CN114690116B - Passive target positioning method and system based on TDOA and FDOA measurement - Google Patents
Passive target positioning method and system based on TDOA and FDOA measurement Download PDFInfo
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Abstract
A passive target positioning method and system based on TDOA and FDOA measurement, the method comprises the following steps: acquiring measurement information and receiving station position information; converting the position information of the receiving station into a geocentric and geocentric fixed coordinate system; establishing a measurement equation according to the measurement information and the position information of the receiving station under the geocentric and geodetic fixed coordinate system; carrying out deformation processing on the measurement equation by combining prior information; and solving the target position vector by using the measurement equation after deformation processing to obtain an estimated value of the target coordinate. The invention introduces the prior range information of the target, converts the prior range information into an approximate value of the height coordinate of the target to be positioned after processing the prior range information, and avoids the ambiguity of positioning the three-station TDOA and the two-station TDOA-FDOA because of the acquisition of the additional coordinate. In the process of solving the target coordinates, the method directly brings the parameter-containing coordinate result to the theoretical definition constraint solving parameter, avoids the introduction of additional errors, and reduces the final positioning error.
Description
Technical Field
The invention belongs to the technical field of target positioning, and particularly relates to a passive target positioning method and system based on TDOA and FDOA measurement.
Background
Passive positioning techniques refer to a technique in which the observation station does not actively radiate electromagnetic signals, but rather by measuring parameters of electromagnetic signals emitted by an external radiation source or measuring its visible and infrared parameters and determining its position in space therefrom. The external radiation source signals available to the work platform are generally divided into two types: from the target itself [1] or with signals transmitted from television, radio, etc.
Passive positioning systems have many advantages [2] over active positioning systems: (1) The survival ability is strong, and the observation station cannot radiate electromagnetic waves to the target, so that the discovery probability of the opposite party is reduced; (2) The anti-interference capability is strong, and the opposite side cannot apply targeted interference because the observation station is not easy to find by the opposite side; (3) The coverage area of the airspace is wide, and the signal interception probability [3] is high; (4) Light weight, small size, low cost, and no need to build a bulky high power transmitter since no high power electromagnetic wave signal is transmitted to the location. These advantages increase the operational efficiency and viability of passive positioning systems, which have become an important way to conceal detection and achieve accurate strikes for locating or tracking target radiation sources.
In a passive positioning system, an observation station may locate [4] a target by measuring the energy intensity of a signal emitted by a radiation source, the angle of direction (AOA) to the observation station, the time of arrival (TOA), or by measuring the time difference of arrival (TDOA) of the radiation source signal at a plurality of receiving stations. The difference in frequency of arrival (FDOA) of the signal at multiple receiving stations may also be used to locate the target when there is relative motion between the source and the receiving stations. The positioning algorithm based on TDOA measurement is to combine the arrival time [5] of the target emission source signals measured by a plurality of receiving stations, calculate the time difference of reaching different observation stations, and then construct a positioning equation about the target position state to realize the passive positioning of the space target. In a positioning system based on the arrival time difference, each receiving station does not need complex gesture measuring equipment, only needs a single receiving channel, and the accuracy of the current arrival time measuring instrument is very high, so that the positioning method based on TDOA measurement can obtain higher positioning accuracy. The positioning algorithm based on the reaching frequency difference FDOA is suitable for [6] in a positioning scene with relative motion between the receiving stations and the target radiation source, and the frequency difference of the radiation source signals reaching different receiving stations is obtained by combining the radiation source signals detected by a plurality of receiving stations, so that a positioning equation set about the state parameters of the target radiation source is constructed, and the positioning equation set is solved to obtain the state information of the target radiation source. Like the time difference of arrival based positioning system, each receiving station in such a positioning system does not need an attitude measurement device, only a single receiving channel is needed.
Since the target positioning algorithm based on the two measurements is always a research hotspot in the positioning field, a series of researches are also obtained for the solving method of the positioning algorithm, including a taylor expansion method, a least square polynomial solving method [7][8], various weighting methods [9] and the like. However, in practical applications, due to the consideration of cost and the like, there may be a problem of positioning ambiguity caused by an insufficient number of observation stations, and the research on the problem is not sufficient at present. When the number of observation stations is insufficient, some priori information of the positioning target (for example, the target height is 0 or the positioning target can be measured by an altimeter in advance) can be obtained, and at this time, due to the problems of insufficient observation stations, only the estimation effect of the x and y coordinates of the space target is often concerned. In literature [10], this problem has been studied, but it is necessary to know the height of the target in advance and establish a constraint relationship in a geocentric fixed coordinate system, and solve in conjunction with the earth radius, which introduces a large error due to the approximation of the earth radius.
Reference to the literature
[1] Zeng Hui, zeng Fangling. Ambiguous and non-solvable problem of spatial three-station moveout positioning [ J ]. Terahertz science and electronic informatics report, 2010,8 (2): 139-142.
[2] Feng Tianjun double machine time difference-frequency difference combined positioning research [ D ]. National defense science and technology university.
[3] Dong Quan, wang Hong, wang Shunan. Double station time difference and frequency difference positioning technique [ C ]. China society of electronics, 2017.
[4]Fang B T.Simple solutions for hyperbolic and related position fixes[J].Aerospace&Electronic Systems IEEE Transactions on,1990,26(5):748-753.
[5] Yan Zhenya, chen Yi, chen Xinnian, et al, three-station time difference and frequency difference positioning accuracy analysis [ J ], modern radar 2018,40 (9): 4.
[6] Zhu Huajin, zhang Yang, eje, et al. Time difference and frequency difference joint positioning algorithm based on constraint weighted least square [ J ]. Telecommunication technology, 2013,53 (4): 7.
[7]Friedlander,B.A passive localization algorithm and its accuracy analysis[J].IEEE Journal of Oceanic Engineering,1987,12(1):234-245.
[8]Smith,J,Abel.Closed-form least-squares source location estimation from range-difference measurements[J].Acoustics,Speech and Signal Processing,IEEE Transactions on,1987,35(12):1661-1669.
[9]Chan Y T,Ho K C.A simple and efficient estimator for hyperbolic location[J].IEEE Transactions on Signal Processing,2002,42(8):1905-1915.
[10]Ho K C,Chan Y T.Geolocation of a known altitude object from TDOA and FDOA measurements[J].IEEE Transactions on Aerospace and Electronic Systems,1997,33(3):770-783.
Disclosure of Invention
The present invention is directed to a passive target positioning method and system based on TDOA and FDOA measurement, which uses a signal from the target itself as an external radiation source signal, and includes two positioning systems, namely TDOA measurement and TDOA and FDOA measurement, which are used separately, so as to reduce positioning errors.
In order to achieve the above purpose, the present invention has the following technical scheme:
In a first aspect, a passive target positioning method based on TDOA and FDOA measurements is provided, including the steps of:
acquiring measurement information and receiving station position information;
converting the position information of the receiving station into a geocentric and geocentric fixed coordinate system;
Establishing a measurement equation according to the measurement information and the position information of the receiving station under the geocentric and geodetic fixed coordinate system;
carrying out deformation processing on the measurement equation by combining prior information;
and solving the target position vector by using the measurement equation after deformation processing to obtain an estimated value of the target coordinate.
As a preferred embodiment of the passive object positioning method of the present invention, the measurement information includes TDOA measurement t i1 and FDOA measurementThe receiving station position information comprises longitude and latitude high coordinates of the observation stationThe receiving station position information is converted into a geocentric and geodetic fixed coordinate system as follows:
Wherein R is the curvature radius of the reference ellipsoid, E is the first eccentricity of the ellipsoid,The major half-axis radius of the ellipsoid is a= 6378137m and the minor half-axis radius is b= 6356752m.
As a preferred embodiment of the passive target positioning method of the present invention, the step of establishing a measurement equation according to measurement information and position information of a receiving station in a geocentric fixed coordinate system includes:
let N receiving stations s i after coordinate conversion have position speeds of x si＝[xsi,ysi,zsi]T and x si＝[xsi,ysi,zsi]T respectively I=1, 2,..n, and the receiving stations are not collinear, coplanar, the undetermined source position and velocity are denoted as x= [ x, y, z ] T and x= [ x, y, z ] T, respectivelyThe distance between the radiation source x and the receiving station s i is:
The receiving station s 1 is selected as a reference receiving station, and the measurement equations of TDOA and FDOA between the radiation source emission signal reaching the ith receiving station and the reference receiving station are expressed as follows:
Wherein t i and t 1 are the time when the signal arrives at the receiving stations s i and s 1, respectively, from the radiation source, c is the propagation speed of the electromagnetic wave, f 0 is the frequency of the signal emitted by the target radiation source, r i is the distance from the target radiation source to each receiving station, For the rate of change of the distance of the target radiation source to each receiving station, v i represents the radial relative velocity of the receiving station to the target, the expression is calculated as follows:
As a preferred solution of the passive target positioning method of the present invention, the linearizing the measurement equation before the deformation processing is performed on the measurement equation by combining prior information includes:
The TDOA measurement information is converted into a distance difference RDOA between the radiation source and the two receiving stations:
According to AndThe equivalent equation to obtain the RDOA equation is as follows:
The time t is derived to obtain a linear FDOA positioning equation:
as a preferred solution of the passive target positioning method of the present invention, the step of performing deformation processing on the measurement equation by combining prior information includes: obtaining a coordinate range of the area where the target source is located according to the position information of the receiving station under the geocentric earth fixed coordinate system, and taking As a priori z-coordinates, the equivalent equation of the RDOA equation is transformed into the form:
in the method, in the process of the invention, xi1＝xsi-xs1,yi1＝ysi-ys1,zi1＝zsi-zs1；
If the target motion is not considered, assume thatThe linearized FDOA location equation is transformed into the following form:
Order the X i1＝xsi-xs1,yi1＝ysi-ys1,zi1＝zsi-zs1 after obtaining a priori z coordinates of the target to be determined, the FDOA location equation of the above formula is then morphed into the form:
As a preferable scheme of the passive target positioning method, the step of solving the target position vector by using the measurement equation after deformation processing comprises the following steps: if the positioning is completed by using only TDOA measurement, writing the determined RDOA equation of different sensor pairs into a matrix form, and then solving; when relative motion exists between the observation station and the target source, the Doppler effect caused by the relative motion between the radiation source and the receiving station is utilized to estimate the frequency difference of signals reaching different receiving stations, and the determined RDOA and FDOA equations of different sensor pairs are combined into a matrix form to be solved.
As a preferred scheme of the passive target positioning method, if the receiving station has only three receiving stations and no relative motion exists between the receiving station and the target, the RDOA equation determined by different sensor pairs is written in a matrix form as follows:
h＝Gxa
Wherein each matrix vector is respectively:
xa＝[x,y]T
xa＝G-1h
From the above equation, the calculation result of the x, y coordinates of the target is obtained, and since r 1 is an unknown quantity, the x, y coordinates of the target are expressed as a function of r 1, and then the obtained result containing r 1 is brought into the defined equation A quadratic equation about r 1 is obtained, the value of r 1 is obtained by solving the equation, and r 1 is brought into the calculation result again to obtain the estimated value of the x and y coordinates of the target.
As a preferred scheme of the passive target positioning method, the value of r 1 is a positive real root, and if both solutions of the equation are positive real roots, an ideal solution is determined through priori information.
As a preferred scheme of the passive target positioning method, if the receiving stations have only two and relative motion exists between the receiving stations and the target, the prior range of the target and the z coordinate approximation value of the target are obtained, and the RDOA equation and the FDOA equation measured by the two stations are jointly written into a matrix form as follows:
from the above equation, the calculation result of the x, y coordinates of the object is obtained, due to r 1 and Are all a function of the unknown variable x, thus r 1 andAre also unknowns, and the x and y coordinates of the target are expressed as a function of r 1;
Since the target is stationary, the opposite type Deriving, willThe function written as r 1 is derived and then written as a form of multiplication of coordinate vectors as follows:
assuming x' s1＝xs1 (1:2:), Then transform the equation above to:
Will be Written as a function of r 1, the final form is as follows:
The result of the above formula is brought into a matrix, the calculated target position coordinate x only contains an unknown parameter r 1, the x coordinate containing the unknown parameter r 1 is brought into a constraint formula r 1 2＝(x-xs1)T(x-xs1), a four-time equation about r 1 is obtained, the four-time equation is solved, the value of r 1 is obtained, the value of r 1 is brought into a parameter-containing result, and the estimated value of the coordinates x and y of the target is obtained.
In a second aspect, a passive target positioning system based on TDOA and FDOA measurements is provided, comprising:
the information acquisition module is used for acquiring measurement information and receiving station position information;
the coordinate conversion module is used for converting the position information of the receiving station into a geocentric and geodetic fixed coordinate system;
The measurement equation building module is used for building a measurement equation according to the measurement information and the position information of the receiving station under the geocentric fixed coordinate system;
the measurement equation deformation module is used for carrying out deformation processing on the measurement equation by combining prior information;
and the target position estimation module is used for solving the target position vector by utilizing the measurement equation after the deformation processing to obtain the estimated value of the target coordinate.
Compared with the prior art, the invention has at least the following beneficial effects:
In the three-station TDOA and double-station TDOA-FDOA space target positioning algorithm, an altimeter is often required to obtain an approximate value of the altitude coordinate of a target, then a TDOA or FDOA measurement equation is used for solving the two-dimensional position coordinate of the target, otherwise, the three-station TDOA and double-station TDOA-FDOA positioning is a fuzzy problem that a determined solution cannot be obtained. In the process of solving the target coordinates, the method directly brings the parameter-containing coordinate result to the theoretical definition constraint solving parameter, avoids the introduction of additional errors, reduces the final positioning error and improves the estimation effect of passive target positioning.
Drawings
FIG. 1 is a flow chart of a method for passive target positioning based on TDOA and FDOA measurements according to the present invention;
FIG. 2 is a graph of percent 3TDOA positioning error at different noise levels;
FIG. 3 is a graph of 3TDOA positioning error percentiles at different height errors;
FIG. 4 is a plot of 3TDOA error versus noise level σ 2＝10-6;
FIG. 5 is a plot of 3TDOA error versus noise level σ 2＝10-2;
FIG. 6 is a graph of 3TDOA positioning error versus noise level;
FIG. 7 is a graph of percent 2TDOA-FDOA positioning error at various noise levels;
FIG. 8 is a graph of percent 2TDOA-FDOA positioning error at different height errors;
FIG. 9 is a plot of 2TDOA-FDOA error versus noise level σ 2＝10-6;
FIG. 10 is a plot of 2TDOA-FDOA error versus noise level σ 2＝10-3;
FIG. 11 is a graph of 2TDOA-FDOA positioning error versus noise level.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
Referring to fig. 1, the passive target positioning method based on TDOA and FDOA measurement of the present invention includes the following steps:
s1, acquiring measurement information and receiving station position information (longitude and latitude height);
S2, converting the position information of the receiving station into a geocentric and geodetic fixed coordinate system;
In the conventional TDOA/FDOA positioning algorithm, cartesian coordinates x, y and z of the target and the observation station are generally used for calculation and solution, but in many engineering applications, longitude and latitude height information of the observation station is often given, so that when the longitude and latitude height coordinates of the observation station are obtained After that, it should first be converted all into cartesian coordinates (x, y, z) in the geocentric fixed coordinate system, and the specific conversion formula is as follows:
Wherein R is the curvature radius of the reference ellipsoid, E is the first eccentricity of the ellipsoid,The major half-axis radius of the ellipsoid is a= 6378137m and the minor half-axis radius is b= 6356752m.
S3, establishing a measurement equation according to the measurement information and the position information of the receiving station under the geocentric fixed coordinate system;
Based on the observation station coordinates in the geocentric earth fixed coordinate system obtained in the step S1, TDOA measurement values t i1 and FDOA measurement are obtained Then, a measurement equation about the position of the target source is established, and the speeds of the positions of the N receiving stations s i after coordinate conversion are respectively x si＝[xsi,ysi,zsi]T and x si＝[xsi,ysi,zsi]T And consider that the receiving stations are not collinear, coplanar, and the undetermined source position and velocity are represented as x= [ x, y, z ] T andThe distance between the radiation source x and the receiving station s i is:
The receiving station s 1 is selected as a reference receiving station, and the measurement equations of TDOA and FDOA between the radiation source emission signal reaching the ith receiving station and the reference receiving station can be expressed as follows:
Wherein t i and t 1 are the time when the signal arrives at the receiving stations s i and s 1, respectively, from the radiation source, c is the propagation speed of the electromagnetic wave, f 0 is the frequency of the signal emitted by the target radiation source, r i is the distance from the target radiation source to each receiving station, For the rate of change of the distance of the target radiation source to each receiving station, v i represents the radial relative velocity of the receiving station to the target, the expression is calculated as follows:
since the above measurement equation is nonlinear and difficult to solve, the simultaneous multiplication of the signal propagation speed c on both sides of equation (3) converts the TDOA measurement information into the difference in distance RDOA between the radiation source and the two receiving stations by linearization:
Then the right end r 1 of the formula (6) is moved to the left end of the equation, then the square is simultaneously carried out on the two sides of the equation, and the relational expression is utilized AndEquivalent positioning equation RDOA equation for TDOA is obtained as follows:
the time t is derived from the above equation, and the FDOA positioning equation after linearization is obtained as follows:
S4, carrying out deformation processing on the measurement equation by combining prior information;
In practical engineering application, aiming at the problem of three-station TDOA positioning or two-station TDOA-FDOA combined positioning, due to the insufficient number of observation stations, a priori longitude and latitude high area of a target source is usually given, the longitude and latitude high area is transformed into a geocentric earth fixed coordinate system, then a coordinate range of the area where the target source is located can be obtained, and the coordinate range is assumed to be [ x min,ymin,zmin]～[xmax,ymax,zmax ], and the coordinate range is taken As a priori z-coordinate, the RDOA equation of equation (7) above can now be changed to the following form:
Wherein the method comprises the steps of xi1＝xsi-xs1,yi1＝ysi-ys1,zi1＝zsi-zs1。
If the movement of the target is not considered, i.e. the assumption is thatThe above formula (8) can be written as follows:
Order the X i1＝xsi-xs1,yi1＝ysi-ys1,zi1＝zsi-zs1 after obtaining a priori z coordinates of the target to be determined, the FDOA equation of formula (10) above can be further written as follows:
s5, solving a target position vector by using the measurement equation after deformation processing to obtain an estimated value of a target coordinate;
In general, if positioning is completed by using only TDOA measurement, the RDOA equations determined by different sensor pairs are written into a matrix form, and then solved. When there is relative motion between the observation station and the target source, for example, the positioning system is installed on a mobile platform, the Doppler effect caused by the relative motion between the radiation source and the receiving station can be used to estimate the Frequency Difference (FDOA) of signals reaching different receiving stations, and then the state parameters of the radiation source are estimated by combining the TDOA and the FDOA. In this case, the determined RDOA and FDOA equations of different sensor pairs need to be combined into a matrix form, and then solved.
The passive target positioning method aims at solving the problem of estimating [ x, y, z ] coordinates of three-dimensional coordinates when the number of observation stations is insufficient in practical engineering application, meanwhile, in order to improve calculation efficiency, a linear least square analysis solution mode is used for solving, and an additional variable r 1 is required to be introduced in a linear solving process, so that in the solving process, the method firstly takes r 1 as a known quantity, then represents the coordinates of a target source to be solved as a function of r 1, and then brings a coordinate vector containing an unknown parameter r 1 into a definition formula r 1 2＝(x-xs1)T(x-xs1) to obtain a high-order equation about r 1, the high-order equation is solved to obtain an estimated value of r 1, and finally the obtained estimated value of r 1 is replaced to obtain an estimated value of a final target coordinate.
The method of the present invention includes using TDOA measurements alone and combining two positioning systems of TDOA and FDOA measurements.
For three-dimensional space object positioning, if only TDOA measurements can be obtained, typically, for objects in space, at least four receiving stations are required to complete the positioning, because four receivers can determine three TDOA measurement equations, thereby determining the x, y, z coordinates of the space object. If there are only three stations, only two TDOA equations can be determined, and the accurate position of the target in space cannot be estimated. However, if the prior range of the target possibly appears is known, the approximate value of the target height coordinate is determined through the known prior range, then the two-dimensional coordinate [ x, y ] of the target is estimated, and the positioning result of the space target [ x, y, z ] based on the three-station TDOA can be realized.
Based on the post-deformation measurement equation (9)) given in step S4, the equations determined for the different sensor pairs are written in matrix form as follows:
h＝Gxa (12)
Wherein each matrix vector is respectively:
xa＝[x,y]T (13)
xa＝G-1h (16)
From equations (12) - (16) above, the calculation result of the x, y coordinates of the target can be obtained, but since r 1 is an unknown quantity, only the x, y coordinates of the target can be expressed as a function of r 1 at this time, then the result including r 1 obtained in equation (16) can be taken into the definition equation r 1 2＝(x-xs1)T(x-xs1), a quadratic equation about r 1 can be obtained, the value of r 1 can be obtained by solving the equation (normally, only one positive root is obtained, if both solutions are positive roots, an ideal solution can be determined by a priori information), at this time, the estimated value of the x, y coordinates of the target can be obtained by taking the obtained r 1 again into the calculation result including the parameters obtained for the first time, and since the estimated value of the coordinate z is already given by a priori information, all the coordinates [ x, y, z ] can be obtained up to this point.
The method of the invention firstly takes the unknown variable r 1 as the known quantity, then the coordinates of the target source are expressed as a function of r 1, and then the coordinate vector containing the unknown parameter r 1 is brought into a definition formula at the beginning for solving. The method is different from the method in the literature [10] in that r 1 is solved by directly utilizing the related definition of r 1, so that errors caused by using the earth radius are avoided, and the positioning accuracy is higher.
Compared with three-station TDOA positioning, the two stations can only obtain one TDOA equation, which makes space positioning impossible, but when relative motion exists between a transmitter and a receiver, an arrival Frequency Difference (FDOA) measurement equation can be obtained, and combined positioning of the two stations TDOA and FDOA on a space target can be completed by combining the two measurement equations and priori height information.
When obtaining the prior range of the target and the z coordinate approximation of the target, the RDOA equation (9) and the FDOA equation (11) measured by the double station can be jointly written into a matrix form as follows:
From equations (17) - (20), the calculation of the target x, y coordinates by the dual-station TDOA-FDOA positioning algorithm can be obtained, but due to r 1 and Are all a function of the unknown variable x, so r 1 andAnd are also unknowns, only the x, y coordinates of the target can be expressed as a function of r 1. The following describes how to solve the two unknowns and obtain the final positioning result.
Since the target is stationary, the two targets can be alignedDeriving, thus canThe function written as r 1 is derived and then written as a form of multiplication of coordinate vectors as follows:
since equation (17) above is only an estimate of the x, y coordinates of the target, i.e., x a = x (1:2,:), if x' s1＝xs1 (1:2,:), Then equation (21) above can be written as:
By combining formulas (17) to (22), it is possible to combine Written as a function of r 1, the final form is as follows:
At this time, the result of the above formula is brought into the formula (19), the calculated target position coordinate x only contains an unknown parameter r 1, at this time, the x coordinate containing the unknown parameter r 1 is brought into the constraint formula r 1 2＝(x-xs1)T(x-xs1), a four-time equation about r 1 can be obtained, the four-time equation is solved, the value of r 1 is obtained, and then the obtained value is brought into the formula (19) and contains the parameter result, so that the final estimated target coordinate can be obtained.
The combined positioning method of the two-station TDOA and the FDOA has the same basic idea as that of the three-station TDOA positioning, namely, the distance r 1 of a target reaching a reference observation station is taken as a known parameter to be brought into an equation set for solving, then r 1 is solved by a method of bringing back the known parameter to a definition type, and the solved r 1 value is brought into a vector to be estimated containing the parameter to solve the final position coordinate of the target. However, in comparison with the TDOA positioning method, the dual-station TDOA-FDOA positioning introduces additional unknown variablesThe method of the invention also uses the derivative formula to calculate the value of the valueExpressed as a function of r 1, ultimately converting the problem into a solution to the problem of the system of equations with the additional variable r 1.
The performance of the method of the present invention is verified by simulation experiments as follows.
Environment: MATLAB R2019b under WIN10 system;
Evaluation index:
The mean square error RMSE, defined as:
wherein x is equal to And respectively representing a true value and an ith Monte Carlo simulation estimated value of the position coordinate of the target to be determined, wherein L is the total number of Monte Carlo simulation times.
Error percent, defined as:
after the experimental RMSE is obtained, the error percentage is calculated by comparing the RMSE with the average euclidean distance from the target to different observation stations.
Simulation experiment one (three-station TDOA location):
First assume that the longitude and latitude high coordinates of 3 observation stations are Setting the true longitude and latitude height of the target to be [75.945.353000], generally giving the prior information range of the target in engineering application, assuming that the z coordinate of the target is known, and the target and the sensor are all stationary, taking the observation station 1 as a reference station, generating two pairs of TDOA values measured by 3 observation stations according to a TDOA definition formula, namely t 21 and t 31, and then adding different levels of TDOA measurement noise (the noise is 0 mean value and the variance is Gaussian white noise of sigma 2), wherein the experimental result is shown in figure 2. All the conditions are unchanged, the measurement noise variance sigma 2＝10-4 is set, namely the TDOA measurement noise variance is 100ns, and under different height errors, the estimation result is shown in figure 3.
As seen from FIG. 2, when the equivalent measurement error is small, the error of the three-station TDOA positioning algorithm based on the prior range information is very small, and the estimation error slowly increases along with the increase of the noise level, but under the condition that the target z coordinate is assumed to be precisely known, the overall positioning error percentage is small, and the positioning result is ideal. Fig. 3 shows the positioning results at a certain noise level at different height errors (i.e. an error of plus or minus 1000 meters added to the actual z-coordinate), the estimated error percentage is almost zero when the error is 0 meters, the positioning error increases continuously as the height error increases, but the overall positioning error is always at a lower level.
The results of comparison with the method in document [10] are shown in fig. 4, fig. 5 and fig. 6.
Fig. 4 and fig. 5 show that when the noise level is fixed, the positioning errors of two algorithms based on the three-station TDOA measurement are different in height errors, range represents the method based on the priori range information proposed by the present invention, height represents the positioning method based on the altitude priori information proposed in document [10], and from the experimental result, the estimation error of the method proposed by the present invention is always smaller than that in document [10], especially when the altitude error is smaller, the superior performance of the scheme proposed by the present invention is more obvious. Fig. 6 shows the trend of the positioning error of two algorithms with noise in the absence of altitude error, from which it is found that the error of the method proposed by the present invention is more pronounced with altitude, since the method in document [10] itself relies on an approximately elliptical model of the earth, with a large inherent error, although the positioning error is insensitive to altitude error, but always with a high positioning error.
Simulation experiment two (double-station TDOA-FDOA joint positioning):
first assume that the longitude and latitude high coordinates of 2 observation stations are The true longitude and latitude height of the target is set to be [75.945.353000], the true longitude and latitude height is consistent with the prior information of the three-station TDOA experiment, the z coordinate of the target is known and the target is static, but relative motion exists between the target and an observation station, and the speed vector of the observation station is expressed asThe real TDOA and FDOA measurement values are given according to the definition of TDOA and FDOA, namely t 21 and FDOAAt different measured noise levels (TDOA noise is 0 mean, variance is a gaussian white noise of σ 2, FDOA noise is 0 mean, variance is a gaussian white noise of 0.1σ 2), the experimental results are shown in fig. 7 as a function of noise.
All the conditions are unchanged, the TDOA measurement noise variance sigma 2＝10-4 (i.e. the TDOA measurement noise variance is 100 ns) is set, the FDOA measurement noise variance is 0.1σ 2, and under different height errors, the estimation result is shown in FIG. 8.
As can be seen from fig. 7, the two-station TDOA-FDOA location error based on the a priori range information increases with increasing noise level, and the estimation error slowly increases, and the overall estimation error percentage is smaller than the three-station TDOA location above due to the introduction of the FDOA measurement information. FIG. 8 shows the positioning results at different height errors (i.e., an error of plus or minus 1000 meters added to the actual z-coordinate) at a certain noise level, similar to the three-station TDOA positioning error result plot, with an estimated error percentage of almost zero when the error is 0 meters, with the positioning error increasing with increasing height error, but the overall positioning error always at a lower level.
The results of comparison with the method in document [10] are shown in fig. 9, 10 and 11. As can be seen from fig. 9 and fig. 10, under the same noise level, the dual-station TDOA-FDOA positioning method provided by the present invention has the same trend as the method in literature [10], but the estimation error of the method provided by the present invention is always smaller than that of the method in literature [10], i.e. the estimation performance is very good; it can also be seen in fig. 11 that as the noise increases, the estimation error increases for both methods, but it is apparent that the estimation error is smaller for the proposed solution of the present invention.
In the two positioning schemes based on prior range information provided by the invention, the values required to be subjectively set are TDOA measurement noise and FDOA measurement noise and Monte Carlo simulation times set in the experimental process. In general, the TDOA measurement error is smaller, the general error is between 30ns and 150ns, and the FDOA error is generally set to be 0.01 to 0.1 times of the TDOA positioning error; regarding the number of Monte Carlo simulations during the experiment, the more positive the number, the better, but for simplicity of calculation, the invention sets the number of Monte Carlo to 1000 for each specific parameter of each experiment. For the positioning method in the document [ 1 ] not only needs to set the parameters, but also needs to set the earth radius in the constraint condition model, generally, a numerical value is selected from the shorter half axis of the earth to the longer half axis of the earth, namely, the numerical value is 6356752 m-6378137 m, and the simulation experiment of the invention selects the earth radius r g =6371 km according to the longitude and latitude of a real target. In practical engineering application, the setting of the value can be carried out by giving an approximate value according to the prior longitude and latitude high range of the target.
Another embodiment of the present invention further provides a passive target positioning system based on TDOA and FDOA measurements, including:
the information acquisition module is used for acquiring measurement information and receiving station position information;
the coordinate conversion module is used for converting the position information of the receiving station into a geocentric and geodetic fixed coordinate system;
The measurement equation building module is used for building a measurement equation according to the measurement information and the position information of the receiving station under the geocentric fixed coordinate system;
the measurement equation deformation module is used for carrying out deformation processing on the measurement equation by combining prior information;
and the target position estimation module is used for solving the target position vector by utilizing the measurement equation after the deformation processing to obtain the estimated value of the target coordinate.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention, which is intended to be covered by the claims.
Claims (7)
1. A passive target positioning method based on TDOA and FDOA measurements, comprising the steps of:
acquiring measurement information and receiving station position information;
converting the position information of the receiving station into a geocentric and geocentric fixed coordinate system;
Establishing a measurement equation according to the measurement information and the position information of the receiving station under the geocentric and geodetic fixed coordinate system;
carrying out deformation processing on the measurement equation by combining prior information;
Solving a target position vector by using the measurement equation after deformation processing to obtain an estimated value of a target coordinate;
The step of establishing a measurement equation according to the measurement information and the position information of the receiving station under the geocentric fixed coordinate system comprises the following steps:
let N receiving stations s i after coordinate conversion have position speeds of x si＝[xsi,ysi,zsi]T and x si＝[xsi,ysi,zsi]T respectively And the receiving stations are not in the same straight line and the same plane, and the undetermined radiation source position and speed are respectively expressed as x= [ x, y, z ] T andThe distance between the radiation source x and the receiving station s i is:
The receiving station s 1 is selected as a reference receiving station, and the measurement equations of TDOA and FDOA between the radiation source emission signal reaching the ith receiving station and the reference receiving station are expressed as follows:
Wherein t i and t 1 are the time when the signal arrives at the receiving stations s i and s 1, respectively, from the radiation source, c is the propagation speed of the electromagnetic wave, f 0 is the frequency of the signal emitted by the target radiation source, r i is the distance from the target radiation source to each receiving station, For the rate of change of the distance of the target radiation source to each receiving station, v i represents the radial relative velocity of the receiving station to the target, the expression is calculated as follows:
linearizing the measurement equation before deforming the measurement equation by combining prior information, including:
The TDOA measurement information is converted into a range difference RDOA equation between the radiation source and the two receiving stations:
The equivalent equation for obtaining the RDOA equation from r i 2＝(x-xsi)T(x-xsi) and r 1 2＝(x-xs1)T(x-xs1) is as follows:
The time t is derived from the above method to obtain a linear FDOA positioning equation:
The step of deforming the measurement equation by combining prior information comprises the following steps: obtaining a coordinate range of the area where the target source is located according to the position information of the receiving station under the geocentric earth fixed coordinate system, and taking As a priori z-coordinates, the equivalent equation of the RDOA equation is transformed into the form:
in the method, in the process of the invention, xi1＝xsi-xs1,yi1＝ysi-ys1,zi1＝zsi-zs1；
Regardless of target motion, assume thatThe linearized FDOA location equation is transformed into the following form:
Order the X i1＝xsi-xs1,yi1＝ysi-ys1,zi1＝zsi-zs1 after obtaining a priori z coordinates of the target to be determined, the FDOA location equation of the above formula is then morphed into the form:
2. The method of claim 1, wherein the measurement information includes TDOA measurements t i1 and FDOA measurements The receiving station position information comprises longitude and latitude high coordinates of the observation stationThe receiving station position information is converted into a geocentric and geodetic fixed coordinate system as follows:
Wherein R is the curvature radius of the reference ellipsoid, E is the first eccentricity of the ellipsoid,The major half-axis radius of the ellipsoid is a= 6378137m and the minor half-axis radius is b= 6356752m.
3. A passive target positioning method based on TDOA and FDOA measurements according to claim 1, wherein the step of solving the target position vector using the deformed measurement equation comprises: if the positioning is completed by using only TDOA measurement, writing the determined RDOA equation of different sensor pairs into a matrix form, and then solving; when relative motion exists between the observation station and the target source, the frequency difference of signals reaching different receiving stations is estimated by using Doppler effect caused by the relative motion between the radiation source and the receiving stations, and the determined RDOA and FDOA equations of different sensor pairs are combined into a matrix form, and then the matrix is solved.
4. A passive target positioning method based on TDOA and FDOA measurements according to claim 3, wherein if there are only three receiving stations and there is no relative motion between the receiving stations and the target, the RDOA equations determined for the different sensor pairs are written in matrix form as follows:
h＝Gxa
Wherein each matrix vector is respectively:
xa＝[x,y]T
xa＝G-1h
From the above equation, the calculation result of the x and y coordinates of the target is obtained, since r 1 is an unknown quantity, the x and y coordinates of the target are expressed as a function of r 1, then the obtained result containing r 1 is brought into the defined equation r 1 2＝(x-xs1)T(x-xs1, a quadratic equation about r 1 is obtained, the value of r 1 is obtained by solving the equation, and r 1 is brought into the calculation result again to obtain the estimated value of the x and y coordinates of the target.
5. A passive target positioning method based on TDOA and FDOA measurements according to claim 4, wherein the value of r 1 is a positive real root, and an ideal solution is determined by a priori information if both solutions of the equation are positive real roots.
6. A passive target positioning method based on TDOA and FDOA measurements according to claim 3, wherein if there are only two receiving stations and there is a relative motion between the receiving stations and the target, when the a priori range of the target and the z coordinate approximation of the target are obtained, the RDOA equations and FDOA equations measured by the two stations are jointly written in matrix form as follows:
from the above equation, the calculation result of the x, y coordinates of the object is obtained, due to r 1 and Are all a function of the unknown variable x, thus r 1 andAre also unknowns, and the x and y coordinates of the target are expressed as a function of r 1;
Since the target is stationary, the opposite type Deriving, willThe function written as r 1 is derived and then written as a form of multiplication of coordinate vectors as follows:
assuming x' s1＝xs1 (1:2:), Then transform the equation above to:
Will be Written as a function of r 1, the final form is as follows:
The result of the above formula is brought into a matrix, the calculated target position coordinate x only contains an unknown parameter r 1, the x coordinate containing the unknown parameter r 1 is brought into a constraint formula r 1 2＝(x-xs1)T(x-xs1), a four-time equation about r 1 is obtained, the four-time equation is solved, the value of r 1 is obtained, the value of r 1 is brought into a parameter-containing result, and the estimated value of the coordinates x and y of the target is obtained.
7. A passive target positioning system based on TDOA and FDOA measurements, comprising:
the information acquisition module is used for acquiring measurement information and receiving station position information;
the coordinate conversion module is used for converting the position information of the receiving station into a geocentric and geodetic fixed coordinate system;
The measurement equation building module is used for building a measurement equation according to the measurement information and the position information of the receiving station under the geocentric fixed coordinate system;
the measurement equation deformation module is used for carrying out deformation processing on the measurement equation by combining prior information;
The target position estimation module is used for solving a target position vector by utilizing the measurement equation after deformation processing to obtain an estimated value of a target coordinate;
The step of establishing a measurement equation according to the measurement information and the position information of the receiving station under the geocentric fixed coordinate system comprises the following steps:
let N receiving stations s i after coordinate conversion have position speeds of x si＝[xsi,ysi,zsi]T and x si＝[xsi,ysi,zsi]T respectively And the receiving stations are not in the same straight line and the same plane, and the undetermined radiation source position and speed are respectively expressed as x= [ x, y, z ] T andThe distance between the radiation source x and the receiving station s i is:
The receiving station s 1 is selected as a reference receiving station, and the measurement equations of TDOA and FDOA between the radiation source emission signal reaching the ith receiving station and the reference receiving station are expressed as follows:
Wherein t i and t 1 are the time when the signal arrives at the receiving stations s i and s 1, respectively, from the radiation source, c is the propagation speed of the electromagnetic wave, f 0 is the frequency of the signal emitted by the target radiation source, r i is the distance from the target radiation source to each receiving station, For the rate of change of the distance of the target radiation source to each receiving station, v i represents the radial relative velocity of the receiving station to the target, the expression is calculated as follows:
linearizing the measurement equation before deforming the measurement equation by combining prior information, including:
The TDOA measurement information is converted into a range difference RDOA equation between the radiation source and the two receiving stations:
The equivalent equation for obtaining the RDOA equation from r i 2＝(x-xsi)T(x-xsi) and r 1 2＝(x-xs1)T(x-xs1) is as follows:
The time t is derived from the above method to obtain a linear FDOA positioning equation:
The step of deforming the measurement equation by combining prior information comprises the following steps: obtaining a coordinate range of the area where the target source is located according to the position information of the receiving station under the geocentric earth fixed coordinate system, and taking As a priori z-coordinates, the equivalent equation of the RDOA equation is transformed into the form:
in the method, in the process of the invention, xi1＝xsi-xs1,yi1＝ysi-ys1,zi1＝zsi-zs1；
Regardless of target motion, assume thatThe linearized FDOA location equation is transformed into the following form:
Order the X i1＝xsi-xs1,yi1＝ysi-ys1,zi1＝zsi-zs1 after obtaining a priori z coordinates of the target to be determined, the FDOA location equation of the above formula is then morphed into the form:
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