Three-dimensional multi-target matching method based on passive sensor network

Abstract

The application provides a three-dimensional multi-target matching method based on a passive sensor network, which comprises the following steps: step one, converting the measurement of each sensor into a common coordinate system; step two, solving a plurality of double passive sensor matching according to the passive sensor network topology; step three, establishing a non-directional weighted graph of the passive sensor network based on the double passive sensor matching; and step four, solving the multi-sensor multi-target measurement matching of the passive sensor network based on the non-directional weighted graph. The application provides a loss function and a loss matrix of the double passive sensor matching, fully utilizes the algebraic property and the geometric property of the passive sensor measurement, and effectively distinguishes the correct matching; a discrete optimization problem corresponding to the double passive sensor matching is constructed and solved, and the calculation complexity is low; a graph theory model of the multi-sensor multi-target measurement matching on the passive sensor network is established, a reasonable definition of the matching is provided, and the calculation complexity of the solving method is also low.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for matching multi-target multi-sensor measurements on passive sensor networks. The method firstly gives the matching cost of multi-target pure angle measurements for dual passive sensors, and then designs a multi-target measurement matching algorithm based on dual passive sensors. Subsequently, a multi-target measurement matching scheme based on passive sensor networks is designed by combining graph theory model and minimum spanning tree technology. BACKGROUND

[0002] Passive sensors are sensors that can only measure the angle information of targets, and cannot obtain the distance information of targets. For a three-dimensional scene, passive sensors can only obtain the high-low angle and azimuth angle measurements of targets to the sensors. Therefore, unlike active sensors, passive sensors lack one dimension of information for target measurement. On the other hand, the measurements of passive sensors on multiple targets often have no labels, i.e., different passive sensors cannot be directly matched. This creates an obstacle for the cooperation between multiple passive sensors, such as cooperative positioning of multiple passive sensors. In some studies, the matching problem is also referred to as the data association problem.

[0003] At the same time, the measurements of passive sensors on targets are inevitably affected by noise. Therefore, the lines of sight corresponding to the pure angle measurements of different passive sensors on targets, even if corresponding to the same target, cannot intersect in space. And because passive sensors lose the distance information of targets, it is not easy to measure whether two sets of pure angle measurements from two passive sensors match, i.e., come from the same target.

[0004] In addition, multi-target measurement matching based on passive sensor networks involves matching of multiple sets of dual passive sensors. Note that the principle of matching is to determine that each set of measurements of different sensors comes from the same target. In order to unify the cooperation of passive sensors on the network, these sets of dual passive sensor matching should be combined to cover all passive sensors on the network without conflict.

[0005] Currently, there are few studies on matching methods for multi-passive sensor multi-target scenes, and there is a lack of research on multi-target measurement matching based on passive sensor networks. Some research contents are as follows: 1. Ye Z H, Li H H, Wang J D, et al. Frontiers and trends of infrared photoelectric detectors [J]. Infrared and Millimeter Waves, 2022, 41(1): 15-39. 2. Qin L, Li J L, Zhou D. Research on near space target based on double station infrared tracking [J]. Modern Defense Technology, 2014, 42(02): 122-127. 3. Yue J, Li F M, Gao S L. Infrared multi-target double station positioning based on track direction maximum density estimation [J]. Optics Precision Engineering, 2022, 30(12): 1509-1522. 4. Wang C, Li S H, Huang H. Multi-target measurement data association of direction finding cross location system [J]. System Engineering and Electronics Technology, 2002, (09): 104-106+117.

[0006] The existing multi-target measurement matching method based on double passive sensors or passive sensor network has the following limitations:

[0007] 1. Some existing methods do not fully utilize the existing measurement information, or the loss function lacks mathematical principle analysis in algebra and geometry.

[0008] 2. Some existing methods involving passive sensor networks assume that there is a central sensor, and only the central sensor and the remaining sub-sensors are matched one by one, thereby simplifying the matching problem of the sensor network to a double sensor matching problem. This method limits the topology of the sensor network, and its effect is affected by the selection of the central sensor, and is not the optimal network topology.

[0009] 3. Some existing methods exhaustively enumerate all possible matching combinations of multi-sensor multi-target measurements, and the computational complexity of such methods increases rapidly with the increase of the number of sensors and targets, which cannot guarantee fast matching of multi-sensor multi-target measurements.

[0010] 4. Some existing methods measure the matching effect based on the positioning effect of multi-sensor measurements on targets,

[0011] The reliability of such methods is affected by the positioning algorithm used.

[0012] In order to solve the above problems, the present application aims at how to match multi-sensor multi-target measurements on passive sensor network, and gives the matching cost of multi-target pure angle measurement based on double passive sensors, and then designs a multi-target measurement matching algorithm based on double passive sensors, and then realizes multi-target measurement matching based on passive sensor network combined with the minimum spanning tree technology. SUMMARY

[0013] The technical problem solved by the present application: for the problem of how to match the multi-sensor multi-target measurement on passive sensor network, the matching cost of multi-target pure angle measurement is given for double passive sensors, and then a multi-target measurement matching algorithm based on double passive sensors is designed, and then the multi-target measurement matching based on passive sensor network is realized by combining graph theory model and minimum spanning tree technology.

[0014] The solution of the present application: for the multi-sensor multi-target measurement on passive sensor network, the matching cost of multi-target pure angle measurement for double passive sensors is designed; based on this cost and passive sensor network, a plurality of double passive sensor matching is solved; then a corresponding undirected weighted graph of passive sensor network is established with the total loss of matching as the edge weight; the minimum spanning tree is found and extracted from the undirected weighted graph, and the multi-target measurement matching of the corresponding passive sensor network is obtained.

[0015] The following describes the specific steps of the present application for the problem. Assuming that the coordinates of the target j centroid position vector in the three-dimensional scene are T j =[x j y j z j ] T , wherein x j , y j , z j are the components of T j in the three coordinate axis directions of the common coordinate system. n is the number of targets. The coordinates of the passive sensor i centroid position vector in the common coordinate system are S i =[x i y i z i ] T , i = 1,..., m, wherein x i , y i , z i are the components of S i in the three coordinate axis directions of the common coordinate system, and m is the number of passive sensors. C i is the rotation matrix of the common coordinate system to the local coordinate system of passive sensor i. Since there is no unified target measurement label, the label of passive sensor i to target j is denoted as φ i (j). Denote the adjacency matrix corresponding to the passive sensor network as A. Without loss of generality, it is assumed that the passive sensor network is connected.

[0016] For a three-dimensional scene, the measurement model of the passive sensor is:

[0017]

[0018] where the azimuth measurement noise are independent and identically distributed (i.i.d.) random variables with mean 0 and variance and are bounded. The high-low measurement noise are independent and identically distributed (i.i.d.) random variables with mean 0 and variance and are bounded, and are independent of are the azimuth measurements of passive sensor i to target j in the local coordinate system of passive sensor i. are the high-low measurements of passive sensor i to target j in the local coordinate system of passive sensor i. i are the labels of the measurements of passive sensor i to target j. i is a bijection from {1,...,n} to {1,...,n}, and different passive sensors have different bijections. are the Cartesian coordinate components of target i in the local coordinate system of passive sensor j, given by the coordinate transformation

[0019]

[0020] Based on the measurement models (1)-(2), the specific steps for matching the multi-sensor multi-target measurements on the passive sensor network are as follows:

[0021] Step 1: Equivalently convert the measurements of each sensor to the common coordinate system

[0022] The measurement of passive sensor i to target j Actually corresponds to a ray in space. According to the rotation matrix of the coordinate system, the unit vector corresponding to this ray in the common coordinate system can be calculated as The calculation formula is as follows:

[0023]

[0024] Further, the equivalent measurement of passive sensor i to target j in the common coordinate system is calculated by the following formula:

[0025]

[0026] Thus, the equivalent measurement set of passive sensor i to all targets in the common coordinate system is

[0027]

[0028] Step 2: Solve several double passive sensor matches according to the passive sensor network topology ​

[0029] The meaning of the adjacency matrix A of the graph corresponding to the passive sensor network is that for a network consisting of m passive sensors, the dimension of the matrix A is m x m, if the (i, l)th element of A is 1, then passive sensor i and passive sensor l need to be matched, if the (i, l)th element of A is 0, then passive sensor i and passive sensor l do not need to be matched.

[0030] Therefore, according to the adjacency matrix A, the passive sensor pairs that need to be matched are matched. The following takes passive sensor i and passive sensor l as an example to illustrate the double passive sensor matching method.

[0031] According to the first step, the equivalent measurement set of passive sensor i in the common coordinate system is obtained respectively and the equivalent measurement set of passive sensor l in the common coordinate system is obtained respectively The double passive sensor matching loss matrix C(i, l) is constructed, which has a dimension of n x n, and the (j, k)th element of C(i, l) is [C(i, l)] j,k The matching loss function of the equivalent measurements in the common system is given by and

[0032]

[0033] Where p(·) is a penalty function:

[0034]

[0035] And, is an auxiliary variable, which is given by the following formula:

[0036]

[0037] In particular, for the more common case, the meaning of the auxiliary variable involved in the matching loss function is that the projection of the measurement of passive sensor i in the x-y plane corresponds to the intersection of the projection of the measurement of passive sensor l in the x-y plane with the projection of the measurement of passive sensor i in the x-y plane. The auxiliary variable has the same meaning.

[0038] After obtaining the loss matrix C of passive sensor i and passive sensor l, the matching is the corresponding relationship between the n groups of measurements that minimize the total loss, that is,

[0039]

[0040] ​Where σ is a bijection from {1,...,n} to {1,...,n}, referring to matching the j-th measurement of passive sensor i with the σ(j)-th measurement of passive sensor l. Equation (9) can be efficiently solved by the KM algorithm.

[0041] Step 3: Establish an undirected weighted graph for the passive sensor network based on dual passive sensor matching.

[0042] For a passive sensor network, consider passive sensor i as node V. i If a match is found between passive sensors i and l in the second step, then at node V... i V l Connected by an edge E i,l The edge weights are the matching loss W between the two passive sensors. i,l Taking passive sensor i and passive sensor l as examples again, if A i,l If the result is 1, then the matching between the two is obtained in the second step. Then the weight W of the edge connecting the two is... i,l for:

[0043]

[0044] Where C(i,l) is the matching loss matrix between passive sensor i and passive sensor l in the second step. Thus, these nodes... edge {E i,l |i,l=1,...,m,A i,l =1} and weight {W i,l |i,l=1,...,m,A i,l =1} forms an undirected weighted graph G.

[0045] Step 4: Solving multi-sensor multi-target measurement matching for passive sensor networks based on undirected weighted graphs

[0046] To ensure that the matching on the network achieves consensus among all passive sensors without contradictions and is optimal, we consider solving for the minimum spanning tree of the undirected weighted graph G established in step three. Since the matching of two passive sensors is based on the assumption that "a set of measurements from each sensor corresponds to the same target," the matching of two passive sensors is transitive. Therefore, two sensors on the network can be matched by several connected edges. Thus, the multi-sensor multi-target measurement matching on the passive sensor network is taken as the set of several two passive sensor matchings corresponding to the minimum spanning tree of the weighted undirected graph G. Specifically, based on the weighted undirected graph G obtained in step three, the minimum spanning tree is:

[0047]

[0048] where ST(G) is the set of spanning trees of graph G, E i,l is the edge connecting passive sensor i and passive sensor l. Equation (11) can be solved effectively by Boruvka algorithm, Prim algorithm, Kruskal algorithm, etc. Thus the multi-sensor multi-target measurement matching on passive sensor network is

[0049] The present application has the advantages compared with the prior art:

[0050] First, the loss function and loss matrix of double passive sensor matching are given, which fully utilizes the algebraic and geometric properties of passive sensor measurement, and can effectively distinguish the correct matching;

[0051] Second, the discrete optimization problem corresponding to the double passive sensor matching is constructed and solved, which has a lower computational complexity;

[0052] Third, based on graph theory technology, a graph theory model of multi-sensor multi-target measurement matching on passive sensor network is established, and a reasonable definition of matching is given, and the computational complexity of the solving method is also lower. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 is a flow chart of the multi-target measurement matching method based on passive sensor network.

[0054] Figure 2 is a passive sensor network topology graph.

[0055] Figure 3 is a graph of the change of the minimum average matching accuracy with the noise standard deviation.

[0056] Figure 4 is a graph of the change of the error matching frequency with the noise standard deviation.

[0057] SYMBOL EXPLANATION:

[0058] A: the adjacency matrix corresponding to the passive sensor network;

[0059] V i : the node corresponding to sensor i in the passive sensor network;

[0060] E i,l : the edge corresponding to the matching of sensors i, l in the passive sensor network;

[0061] A i,l : the (i, l)th component of the adjacency matrix corresponding to the passive sensor network;

[0062] C(i, l): the matching loss matrix of passive sensor i and passive sensor l;

[0063] Multi-target measurement matching of passive sensor i and passive sensor l;

[0064] G: Passive sensor network matching corresponding undirected weighted graph;

[0065] Minimum spanning tree of undirected weighted graph G;

[0066] E i,l : Edge connecting nodes corresponding to passive sensor i and passive sensor l in undirected weighted graph G;

[0067] σ b : Standard deviation of azimuth measurement noise; σ e : Standard deviation of elevation measurement noise. DETAILED DESCRIPTION

[0068] The following is an example of a set of simulations to illustrate the specific implementation of the multi-target measurement matching method based on passive sensor network. First, introduce the simulation scene, in which the passive sensor network is composed of 5 passive sensors, which are:

[0069]

[0070] The network topology is shown in Figure 2 . Among them, node V i corresponds to passive sensor i, and edge E i,l between nodes i, l corresponds to A i,l = 1, i.e. passive sensor i, l needs to be matched. The coordinates of the 6 targets are respectively:

[0071]

[0072] The algorithm first converts the measurements of all passive sensors into a common coordinate system according to equations (3)-(5). Then, according to the adjacency matrix A corresponding to the passive sensor network, for each pair of passive sensors that need to be matched, take passive sensor i and passive sensor l as an example, calculate the double passive sensor matching loss matrix C(i, l) according to equations (6)-(8), and then solve the double passive sensor matching Subsequently, according to the solved double passive sensor matching, a graph theory model of this passive sensor network matching, i.e. undirected weighted graph G, is established. The weight of each edge is given by equation (10). Finally, the minimum spanning tree of undirected weighted graph G is solved according to equation (11) Then the multi-target measurement matching of the passive sensor network is

[0073]

[0074] According to the simulation scene of the present application, 500 experiments are performed for the high-low angle and pitch angle measurement noise standard deviation σ b = σ e = (0.1, 0.2,..., 1.9, 2) x 10 -3 rad respectively. For each experiment, the matching accuracy of each pair of matched dual passive sensors is calculated, i.e. the ratio of the number of correctly matched measurements to the total number of measurements (6 in this simulation scenario), and the average accuracy is calculated for 500 experiments. In addition, for each pair of matched dual passive sensors, the frequency of incorrect matching (i.e. the matching accuracy is not 1) in 500 experiments is calculated. Furthermore, for the matching of the passive sensor network obtained, the frequency of incorrect matching of any pair of dual passive sensors in 500 experiments is calculated.

[0075] Figure 3 The lowest average accuracy of all matched pairs of dual passive sensors changes with the noise standard deviation. It can be seen that the dual passive sensor matching method given by the present application can always guarantee that all dual passive sensor matching is completely correct when the noise is small. When the noise is large, the lowest average accuracy can still be above 90%. This shows that the method given by the present application can effectively complete the multi-target measurement matching between dual passive sensors, and lays a reliable foundation for multi-target measurement matching based on passive sensor networks.

[0076] Figure 4 The maximum error matching frequency of all matched pairs of dual passive sensors, and the error matching frequency of the passive sensor network. It can be seen that the method given by the present application can always guarantee that there is no error matching when the noise is small, and can still guarantee that the error matching frequency is about 0.2 when the noise is large. In addition, the matching of the passive sensor network obtained by the method given by the present application can avoid error matching of dual passive sensors, further reducing the error matching frequency, so that even when the noise standard deviation is large, the error matching frequency is still not more than 0.05. This shows that the method given by the present application can effectively solve the multi-target measurement matching problem based on passive sensor networks.

[0077] In summary, the present application addresses the problem of how to match multi-target measurements based on passive sensor networks, coordinates the measurements of each passive sensor, proposes a dual passive sensor matching method, further establishes a graph theory model for passive sensor network matching, and gives a reasonable scheme for matching multi-target measurements based on passive sensor networks.

Claims

1. A method for 3D multi-target matching based on passive sensor networks, characterized in that: Let the coordinate of the centroid position vector of target j in three-dimensional scene be T j =[x j y j z j ] T , where x j , y j , z j are the components of T j in the three coordinate axes of the common coordinate system respectively; n is the number of targets; the coordinate of the centroid position vector of passive sensor i in the common coordinate system is S i =[x i y i z i ] T , i = 1, …, m, where x i , y i , z i are the components of S i in the three coordinate axes of the common coordinate system respectively, and m is the number of passive sensors; C i is the rotation matrix from the common coordinate system to the local coordinate system of passive sensor i; let the label of passive sensor i to target j be φ i (j); let the corresponding adjacency matrix of the passive sensor network be A; without loss of generality, let the passive sensor network be connected; For three-dimensional scene, the measurement model of passive sensor is: where the azimuth measurement noise are independent and identically distributed with mean 0 and variance and bounded random variables; the elevation measurement noise are independent and identically distributed with mean 0 and variance and bounded random variables, and are independent of is the azimuth measurement of target j by passive sensor i in the local coordinate system of passive sensor i; is the elevation measurement of target j by passive sensor i in the local coordinate system of passive sensor i; φ i (j) e {1,...,n} is the label of the measurement of target j by passive sensor i; φ i (·) is a bijection from {1,...,n} to {1,...,n} and the bijection is different for different passive sensors; is the Cartesian coordinate component of target i in the local coordinate system of passive sensor j, given by the coordinate transformation​ Based on the measurement model (1)-(2), the specific steps of matching multi-sensor multi-target measurement on passive sensor network are as follows: Step one: equivalent conversion of each sensor measurement to the common coordinate system; Step two: according to the topology of passive sensor network, solve several double passive sensor matching; Step three: establish the undirected weighted graph of passive sensor network based on double passive sensor matching; Step four: based on the undirected weighted graph, solve the multi-sensor multi-target measurement matching of passive sensor network.

2. The method of claim 1, wherein: In step one, passive sensor i measures target j Corresponds to a ray in space; according to the coordinate system rotation matrix, calculate the corresponding unit vector of this ray in the common coordinate system The calculation formula is as follows:

3. The method of claim 2, wherein: In step one, passive sensor i measures the equivalent of target j in the common coordinate system is calculated from the equation: Thus obtaining the equivalent set of measurements of passive sensor i for all targets in the common coordinate system 4. The method of claim 1, wherein: In step two, the meaning of the adjacency matrix A of the graph corresponding to the passive sensor network is: for a network composed of m passive sensors, the dimension of matrix A is m x m, if the (i, l) element of A is 1, then passive sensor i and passive sensor l need to be matched, if the (i, l) element of A is 0, then passive sensor i and passive sensor l do not need to be matched.

5. The method of claim 4, wherein: According to the adjacency matrix A, match the passive sensor pairs that need to be matched; The equivalent set of measurements of passive sensor i in the common coordinate frame is and the equivalent set of measurements of passive sensor l in the common coordinate frame is The double passive sensor matching loss matrix C(i, l) is constructed, which has dimensions n x n, and its (j, k)th element [C(i, l)] j,k Given by the matching loss function of the equivalent measurements and ​ Where p(·) is the penalty function: And, For the auxiliary variable, given by the following equation:

6. The three-dimensional multi-target matching method based on passive sensor network according to claim 5, characterized in that: For the case of the auxiliary variable d involved in the matching loss function i j the meaning of the measurement of the passive sensor i The projection of the corresponding ray onto the xy plane, and the measurement of the passive sensor l. The distance from the intersection of the projections of the ray onto the xy plane to the projection of the passive sensor i onto the xy plane.

7. The method of claim 6, wherein: After obtaining the loss matrix C of passive sensor i and passive sensor l, the matching is the corresponding relationship between the n groups of measurements with the minimum total loss, that is Where σ is a bijection from {1,...,n} to {1,...,n}, which means matching the jth measurement of passive sensor i with the σ(j)th measurement of passive sensor l; formula (9) is effectively solved by KM algorithm.

8. The method of claim 1, wherein: In step three, for a passive sensor network, passive sensor i is considered as a node V i If a match is found between passive sensors i, l, then a link E i is drawn between these nodes V l with a weight equal to the match loss W i,l of these two passive sensors; if A i,l = 1, then the weight W i,l of the link between them is: i,l ​​ where C(i, l) is the matching loss matrix of passive sensor i and passive sensor l, by the node Edges {E i,l | i, l = 1,..., m, A i,l = 1} and weights {W i,l | i, l = 1,..., m, A i,l = 1} form an undirected weighted graph G.

9. The method of claim 1, wherein: In step four, in order to ensure that the matching on the network reaches a consensus among all passive sensors and does not appear contradictory and optimal, the minimum spanning tree of the undirected weighted graph G is solved; the multi-sensor multi-target measurement matching on the passive sensor network is taken as the set of several double passive sensor matchings corresponding to the minimum spanning tree of the weighted undirected graph G; according to the weighted undirected graph G, the minimum spanning tree is: Wherein, ST(G) is the set of spanning trees of graph G, E i,l is the edge connecting passive sensor i and passive sensor l; formula (11) is solved by Boruvka algorithm, Prim algorithm, Kruskal algorithm; so that the multi-sensor multi-target measurement matching on the passive sensor network is

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