Dual base joint multi-target positioning method based on external radiation source system

Abstract

The present application relates to radar data processing technical field, specifically a kind of multi-station system suitable for multi-radiation source, under the condition of no bistatic range information, the multi-target measurement value matching of single frame and two frames is carried out, different system multi-target positioning problem of external radiation source has better adaptability, it is favorable for multi-target positioning, real-time tracking, track generation and other processes based on external radiation source system bistatic joint multi-target positioning method of system, it include: matching multi-source multi-station angle measurement value obtains candidate association, estimates angle measurement value intersection position and velocity state;Approximately construct the linear equation of bistatic velocity and angle measurement value error, establish the measurement value error estimation of candidate association and real target, remove false candidate association using association hypothesis decision;According to the measurement value error estimation and state mahalanobis distance of candidate association between two frames, establish cost function, remove two-frame false candidate association using association hypothesis decision.

Description

Technical Field

[0001] This invention relates to the field of radar data processing technology, specifically to a bistatic joint multi-target localization method based on an external radiation source system. This method is applicable to multi-external radiation source multi-station systems, and performs multi-target measurement value matching between single frames and two frames under the condition of no bistatic distance information. It has good adaptability to multi-target localization problems of external radiation source systems of different systems, and is beneficial to processes such as multi-target localization, real-time tracking, and track generation. Background Technology

[0002] Target localization is a crucial method in multi-station radar system data processing, used for target position estimation and continuous tracking. In external radiation source localization systems, some communication signal systems, such as AM signals, do not support high-precision bistatic range measurement-based joint localization. When using angle information to locate multiple targets, at least three receiving stations are required without high-precision elevation angle measurements; similarly, at least five receiving stations are needed when using bistatic velocity information. Furthermore, angle localization requires array-type receivers, significantly increasing the deployment cost of external radiation source radars. To address the multi-target measurement matching problem in the absence of range information without increasing deployment costs, combining angle measurements with bistatic velocity measurements for multi-target correlation is a feasible method. Therefore, how to perform multi-target correlation and localization using only bistatic velocity and angle measurements with two receiving stations, when range measurements are unavailable, has become a pressing issue in this field. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a bistatic joint multi-target localization method based on an external radiation source system. This method is applicable to multi-external radiation source systems with multiple stations, performs multi-target measurement value matching between single and two frames under conditions without bistatic distance information, has good adaptability to multi-target localization problems in external radiation source systems with different systems, and is beneficial for processes such as multi-target localization, real-time tracking, and track generation.

[0004] This invention achieves its purpose through the following measures:

[0005] A bistatic joint multi-target localization method based on an external radiation source system is characterized by the following steps:

[0006] Step 1: Match multi-source, multi-station angle measurements to obtain candidate associations, and estimate the intersection point of angle measurements and velocity status;

[0007] Step 2: Approximately construct a linear equation for the measurement error of the bistatic velocity and angle, establish the measurement error estimate between the candidate association and the real target, and use the association assumption to make a decision to remove erroneous candidate associations;

[0008] Step 3: Establish a cost function based on the measurement error estimate of the candidate association between two frames and the state Mahalanobis distance, and use the association hypothesis decision to remove erroneous candidate associations between the two frames.

[0009] In this invention, matrices and vectors are represented by bold upright symbols; superscript (·) T and(·) H These represent the transpose and conjugate transpose operators, respectively; the symbol E(·) represents the mathematical expectation operation; the symbol Cov(·) represents the covariance operation; the symbol The subscript represents the orthogonal projection matrix of the subspace corresponding to its subscript; the symbol diag(·) represents a diagonal matrix; when processing two frames of data, the superscript k represents the timestamp of the k-th frame; in a multi-target association scenario with multiple external radiation sources on a 2D plane, the carrier frequencies of the signals emitted by each transmitter are different or mutually orthogonal, enabling the receiver to distinguish the signals from different transmitters. Each receiver can receive echo signals from different transmitters and obtain bistatic velocity and azimuth measurements of multiple targets. A transmitter-receiver combination is referred to as a channel. If i represents the transmitter number and j represents the receiver number, then the combination of the i-th transmitter and the j-th receiver is the (i,j)-th channel, and the coordinates of the transmitter and receiver are respectively... and Regarding the azimuth and bistatic velocity measurements, the azimuth is expressed as the angle between the line of sight between the receiving station and the target and the due east direction. The bistatic velocity is the rate of change of the bistatic distance of the target in the corresponding channel. Assuming the target's position and velocity state are as follows:

[0010] x = [u T ,v T ] T =[x,y,v x ,v y ] T ,

[0011] The expression for the bistatic velocity and azimuth measurement equations for the (i,j)th channel is:

[0012]

[0013] Where θ i,j Represents azimuth. φ represents the bistatic distance, the superscript indicates that the measurement comes from the (i,j)th channel, ||·|| represents the Euclidean norm, and atan2 represents the four-quadrant arctangent function. To simplify the equation for bistatic velocity, φ is used. i,j (u) indicates Due to the influence of measurement noise, the actual bistatic velocity and angle measurements obtained are as follows:

[0014] z i,j=h i,j (x)+n i,j ,

[0015] in, For measurement noise, it is assumed that the noise in the bistatic velocity and angle measurements is independent Gaussian white noise between channels, with noise energies of respectively. and

[0016] In step 2 of this invention, for any real target, the target azimuth measurement values ​​obtained from observations at different channels of any receiving station j should be approximately the same. Considering the influence of azimuth measurement noise, based on the azimuth measurement noise energy, the following normalized azimuth measurement error function is established.

[0017]

[0018] Since the noise in the measurement values ​​follows a Gaussian distribution Following a chi-square distribution with 1 degree of freedom, the corresponding azimuth measurement matching threshold is as follows:

[0019]

[0020] Where γ θ The upper quantile of the chi-square distribution can be calculated using a 99.5% confidence interval. All azimuth measurement pairs are examined at each receiving station, and azimuth measurement pairs from different receiving stations are combined to generate candidate associations.

[0021] For any candidate association, azimuth measurements from different receiving stations can be cross-referenced to obtain the target position estimate, and combined with bistatic velocity measurements, the target vector velocity estimate can be obtained.

[0022]

[0023] Furthermore, an approximate linear equation is constructed for the error between the bistatic velocity and angle measurements. For any real target A, the true state of the target is: The target state estimated by launch station i is The errors in the bistatic velocity and azimuth measurements can be approximated using a first-order Taylor expansion:

[0024]

[0025]

[0026] The linear equation for combining the errors of azimuth measurements and bistatic measurements yields:

[0027]

[0028] in:

[0029]

[0030] The error equations of linear measurements obtained from multiple channels are combined, i.e.

[0031] and get:

[0032]

[0033] The error level between the state of target A and the corresponding measurement value is estimated using the weighted least squares (WLS) method:

[0034]

[0035] Where ∑ is the measurement error weighting matrix, which is typically the diagonal matrix of measurement error intensity for independent measurement noise of known strength. The covariance matrix of the target state estimation is approximately:

[0036]

[0037] The level of measurement error is estimated as a weighted sum of squares (WSOS) as follows:

[0038]

[0039] For Δz A The projection of S onto subspace Q approximately follows a chi-square distribution with degrees of freedom Δz. A The difference in dimension between the subspace Q and the measurement space is the difference in dimension between the measurement space and the state space (2D plane is fixed at 4). The following correlation hypothesis decision is established:

[0040] S≤γ S ,

[0041] Where γ S The upper fraction of the chi-square distribution can be calculated using a 99% confidence interval.

[0042] In step 3 of this invention, the Mahalanobis distance between candidate associations between the k-th and k+1-th frames is given by the following formula:

[0043]

[0044] in

[0045]

[0046] The expression for the inter-frame association cost function constructed based on Mahalanobis distance and WSOS is as follows:

[0047] c = S k +S k+1 +d 2 ,

[0048] The cost function approximately follows a chi-square distribution, and the degrees of freedom are the sum of the dimensions of the measurement space of the two frames minus the dimension of the state space. The following association hypothesis decision is established:

[0049] c≤γ c ,

[0050] Where γ c The upper quantile of the chi-square distribution can be calculated using a 99% confidence interval.

[0051] Simulation results confirm that the proposed technical solution is effective and realizes multi-target association based on multiple external radiation sources and multiple stations, which is beneficial for applications such as multi-target positioning, real-time tracking, and trajectory generation. Attached Figure Description

[0052] Figure 1 This is a flowchart of an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram of a two-source, two-station, multi-target association model in an embodiment of the present invention.

[0054] Figure 3 This is a diagram showing the location distribution of the simulated transmitter and receiver station and multiple random velocity targets in an embodiment of the present invention.

[0055] Figure 4 This is a graph showing the change in the correct correlation probability of different bistatic velocity errors under a fixed 1° angular error in an embodiment of the present invention.

[0056] Figure 5 This is a graph showing the variation of the average number of errors associated with different bistatic velocity errors under a fixed 1° angle error in an embodiment of the present invention.

[0057] Figure 6 This is a graph showing the change in the probability of correct correlation of different angle errors in an embodiment of the present invention, under the condition of a fixed bistatic velocity error of 3 m / s.

[0058] Figure 7 This is a graph showing the variation of the average number of error associations at different angles under a fixed bistatic velocity error of 3 m / s in an embodiment of the present invention.

[0059] Figure 8This is a graph showing the change in the correct association probability under different frame time intervals in an embodiment of the present invention.

[0060] Figure 9 This is a graph showing the variation of the average number of error associations under different frame time intervals in an embodiment of the present invention. Detailed Implementation

[0061] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0062] Example:

[0063] See Figure 1 In some embodiments, a bistatic velocity and angle joint multi-target correlation method based on an external radiation source system is provided, including:

[0064] S1. Match multi-source, multi-station angle measurements to obtain candidate associations and estimate the intersection point of angle measurements and velocity status;

[0065] S2. Approximately construct a linear equation for the measurement error of the bistatic velocity and angle, establish the measurement error estimate between the candidate association and the real target, and use the association assumption to make a decision to remove erroneous candidate associations;

[0066] S3. Establish a cost function based on the measurement error estimate of the candidate association between two frames and the state Mahalanobis distance, and use the association assumption decision to remove the erroneous candidate associations between the two frames.

[0067] It should be noted that the multi-target association scenario in this embodiment considers a 2D planar model. The carrier frequencies of the signals transmitted by each transmitting station are different or mutually orthogonal, which enables the receiver to distinguish the signals of different receiving stations. Each receiving station can receive echo signals from different transmitting stations and obtain the bistatic velocity and azimuth angle measurements of multiple targets from them.

[0068] Optionally, in step S1, a 2-transmitter, 2-receiver model is used. See the schematic diagram for the model. Figure 2 As shown. A transmitter-receiver combination is referred to as a channel. If i (i = 1, 2) represents the transmitter number and j (j = 1, 2) represents the receiver number, then the combination of the i-th transmitter and the j-th receiver is the (i, j)-th channel. The coordinates of the transmitter and receiver are respectively... and A 2-transmitter, 2-receiver system can be configured with a total of 4 channels. Assume the target's position and velocity are as follows:

[0069] x = [u T ,v T ] T =[x,y,vx ,v y ] T

[0070] The expression for the azimuth angle and bistatic velocity observation equations after the electromagnetic wave travels from the i-th transmitting station, passes through the target, and reaches the j-th receiving station is:

[0071]

[0072] Where θ i,j Represents azimuth. φ represents the bistatic distance, the superscript indicates that the measurement comes from the (i,j)th channel, ||·|| represents the Euclidean norm, and atan2 represents the fourth-quadrant arctangent function. To simplify the equation representation of the bistatic velocity, φ is used in the remainder of this example. i,j (u) indicates Due to the influence of measurement noise, the actual bistatic velocity and angle measurements obtained are as follows:

[0073] z i,j =h i,j (x)+n i,j

[0074] in, For measurement noise, it is assumed that the noise in the bistatic velocity and angle measurements is independent Gaussian white noise between channels, with noise energies of respectively. and

[0075] Specifically, in step S1, according to the pre-set association threshold, the azimuth angle measurement values ​​of multiple targets and false alarms obtained from observations of various channels of the same receiving station are matched, and the matching results obtained from different receiving stations are combined to obtain candidate associations. For each candidate association, the intersection point position and velocity state obtained by the intersection of the angle measurement values ​​of different receiving stations are estimated.

[0076] S11, Stage 1: Matching multiple targets and false alarm azimuth measurements obtained from observations of various channels at the same receiving station, and combining the matching results from different receiving stations to obtain candidate associations. The angle matching method is performed according to the following steps:

[0077] For a given receiving station j, the azimuth angle measurements θ from the same target on different transmitting station channels. 1,j With θ 2,j There should be the same expected value, which is the true direction θ of the target. j The magnitude of the difference between the measured values ​​is related to the noise energy of the measured values. For any given azimuth measurement θ... 1,j With θ 2,j The correlation can be measured by the following normalized azimuth measurement error function.

[0078]

[0079] Obviously, assuming the measured noise is independent Gaussian white noise, It follows a chi-square distribution with 1 degree of freedom. When a pair of azimuth measurements θ 1,j With θ 2,j When the difference between the two azimuth angles does not exceed a certain threshold, these two azimuth angles are considered to originate from the same target. This threshold can be given by the following formula:

[0080]

[0081] Where γ θ For the upper quantile of a chi-square distribution with 1 degree of freedom, step S21 is the initial matching step, therefore the threshold should be set as loosely as possible, hence γ θ It can be calculated using a 99.5% confidence interval. All azimuth measurement pairs are examined at each receiving station. Since the measurements from different receiving stations cannot be correlated using azimuth information under a 2-receiving-station condition, the azimuth measurement pairs from different receiving stations are permuted and combined to generate candidate correlations.

[0082] S12: For each candidate measurement value association, the position and velocity state of the intersection point of the azimuth measurement lines are solved by cross-location of azimuth measurement values ​​and bistatic velocity equations:

[0083]

[0084] This is the initial estimate of the target state when the candidate target corresponds to the real target.

[0085] Specifically, in step S2, for the candidate associations obtained by the first-stage angle matching, a linear equation is constructed for the error between the bibase velocity and the angle measurement value. The measurement error level of each candidate association is estimated. The position and velocity state of the candidate associations are further estimated by combining the bibase velocity and angle measurement value information. The candidate associations with low confidence are removed by using the association hypothesis decision.

[0086] S21. Stage Two: Construct a linear equation for the error of bistatic velocity and angle measurements, estimate the error level of each candidate association, and further estimate the position and velocity state of the candidate association by combining the bistatic velocity and angle measurement information. The estimation is performed according to the following steps:

[0087] For each candidate measurement association, to verify whether it originates from the real target, estimating the measurement error when the association is assumed to originate from the real target can determine the probability that the measurement comes from the real target. Assume a real target A, whose true state is... The target state estimated by the corresponding launch station i in step 1 is: After completing S1, firstly, regarding the intersection position error of target A caused by the azimuth error, it can be approximated by a first-order Taylor expansion as follows:

[0088]

[0089] Then, for the vector velocity error caused by the bistatic velocity error, we can obtain...

[0090]

[0091] Because of which Since the value is unknown, we also use a first-order Taylor expansion to obtain an approximate value.

[0092]

[0093] The error equation for the bistatic velocity measurements can then be rewritten as follows:

[0094]

[0095] By integrating the error equations of the two types of measurements, we can obtain:

[0096]

[0097] Among them are

[0098]

[0099] Then, combining the error equations of each channel, i.e. and We can obtain the weighted least squares (WLS) estimate of the target state and the corresponding measurement error level estimate:

[0100]

[0101] Where ∑ is the measurement error weighting matrix, which is typically the diagonal matrix of measurement error intensity for independent measurement noise of known strength. The covariance matrix of the target state estimation can be approximated as:

[0102]

[0103] It should be noted that because a first-order Taylor expansion approximation is used in the establishment of the linear equation, the estimated value of the target state is biased and is only a rough estimate obtained for target matching.

[0104] S22. For the estimated measurement error level, the weighted sum of squares (WSOS) is used to measure the magnitude of the measurement error. The weighted sum of squares for estimating the measurement error level can be expressed as:

[0105]

[0106] Assume the error of the actual measurement is Δz A Then the estimated measurement error level can be expressed as the actual measurement error.

[0107]

[0108] Obviously, the level of measurement error is estimated. The error Δz of the actual measurement value A The orthogonal projection onto the subspace composed of Q, based on the properties of the orthogonal projection operator, allows WSOS to be considered to approximately follow a chi-square distribution. Its degrees of freedom are the spatial dimension of the measured values ​​minus the spatial dimension of the target state. In the current scene, the dimension of Q is 4, and the dimension of the measured values ​​is 8. Therefore, the degrees of freedom of WSOS can be considered approximately 4, S ~ X. 2 (4). Therefore, the condition for accepting this candidate measurement as associated with the assumed target is:

[0109] S≤γ S

[0110] Where γ S The upper quantile can be obtained from the chi-square probability distribution function with 4 degrees of freedom, below a set association probability such as 99%.

[0111] Specifically, in step S3, for the candidate associations of two frames, the Mahalanobis distance between their states is calculated to find possible inter-frame candidate associations, and a cost function is constructed based on the Mahalanobis distance and the measurement error level within the two frames. Inter-frame candidate associations with low confidence are removed using the association hypothesis decision.

[0112] S31. Stage 3: Calculate the Mahalanobis distance between two candidate association states in two frames, and find possible inter-frame candidate associations. The inter-frame association is performed according to the following steps:

[0113] After processing each frame of the obtained data through stages one and two, each frame retains a portion of candidate associations for real targets. This includes erroneous associations that could not be successfully removed within a single frame, as seen in the current instance. Assuming the timestamps of two frames are k and k+1, the time interval between the two frames is T, and the actual velocities of multiple real targets remain constant between the two frames, the state transition equation is:

[0114] x k+1 =Fx k

[0115] Among them are

[0116]

[0117] The Mahalanobis distance between candidate associations between two frames can be calculated by the following formula.

[0118]

[0119] Generally speaking, the Mahalanobis distance can be considered to approximately follow a chi-square distribution with degrees of freedom equal to the dimension of the target state, i.e., d 2 ~χ 2 (4) When the Mahalanobis distance is calculated, a threshold can be given under a certain correct association probability. It is assumed that inter-frame associations that pass the threshold may correspond to a real target. All candidate associations in frames k and k+1 are permuted and combined, and the Mahalanobis distance of each combination is calculated. Those with Mahalanobis distances below the threshold are considered inter-frame candidate associations. The motion state and velocity estimation of the real target should be consistent, while erroneous associations do not necessarily satisfy this. Therefore, for any candidate association in frame k, some erroneous associations can be eliminated by checking whether there is a candidate association in frame k+1 whose Mahalanobis distance passes the threshold. In order to retain as many correct inter-frame association combinations as possible, the association probability should be set as high as possible, such as 99.5%.

[0120] S32. Based on Mahalanobis distance and the measurement error level between two frames, the following cost function is proposed to measure the probability that the inter-frame association combination corresponds to a real target:

[0121] c = S k +S k+1 +d 2

[0122] Where S k Let represent the WSOS of the hypothetical target in frame k. It must be noted that in the above cost function, the three cost terms are actually estimates of the noise levels of the measurements in the two frames. For the real target, the source of these costs is the measurement error of the target in the two frames. Since the source is the same, it is necessary to discuss the statistical characteristics of the equal-weighted sum of the three terms in this cost function.

[0123] The three terms in the cost function can be approximated by the measurement errors of the two frames as follows:

[0124]

[0125] Where, Δz k This represents the error of the actual measurement value in the k-th frame. The formula for finding the inverse of the sum of invertible matrices (A+B) -1=A -1 (A -1 +B -1 ) -1 B -1 The formula for the cost function can be reorganized as follows:

[0126] c≈Δz T ∑ -1 Δz-Δz T ∑ -1 Q(Q T ∑ -1 Q) -1 Q T ∑ -1 Δz

[0127] in:

[0128]

[0129] Based on the above equation, the cost function can be approximated as the WSOS of the projection of the true measurement errors of the two frames onto the error matrix Q of the two frames. The projection subspace has a dimension of 4, and the measurement subspace has a dimension of 16. Therefore, the cost function should follow a chi-square distribution with 12 degrees of freedom, i.e., c ~ χ. 2 (12), from which the inter-frame correlation hypothesis decision can be established:

[0130] c≤γ c

[0131] Decision threshold γ c The upper quantile of the chi-square distribution with 12 degrees of freedom corresponds to a confidence level, i.e., the inter-frame correlation probability, which can be set to 99%.

[0132] The following section presents a numerical simulation performance verification and analysis of the target localization method provided in this embodiment.

[0133] The error ranges during the test were as follows: angle error 0.1°~2°; bistatic velocity error 1m / s~10m / s; time interval between two frames 10s~120s; the default standard deviation of the angle error in the simulation parameters was 1°, the standard deviation of the bistatic velocity error was 3m / s, and the time interval between two frames was 60s.

[0134] The geographical locations of the receiving and transmitting stations are shown in Table 1. There are a total of 22 external radiation source transmitting stations and 22 external radiation source receiving stations. All channels are equipped with bistatic velocity and angle observation capabilities.

[0135] Table 1 Geographic coordinates of the transmitting and receiving stations

[0136] Tx1 (-100,20) Rx1 (0,0) Tx2 (-57.7,-100) Rx2 (-100,20)

[0137] Eight random targets are set in the scene. The position and velocity information of the random targets are shown in Table 2. Figure 3 As shown, in each channel of each frame, a number of random false alarm measurements are added, which follow a Poisson distribution with an expected value of 2.

[0138] Table 2. Location and velocity information of random targets

[0139] 1 (-13.2,128.6) (505.1,153.2) 2 (-62.6,128.1) (-467.9,273.8) 3 (-16.7,109.4) (-535.3,235.7) 4 (-65,320.8) (447.6,-360) 5 (-22.8,149.6) (-559.2,-113.4) 6 (-68.2,91.2) (-227,456.4) 7 (-45.2,189.8) (-581.1,-127.8) 8 (64,204.7) (-161.5,553.5)

[0140] The statistical results of 1000 Monte Carlo experiments were used as the experimental test results. The performance of the algorithm was described by the correct association probability and the average number of incorrect associations. The correct association probability is the average statistical probability that all measurements of each target are correctly associated in multiple Monte Carlo experiments. The average number of incorrect associations is the average number of incorrect associations generated by multiple targets in different Monte Carlo experiments.

[0141] The impact of angle measurement error on multi-target correlation performance is analyzed below. With the standard deviation of the bistatic velocity error fixed at 3 m / s, only the angle measurement error is changed, while other conditions remain unchanged. The test results are as follows: Figure 4 and Figure 5 As shown.

[0142] analyze Figure 4 and Figure 5 The results show that the correct association probability of a single frame and two frames remains stable under different angle error conditions, close to the preset association probability of 99%. The correct association probability of two frames is significantly lower than that of a single frame, only close to 97%. This is because the correct association of the target between two frames requires that the target be correctly associated in each of the two frames. Therefore, the correct association probability of two frames will not be higher than the square of the single frame case, resulting in a lower probability. As the angle measurement error increases, the number of incorrect matches will increase. This is because a larger angle measurement error raises the threshold of the association hypothesis decision, allowing more incorrect matches to pass the decision. The number of incorrect associations in two frames is significantly lower than that in a single frame. This is because two frames further remove incorrect associations through additional inter-frame association hypothesis decisions.

[0143] The impact of bistatic velocity measurement error on multi-target correlation performance is analyzed as follows. With the standard deviation of the angular error fixed at 1°, only the bistatic velocity measurement error is changed, while other conditions remain unchanged. The test results are as follows: Figure 6 and Figure 7 As shown.

[0144] analyze Figure 4 and Figure 5The results show that the correct association probability of a single frame and two frames remains stable under different bistatic velocity error conditions, close to the preset association probability of 99%. The correct association probability of two frames is significantly lower than that of a single frame, only close to 97%. The analysis of this phenomenon is the same as the previous analysis of the angle measurement error. As the bistatic velocity measurement error increases, the number of incorrect matches will increase. This is because a larger bistatic velocity measurement error raises the threshold of the association hypothesis decision, resulting in more incorrect matches passing the decision. The number of incorrect associations between two frames is significantly lower than that of a single frame when the bistatic velocity error is less than 4 m / s, but the opposite is true when it exceeds 5 m / s. This is because when the bistatic velocity is accurate, the two frames further remove incorrect associations through additional inter-frame association hypothesis decisions. However, when the error exceeds 5 m / s, the process of candidate association between two frames will also introduce additional incorrect associations, and the probability of this incorrect association will also increase with the increase of the bistatic velocity error.

[0145] The impact of the two-frame time interval on multi-target correlation performance is analyzed as follows. With the standard deviation of the angle error fixed at 1° and the standard deviation of the bistatic velocity error fixed at 3 m / s, only the two-frame time interval is changed, while other conditions remain unchanged. The test results are as follows: Figure 8 and Figure 9 As shown.

[0146] analyze Figure 4 and Figure 5 The results show that the probability of correct association remains stable under different two-frame time intervals, all close to 97%. The number of incorrect associations increases with the increase of the two-frame time interval. This is because when the two-frame time interval increases, the error of the predicted value of the candidate association state generated by the previous frame will also increase, which leads to an increase in the threshold of Mahalanobis distance when searching for inter-frame candidate associations. This, in turn, increases the probability of incorrect inter-frame candidate associations passing the threshold, resulting in an increase in the number of incorrect associations between two frames.

[0147] In summary, the technical solution of this invention is practical and effective, realizing multi-target association based on multiple external radiation sources and multiple stations. The correct association probability has high robustness to different measurement noise and two-frame time interval conditions, while the number of incorrect matches will increase with the increase of measurement noise and two-frame time interval. However, within the above example conditions, the method is still effective in removing incorrect associations.

Claims

1. A dual-base joint multi-target localization method based on an external radiation source system, characterized in that, Includes the following steps: Step 1: Match multi-source, multi-station angle measurements to obtain candidate associations, acquire bistatic velocity measurements, and estimate the intersection point of angle measurements and velocity state. Hereinafter, a transmitter-receiver combination is referred to as a channel. i Represents the launch station serial number. j Representing the receiving station sequence number, then the... i The launch site and the first j The combination of the receiving stations is the () i , j The coordinates of the transmitting station and the receiving station are as follows: and ; superscript Indicates the transpose operator; The azimuth angle is represented by the angle between the line of sight between the receiving station and the target and the due east direction. The bistatic velocity is the rate of change of the bistatic distance of the target in the corresponding channel. Assume the target's position and velocity state are as follows: ， The expression for the bistatic velocity and azimuth measurement equations for the (i, j)th channel is: ， in Represents azimuth. Represents bistatic velocity; the superscript indicates that the measurement comes from the ( )th ______. i , j )aisle, Representing the Euclidean norm, atan2 represents the arctangent function in the fourth quadrant. express Due to the influence of measurement noise, the actual bistatic velocity and angle measurements are expressed as follows: ， in, For measurement noise, it is assumed that the noise in both bistatic velocity and angle measurements is independent Gaussian white noise between channels, with noise energies of respectively. and ; Step 2: Approximately construct the linear equations for the errors in bistatic velocity and angle measurements, establish error estimates between candidate associations and the true target measurements, and use the association assumption decision to remove erroneous candidate associations; the approximate construction method for the linear equations for the errors in bistatic velocity and angle measurements is as follows: For any real target A, the real state of the target is: The target state estimated by launch station i is The errors in azimuth measurement and bistatic velocity measurement can be approximated using a first-order Taylor expansion as follows: ， ， symbol The orthogonal projection matrix representing the subspace corresponding to its subscript, combined with the linear equation of the azimuth measurement error and the bistatic velocity measurement error, yields: ， in: ， The error equations of linear measurements obtained from multiple channels are combined, i.e. , and ,get: ； Step 3: Establish a cost function based on the measurement error estimate of the candidate association between two frames and the state Mahalanobis distance, and use the association hypothesis decision to remove erroneous candidate associations between the two frames.

2. The dual-base joint multi-target localization method based on an external radiation source system according to claim 1, characterized in that, The multi-target association method and observation model are based on a two-dimensional plane. The signals transmitted by each transmitter station have different or mutually orthogonal carrier frequencies, which enables the receiver to distinguish the signals from different transmitter stations. Each receiver station receives echo signals from different transmitter stations and obtains bistatic velocity and azimuth measurements of multiple targets from them.

3. The dual-base joint multi-target localization method based on an external radiation source system according to claim 1, characterized in that, In step 1, for any real target, at any receiving station j The target azimuth measurements obtained from observations through different channels are approximate, and a normalized azimuth measurement error function is established. as follows: ， symbol This represents the mathematical expectation operation; since the measurement noise follows a Gaussian distribution, Following a chi-square distribution with 1 degree of freedom, the corresponding azimuth measurement matching threshold is expressed as: ， in The upper quantile of the chi-square distribution is used to calculate the expected angular association probability by pre-setting the confidence interval. All azimuth measurement pairs are examined at each receiving station, and azimuth measurement pairs from different receiving stations are combined to generate candidate associations.

4. The dual-base joint multi-target localization method based on an external radiation source system according to claim 3, characterized in that, For any candidate association, the target position estimate is obtained by cross-locating azimuth measurements from different receiving stations. ， The target vector velocity estimate was obtained by joint bistatic velocity measurement. 。 5. The dual-base joint multi-target localization method based on an external radiation source system according to claim 4, characterized in that, The error level between the state of target A and the corresponding measurement value is estimated using the weighted least squares method: ， ， in This is the measurement error weighting matrix. For independent measurement noise of known intensity, this matrix is ​​the diagonal matrix of the measurement error intensity, i.e. ,symbol Representing a diagonal matrix, the covariance matrix of the target state estimation is approximately: ， symbol Indicates covariance operation; The level of error in the measured values ​​is estimated as a weighted sum of squares as follows: ， for To subspace The projection, S It approximately follows a chi-square distribution with degrees of freedom. The dimensional difference between the subspace Q and the measurement space is the dimensional difference between the measurement space and the state space. With the 2D plane fixed at 4, the following correlation hypothesis decision is established: ， in The upper quantile of the chi-square distribution is calculated using a pre-set confidence interval based on the expected correct association probability.

6. The dual-base joint multi-target localization method based on an external radiation source system according to claim 5, characterized in that, In step 3, the Mahalanobis distance between candidate associations between the k-th and (k+1)-th frames is given by the following formula: ， When processing two frames of data, the superscript... k Indicates the first k Frame timestamp, and: ， ， The expression for the inter-frame association cost function constructed based on Mahalanobis distance and WSOS is as follows: ， The cost function approximately follows a chi-square distribution, and the degrees of freedom are the sum of the dimensions of the measurement space of the two frames minus the dimension of the state space. The following association hypothesis decision is established: ， in The upper quantile of the chi-square distribution is calculated based on a pre-set confidence interval according to the expected probability of correct association between two frames.

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