Target track and electronic reconnaissance information data association method based on multi-dimensional distribution

Abstract

The invention discloses a target track and electronic reconnaissance information data association method based on multi-dimensional distribution. A detection system and an electronic reconnaissance system are included. The detection system obtains aerial target information, and the electronic reconnaissance system obtains carrying target information. With the position of the electronic reconnaissance system as a reference, calculating a direction value of a target track point detected by the detection system relative to the reference position; taking a target track point time scale detected by the detection system as a reference, and extrapolating and interpolating a target direction finding value detected by the electronic reconnaissance system; taking the registered target track point direction value and the reconnaissance target direction finding value as associated objects; taking an ellipsoid threshold as a distance threshold of the associated object; calculating data of the associated objects by adopting a multi-dimensional distribution method; and accumulating the detection matrix for multiple times and outputting a judgment result. According to the method, data association of a detection target and a reconnaissance target can be completed, and the method has a relatively high judgment correct probability and a relatively small false alarm probability.

Description

Technical Field

[0001] The present invention belongs to the technical fields of radar and electronic countermeasure, and particularly relates to a method for associating target track and electronic reconnaissance information data based on multi-dimensional assignment. Background Technique

[0002] A detection system (such as a radar) can detect, locate, and track a target using the target echo to form target position information, but it cannot identify the target identity. An electronic reconnaissance system can use the signals radiated by the radiation sources carried on the target to measure the direction of the target and identify its identity to form electronic reconnaissance information. However, it cannot obtain the distance and position information of the reconnaissance target.

[0003] Associating the target track detected by the detection system and the target identity information detected by the electronic reconnaissance system, and simultaneously obtaining the position and identity information of the target to enhance the dimension of the target information has great application prospects. Currently, there are various data association algorithms, and different methods are adopted according to different purposes and usage conditions. Among them, the multi-dimensional assignment method can transform the multi-dimensional data association problem into a 0-1 linear programming solution problem under certain constraint conditions, which is an optimal data association method for solving the data association problem and has the advantages of simplicity, effectiveness, and easy implementation. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a method for associating target track and electronic reconnaissance information data based on multi-dimensional assignment.

[0005] The present invention performs spatial registration and time registration on the target track point data and the target direction measurement value data of the electronic reconnaissance information. Combining the requirements of easy implementation in engineering, using the modified ellipsoid threshold as the statistical distance of the associated object, associates the target track point direction value detected by the detection system and the target direction measurement value detected by the electronic reconnaissance system through the multi-dimensional assignment data association method, constructs a data association discrimination matrix, and adopts a continuous multiple accumulation detection method. Taking more than N successful associations in M detections as the discrimination basis to improve the association correct rate. The specific method is as follows:

[0006] S1, taking the site deployment position of the electronic reconnaissance system as the reference position, calculates the direction value of the target track point detected by the detection system relative to the reference position to ensure that the target track point and the target direction measurement value have a unified reference position and achieve spatial registration; taking the time scale of the target track point of the detection system as the benchmark, extrapolates and interpolates the target direction measurement value of the electronic reconnaissance system to obtain the direction measurement value of the electronic reconnaissance system at the benchmark time scale to ensure that the target track point and the target direction measurement value have a unified time scale and achieve time registration;

[0007] S2. Calculate the statistical distance between the target direction finding values of the electronic reconnaissance system and the target track point direction values of the detection system, and correct the statistical distance to reduce the computational amount of the algorithm;

[0008] S3. Construct an association discrimination matrix for the target direction finding values of the electronic reconnaissance system and the target track point direction values of the detection system based on the multi-dimensional assignment algorithm

[0009] S4. Adopt the method of continuous multiple accumulation detection to detect the association discrimination matrix and output the discrimination result according to the discrimination matrix.

[0010] Furthermore, the specific content of step S1 includes:

[0011] S11. At time k, the position measurement set of N k target track points output by the detection system is: where x k，j , j = 1, 2,..., N k obeys the normal distribution with the mean of and the variance of p k，j . The measurement set of M k target direction finding values detected by the electronic reconnaissance system is: where z k，i , i = 1, 2,..., M k , z k，i obeys the normal distribution with the mean of and the variance of q k，i . Assume that the position of a certain target track point in the rectangular coordinate system at time t is (x a , y a ), and the coordinate of the deployment position of the electronic reconnaissance system is (x0, y0). Then the direction value of this target track point relative to the reference position is

[0012] β pt = arctan((y a - y0) / (x a - x0)) (3)

[0013] where p is the track number. After spatial registration, the direction value set of the target track point relative to the reference position can be obtained as

[0014]

[0015] β k,j , j = 1, 2,..., N k represents the direction value of the jth detected target relative to the electronic reconnaissance system at time k. β k,j , j = 1, 2,..., N k obeys the normal distribution with the mean of m k,j and the variance of σk，i Gaussian distribution

[0016] S12. Suppose the time scale of the target track points detected by the detection system is {T1, T2, … T k …}, and the time scale of the target direction-finding values detected by the electronic reconnaissance system is {T1′, T2′, … T k ′…}. Based on the time scale {T1, T2, … T k …} of the target track points detected by the detection system, interpolate or extrapolate the target direction-finding values detected by the electronic reconnaissance system to ensure that the time scale of the target direction-finding values detected by the electronic reconnaissance system is consistent with that of the target track points detected by the detection system, and achieve time registration. For example, the data rate of the track point data of the detection system is once every 10 seconds, and the data rate of the direction-finding data of the electronic reconnaissance system is once every 1 second, as Figure 3 shown. For the time scale T k of the detection system, the target direction-finding value obtained at the previous time point T k ′ of T k-1 in the reconnaissance data sequence of the electronic reconnaissance system is z2, and the target direction-finding value obtained at the next time point T k of T k+1 ′ is z3. By interpolating the direction-finding values z2 and z3 obtained by the electronic reconnaissance system, the direction-finding value of the electronic reconnaissance system at the moment can be obtained. This process can be approximately regarded as linear and is expressed as

[0017]

[0018] Through the above method, after achieving time registration, at the kth moment, denote the set of M k target direction-finding values detected by the electronic reconnaissance system as

[0019]

[0020] where α k，i , i = 1, 2, …, M k , α k，i follows a normal distribution with a mean of and a variance of σ k，i .

[0021] Furthermore, the specific content of step S2 includes:

[0022] S21. The ellipsoidal threshold is used as the statistical distance of the associated object. When the distance threshold of the associated object is 2°, correct the distance threshold to ensure that only the associated objects that meet the corrected distance threshold are data-associated, reducing the computational amount. Suppose the target detected by the detection system and the target detected by the electronic reconnaissance system are the same target. Then the random variable (α k，i - βk，j ) follows a Gaussian distribution with a mean of zero and a variance of σ k，j +σ k，i . Define the statistical distance between α k,i and β k，j as follows:

[0023] ||α k，i - β k，j || = (α k，i - β k，j )(σ T + σ k，j + σ k，i )(α -1 - β k，i - β k，j )(7)

[0024] For S22, to reduce the computational complexity of the algorithm and improve the real-time performance of processing, only the data whose statistical distance meets certain threshold requirements is associated, and the statistical distance exceeding the threshold is specified as a constant. When 2σ = 4°, the corrected statistical distance is

[0025]

[0026] where σ = σ k，j + σ k，i . In this way, a threshold is set for the distance between two angle values, that is, when the distance between the direction value of the target detected by the detection system and the direction finding value of the target detected by the electronic reconnaissance system is greater than two standard deviations, data association is not performed. To ensure the integrity and feasibility of the algorithm, when the statistical distance between α k，i and β k，j is greater than two standard deviations, let d ij = 100σ, so that in the actual calculation process, this situation is excluded.

[0027] Furthermore, the specific content of step S3 includes:

[0028] S31, transform the problem of associating the direction value of the target track point based on the multi-dimensional assignment algorithm with the direction finding value of the target into a global discrete optimization problem under certain constraint conditions, and its objective function is

[0029]

[0030] where d ij is as shown in formula (8). The constraint conditions are

[0031]

[0032] where C ij = 0 or 1, is the association discrimination matrix, used to represent α k，i and βk，j Is it associated? If it is associated, then C ij = 1, otherwise C ij = 0. The objective function in formula (9) represents the minimum multi-dimensional assignment cost, that is, the total cost of the association between the direction value of the target detected by the detection system and the direction finding value of the target detected by the electronic reconnaissance system is minimized. The constraint condition in formula (10) indicates the uniqueness of the assignment, that is, the direction value of the detected target and the direction finding value of the detected target can only appear in one target association relationship pair, thus ensuring the uniqueness of the association relationship.

[0033] The solution of formula (9) for C ij can be transformed into the solution of a multi-0-1 linear programming problem. For example, when M k = 3 and N k = 3, the objective function D(α k , β k ) * is

[0034] min C (d 11 C 11 + d 12 C 13 + d 13 + C 13 + d 21 C 21 + d 22 C 22 + d 23 C 23 + d 31 C 31 + d 32 C 32 + d 33 C 33 ) (11)

[0035] Let d and C be respectively

[0036] d = [d 11 d 12 d 13 d 21 d 22 d 23 d 31 d 32 d 33 (12)

[0037] C = [C 11 C 12 C 13 C 21 C 22 C 23 C 31 C 32C 33 ] (13)

[0038] Where T is the transposition operator symbol, then the objective function D(α k , β k ) * It can be transformed into the solution of the matrix equation (14).

[0039]

[0040] In this way, we can solve equation (14) to obtain C = {c ij}, it is possible to determine the correlation between the target track data detected by the detection system and the target direction finding data detected by the electronic reconnaissance system.

[0041] S32, remove the distance d of the associated object ij The value of 100σ is used in the equation, and the modified correlation matrix is in,

[0042]

[0043] pass Determine whether the target direction value detected by the detection system and the target direction finding angle detected by the electronic reconnaissance system are successfully correlated.

[0044] Furthermore, the specific contents of step S4 include:

[0045] S41, if the target detected by the detection system and the target detected by the electronic reconnaissance system are the same target, the random variable (α k，i -β k，j ) obeys a Gaussian distribution with a mean of zero and a standard deviation of σ, so (α k，i -β k，j The probability that ) is less than 2σ is The probability of being greater than 2σ is 1-p1=0.0455. If the target detected by the detection system is not the same as the target detected by the electronic reconnaissance system, assuming that α k，i ~N(m k，i , σ k，i ), β k，i ~N(m k，j , σ k，j ),but

[0046] (α k，i -β k，j )~N(m k，i -m k，j , σ k，i -σ k，j ) (16)

[0047] Considering m k，i and mk，j obeys a uniform distribution within the range of [0, 2π], then (m k，i -m k，j ) obeys a uniform distribution within the range of [-2π, 2π]. Therefore, the probability that the distance between associated objects is less than 2σ is In this case, the two targets will be wrongly associated together.

[0048] S42. Calculate the correct association probability and false association probability of the targets detected by the detection system and the targets reconnoitered by the electronic reconnaissance system. For the targets detected by the detection system and the targets reconnoitered by the electronic reconnaissance system, if for two targets, after m consecutive detections, they are associated more than n times, then they are considered to be the same target. Denote the correct detection probability as P R , and the false alarm probability as P F , then

[0049]

[0050] In practical engineering applications, appropriate m and n can be selected according to different detection probabilities and false alarms, and the values of P R and P F can be calculated. For example, when σ k，j = 1°, σ k，i = 1°, p1 = 0.9545, p2 = 0.0111. The detection probability P R and the false alarm probability P F in several typical cases of m and n values are as follows:

[0051] The detection probability P R and the false alarm probability P F

[0052]

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0054] (1) The method of the present invention can complete the data association of the detected target and the reconnoitered target under the condition of low detection probability, and has a high correct discrimination probability and a small false alarm probability.

[0055] (2) When the measurement data probability of the electronic reconnaissance is greater than 0.9, the method of the present invention can complete the attribute discrimination and there will be no wrong discrimination. Description of the Drawings

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0057] In the drawings:

[0058] Figure 1 is a flowchart of a method for data association between a target track and electronic reconnaissance information based on multi-dimensional assignment provided by an embodiment of the present invention;

[0059] Figure 2 is a typical scenario diagram of data association between a detection system and an electronic reconnaissance system in the specific implementation method of the present invention;

[0060] Figure 3 are the time scales of the target track points of the detection system and the target direction measurement values of the electronic reconnaissance system;

[0061] Figure 4 is the true motion trajectory of the target;

[0062] Figure 5 are the target track points detected by the detection system (distance root mean square error RMS = 1 km, angle root mean square error RMS = 1°);

[0063] Figure 6 is the relative direction value of the target track point with the deployment position of the electronic reconnaissance system station as the reference position;

[0064] Figure 7(a) shows the direction finding result when the direction finding correct probability of the electronic reconnaissance system for the target is 1, Figure 7(b) shows the direction finding result when the direction finding correct probability of the electronic reconnaissance system for the target is 0.9, Figure 7(c) shows the direction finding result when the direction finding correct probability of the electronic reconnaissance system for the target is 0.8; Figure 7(d) shows the direction finding result when the direction finding correct probability of the electronic reconnaissance system for the target is 0.5;

[0065] Figure 8 shows the association result of the target detected by the detection system and the target reconnoitered by the electronic reconnaissance system when the direction finding correct probability of the electronic reconnaissance system for the target is 1 in the simulation experiment of the present invention; among them, Figure 8(a) shows the association result of detection target 1 and reconnaissance target 1, Figure 8(b) shows the association result of detection target 2 and reconnaissance target 2, Figure 8(c) shows the association result of detection target 3 and reconnaissance target 3, Figure 8(d) shows the association result of detection target 1 and reconnaissance target 2, Figure 8(e) shows the association result of detection target 1 and reconnaissance target 3, Figure 8(f) shows the association result of detection target 2 and reconnaissance target 3;

[0066] Figure 9 shows the association results of the detected target and the electronic reconnaissance target when the correct direction-finding probability of the electronic reconnaissance system for the target is 0.9 in the simulation experiment of the present invention. Among them, Figure 9(a) shows the association result of detected target 1 and reconnaissance target 1, Figure 9(b) shows the association result of detected target 2 and reconnaissance target 2, Figure 9(c) shows the association result of detected target 3 and reconnaissance target 3, Figure 9(d) shows the association result of detected target 1 and reconnaissance target 2, Figure 9(e) shows the association result of detected target 1 and reconnaissance target 3, and Figure 9(f) shows the association result of detected target 2 and reconnaissance target 3;

[0067] Figure 10 shows the association results of the detected target and the electronic reconnaissance target when the direction-finding probability of the reconnaissance system for the radiation source target is 0.8 in the simulation experiment of the present invention. Among them, Figure 10(a) shows the association result of detected target 1 and reconnaissance target 1, Figure 10(b) shows the association result of detected target 2 and reconnaissance target 2, Figure 10(c) shows the association result of detected target 3 and reconnaissance target 3, Figure 10(d) shows the association result of detected target 1 and reconnaissance target 2, Figure 10(e) shows the association result of detected target 1 and reconnaissance target 3, and Figure 10(f) shows the association result of detected target 2 and reconnaissance target 3.

[0068] Detailed implementation manners

[0069] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0070] It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Therefore, only the components related to the present invention are shown in the diagrams, rather than being drawn according to the number, shape, and size of the components in actual implementation. The types, quantities, and proportions of the components in actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0071] An embodiment of the present invention provides a method for associating target track and electronic reconnaissance information data based on multi-dimensional assignment. The process schematic diagram is as Figure 1 shown, and the data association method includes:

[0072] S1. Taking the site deployment location of the electronic reconnaissance system as the reference location, calculate the direction value of the target track point detected by the detection system relative to the reference location, ensure that the target track point and the target direction measurement value have a unified reference location, and achieve spatial registration; taking the time scale of the target track point of the detection system as the benchmark, extrapolate and interpolate the target direction measurement value of the electronic reconnaissance system to obtain the direction measurement value of the electronic reconnaissance system at the reference time scale, ensure that the target track point and the target direction measurement value have a unified time scale, and achieve time registration;

[0073] S2. Calculate the statistical distance between the target direction measurement value of the electronic reconnaissance system and the direction value of the target track point of the detection system, and correct the statistical distance to reduce the computational complexity of the algorithm;

[0074] S3. Construct an association discrimination matrix for the target direction measurement value of the electronic reconnaissance system and the direction value of the target track point of the detection system based on the multi-dimensional assignment algorithm

[0075] S4. Adopt the continuous multiple accumulation detection method to detect the association discrimination matrix, and output the discrimination result according to the discrimination matrix.

[0076] Furthermore, the specific content of step S1 includes:

[0077] S11. At time k, the position measurement set of N k target track points output by the detection system is: where x k,j , j = 1, 2,... N k obeys a normal distribution with a mean of and a variance of p k,j . The measurement set of M k target direction measurement values detected by the electronic reconnaissance system is: where z k,i , i = 1, 2…, M k , z k，i obeys a normal distribution with a mean of and a variance of q k，i . Assuming that the position of a certain target track point in the rectangular coordinate system at time t is (x a , y a ), and the deployment position coordinates of the electronic reconnaissance system are (x0, y0), then the direction value of this target track point relative to the reference location is

[0078] β pt = arctan((y a - y0) / (x a - x0)) (3)

[0079] where p is the track number. After spatial registration, the set of direction values of the target track point relative to the reference location can be obtained as

[0080]

[0081] β k，j , j = 1, 2...N k represents the direction value of the j-th detected target relative to the electronic reconnaissance system at time k. β k，j , j = 1, 2…N k , subject to a Gaussian distribution with a mean of m k，j and a variance of σ k，j .

[0082] S12. Assume that the time scales of the target track points detected by the detection system are {T1, T2, … T k …}, and the time scales of the target direction measurement values detected by the electronic reconnaissance system are {T1′, T2′, … T k ′…}. Based on the time scale {T1, T2, … T k …} of the target track points detected by the detection system, interpolate or extrapolate the target direction measurement values detected by the electronic reconnaissance system to ensure that the time scales of the target direction measurement values detected by the electronic reconnaissance system and the target track points detected by the detection system are consistent, thereby achieving time registration. For example, the data rate of the track point data of the detection system is once every 10 seconds, and the data rate of the direction measurement data of the electronic reconnaissance system is once every 1 second, as Figure 3 shown. For the time scale T k of the detection system, the target direction measurement value obtained at the previous time point T k ′ in the reconnaissance data sequence of the electronic reconnaissance system is z2, and the target direction measurement value obtained at the next time point T k-1 ′ after T k is z3. By performing interpolation processing on the direction measurement values z2 and z3 obtained by the electronic reconnaissance system, the direction measurement value of the electronic reconnaissance system at k+1 time can be obtained. This process can be approximately regarded as linear and is expressed as

[0083]

[0084] Through the above method, after achieving time registration, at time k, denote the set of M k target direction measurement values detected by the electronic reconnaissance system as

[0085]

[0086] where α k，i , i = 1, 2..., M k k，i α k，i is subject to a normal distribution with a mean of and a variance of σ k，i .

[0087] Furthermore, the specific content of step S2 includes:

[0088] S21. The ellipsoidal threshold is used as the statistical distance of the associated object. When the distance threshold of the associated object is 2°, the distance threshold is corrected to ensure that data association is only performed on the associated objects that meet the corrected distance threshold, reducing the computational amount. Assume that the target detected by the detection system and the target detected by the electronic reconnaissance system are the same target. Then the random variable (α k，i -β k，j ) follows a Gaussian distribution with a mean of zero and a variance of σ k，j +σ k，i . Define the statistical distance between α k，i and β k，j as:

[0089] ||α k，i -β k，j ||=(α k，i -β k，j ) T (σ k，j +σ k，i ) -1 (α k，i -β k，j ) (7)

[0090] S22. To reduce the computational amount of the algorithm and improve the real-time performance of processing, only the data whose statistical distance meets certain threshold requirements is associated, and the statistical distance exceeding the threshold is specified as a constant. When 2σ = 4°, the corrected statistical distance is

[0091]

[0092] where σ = σ k，j +σ k，i . In this way, a threshold is set for the distance between two angle values, that is, data association is not performed when the distance between the direction value of the target detected by the detection system and the direction finding value of the target detected by the electronic reconnaissance system is greater than two standard deviations. To ensure the integrity and feasibility of the algorithm, when the statistical distance between α k，i and β k，j is greater than two standard deviations, let d ij = 100σ, so that in the actual calculation process, this situation is excluded.

[0093] Furthermore, the specific content of step S3 includes:

[0094] S31. Transform the problem of associating the direction value of the target track point based on the multi-dimensional assignment algorithm with the direction finding value of the target into a global discrete optimization problem under certain constraint conditions, and its objective function is

[0095]

[0096] where d ij is as shown in formula (8). The constraint conditions are

[0097]

[0098] where C ij = 0 or 1, is the association discrimination matrix, used to represent whether α k，j and β k，j are associated. If they are associated, then c ij = 1, otherwise c ij = 0. The objective function in formula (9) represents the minimum multi-dimensional assignment cost, that is, the total association cost between the direction value of the target detected by the detection system and the direction finding value of the target detected by the electronic reconnaissance system is minimized. The constraint conditions in formula (10) indicate the uniqueness of the assignment, that is, the direction value of the detected target and the direction finding value of the detected target can only appear in one target association relationship pair, thus ensuring the uniqueness of the association relationship.

[0099] The solution of C in formula (9) ij can be transformed into the solution of a multi-0-1 linear programming problem. For example, when M k = 3 and N k = 3, the objective function D(α k , β k ) * is

[0100] min C (d 11 C 11 + d 12 C 12 + d 13 C 13 + d 21 C 21 + d 22 C 22 + d 23 C 23 + d 31 C 31 + d 32 C 32 + d 33 C 33 ) (11)

[0101] Denote d and C as

[0102] d = [d 11 d 12 d 13 d 21 d 22 d 23d 31 d 32 d 33 (12)

[0103] C = [C 11 C 12 C 13 C 21 C 22 C 23 C 31 C 32 C 33 T (13)

[0104] where T is the transpose operator, then the objective function D(α k , β k ) * can be transformed into the solution of the matrix equation (14).

[0105]

[0106] In this way, by solving the system of equations (14), C = {c ij} can be obtained, and the correlation result between the target track data detected by the detection system and the target direction-finding data detected by the electronic reconnaissance system can be determined.

[0107] S32. Eliminate the value of 100σ in the distance d ij of the associated object, and correct the association matrix to where

[0108]

[0109] By determine whether the target direction value detected by the detection system and the target direction-finding angle detected by the electronic reconnaissance system are successfully associated.

[0110] Furthermore, the specific content of step S4 includes:

[0111] S41. If the target detected by the detection system and the target detected by the electronic reconnaissance system are the same target, the random variable (α k，i - β k，j ) follows a Gaussian distribution with a mean of zero and a standard deviation of σ. Therefore, the probability that (α k，i - β k，j ) is less than 2σ is and the probability of being greater than 2σ is 1 - p1 = 0.0455. If the target detected by the detection system and the target detected by the electronic reconnaissance system are not the same target, assume α k，i ~N(m k，i , σ k，i ), β​k，i ~N(m k，j ,σ k，j ), then

[0112] (α k，i -β k，j )~N(m k，i -m k，j ,σ k，i -σ k，j ) (16)

[0113] Considering that m k，i and m k，j are uniformly distributed in the range of [0, 2π], then (m k，i -m k，j ) is uniformly distributed in the range of [-2π, 2π]. Therefore, the probability that the distance between associated objects is less than 2σ is In this case, the two targets will be misassociated together.

[0114] S42. Calculate the correct association probability and misassociation probability of the detection target by the detection system and the reconnaissance target by the electronic reconnaissance system. For the detection target by the detection system and the reconnaissance target by the electronic reconnaissance system, if for two targets, after m consecutive detections and being associated more than n times, they are considered to be the same target. Denote the correct detection probability as P R , and the false alarm probability as P F , then

[0115]

[0116] In practical engineering applications, appropriate m and n can be selected according to different detection probabilities and false alarms, and the values of P R and P F can be calculated. For example, when σ k，j = 1°, σ k,i = 1°, p1 = 0.9545, p2 = 0.0111. The detection probability P R and the false alarm probability P F in several typical cases of m and n values are shown in the following table:

[0117] Detection probability P R and false alarm probability P F

[0118]

[0119] 1. Simulation conditions of the embodiments of the present invention:

[0120] Assume that in the experiment of the present invention, the site deployments of the detection system and the electronic reconnaissance system are at the same location, with the coordinate position being (0, 0). The number of targets is 3, and the initial positions of Targets 1 to 3 are (0, 100000 m), (0, 150000 m), and (30000 m, 150000 m) respectively. The motion trajectory equations are determined by Formulas (52) to (54) respectively:

[0121]

[0122] Assume that after completing the spatial registration and time registration, the number of target track points detected by the detection system and the number of target direction measurement values detected by the electronic reconnaissance system are 50, and the time scale interval is 10 seconds. Assume that the root mean square error of the distance measurement of the target track points detected by the detection system is 1 km, and the root mean square error of the direction value is 1°. Then the target track points detected by the detection system are as Figure 4 shown. Convert the position of the target track points to the direction value relative to the reference position (the position of the electronic reconnaissance system), as Figure 5 shown.

[0123] Assume that the correct probabilities of the electronic reconnaissance system for target direction finding are 1, 0.9, and 0.8 respectively. Under different probabilities, Figure 7(a) shows the direction measurement values of the target when the probability is 1, Figure 7(b) shows the direction measurement values of the target when the probability is 0.9, Figure 7(c) shows the direction measurement values of the target when the probability is 0.8, and Figure 7(d) shows the direction measurement values of the target when the probability is 0.5.

[0124] 2. Analysis of the simulation results of the experiment of the present invention:

[0125] Figures 8 to 10 show the simulation results of the data association algorithm based on multi-dimensional assignment for associating the direction values of the 3 detected target track points and the target direction measurement values detected by the electronic reconnaissance system, and continuously accumulating the association detection rule for 5 times when the probabilities of the reconnaissance system for direction finding of the radiation source target are 1, 0.9, and 0.8 respectively. Among them, Figure 8 shows the simulation results when the probability is 1, Figure 9 shows the simulation results when the probability is 0.9, and Figure 10 shows the simulation results when the probability is 0.8. Figure 8(a), Figure 9(a), and Figure 10(a) show the association results between Detected Target 1 and Reconnaissance Target 1, Figure 8(b), Figure 9(b), and Figure 10(b) show the association results between Detected Target 2 and Reconnaissance Target 2, Figure 8(c), Figure 9(c), and Figure 10(c) show the association results between Detected Target 3 and Reconnaissance Target 3, Figure 8(d), Figure 9(d), and Figure 10(d) show the association results between Detected Target 1 and Reconnaissance Target 2, Figure 8(e), Figure 9(e), and Figure 10(e) show the association results between Detected Target 1 and Reconnaissance Target 3, and Figure 8(f), Figure 9(f), and Figure 10(f) show the association results between Detected Target 2 and Reconnaissance Target 3.

[0126] The embodiments of the present invention described above are only used to help illustrate the present invention. These embodiments are selected and specifically described in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can well understand and utilize the present invention. The embodiments do not describe all the details in detail, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification, and these all belong to the protection scope of the present invention.

Claims

1. A method for data association between target tracks and electronic reconnaissance information based on multi-dimensional assignment, characterized in that, It includes a detection system and an electronic reconnaissance system; the detection system obtains the direction and distance information of the aerial target track, and the electronic reconnaissance system obtains the direction and identity information of the radiation source carried on the target. The method for data association between the target track and the electronic reconnaissance information based on multi-dimensional assignment includes the following steps: S1. Taking the position of the electronic reconnaissance system as the reference position, calculate the direction value of the target track point detected by the detection system relative to the reference position to achieve spatial registration; taking the time scale of the target track point detected by the detection system as the benchmark, extrapolate and interpolate the target direction-finding value detected by the electronic reconnaissance system to achieve time registration; using the direction value of the registered target track point and the detected target direction-finding value as the association objects; S2. Use the elliptical threshold as the distance threshold d for the associated object ij ; S3. Calculate the data association discrimination matrix of associated objects by using a multi-dimensional allocation method S4. Adopt the multiple accumulation detection method to detect the discrimination matrix and output the discrimination result.

2. A method for associating target track and electronic reconnaissance information data based on multi-dimensional assignment according to claim 1, characterized in that, In step S2, when the distance threshold of the association object is 2°, correct the distance threshold to ensure that only the association objects that meet the corrected distance threshold are subjected to data association, reducing the calculation amount.

3. A method for correlating target track and electronic reconnaissance information data based on multi-dimensional assignment according to claim 1, characterized in that, Step S1 specifically includes: Assume that the detection system and the electronic reconnaissance system monitor the same airspace. The detection system and the electronic reconnaissance system are deployed at different locations, and data is transmitted between the two systems through a data transmission link. There are N targets in the monitored airspace, and it is assumed that the radiation sources carried by the targets are all turned on to emit radiation signals. At time k, the non-cooperative detection system detects N k sets of target position measurements as where x k，j , j = 1, 2…, N k , x k，j obeys a normal distribution with a mean of and a variance of p k，j ; the electronic reconnaissance system detects M k sets of target direction-finding values as where z k，i , i = 1, 2…, M k , z k，i obeys a normal distribution with a mean of and a variance of q k，i ; Suppose that at time t, the position of a target track point in the rectangular coordinate system is (x a , y a ), and the coordinate of the deployment position of the electronic reconnaissance system is (x0, y0). Then the direction value of the target track point relative to the reference position is β pt = arctan((y a - y0) / (x a - x0)) (3) where p is the track number; after spatial registration, the set of direction values of the target track point relative to the reference position can be obtained as β k，j where \(j = 1, 2,\cdots,N\) k represents the direction value of the \(j\)-th detected target relative to the electronic reconnaissance system at time \(k\); \(\beta\) k，j where \(j = 1, 2,\cdots,N\) k follows a Gaussian distribution with a mean of \(m\) k，j and a variance of \(\sigma\) k，j . Suppose the time scales of the target track points detected by the detection system are {T1, T2, … T k …}, and the time scales of the target direction-finding values detected by the electronic reconnaissance system are {T1′, T2′, … T k ′…}; based on the time scales {T1, T2, … T k …} of the target track points detected by the detection system, interpolation or extrapolation is performed on the target direction-finding values detected by the electronic reconnaissance system.

4. A method for correlating target track and electronic reconnaissance information data based on multi-dimensional assignment according to claim 3, characterized in that The data rate of the detection system track point data is 10 seconds per time, and the data rate of the electronic reconnaissance system direction finding data is 1 second per time. k , in the electronic reconnaissance system reconnaissance data sequence, k The previous time point T k-1 ′The target direction finding value obtained is z2, at T k The next moment T k+1 ′ The target direction finding value obtained is z3; interpolation processing is performed on the direction finding values ​​z2 and z3 obtained by the electronic reconnaissance system to obtain The direction finding value of the electronic reconnaissance system at the moment, this process can be approximately regarded as linear, expressed as After achieving time registration through the above method, at time k, denote the set of M k target direction measurement values detected by the electronic reconnaissance system as Among them, α k，i , i = 1, 2..., M k , α k，i obeys a normal distribution with a mean of and a variance of σ k，i .

5. A method for correlating target track and electronic reconnaissance information data based on multi-dimensional assignment according to claim 1, characterized in that Step S2 specifically includes: S21, using the elliptical threshold as the statistical distance of the associated object. Assume that the target detected by the detection system and the target detected by the electronic reconnaissance system are the same target. Then the random variable (α k，i -β k，j ) follows a Gaussian distribution with a mean of zero and a variance of σ k，j +σ k，i . Define the statistical distance between α k，i and β k，j as: ||α k，i -β k，j ||-(α k，i -β k，j ) T (σ k，j +σ k，i ) -1 (α k，i -β k，j ) (7) S22. To reduce the calculation amount of the algorithm and improve the real-time performance of processing, only associate the data whose statistical distance meets certain threshold requirements, and stipulate the statistical distance exceeding the threshold as a constant. When 2σ = 4°, the corrected statistical distance is where σ = σ k,j + σ k,i , which sets a threshold for the distance between the two angular values. That is, when the distance between the direction value of the target detected by the detection system and the direction finding value of the target detected by the electronic reconnaissance system is greater than two standard deviations, data association is cancelled. To ensure the integrity and feasibility of the algorithm, when the statistical distance between α k,i and β k，j is greater than two standard deviations, let d ij = 100σ, so that in the actual calculation process, this situation is excluded.

6. The method for associating target track and electronic reconnaissance information data based on multi-dimensional assignment according to claim 1, wherein Step S3 specifically includes: S31. Convert the problem of associating the direction value of the target track point and the target direction-finding value based on the multi-dimensional assignment algorithm into a global discrete optimization problem under certain constraint conditions, and its objective function is where d ij is as shown in formula (8). The constraint condition is Among them, C ij = 0 or 1, is an association discrimination matrix, used to represent α k,i and β k，j whether they are associated. If they are associated, then C ij = 1, otherwise C ij = 0. The objective function in formula (9) represents the minimum multi-dimensional allocation cost, that is, the minimum total association cost between the direction value of the target detected by the detection system and the direction finding value of the target detected by the electronic reconnaissance system; the constraint condition in formula (10) indicates the uniqueness of the allocation, that is, the direction value of the detected target and the direction finding value of the detected target can only appear in one target association relationship pair, so as to ensure the uniqueness of the association relationship; Solving C in Formula (9) ij can be transformed into solving a multi 0-1 linear programming problem; for example, when M k = 3, N k = 3, the objective function D(α k , β k ) * is min c (d 11 C 11 +d 12 C 12 +d 13 C 13 +d 21 C 21 +d 22 C 22 +d 23 C 23 +d 31 C 31 +d 32 C 32 +d 33 C 33 ) (11) Denote d and C as respectively d = [d 11 d 12 d 13 d 21 d 22 d 23 d 31 d 32 d 33 (12) C = [C 11 C 12 C 13 C 21 C 22 C 23 C 31 C 32 C 33 T (13)​ where T is the transpose operator, the objective function D(α k , β k ) * can be transformed into the solution of the matrix equation (14); In this way, C = {c ij} can be obtained by solving the system of equations (14), and the correlation result between the target track data detected by the detection system and the target direction-finding data detected by the electronic reconnaissance system can be discriminated; S32, eliminate the distance d of the associated object ij The value is 100σ, and correct the association matrix to wherein By Determine whether the target direction value detected by the detection system is successfully associated with the target direction-finding angle detected by the electronic reconnaissance system.

7. A method for associating target track and electronic reconnaissance information data based on multi-dimensional allocation according to claim 1, characterized in that Step S4 specifically includes: S41, the random variable (α k，i -β k，j ) follows a Gaussian distribution with a mean of zero and a standard deviation of σ. Therefore, the probability that (α k，i -β k，j ) is less than 2σ is The probability of being greater than 2σ is 1 - p1 = 0.0455, which proves that the target detected by the detection system and the target reconnoitered by the electronic reconnaissance system are the same target.

8. A method for associating target track and electronic reconnaissance information data based on multi-dimensional assignment according to claim 1, characterized in that Step S4 specifically includes: Suppose α k，i ~N(m k，i ,σ k，i ), β k，i ~N(m k，j ,σ k，j ), then (α k，i -β k，j )~N(m k，i -m k，j ,σ k,i -σ k，j ) (16) Considering m k，i and m k，j are uniformly distributed in the range of [0, 2π], then (m k，i - m k，j ) is uniformly distributed in the range of [-2π, 2π]. Therefore, the probability that the associated object distance is less than 2σ is It means that the target detected by the detection system and the target detected by the electronic reconnaissance system are not the same target.

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