A Multi-Station Passive Sensor Target Localization Method Based on Angle Measurement

Abstract

This invention proposes a multi-station passive sensor target localization method based on angle measurement. The steps are as follows: constructing a target localization scenario based on angle measurement; an information acquisition module collects angle information and sensor position observation information; an information processing module constructs a pseudo-linear observation matrix and a pseudo-linear measurement vector; obtaining the least squares estimate of the target position coordinates; calculating the total measurement variance of the azimuth and elevation angles; calculating the weight matrix; calculating the weighted least squares estimate of the target position coordinates; and performing deviation compensation on the weighted least squares estimate. This invention effectively improves the target localization accuracy by compensating for the deviation of the weighted least squares estimate of the target position coordinates. Furthermore, when using weighted least squares to estimate the target position coordinates, it considers both angle measurement errors and the sensor's own localization errors, further enhancing the target localization accuracy.

Description

Technical Field

[0001] This invention belongs to the field of passive positioning technology and relates to a multi-station passive sensor target positioning method, specifically a multi-station passive sensor target positioning method based on angle measurement, which can be used for target positioning of multi-station passive sensors based on angle measurement. Background Technology

[0002] Target localization, which uses sensors to measure a target and estimate its position, is a crucial research area in signal processing. Based on sensor type, target localization methods can be categorized into active and passive localization techniques. Passive sensors, which do not emit electromagnetic signals, offer advantages such as good concealment and strong anti-interference capabilities, making them a research hotspot in recent years.

[0003] Passive positioning technology can be categorized based on sensor measurement information into target positioning based on time difference information, target positioning based on frequency domain information, target positioning based on angle measurement, and target positioning using a combination of these measurement information. Time difference-based target positioning utilizes the time difference in signal reception by passive sensors to locate the target, requiring high sensitivity of the receiving system and the ability to detect target radiation. Frequency domain-based target positioning primarily uses the sensor's measurement of the target's Doppler frequency to locate the target, but it relies on the signal's inherent frequency and has poor adaptability to different signal types. Compared to time difference-based and frequency domain-based target positioning, it does not require the target to emit its own radiation signal, and passive sensors with angle measurement capabilities are typically small, resulting in low payload capacity for the mounting platform. With the rapid development of passive sensors with angle measurement capabilities, such as optoelectronic platforms, infrared angle measurement systems, and passive radar, angle-based target positioning methods have also found widespread application in practice.

[0004] Positioning accuracy is a crucial metric for evaluating positioning algorithms. To improve target position estimation accuracy, angle-based target positioning methods require precise angle measurements. However, since sensor position measurements are used in the target position calculation process, and these sensors obtain their positions through positioning systems like GPS, they inherently contain measurement errors. Therefore, the observations in angle-based positioning typically include both angle measurement errors and the sensor's own positioning errors. Common angle-based target positioning methods include cross-positioning, least squares, and weighted least squares algorithms. Because cross-positioning and least squares algorithms do not consider measurement errors during the positioning process, relying solely on equations constructed from multiple sensor measurements to estimate the target position, and then solving these equations, the target position estimates obtained by these two algorithms tend to have poor accuracy. Weighted least squares algorithms pseudo-linearize the angle measurement equation to obtain a pseudo-linear equation about the target position, and then solve the pseudo-linear equation to obtain a target position estimate. For example, patent application CN109991572A, entitled "A Dual-Machine Passive Positioning Method Based on Azimuth and Pitch Angle Information," discloses a target positioning method based on angle measurement using weighted least squares. This method first pseudo-linearizes the angle measurement equation to obtain a pseudo-linear equation about the target position, and then uses a weighted least squares algorithm to solve the equation to obtain a target position estimate. However, because the pseudo-linear observation matrix and pseudo-linear measurement noise vector in the pseudo-linear equation constructed by the weighted least squares algorithm are correlated, the target position estimate obtained by the weighted least squares algorithm will have a bias, resulting in poor positioning accuracy. Secondly, because this algorithm considers angle measurement errors in the solution process, its positioning accuracy is improved compared to cross-positioning methods and least squares algorithms. However, because it does not consider the sensor's own positioning error, its target positioning accuracy will decrease when the sensor's own positioning error exists. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and propose a multi-station passive sensor target localization method based on angle measurement, which aims to improve the accuracy of multi-station passive sensor target position estimation based on angle measurement.

[0006] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0007] (1) Construct a target localization scenario based on angle measurement:

[0008] A target localization system and a target localization scenario are constructed, distributed in a spatial rectangular coordinate system OXYZ. The target localization system includes an information acquisition module based on angle measurements and an information processing module. The information acquisition module includes an angle information acquisition module and a position information acquisition module. The angle information acquisition module includes N passive sensors Z = {z1, z2, ..., z...} mounted on flight platforms at different locations. n ,···,z N}, where N≥2, z n This represents the nth passive sensor;

[0009] (2) The information acquisition module acquires angle information and sensor position observation information:

[0010] Each passive sensor z in the angle information acquisition module n Collect target angle information and angle information φ n The data is sent to the information processing module, while the location information acquisition module collects data from each passive sensor. n Location observation information s n =[x sn ,y sn ,z sn ] T and s n Send to the information processing module, where θ n , They represent z respectively n The acquired azimuth and elevation angle information of the target, [·] T Indicates the transpose operation, x sn y sn z sn They represent s respectively n Position observation components on the X-axis, Y-axis, and Z-axis in the spatial rectangular coordinate system OXYZ;

[0011] (3) The information processing module constructs a pseudo-linear observation matrix and a pseudo-linear measurement vector:

[0012] The information processing module uses the angle information φ n Construct a pseudo-linear observation matrix A with dimension 2N×3, and simultaneously based on the angle information φ n and passive sensor z n Location observation information s n Construct a pseudo-linear measurement vector h with dimension 2N×1:

[0013]

[0014] u θ,n =[sinθ n,-cosθ n ,0] T

[0015]

[0016]

[0017] Where, the 2nth line in A Act 2n-1 The 2nth element in h is The (2n-1)th element is

[0018] (4) The information processing module obtains the least squares estimate of the target location coordinates:

[0019] The information processing module uses the transpose of the pseudolinear observation matrix A as the input. T The least squares estimate of the target position coordinates p is obtained by using the pseudolinear measurement vector h as the basis for estimation.

[0020]

[0021] in, Let represent the estimated position components of the target on the X, Y, and Z axes in the Cartesian coordinate system OXYZ, respectively. -1 This represents the inverse operation;

[0022] (5) The information processing module calculates the total measurement variance of azimuth and elevation angles:

[0023] (5a) The information processing module calculates the least squares estimate of the target position coordinates p. Relative to each passive sensor z n Location observations s n slant distance Azimuth and pitch angle and through and s n Calculate the azimuth angle θ n and pitch angle Regarding each passive sensor z n Location observations s n azimuth deflection vector b θ,n and pitch angle deflection

[0024] (5b) The information processing module uses the azimuth angle deviation amount b θ,n and pitch angle deflection Calculate the azimuth angle θ n and pitch angle Total measurement variance and

[0025]

[0026]

[0027] in, These are passive sensors z n The variance of azimuth measurement, the variance of elevation measurement, R s,n For passive sensor z n Location observations s n The error covariance matrix;

[0028] (6) The information processing module calculates the weight matrix:

[0029] The information processing module calculates z for each passive sensor. n The weight matrix W has a dimension of 2×2. n And construct N weight matrices W1, W2, ..., W n ,···,W N The weight matrix W has a dimension of 2N×2N along its main diagonal:

[0030] W = blkdiag(W1, W2, ..., W n ,···,W N )

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] Where blkdiag(·) represents the operation of generating a block diagonal matrix, and diag(·) represents the operation of generating a diagonal matrix;

[0038] (7) The information processing module calculates the weighted least squares estimate of the target location coordinates:

[0039] The information processing module estimates the target position coordinates p based on the weighted least squares algorithm, obtaining the weighted least squares estimate.

[0040]

[0041] (8) The information processing module performs bias compensation on the weighted least squares estimate:

[0042] The information processing module calculates the weighted least squares estimate of the target position coordinates p. The estimation bias e, and through e to Perform deviation compensation to obtain the target positioning result after deviation compensation.

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] a n =W n (1,1)

[0051] b n =W n (1,2)

[0052] c n =W n (2,2);

[0053] Where ∑ represents the summation operation, W n (i,j) represents matrix W n The element in the i-th row and j-th column, i∈{1,2}, j∈{1,2}.

[0054] Compared with the prior art, the present invention has the following advantages:

[0055] 1) This invention compensates for the deviation of the weighted least squares estimate by the estimation deviation of the target position coordinates to obtain the target positioning result after deviation compensation. This reduces the impact of the deviation in the solution result caused by the correlation between the pseudo-linear observation matrix and the pseudo-linear measurement noise vector in the pseudo-linear equation constructed by the weighted least squares algorithm on the positioning accuracy. Compared with the prior art, it effectively improves the accuracy of target positioning.

[0056] 2) This invention estimates the influence of the sensor's own positioning error on the angle measurement variance by calculating the azimuth and elevation angles of the observed values ​​of the passive sensor position. In turn, it obtains the total measurement variance of the azimuth and elevation angles. When the information processing module calculates the weight matrix, it uses the total measurement variance of the azimuth and elevation angles and considers the sensor's own positioning error, making the calculated weight matrix more accurate and further improving the accuracy of target positioning. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0058] Figure 2 This is a comparison chart of simulation results of the positioning accuracy of the present invention and existing technologies. Detailed Implementation

[0059] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Reference Figure 1 The present invention includes the following steps:

[0061] Step 1) Construct a target localization scenario based on angle measurement:

[0062] A target localization system and a target localization scenario are constructed, distributed in a spatial rectangular coordinate system OXYZ. The target localization system includes an information acquisition module based on angle measurements and an information processing module. The information acquisition module includes an angle information acquisition module and a position information acquisition module. The angle information acquisition module includes N passive sensors Z = {z1, z2, ..., z...} mounted on flight platforms at different locations. n ,···,z N}, where N≥2, z n This represents the nth passive sensor; in this example, N = 4.

[0063] Step 2) The information acquisition module acquires angle information and sensor position observation information:

[0064] Each passive sensor z in the angle information acquisition module n Collect target angle information and angle information φ n The data is sent to the information processing module, while the location information acquisition module collects data from each passive sensor. n Location observation information s n =[x sn ,y sn ,z sn ] T and sn Send to the information processing module, where θ n , They represent z respectively n The acquired azimuth and elevation angle information of the target, [·] T Indicates the transpose operation, x sn y sn z sn They represent s respectively n The positional observation components on the X-axis, Y-axis, and Z-axis in the spatial rectangular coordinate system OXYZ; in this example, s1 = (50,0,0) meters, s2 = (150,150,0) meters, s3 = (1500,3000,0) meters, and s4 = (500,1000,0) meters.

[0065] Step 3) The information processing module constructs a pseudo-linear observation matrix and a pseudo-linear measurement vector:

[0066] The information processing module uses the angle information φ n Construct a pseudo-linear observation matrix A with dimension 2N×3, and simultaneously based on the angle information φ n and passive sensor z n Location observation information s n Construct a pseudo-linear measurement vector h with dimension 2N×1:

[0067]

[0068] u θ,n =[sinθ n ,-cosθ n ,0] T

[0069]

[0070]

[0071] Where, the 2nth line in A Act 2n-1 The 2nth element in h is The (2n-1)th element is

[0072] Step 4) The information processing module obtains the least squares estimate of the target location coordinates:

[0073] The information processing module uses the transpose of the pseudolinear observation matrix A as the input. T The least squares estimate of the target position coordinates p is obtained by using the pseudolinear measurement vector h as the basis for estimation.

[0074]

[0075] in, Let represent the estimated position components of the target on the X, Y, and Z axes in the Cartesian coordinate system OXYZ, respectively. -1 This indicates the inverse operation; in this example, the target location coordinates are p = (1000, 2000, 1000) meters;

[0076] Step 5) The information processing module calculates the total measurement variance of the azimuth and elevation angles:

[0077] (5a) The information processing module calculates the least squares estimate of the target position coordinates p. Relative to each passive sensor z n Location observations s n slant distance Azimuth and pitch angle and through and s n Calculate the azimuth angle θ n and pitch angle Regarding each passive sensor z n Location observations s n azimuth deflection vector b θ,n and pitch angle deflection Slope distance Azimuth and pitch angle And azimuth deflection vector b θ,n and pitch angle deflection The calculation formulas are as follows:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] Where arctan(·) represents the arctangent operation, δ x,n δ y,n and δz,n These represent the estimated target position coordinates. With passive sensor z n Position coordinate measurement s n The coordinate differences on the X, Y, and Z axes;

[0087] (5b) The information processing module uses the azimuth angle deviation amount b θn and pitch angle deflection Calculate the azimuth angle θ n and pitch angle Total measurement variance and

[0088]

[0089]

[0090] in, These are passive sensors z n The variance of azimuth measurement, the variance of elevation measurement, R s,n For passive sensor z n Location observations s n The error covariance matrix;

[0091] In calculating the azimuth angle θ n and pitch angle Total measurement variance and In addition to considering the measurement errors of azimuth and elevation angles, the influence of the sensor's own positioning error on the measurement accuracy of azimuth and elevation angles is also taken into account, which makes the measurement variance of azimuth and elevation angles more accurate and helps to improve the positioning accuracy of the target.

[0092] Step 6) The information processing module calculates the weight matrix:

[0093] The information processing module calculates z for each passive sensor. n The weight matrix W has a dimension of 2×2. n And construct N weight matrices W1, W2, ..., W n ,···,W N The weight matrix W has a dimension of 2N×2N along its main diagonal:

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] Where blkdiag(·) represents the operation of generating a block diagonal matrix, and W is a matrix (W1, W2, ..., W...). n ,···,W N A matrix with elements on the main diagonal, 0 2×2 It is a zero matrix of dimension 2×2, and diag(·) represents the operation of generating a diagonal matrix;

[0102] The total measurement variance of azimuth and elevation angles was used in the calculation of the weight matrix W, which makes the estimation of the weight matrix W of the passive sensor more accurate and helps to improve the target positioning accuracy.

[0103] Step 7) The information processing module calculates the weighted least squares estimate of the target location coordinates:

[0104] (7a) Construct the objective function J(p) with respect to the target position coordinates p:

[0105] J(p)=(h-Ap) T W(h-Ap);

[0106] (7b) Obtain the partial derivative function d(p) with respect to the target position coordinates p:

[0107] d(p)=A T W(h-Ap);

[0108] (7c) Let the partial derivative function d(p) equal to 0, and construct the equation U about the target position coordinates p:

[0109] U:d(p)=A T W(h-Ap)=0

[0110] Where 0 represents a zero vector with dimension 3×1;

[0111] (7d) Solve equation U to obtain the target position coordinate estimate.

[0112]

[0113] Target position coordinate estimation This initial target position coordinate estimation during target localization ignores the correlation between the pseudo-linear observation matrix and the pseudo-linear measurement noise vector, leading to inaccurate target position coordinate estimation. There are discrepancies;

[0114] Step 8) The information processing module performs bias compensation on the weighted least squares estimate:

[0115] The information processing module calculates the weighted least squares estimate of the target position coordinates p. The estimation bias e, and through e to Perform deviation compensation to obtain the target positioning result after deviation compensation.

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] a n =W n (1,1)

[0124] b n =W n (1,2)

[0125] c n =W n (2,2);

[0126] Where ∑ represents the summation operation, W n (i,j) represents matrix W n The element in the i-th row and j-th column, i∈{1,2}, j∈{1,2}.

[0127] Weighted least squares estimate The estimation bias e is caused by the correlation between the pseudolinear observation matrix and the pseudolinear measurement noise vector. This invention calculates the estimation bias e to... By performing bias compensation, the impact of the deviation in the solution results caused by the correlation between the pseudolinear observation matrix and the pseudolinear measurement noise vector in the pseudolinear equation constructed by the weighted least squares algorithm on the positioning accuracy is reduced, which is beneficial to improving the positioning accuracy of the target.

[0128] The technical effects of the present invention will be explained by combining the following simulation experiments.

[0129] 1. Simulation conditions and content:

[0130] The simulation uses an Intel Core i7 6500U CPU with a clock speed of 2.50GHz, 8.0GB of memory, a 64-bit operating system, Microsoft Windows 10 Professional Edition, and MATLAB 2020a simulation software.

[0131] There are 4 passive sensors, N, whose coordinates in the Cartesian coordinate system OXYZ are s1 = (50, 0, 0) meters, s2 = (150, 150, 0) meters, s3 = (1500, 3000, 0) meters, and s4 = (500, 1000, 0) meters, respectively; the target's position coordinates are p = (1000, 2000, 1000) meters. Assume the positioning error of the passive sensors follows a zero-mean Gaussian distribution, and the error covariance matrix R... s,n =diag(10 2 10 2 10 2 ), n = 1, 2, 3, 4; Assume that the azimuth and elevation measurement errors both follow a zero-mean Gaussian distribution, collectively referred to as angle measurement errors. The standard deviation of the angle measurement errors increases from 0.1° to 10.1° in 1° increments. After each change in angle measurement error, 100,000 Monte Carlo experiments are conducted. The deviation of the target position estimation is defined as BNorm, and its expression is:

[0132]

[0133] in, This represents the estimation of the target position coordinates p by the localization algorithm, and ||·|| represents the 2-norm operation.

[0134] A simulation was performed to compare the target position estimation deviation BNorm of this invention with that of existing dual-machine passive positioning methods based on azimuth and elevation angle information. The results are as follows: Figure 2 As shown.

[0135] 2. Simulation Result Analysis:

[0136] Reference Figure 2 The horizontal axis represents the angle measurement error, in degrees, and the vertical axis represents the target position estimation deviation, BNorm. From Figure 2It can be seen that within the angle measurement error range of 0.1° to 2.1°, the target position estimation deviation of the present invention is very close to that of the prior art. However, as the angle measurement error increases, the target position estimation deviation of the present invention is significantly reduced compared to the prior art. Moreover, the larger the angle measurement error, the more obvious the reduction in target position estimation deviation. When the angle measurement error is 10.1°, the target position estimation deviation of the prior art is 175.2 meters, while the target position estimation deviation of the present invention is only 40.61 meters, a decrease of about 76.8%, which improves the estimation accuracy of the target position coordinates.

[0137] In summary, simulations have demonstrated that the method of this invention can locate the target, and at the same time improves the target positioning accuracy compared with the prior art.

Claims

1. A method for target localization based on angle measurement multi-static passive sensor, characterized in that, Comprising the following steps: (1) Constructing an angle-measurement-based positioning scenario: Construct a spatial rectangular coordinate system The target positioning system and the target positioning scene are described. The target positioning system includes an information acquisition module and an information processing module. The information acquisition module includes an angle information acquisition module and a position information acquisition module. The angle information acquisition module includes... Passive sensors mounted on flight platforms at different locations ,in, , Indicates the first One passive sensor; (2) An information acquisition module acquires angle information and observation value information of sensor positions: Each passive sensor in the angle information acquisition module Acquire angle information of the target And send the angle information To the information processing module, while the position information acquisition module acquires the observation value Of the position of each passive sensor And send To the information processing module. ； wherein, , respectively represent azimuth and elevation information of the target collected, represents a transpose operation, , , respectively represent components on the x-axis, x-axis, y-axis, z-axis of the spatial rectangular coordinate system (3) An information processing module constructs a pseudo-linear observation matrix and a pseudo-linear measurement value vector: The information processing module uses angle information Construction dimension is pseudolinear observation matrix At the same time, based on angle information and passive sensors Location observations Construction dimension is pseudolinear measurement vector : ； ； ； ； wherein the first behavior , the behavior , the first element is , the element is ; (4) The information processing module obtains a least squares estimation value of a target position coordinate: The information processing module uses a pseudo-linear observation matrix. transpose result and pseudolinear measurement vector For the target position coordinates Perform least squares estimation to obtain the least squares estimate. : ； wherein , , respectively denote the coordinate estimates of the target in the Cartesian coordinate system axis, axis, axis, denotes the inverse operation; (5) The information processing module calculates a total measurement variance of an azimuth angle and a pitch angle: (5a) The information processing module calculates target position coordinates least square estimates of the range observation of the position of each passive sensor observation of the position of each passive sensor range, azimuth, and elevation azimuth, and elevation azimuth, and elevation azimuth, and elevation , and azimuth, and elevation azimuth, and elevation azimuth, and elevation azimuth, and elevation azimuth, and elevation azimuth, and elevation azimuth, and elevation (5b) Azimuthal angle bias vector of information processing module and pitch angle bias vector Azimuthal angle and pitch angle total measurement variance and : ； ； wherein , are the azimuth measurement variance, the pitch measurement variance, respectively, of a passive sensor , is the error covariance matrix of the position coordinates measurement of a passive sensor , . (6) The information processing module calculates a weight matrix: The information processing module calculates a weight matrix of dimension 2x2 for each passive sensor The information processing module calculates a weight matrix of dimension 2x2 for each passive sensor and builds a weight matrix of dimension with the weight matrix as main diagonal : ； ； ； ； ； ； ； wherein, denotes a generating block-diagonal matrix operation, denotes a generating diagonal matrix operation; (7) The information processing module calculates a weighted least squares estimation value of the target position coordinate: The information processing module estimates the target position coordinates based on a weighted least squares algorithm to obtain a weighted least squares estimate : ； (8) The information processing module performs bias compensation on the weighted least squares estimation value: The information processing module calculates the target location coordinates. Weighted least squares estimate estimation bias and through right Perform deviation compensation, and then analyze the deviation compensation results. As a result of target location: ； ； ； ； ； ； ； ； ； ； wherein denotes a summation operation, denotes a matrix the element in the the element in the column of the matrix, , .

2. The method of claim 1, wherein, The least squares estimate described in step (5a) Relative to each passive sensor Location observations slant distance Azimuth and pitch angle and azimuth deflection vector and pitch angle deflection The calculation formulas are as follows: ； ； ； ； ； ； ； ； wherein, represents an inverse tangent operation, , and respectively represent target position coordinate estimates and passive sensor position coordinate measurements in an x-axis, a y-axis, a z-axis.

3. The method of claim 1, wherein, The information processing module described in step (7) uses a weighted least squares algorithm to process the target position coordinates. The estimation process involves the following steps: (7a) constructing an objective function with respect to target position coordinates of the target : ； (7b) obtaining a partial derivative function of the target position coordinates with respect to the control variables : ； (7c) partial derivative is equal to , construct an equation about the target position coordinates : ； wherein represents a zero vector of dimension ​ (7c) solving the equation for the target position estimate : 。

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