the same straight line. By measuring, the position of the transponder 43 can be uniquely determined in the plane.

Here, the number of transponders 43 is set to N, and each transponder 43 is distinguished by the subscript n. For example, the n-th transponder 43 among the plurality of transponders 43 is referred to as an n-th transponder 43. When the positioning system 40 includes one transponder 43, this transponder 43 is referred to as a first transponder 43. Further, the number of positioning device antennas 42 is denoted by M, and each positioning device antenna 42 is distinguished by a subscript m. For example, among the plurality of positioning device antennas 42, the m-th positioning device antenna 42 is referred to as an m-th positioning device antenna 42. The r _n Distant by the position of the n transponder 43 is expressed by two-dimensional vector, placing s _m represent the position of the m positioning device antenna 42 in a two-dimensional vector.

If the received signal of the interference wave signal v at the m-th positioning device antenna 42 is v _m (k), the received signal z _m (k) at the m-th positioning device antenna 42 is the radio signal from the transponder 43. 45 is w (t), radio wave signal w (t) from the n-th transponder 43 is w _n (t), and noise x (k) received by the m-th positioning device antenna 42 is x _m (k). Is expressed by the following formula (40).

Α _{m, n} in Expression (40) is a propagation coefficient of the radio wave signal 45 from the n-th transponder 43 to the m-th positioning device antenna 42 when the transponder 43 is realized by a wireless device. When realized by a radio wave reflector, the square of the propagation coefficient of the radio wave signal 45 from the n-th transponder 43 to the m-th positioning device antenna 42 is multiplied by the reflection coefficient of the n-th transponder 43. K, h, c, and β in Formula (40) are the same as in Formula (17).

Since a matrix in which z ₁ (k) to z _M (k) are vertically arranged is z (k), the probability density function that the received signal z follows is represented by the product of the probability density functions that z _m follows. , R ₁ to r _N are arranged as r, and σ ₁ to σ _M are arranged as σ, and the probability density function f˜ of the distribution followed by the received signal z is expressed by the following equation (41). expressed. However, u _m (k) in the equation (41) is defined by the following equation (42).

However, u _m (k) in the equations (41) and (42) means the m-th element of u (k). The ideal probability density function f when there is no model error is equal to the probability density function f˜ of equation (41) when v = 0 in equation (42).

  In the present embodiment, the observation means 12 of the positioning device 41 receives the radio signal 45 from the transponder 43. The estimation means 13 estimates the position of the transponder 43 from the received signal that is the radio wave signal 45 received by the observation means 12, for example, by a known means described in Non-Patent Document 1. The maximum error evaluation means 11 is the maximum estimation which is the maximum error of the estimated value caused by the interference wave signal 46 from at least the estimated position of the transponder 43 estimated by the estimating means 13 by the method described in the first embodiment. Quantify the error. The display means 14 provides the user of the positioning device 41 by displaying the estimated value estimated by the estimating means 13 and the maximum estimated error quantified by the maximum error evaluating means 11 together.

Also in the present embodiment, as described in the second or third embodiment, the calculation amount is reduced by analytically obtaining the proportionality coefficient Λ or ΛΛ ^T and configuring the maximum error evaluation means 11. can do.

  As described above, according to the positioning device 41 of the present embodiment, the position of the transponder 43 is measured using the radio wave signal 45 in an actual observation environment where a large number of interference wave signals 46 exist, and the interference wave signal The maximum estimation error which is the maximum positioning error caused by 46 can be quantified, and the information can be provided to the user of the positioning device 41. Further, by using the maximum error evaluation unit 11 of the second or third embodiment as the maximum error evaluation unit 11, the estimated value and the maximum estimation error can be provided with a smaller calculation amount.

  In the present embodiment, the maximum error evaluation unit 11 is configured using the interference wave signal as a model error. However, the maximum error evaluation unit 11 may be configured by a similar method for other model errors such as a manufacturing error. .

<Seventh embodiment>
Next, a positioning device according to a seventh embodiment of the present invention will be described. The positioning device of this embodiment is obtained by extending the positioning device 41 of the sixth embodiment shown in FIG. 4 to a positioning device that measures a position in a three-dimensional space. The positioning device of the present embodiment is the same as the positioning device 41 of the sixth embodiment except that the position to be measured is a position in a three-dimensional space. Similar explanations are omitted.

Positioning device 41 of the sixth embodiment described above, in formula (42), as a vector representing the position of the n transponder 43, using a two-dimensional vector r _n, represents the position of the m positioning device antenna 42 as a vector, and using the two-dimensional vector s _m. In this formula (42), by a two-dimensional vector s _m which represents the position of the two-dimensional vector r _n and the m positioning device antenna 42 representative of the position of the n transponder 43, to change the three-dimensional vector, respectively, the The positioning device 41 in the sixth embodiment can be easily extended to a positioning device that measures a position in a three-dimensional space. In this way, the positioning device according to the present embodiment is obtained by expanding the positioning device 41 according to the sixth embodiment to a positioning device that measures a position in a three-dimensional space.

  Also in the positioning device of the present embodiment, the position of the transponder 43 can be uniquely determined by the positioning device antennas 42 installed at three positions that are not on the same straight line.

  According to the positioning device of the present embodiment, the same effect as the positioning device 41 of the sixth embodiment is achieved. Specifically, the position of the transponder 43 is measured using the radio wave signal 45 even in a situation where there are many weak interference wave signals 46 and model errors such as manufacturing errors of the observation means 12 that is the radio wave receiver. At the same time, the maximum estimation error that is the maximum positioning error caused by the model error can be quantified, and the information can be provided to the user of the positioning device.

<Eighth Embodiment>
Next, a positioning device according to an eighth embodiment of the present invention will be described. The positioning device according to the present embodiment is the same as the positioning device 41 according to the sixth embodiment shown in FIG. 4 described above or the seventh device described above except that the position of the positioning device is measured instead of the position of the transponder 43. Since it is the same as the positioning device of the embodiment, different parts will be described, and illustration and similar description will be omitted. Hereinafter, the positioning device of the present embodiment may also be referred to as “positioning device 41”.

  In the above-described sixth and seventh embodiments, the transponder 43 is installed at a point where the position is desired to be measured, and the position of the transponder 43 is measured by the positioning device 41. In the present embodiment, transponders 43 are installed at a plurality of points whose position coordinates are known, and the position of the positioning device 41 is measured by the positioning device 41. In this case, the positioning system 40 includes a positioning device 41 and a plurality of transponders 43.

  The transponder 43 may be configured as a wireless device or a radio wave reflector, but is configured so that a plurality of transponders 43 can be identified from the observed radio signal 45. For example, when the transponder 43 is configured as a wireless device, a plurality of types of trigger signals are prepared, and only a specific transponder 43 returns a radio signal 45 as a response signal with respect to a specific trigger signal, or A response signal unique to each transponder 43 is returned as a radio signal 45 for one type of trigger signal. When the transponder 43 is configured as a radio wave reflector, for example, the positioning device antenna 42 of the positioning device 41 has directivity, and the response of the transponder 43 in a specific direction as viewed from the positioning device 41 in one measurement. Only the signal can be received as the radio wave signal 45.

  In the present embodiment, the distance between each transponder 43 and the positioning device 41 is measured based on the propagation time of the radio signal between each transponder 43 and the positioning device antenna 42 of the positioning device 41. The positioning device 41 can specify the position of its own device, that is, the position of the positioning device 41 by measuring the distance between at least two transponders 43 whose position coordinates are known.

  As described above, according to the positioning device 41 of the present embodiment, the radio wave signal 45 is present even in the presence of a number of weak interference wave signals and model errors such as manufacturing errors of the observation means 12 that is a radio wave receiver. Is used to measure the position of the positioning device 41, to quantify the maximum estimation error, which is the maximum positioning error caused by the model error, and to provide the information to the user of the positioning device 41.

<Ninth embodiment>
Next, a positioning device according to a ninth embodiment of the present invention is described. In this embodiment, a positioning device that uses a difference in arrival times of radio signals will be described. FIG. 5 is a diagram schematically showing a configuration of a positioning system 50 including a positioning device 51 according to the ninth embodiment of the present invention. The positioning system 50 includes a positioning device 51 and a transmitter 53. The positioning device 51 of the present embodiment is a positioning device to which the measuring device 1 of the first embodiment described above is applied. Therefore, the positioning device 51 includes the maximum error evaluation means 11, the observation means 12, the estimation means 13, the display means 14, and the sensor 19 shown in FIG. In the present embodiment, the positioning device 51 considers the influence of the weak interference wave signal 56 as a model error.

  The positioning device 51 includes positioning device antennas 52 at three or more different positions. In other words, the positioning device 51 includes three or more positioning device antennas 52, and these positioning device antennas 52 are provided at different positions. The positioning device antenna 52 is provided in the observation means 12 shown in FIG.

  The transmitter 53 includes a transmitter antenna 54. The transmitter 53 is installed at a point where the position is desired to be measured. In the positioning system 50, a plurality of transmitters 53 may be installed at different positions with respect to one positioning device 51. In FIG. 5, for ease of understanding, the positioning system 50 including one transmitter 53 is illustrated, but two or more transmitters 53 may be provided.

  The positioning device antenna 52 receives the radio wave signal 55 transmitted from the transmitter 53. In the present embodiment, when the radio wave signal 55 transmitted from the transmitter 53 is received, the weak interference wave signal 56 is superimposed on the reception signal that is the radio wave signal 55 received by each positioning device antenna 52. . Since the radio signal 55 propagates at the speed of light c, the received signal, which is the radio signal 55 received by each positioning device antenna 52, has a delay according to the distance between the transmitter 53 and each positioning device antenna 52. .

  Now, since the exact time at which the transmitter 53 transmits the radio signal 55 is unknown, the delay of the received signal cannot be measured by the single positioning device antenna 52. However, the difference in the delay of the received signal among the plurality of positioning device antennas 52 can be measured. That is, the distance between the positioning device antenna 52 and the transmitter 53 cannot be measured, but the distance between the transmitter 53 and one positioning device antenna 52 determined in advance, and the transmitter 53 and another positioning device antenna 52 determined in advance. The difference in distance from can be measured.

  In the present embodiment, the position of the transmitter 53 can be limited to one hyperbola by measuring the difference between the delays of the received signals with the two positioning device antennas 52. Therefore, the position of the transmitter 53 can be uniquely estimated by measuring the difference in the delay of the received signal between two different positioning device antennas 52.

Here, the number of transmitters 53 is set to N, and each transmitter 53 is distinguished by the subscript n. For example, the n-th transmitter 53 among the plurality of transmitters 53 is referred to as an n-th transmitter 53. When the positioning system 50 includes one transmitter 53, this transmitter 53 is referred to as a first transmitter 53. Further, the number of positioning device antennas 52 is denoted by M, and each positioning device antenna 52 is distinguished by a subscript m. For example, of the three or more positioning device antennas 52, the m-th positioning device antenna 52 is referred to as an m-th positioning device antenna 52. The addition position coordinates of the n transmitter 53, put the r _n represents a two-dimensional vector. Also, placing a s _m represents the position coordinates of each positioning device antenna 52 similarly in a two-dimensional vector.

At this time, the received signal z _m (k) at the m-th positioning device antenna 52 is expressed by the following equation (43), where the transmission signal 55 of the n-th transmitter 53 is w _n (t). In Equation (43), h is a sampling period, v _m (k) is an interference wave signal superimposed on the m-th positioning device antenna 52, and α _{m, n} is _m-th from the n-th transmitter 53. It is a propagation coefficient to the positioning device antenna 52, and x _m (k) is complex Gaussian noise.

A matrix in which z ₁ (k) to z _M (k) are arranged vertically is z (k), and the probability density function f˜ following the received signal z is r, and the matrix in which r ₁ to r _N are arranged is r When the standard deviation of noise at the m positioning device antenna 52 is σ _m and a matrix in which σ ₁ to σ _M are arranged vertically is σ, the following equation (44) is obtained. However, u _m (k) in the equation (44) is defined by the following equation (45).

U _m (k) in Expression (44) and Expression (45) means the m-th element of u (k). The ideal probability density function f when there is no model error is equal to the probability density function f˜ of equation (44) when v = 0 in equation (45).

Here, there is a problem if the maximum error evaluation means 11 is configured using the probability density function f˜ shown in Expression (44) in the same manner as in the first embodiment described above. As can be seen from the equation (43), w _n and α _{m, n} are arbitrary _, and there can be a plurality of combinations of α _{m, n} and w _n that give exactly the same z (k). Since transmission signal w _n of the transmitter 53 is a continuous signal, discretely sampled received signal z (k), it can not be uniquely estimate the transmitted signal w _n. This first causes the problem that the parameter of w _n (k) is made infinite, and Ω ₂₂ in equation (6) of the first embodiment becomes a singular matrix, making it impossible to calculate the inverse matrix.

In the positioning device using the arrival time difference of the radio signal, the probability density of the known means for estimating the position r _n of the transmitter 53, when the received signal z as in the present embodiment has an actual observed signal Instead of obtaining r, α, σ, and w that maximize the function f, only r is estimated by another means. Therefore, it is not necessary to calculate the inverse matrix described above. However, in the present embodiment, when the maximum error evaluation means 11 is configured according to the first embodiment described above, it becomes an obstacle because it is necessary to calculate the aforementioned inverse matrix.

Therefore, first, discrete Fourier transform is performed on both sides of the equation (43). When the discrete Fourier transform is performed, the following expression (46) is obtained. However, z _m ^ represents a discrete Fourier transform of z _m, w _n ^ represents a discrete Fourier transform of w _n, v _m ^ represents a discrete Fourier transform of v _m, discrete Fourier x _m ^ is x _m Represents a conversion. “Z _m ^”, “w _n ^”, “v _m ^”, and “x _m ^” are symbols obtained by adding a symbol “∧” on the symbols z _m , w _n , v _m, and x _m , respectively. To express.

  Since ＾ (k) becomes a discrete signal according to the equation (46), it is possible to perform parametrization as a part of ζ in the first embodiment described above.

  Next, the probability density functions f˜ shown in the equations (44) and (45) are expressed as shown in the following equations (47) and (48).

  In the present embodiment, the observation means 12 of the positioning device 51 receives the radio signal 55 transmitted from the transmitter 53. The estimation means 13 estimates at least the position of the transmitter 53 from the received signal, which is the radio wave signal 55 received by the observation means 12, for example, by a known means described in Reference Document 1 described above. The maximum error evaluation means 11 calculates z ^ (l) from the observation signal z (k) using fast Fourier transform or the like, and the maximum that the model error gives to the estimated value by the method described in the first embodiment. The maximum estimation error that is the error of is quantified. The fast Fourier transform can be performed by a known method described in Reference Document 3 described above. For quantifying the maximum estimation error, the method described in the second or third embodiment may be applied instead of the method described in the first embodiment.

When the methods of the first to third embodiments are applied, the probability density functions f˜ represented by the equations (47) and (48) are used as the probability density functions f˜. Also with respect to the first embodiment of formula (6) Omega ₂₂ is singular in the problem, when the calculation of the proportional coefficient lambda, deform equation (8) as shown in the following equation (49) . However, the Omega ⁺ _22, means a Moore-Penrose type pseudo-inverse of the Omega _22. The Moore-Penrose-type pseudo inverse matrix can be obtained by, for example, the singular value decomposition method which is a known method described in the above-mentioned Reference 3.

  When the maximum error evaluation means 11 of the second or third embodiment is applied to this embodiment, the second and third embodiments are the same except that the equation (49) is adopted as the definition of the proportional coefficient Λ. It is the same as the form.

  According to the positioning device 51 of the present embodiment, the position of the transmitter 53 is measured based on the arrival time difference of the radio wave signal 55 in an environment where many weak interference wave signals 56 arrive, and the interference wave signal The maximum estimation error, which is the maximum positioning error caused by 56, is quantified, and the information can be provided to the user of the positioning device 51.

  In the present embodiment, the maximum error evaluation unit 11 is configured using the interference wave signal as a model error. However, the maximum error evaluation unit can be configured by a similar method for other model errors such as a manufacturing error. .

<Tenth Embodiment>
Next, a positioning device according to a tenth embodiment of the present invention will be described. The positioning device of the present embodiment is obtained by extending the positioning device 51 of the ninth embodiment shown in FIG. 5 to a positioning device that measures a position in a three-dimensional space. The positioning device of the present embodiment is the same as the positioning device 51 of the ninth embodiment except that the position to be measured is a position in a three-dimensional space. Similar explanations are omitted.

Positioning device 51 of the ninth embodiment described above, each of the three-dimensional two-dimensional vectors s _m representing the position coordinates of the two-dimensional vector r _n and the positioning device antenna 52 which represents the position coordinates of the n transmitter 53 By using a vector, it can be easily extended to a positioning device that measures a position in a three-dimensional space. In this way, the positioning device according to the present embodiment is obtained by expanding the positioning device 51 according to the ninth embodiment to a positioning device that measures a position in a three-dimensional space. In the present embodiment, the position of the transmitter 53 can be determined by installing the positioning device antenna 52 at four different positions.

  According to the positioning device of the present embodiment, the same effect as the positioning device 41 of the ninth embodiment is achieved. Specifically, the position of the transmitter 53 is measured using the radio wave signal 55 even in the presence of a number of weak interference wave signals 56 and model errors such as manufacturing errors of the observation means 12 that is the radio wave receiver. In addition, the maximum estimation error, which is the maximum positioning error caused by the model error, can be quantified and the information can be provided to the user of the positioning device.

<Eleventh embodiment>
Next, a positioning device according to an eleventh embodiment of the present invention is described. The positioning device according to the present embodiment is the same as the positioning device 51 according to the ninth embodiment shown in FIG. 5 described above or the above-described first device except that the position of the positioning device is measured instead of the position of the transmitter 53. Since it is the same as that of the positioning apparatus of 10 embodiment, a different part is demonstrated and illustration and the same description are abbreviate | omitted. Hereinafter, the positioning device of the present embodiment may also be referred to as “positioning device 51”.

  In the ninth and tenth embodiments described above, the transmitter 53 is installed at a point where the position is to be measured, and the position of the transmitter 53 is measured by the positioning device 51. In the present embodiment, the transmitter 53 is installed at three or more points whose position coordinates are known, the positioning device 51 is installed at the position where the position is desired to be measured, and the position of the positioning device 51 is measured. In this case, the positioning system 50 includes a transmitter 53 installed at three or more points whose position coordinates are known, and a positioning device 51 installed at a point whose position is to be measured.

  In the present embodiment, the transmitter 53 is configured in the positioning device 51 so that the radio wave signal 55 transmitted from each transmitter 53 can be distinguished from which transmitter 53 is transmitted. In order to realize this configuration, the transmitter 53 transmits, for example, the radio signals 55 at different timings, the radio signals 55 transmitted at different frequencies, or different signals with small correlation. It is configured to transmit as a radio wave signal 55.

  In the present embodiment, the position of the positioning device 51 is on one hyperbola due to the difference between the distance between the positioning device 51 and one transmitter 53 and the distance between the positioning device 51 and another transmitter 53. Limited. Therefore, the position of the positioning device 51 can be uniquely determined by using at least three or more transmitters 53.

  According to the positioning device 51 of the present embodiment, the radio wave signal 55 is used even under a situation where there are many weak interference wave signals 56 and model errors such as manufacturing errors of the observation means 12 that is a radio wave receiver. While measuring the position of the positioning device 51, the maximum estimation error that is the maximum positioning error caused by the model error can be quantified, and the information can be provided to the user of the positioning device 51.

<Twelfth embodiment>
Next, a twelfth embodiment of the present invention will be described. FIG. 6 is a diagram schematically showing the configuration of the angle measuring device 61 according to the twelfth embodiment of the present invention. The angle measuring device 61 of the present embodiment is a angle measuring device to which the measuring device 1 of the first embodiment described above is applied. Accordingly, the angle measuring device 61 includes the maximum error evaluation unit 11, the observation unit 12, the estimation unit 13, the display unit 14, and the sensor 19 shown in FIG. The angle measuring device 61 estimates the arrival direction of a radio signal 63 coming from a radio source (not shown). In the present embodiment, the angle measuring device 61 considers the influence of many weak interference wave signals 64, that is, an error caused by the interference wave signal 64 as a model error.

  The angle measuring device 61 includes a plurality of, ie, two or more angle measuring device antennas 62. The plurality of angle measuring device antennas 62 are installed close to each other. The plurality of angle measuring device antennas 62 are provided in the observation means 12 shown in FIG.

  The angle measuring device 61 estimates the arrival direction of the incoming radio signal 63. The number of incoming radio signals 63 is denoted by N, and each radio signal is distinguished by a subscript n. For example, the nth radio signal 63 among a plurality of incoming radio signals 63 is referred to as an nth radio signal 63. In FIG. 6, one radio wave signal 63 is shown for easy understanding. In this case, this one radio signal 63 becomes the first radio signal 63.

  Further, the number of angle measuring device antennas 62 is denoted by M, and each angle measuring device antenna 62 is distinguished by the subscript m. For example, among the plurality of angle measuring device antennas 62, the m-th angle measuring device antenna 62 is referred to as an m-th angle measuring device antenna 62. In the present embodiment, the plurality of angle measuring device antennas 62 are close enough that the reception intensity of one radio wave signal 63 does not change in each angle measuring device antenna 62 and the waveform of the baseband signal can be regarded as the same. It shall be installed. In the present embodiment, it is assumed that the interference wave signal 64 is superimposed on the radio wave signal 63 received by each angle measuring device antenna 62 as a model error.

Here, one reference position of the angle measuring device 61 is taken and its coordinates are set as a two-dimensional vector s ₀ . Further m-th angle measuring device antenna 62 (m = 1, ···, M) is denoted by 2-dimensional vectors s _m position coordinates of. Here, a received signal assuming that the n-th radio signal 63 is received at the position s ₀ is set to w _n (k). Assuming that the n-th radio signal 63 arrives from the direction of the angle θ counterclockwise with the positive direction of the x-axis as 0 ° on the xy coordinate plane, the n-th radio signal 63 at the m-th angle measuring device antenna 62 is obtained. The received signal has a phase difference expressed by the following equations (50) and (51) with respect to w _n (k). However, in Formula (50) and Formula (51), λ is the wavelength of the center frequency of the radio signal 63.

From Equation (50) and Equation (51), if the received signal at the antenna 62 for the m-th angle measuring device is z _m (k) and a matrix in which z ₁ to z _M are arranged vertically is z, The reception signal z (k) of the device 61 is expressed by the following equations (52) and (53). However, in Formula (52) and Formula (53), w (k) is a matrix in which w _n (k) is vertically arranged, v is a matrix in which v _m (k) is vertically arranged, and v _m (K) is an interference wave signal 64 received by the m-th angle measuring device antenna 62, and x (k) is noise, which can be considered to follow an m-dimensional complex Gaussian distribution.

From Expression (50) and Expression (51), the probability density function f˜ of the distribution that the received signal z follows is expressed by the following Expression (54). However, in Expression (54), θ is a matrix in which θ _n is arranged vertically.

  The ideal probability density function f followed by the received signal z when there is no model error is equal to the probability density function f˜ when v = 0 in the equation (54).

  In the present embodiment, the observation means 12 receives a radio signal 63 coming from a radio source (not shown). The estimation unit 13 obtains at least θ among θ, σ, and w that maximizes the probability density function f, for example, by a known unit described in the above-mentioned Reference Document 1, where z is an actual received signal. Estimated values of σ and w can be obtained from θ. The maximum error evaluation means 11 is configured in the same manner as in the first embodiment based on the probability density function f˜.

Also in the present embodiment, the maximum error evaluation means 11 may be configured by analytically obtaining the proportional coefficient Λ or ΛΛ ^T as in the second or third embodiment. Thereby, the amount of calculation can be reduced.

  According to the angle measuring device 61 of the present embodiment, even in an environment where a large number of weak interference wave signals 64 arrive, the arrival angle of the radio wave signal 63 is measured and the maximum angle measurement caused by the interference wave signal 64 is achieved. The maximum estimation error, which is an error, is quantified, and the information can be provided to the user of the angle measuring device 61. Further, by using the maximum error evaluation means 11 of the second or third embodiment as the maximum error evaluation means 11, the arrival direction and the maximum estimation error of the radio wave signal 63, which are estimated values, can be reduced with a smaller calculation amount. Can be provided.

  In the present embodiment, the maximum error evaluation unit 11 is configured using the interference wave signal as a model error. However, the maximum error evaluation unit 11 can be configured similarly for other model errors such as a manufacturing error.

<Thirteenth embodiment>
Next, an angle measuring apparatus according to a thirteenth embodiment of the present invention will be described. The angle measuring device of the present embodiment is obtained by extending the angle measuring device 61 of the twelfth embodiment shown in FIG. 6 to a angle measuring device that measures the arrival direction of the radio signal 63 in a three-dimensional space. It is. The angle measuring device according to the present embodiment is the same as the angle measuring device 61 according to the twelfth embodiment except that the range in which the arrival direction of the radio signal 63 is measured is in a three-dimensional space. The illustration and the similar description are omitted.

Angle measuring device of the present embodiment, the angle measuring device 61 of the twelfth embodiment described above, measuring the position coordinates s _m corner device antenna 62 and a three-dimensional vector, the following equation [pi _n (55 ) Can be realized.

  Specifically, the angle measuring device of the present embodiment has a three-dimensional space when the azimuth is taken counterclockwise on the xy plane with respect to the positive direction in the x-axis direction and the elevation angle is taken in the z-axis direction. The arrival direction of the radio signal 63, specifically, the azimuth angle θ and the elevation angle ρ are estimated.

  According to the angle measuring device of the present embodiment, the radio wave signal 63 is used even under a situation where there are many weak interference wave signals 64 and model errors such as manufacturing errors of the observation means 12 that is a radio wave receiver. While measuring the arrival direction of the radio wave signal 63, the maximum estimation error, which is the maximum angle measurement error caused by the model error, is quantified, and the information can be provided to the user of the angle measuring device.

<Fourteenth embodiment>
Next, a positioning apparatus according to a fourteenth embodiment of the present invention is described. FIG. 7 is a diagram schematically showing a configuration of a positioning system 70 including a positioning device 71 according to the fourteenth embodiment of the present invention. The positioning system 70 includes a positioning device 71 and a transponder 73. The positioning device 71 of the present embodiment is a positioning device to which the measuring device 1 of the first embodiment described above is applied. Therefore, the positioning device 71 includes the maximum error evaluation means 11, the observation means 12, the estimation means 13, the display means 14, and the sensor 19 shown in FIG. The positioning device 71 measures the position of the transponder 73 by estimating the arrival angle of the radio signal 76 and estimating the arrival time.

  The transponder 73 is installed at a point whose position is to be measured. In the positioning system 70, a plurality of transponders 73 may be installed at different positions with respect to one positioning device 71. In FIG. 7, for ease of understanding, a positioning system 70 including one transponder 73 is illustrated, but two or more transponders 73 may be provided.

  The positioning device 71 includes a plurality of positioning device antennas 72. In the present embodiment, the positioning device 71 includes three positioning device antennas 72. The plurality of positioning device antennas 72 are installed close to each other. The positioning device antenna 72 is provided in the observation means 12 shown in FIG. The positioning device 71 transmits a trigger signal 75 to the transponder 73 from at least one of the plurality of positioning device antennas 72 or another antenna other than the plurality of positioning device antennas 72.

  The transponder 73 includes a transponder antenna 74. The positioning system 70 may be realized by a wireless device including a radio signal transmitter / receiver and an amplifier, as in the case of the transponder 23 in the above-described fourth embodiment, or may be realized by a simple radio wave reflector. Good.

  In the present embodiment, a case is considered in which an interference wave signal 77 is received by an individual positioning device antenna 72 as a model error. When the transponder 73 receives the trigger signal 75 transmitted from the positioning device 71, the radio signal 76 is sent as a response signal to the positioning device 71 via the transponder antenna 74 immediately or after a predetermined time β has elapsed. Send. The positioning device 71 receives the response signal 76 transmitted from the transponder 73 via a plurality of positioning device antennas 72.

  Here, the number of positioning device antennas 72 is denoted by M, and each positioning device antenna 72 is distinguished by a suffix m. For example, among the plurality of positioning device antennas 72, the m-th positioning device antenna 72 is referred to as an m-th positioning device antenna 72. Further, the number of transponders 73 is set to N, and each transponder 73 is distinguished by the subscript n. For example, the n-th transponder 73 among the plurality of transponders 73 is referred to as an n-th transponder 73. When the positioning system 70 includes one transponder 73, this transponder 73 is referred to as a first transponder 73.

When the response signal 76 from the n-th transponder 73 is set to w _n (t), the received signal z _m (k) at the m-th positioning device antenna 72 is expressed by the following equation (56).

However, s ₀ in the formula (56) are the coordinates of the reference position of the positioning apparatus 71, s _m is the coordinates of the m positioning device antenna 72, r _n are the coordinates of the n transponder 73. In addition, α _n in the equation (56) is a propagation coefficient of the response signal 76 from the n-th transponder 73 to the reference position of the positioning device 71 when the transponder 73 is realized by a wireless device. In this case, the square of the propagation coefficient of the response signal 76 from the nth transponder 73 to the reference position of the positioning device 71 is multiplied by the reflection coefficient of the nth transponder 73. In Equation (56), θ _n is the direction of the n-th transponder 73 viewed from the reference position of the positioning device 71, and φ _m (θ _n ) is caused by the arrival direction of the response signal 76 that is a radio signal. This is the phase difference at each positioning device antenna 72.

The phase difference φ _m (θ _n ) at each positioning device antenna 72 is specifically expressed by the following equation (57). Θ _n in the equation (57) is expressed by the following equation (58). E ₁ in the formula (58) is represented by the following formula (59), and E ₂ is represented by the following formula (60). However, Π _n is the same as in equation (51).

In Expression (56), v _m (k) is an interference wave signal 77 superimposed on the received signal received by the m-th positioning device antenna 72, and x _m (k) is noise that can be regarded as following a Gaussian distribution. It is.

From the above, the probability density function f˜ of the distribution that the received signal z follows is expressed by the following equations (61) and (62). However, in the formula (61) and formula (62), r is a matrix obtained by arranging r _n, sigma is the standard deviation of the noise. Z (k) is a matrix in which z ₁ (k) to z _M (k) are vertically arranged, and v (k) is a matrix in which v ₁ (k) to v _M (k) are vertically arranged. It is.

  The ideal probability density function f followed by the received signal z when there is no model error is equal to the probability density function f˜ when v = 0 in the equation (61).

  In the present embodiment, the observation means 12 of the positioning device 71 receives the response signal 76 transmitted from the transponder 73. The estimation means 13 obtains at least r out of r and σ that maximizes the probability density function f, for example, by a known means described in Reference Document 1 described above, where z is the actual received signal. The estimated value of σ can be obtained from r. The maximum error evaluation means 11 is configured in the same manner as in the first embodiment based on the probability density function f˜.

  Also in the present embodiment, the maximum error evaluation means 11 of the second or third embodiment may be used instead of the maximum error evaluation means 11 of the first embodiment.

  According to the positioning device 71 of the present embodiment, the position of the transponder 73 is measured and the maximum positioning error that is caused by the interference wave signal 77 is obtained even in an environment where many weak interference wave signals 77 arrive. The estimation error can be quantified and the information can be provided to the user of the positioning device 71.

  In the present embodiment, the maximum error evaluation unit 11 is configured using the interference wave signal 77 as a model error. However, the maximum error evaluation unit 11 may be configured in the same manner for other model errors such as a manufacturing error. it can.

<Fifteenth embodiment>
Next, a positioning device according to a fifteenth embodiment of the present invention is described. The positioning device of the present embodiment is obtained by extending the positioning device 71 of the fourteenth embodiment shown in FIG. 7 described above to a positioning device that measures the position of the transponder 73 in a three-dimensional space. The positioning device according to the present embodiment is the same as the positioning device 71 according to the fourteenth embodiment except that the position is measured in a three-dimensional space. Omitted.

Positioning device of the present embodiment, the positioning device 71 of the fourteenth embodiment described above represents the position coordinates of the two-dimensional vectors s _m and the n transponder 73 which represents the position coordinates of the m positioning device antenna 72 the two-dimensional vector r _n a 3-dimensional vector, respectively, and [pi _n of the formula (55) in the thirteenth embodiment of the [pi _n of the foregoing, further azimuth and theta _n of the n transponder 73, the elevation angle By setting ρ _n , it can be easily realized.

  According to the positioning device of the present embodiment, the same effect as the positioning device 71 of the fourteenth embodiment is achieved. Specifically, the position of the transponder 73 is measured by using the response signal 76 that is a radio wave signal even in an environment where a large number of weak interference wave signals 77 arrive and in a situation where manufacturing errors of the observation means 12 exist. In addition, the maximum positioning error caused by the model error can be quantified as the maximum estimation error, and the information can be provided to the user of the positioning device.

<Sixteenth Embodiment>
Next, a positioning device according to a sixteenth embodiment of the present invention is described. FIG. 8 is a diagram schematically showing a configuration of a positioning system 80 including a positioning device 81 according to the sixteenth embodiment of the present invention. The positioning system 80 includes a positioning device 81 and a transmitter 83. The positioning device 81 of the present embodiment is a positioning device to which the measuring device 1 of the first embodiment described above is applied. Therefore, the positioning device 81 includes the maximum error evaluation unit 11, the observation unit 12, the estimation unit 13, the display unit 14, and the sensor 19 shown in FIG. The positioning device 81 measures the position of the transmitter 83. In the present embodiment, the positioning device 81 considers the influence of many weak interference wave signals 86 as model errors.

  In the positioning system 80, a plurality of positioning devices 81 are installed at sufficiently separated positions. In FIG. 8, for ease of understanding, a positioning system 80 including two positioning devices 81 is illustrated, but three or more positioning devices 81 may be provided. Each positioning device 81 includes a plurality of positioning device antennas 82. In each positioning device 81, a plurality of positioning device antennas 82 are installed close to each other. Each positioning device 81 includes at least two positioning device antennas 82. FIG. 8 illustrates a case where each positioning device 81 includes three positioning device antennas 82. The positioning device antenna 82 is provided in the observation means 12 shown in FIG. The positioning device 81 receives a radio wave signal 85 transmitted from the transmitter 83 via each positioning device antenna 82.

  The transmitter 83 includes a transmitter antenna 84. The transmitter 83 is installed at a point where the position is desired to be measured. In FIG. 8, for ease of understanding, a positioning system 80 including one transmitter 83 is illustrated. However, the positioning system 80 includes a plurality of transmitters 83, and each transmitter 83 is configured with each transmitter 83. It may be installed at different positions.

  In the present embodiment, when the positioning device 81 receives a radio wave signal 85 transmitted from the transmitter 83 via each positioning device antenna 82, a number of weak interference wave signals 86 are also generated as model errors. Consider the case of receiving.

Here, the number of positioning devices 81 is set to L, and each positioning device 81 is distinguished by the subscript L (l). For example, the l-th positioning device 81 among the plurality of positioning devices 81 is referred to as an l-th positioning device 81. Further, the number of positioning device antennas 82 provided in the l-th positioning device 81 is set as M _l , and each positioning device antenna 82 is distinguished by the suffix m. For example, of the plurality of positioning device antennas 82, the m-th positioning device antenna 82 is referred to as an m-th positioning device antenna 82. Further, the number of transmitters 83 is set as N, and each transmitter 83 is distinguished by a subscript n. For example, the n-th transmitter 83 among the plurality of transmitters 83 is referred to as an n-th transmitter 83. When the positioning system 80 includes one transmitter 83, this transmitter 83 is referred to as a first transmitter 83.

Determining one coordinate to the l positioning device 81, placing it and b _l. Further, if the position of the m-th positioning device antenna 82 of the l-th positioning device 81 is set to r _{l, m} , the received signal z _{l, m} (k) at the m-th positioning device antenna 82 of the l-th positioning device 81 is And expressed by the following equation (63). In Equation (63), w _{l, n} is a received signal at the reference position of the l-th positioning device 81, v _{l, m} is an interference wave signal, and x _{l, m} follows a Gaussian distribution. It can be regarded as noise.

Also, φ _{l, m} (θ _{l, n} ), θ _{l, n} and Π _{l, n} in equation (63) are represented by the following equations (64), (65) and (66), respectively. .

  From Expression (63) to Expression (66), the probability density function f to the distribution that the received signal z follows is expressed by the following Expression (67).

However, in the formula (67), r is a matrix obtained by arranging r _n, sigma is a matrix obtained by arranging sigma _l, the sigma _l is the standard deviation of noise at the l positioning device 81. Further, z is a matrix obtained by arranging z _l, z _l is a matrix obtained by arranging z _{l, m.} w is a matrix obtained by arranging w _l, w _l is a matrix obtained by arranging w _{l, m.} v is a matrix composed of an array of the v _l, v _l is the matrix obtained by arranging v _{l, m.}

Furthermore, A _l in the formula (67) is represented by the following formula (68).

  The probability density function f of an ideal distribution that the received signal z follows when there is no model error is equal to the probability density function f˜ when v = 0 in the equation (67).

  In the present embodiment, the observation means 12 of the positioning device 81 receives the radio wave signal 85 transmitted from the transmitter 83. The estimation unit 13 obtains at least θ among θ, σ, and w that maximizes the probability density function f, for example, by a known unit described in the above-mentioned Reference Document 1, where z is an actual received signal. The estimated values of σ and w can be obtained from the estimated value of θ. The maximum error evaluation means 11 is configured in the same manner as in the first embodiment based on the probability density function f˜.

Also in the present embodiment, the maximum error evaluation means 11 may be configured by analytically obtaining the proportionality coefficient Λ or ΛΛ ^T as in the second or third embodiment. Thereby, the amount of calculation can be reduced.

  According to the positioning device 81 of the present embodiment, the position of the transmitter 83 is measured and the maximum positioning error caused by the interference wave signal 86 is obtained even in an environment where many weak interference wave signals 86 arrive. The maximum estimation error can be quantified and the information can be provided to the user of the positioning device 81.

  In the present embodiment, the maximum error evaluation unit 11 is configured using the interference wave signal 86 as a model error. However, the maximum error evaluation unit 11 can be configured similarly for other model errors such as a manufacturing error. .

<Seventeenth embodiment>
Next, a positioning device according to a seventeenth embodiment of the present invention is described. The positioning device of the present embodiment is obtained by extending the positioning device 81 of the sixteenth embodiment shown in FIG. 8 described above to a positioning device that measures the position of the transmitter 83 in a three-dimensional space. Since the positioning device of the present embodiment is the same as the positioning device 81 of the sixteenth embodiment except that the position is measured in a three-dimensional space, different parts will be described, and the illustration and the similar description will be given. Omitted.

  The positioning device according to the present embodiment can be easily realized by configuring the positioning device 81 according to the sixteenth embodiment so that the coordinates are handled as a three-dimensional vector and the angles are handled as an azimuth angle and an elevation angle. Can do.

  According to the positioning device of the present embodiment, the same effect as the positioning device 81 of the sixteenth embodiment is achieved. More specifically, the position of the transmitter 83 is measured and the maximum positioning error caused by the model error even in a situation where there are many weak interference wave signals 86 and model errors such as manufacturing errors of the observation means 12. Can be quantified as the maximum estimation error, and the information can be provided to the user of the positioning device.

  In each of the above embodiments, the maximum estimation error that is the maximum value of the estimation error that occurs in the estimation amount due to the model error is provided as the error information. The measurement apparatus is not limited to this, and the measurement apparatus may be configured to provide the model error amount as error information, or may be configured to provide both the maximum estimated error and the model error amount as error information. . When configured to provide both the maximum estimated error and the model error amount, the measuring apparatus outputs the model error amount from the model error amount estimating means 18 shown in FIG. Configured to display. When configured to provide a model error amount, the measurement apparatus is configured to include a model error amount estimation unit 18 instead of the maximum error evaluation unit 11 illustrated in FIG. 1, for example.

  DESCRIPTION OF SYMBOLS 1 Measurement apparatus, 11 Maximum error evaluation means, 12 Observation means, 13 Estimation means, 14 Display means, 15 Proportional coefficient calculation means, 16 Estimation model memory | storage means, 17 Maximum error calculation means, 18 Model error amount estimation means, 19 Sensor, 20 Ranging system, 21 Ranging device, 22 Ranging device antenna, 23, 43, 73 Transponder, 24, 44, 74 Transponder antenna, 25, 75 Trigger signal, 26, 45, 55, 76, 85 Response signal (Radio signal), 27, 46, 56, 64, 77, 86 Interference wave signal, 32 I detector, 34 Q detector, 40, 50, 70, 80 positioning system, 41, 51, 71, 81 positioning device, 42, 52, 72, 82 Antenna for positioning device, 51 Positioning device, 53, 83 Transmitter, 54, 84 Transmitter antenna, 61 Angle measuring device, 62 Antenna for angle measuring device, 63 radio wave signal.

Claims (9)

An acquisition means for acquiring related information related to measurement information to be measured;
Estimating means for estimating the measurement information based on the relationship information acquired by the acquiring means;
Error evaluation means for obtaining error information representing an error included in the measurement information estimated by the estimation means;
A measurement apparatus comprising: display means for displaying the measurement information estimated by the estimation means and the error information obtained by the error evaluation means. The estimation means estimates the measurement information using a model function that represents the relationship information as a model,
The error evaluation unit calculates a proportional coefficient from a model error that is an error from the model function included in the relationship information acquired by the acquisition unit to an estimation error that is an error generated in the measurement information due to the model error. The measuring apparatus according to claim 1, wherein a maximum value of an estimation error that can occur in the measurement information due to the model error is obtained as the error information using the obtained proportional coefficient.   The error evaluation unit is configured to hold a result of analytically obtaining a proportional coefficient from the model error to the estimation error, and the measurement information estimated by the estimation unit to the analytically obtained result The measurement apparatus according to claim 2, wherein the proportionality coefficient is obtained by substituting.   The measurement apparatus according to claim 1, wherein the acquisition unit is a reception unit that receives a radio signal, and acquires the related information from the received radio signal. The acquisition means is a reception means for receiving a radio signal, acquires the related information from the received radio signal,
The measuring apparatus according to claim 2, wherein the model error includes an error caused by an interference wave signal included in a radio wave signal received by the acquisition unit. The acquisition means is a reception means for receiving a radio signal, acquires the related information from the received radio signal,
The measurement apparatus according to claim 2, wherein the model error includes a manufacturing error that occurs when the acquisition unit is manufactured.   The measurement apparatus according to claim 4, wherein the measurement information includes a distance to a transmission source of the radio signal.   The measurement apparatus according to claim 4, wherein the measurement information includes an arrival direction of the radio signal.   The measurement apparatus according to claim 4, wherein the measurement information includes a position of a transmission source of the radio signal.

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