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

Abstract

The invention provides a three-dimensional multi-target matching method based on a passive sensor network. The three-dimensional multi-target matching method comprises the following steps: step 1, equivalently converting measurement of each sensor to a common coordinate system; 2, solving matching of a plurality of double passive sensors according to the passive sensor network topology; step 3, establishing an undirected weighted graph of the passive sensor network based on dual passive sensor matching; and 4, solving multi-sensor multi-target measurement matching of the passive sensor network based on the undirected weighted graph. According to the method, a loss function and a loss matrix matched with the double passive sensors are given, algebraic properties and geometric properties measured by the passive sensors are fully utilized, and correct matching is effectively distinguished; a discrete optimization problem corresponding to double passive sensor matching is constructed and solved, and the calculation complexity is low; a matched graph theory model of multi-sensor multi-target measurement on the passive sensor network is established, a reasonable definition of matching is given, and the calculation complexity of the solving method is low.

Description

Technical Field

[0001] The present invention relates to a method for matching multi-sensor multi-target measurements on a passive sensor network. The method first 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 a passive sensor network is designed by combining a graph theory model and a minimum spanning tree technology. Background Art

[0002] Passive sensors refer to a type of sensor that can only measure the angle information of the target but cannot obtain the distance to the target. For three-dimensional scenes, passive sensors can only obtain the elevation and azimuth angles from the target to the sensor. Therefore, unlike active sensors, passive sensors lack one dimension of information when measuring the target. On the other hand, passive sensors often do not have labels for measuring multiple targets, which means that it is impossible to directly match the measurements of different passive sensors. This creates obstacles for the collaboration between multiple passive sensors, such as the collaborative positioning of multiple passive sensors. In some studies, the matching problem is also called the data association problem.

[0003] At the same time, the measurement of the target by the passive sensor is often inevitably affected by noise. Therefore, the lines of sight corresponding to the pure angle measurement of the target by different passive sensors cannot intersect in space even if they correspond to the same target. And because the passive sensor loses the distance information of the target, it is not easy to measure whether the two sets of pure angle measurements from two passive sensors match, that is, whether they come from the same target.

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

[0005] At present, there are few studies on matching methods in multi-passive sensor multi-target scenarios, and there is a lack of research results on multi-target measurement matching based on passive sensor networks. For some research contents, see: 1. Ye Zhenhua, Li Huihao, Wang Jindong, et al. Frontier hotspots and transformation trends of infrared photoelectric detectors [J]. Journal of Infrared and Millimeter Waves, 2022, 41(1): 15-39. 2. Qin Lei, Li Junlong, Zhou Di. Research on dual-station infrared tracking of near-space targets [J]. Modern Defense Technology, 2014, 42(02): 122-127. 3. Yue Juan, Li Fanming, Gao Sili. Dual-station positioning of infrared multi-targets based on maximum density estimation of track direction [J]. Optical Precision Engineering, 2022, 30(12): 1509-1522. 4. Wang Cheng, Li Shaohong, Huang Huai. Multi-target measurement data association of direction finding cross-positioning system [J]. Systems Engineering and Electronic Technology, 2002, (09): 104-106+117.

[0006] The existing multi-target measurement matching methods based on dual passive sensors or passive sensor networks have the following limitations:

[0007] 1. The loss functions given by some existing methods to measure the correctness of matching do not make full use of the existing measurement information, or the proposed loss functions lack 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 match the central sensor with the remaining sub-sensors one by one, thereby simplifying the matching problem of the sensor network to a dual-sensor matching problem. Such methods limit the topology of the sensor network, and their effects are affected by the selection of the central sensor, and are not the optimal network topology.

[0009] 3. Some existing methods exhaustively enumerate all possible matching combinations of multi-sensor measurements of multiple targets. The computational complexity of such methods increases rapidly with the number of sensors and targets, and 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 measurement on the target.

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

[0012] In order to solve the above problems, the present invention aims at the problem of how to match multi-target measurements of multiple sensors on a passive sensor network, gives the matching cost of multi-target pure angle measurement for dual passive sensors, and then designs a multi-target measurement matching algorithm based on dual passive sensors. Subsequently, combined with the minimum spanning tree technology, multi-target measurement matching based on a passive sensor network is realized. Summary of the invention

[0013] The technical problem solved by the present invention is as follows: In order to solve the problem of how to match the measurements of multiple targets by multiple sensors on a passive sensor network, the matching cost of pure angle measurements of multiple targets is given for dual passive sensors, and then a multi-target measurement matching algorithm based on dual passive sensors is designed. Subsequently, a graph theory model and minimum spanning tree technology are combined to realize multi-target measurement matching based on a passive sensor network.

[0014] The solution of the present invention is as follows: for the measurement of multiple targets by multiple sensors on a passive sensor network, a matching cost for the pure angle measurement of multiple targets of dual passive sensors is designed; based on this cost and the passive sensor network, a number of dual passive sensor matchings are solved; then an undirected weighted graph corresponding to the passive sensor network is established with the total matching loss as the edge weight; for this undirected weighted graph, a minimum spanning tree is found and extracted to obtain the corresponding multi-target measurement matching of the passive sensor network.

[0015] The following is a description of the specific steps proposed by the present invention. Assume that in a three-dimensional scene, the coordinates of the centroid position vector of target j are T j =[x j y j z j ] T , where x j ,y j ,z j T j The components of the three coordinate axes in the common coordinate system. n is the number of targets. The coordinates of the center of mass position vector of passive sensor i in the common coordinate system are S i =[x i y i z i ] T ,i=1,...,m, where x i ,y i ,z i S i The components in the three coordinate axis directions of the common coordinate system, m is the number of passive sensors. i is the rotation matrix from the public coordinate system to the local coordinate system of passive sensor i. Because there is no unified target measurement label, the label of passive sensor i to target j is φ i (j). Let the adjacency matrix corresponding to the passive sensor network be A. Without loss of generality, assume that the passive sensor network is connected.

[0016] For three-dimensional scenes, the measurement model of passive sensors is:

[0017]

[0018] Among them, the azimuth measurement noise are independent and identically distributed, with a mean of 0 and a variance of and bounded random variables. High and low angle measurement noise are independent and identically distributed, with a mean of 0 and a variance of and bounded random variables, and independent. i=1,...,m,j=1,...,n, are the azimuth angle measurements of target j in the local coordinate system of passive sensor i; i=1,...,m,j=1,...,n, are the high and low angle measurements of target j in the local coordinate system of passive sensor i. φ i (j)∈{1,...,n} is the label of passive sensor i measuring target j. i (·) is a bijection from {1, ..., n} to {1, ..., n}, and different passive sensors have different bijections. is the Cartesian coordinate component of target i in the local coordinate system of passive sensor j, which is given by the following coordinate transformation:

[0019]

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

[0021] Step 1: Convert the measurements of each sensor to a common coordinate system

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

[0023]

[0024] Then, the equivalent measurement of passive sensor i on target j in the common coordinate system is Calculated by the following formula:

[0025]

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

[0027]

[0028] Step 2: Solve the matching of several dual passive sensors 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: for a network composed of m passive sensors, the dimension of the matrix A is m×m. If the (i,l)th element of A is 1, passive sensor i and passive sensor l need to be matched. If the (i,l)th element of A is 0, passive sensor i and passive sensor l do not need to be matched.

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

[0031] According to the first step, the equivalent measurement set of passive sensor i in the public coordinate system is obtained respectively: And the equivalent measurement set of passive sensor l in the common coordinate system Construct the dual passive sensor matching loss matrix C(i,l), whose dimension is n×n, and its (j,k)th element [C(i,l)] j,k Equivalent measurement under public system and The matching loss function is given by:

[0032]

[0033] Among them, p(·) is the penalty function:

[0034]

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

[0036]

[0037] In particular, for the more common Case, the auxiliary variables involved in the matching loss function The meaning is: the measurement of passive sensor i The corresponding ray projection on the xy plane and the measurement of the passive sensor l The distance from the intersection of the ray projection on the xy plane to the projection of the passive sensor i on the xy plane. Auxiliary variables Same reason.

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

[0039]

[0040] 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. Equation (9) can be effectively solved by the KM algorithm.

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

[0042] For a passive sensor network, passive sensor i is regarded as node V i If the passive sensors i and l are matched in the second step, then at this node V i ,V l Connect an edge E i,l , whose edge weight is the matching loss W of the two passive sensors i,l . Still taking passive sensor i and passive sensor l as an example, if A i,l =1, then the match between the two is obtained in the second step Then the weight of the edge between the two is W i,l for:

[0043]

[0044] Among them, C(i,l) is the matching loss matrix of passive sensor i and passive sensor l in the second step. 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} form an undirected weighted graph G.

[0045] Step 4: Solve the multi-sensor multi-target measurement matching of passive sensor networks based on undirected weighted graphs

[0046] In order to ensure that the matching on the network allows all passive sensors to reach a consensus without contradiction and is optimal, consider solving the minimum spanning tree of the undirected weighted graph G established in the third step. Because the matching of dual passive sensors is based on the assumption that "a certain set of measurements from each sensor corresponds to the same target", the dual passive sensor matching is transitive. Therefore, the two sensors on the network can be matched by several connected edges. Therefore, the multi-sensor multi-target measurement matching on the passive sensor network is taken as a set of several dual passive sensor matchings corresponding to the minimum spanning tree of the weighted undirected graph G. Specifically, according to the weighted undirected graph G obtained in the third step, the minimum spanning tree is:

[0047]

[0048] Among them, 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 effectively solved by Boruvka algorithm, Prim algorithm, Kruskal algorithm, etc. Therefore, the multi-sensor multi-target measurement matching on the passive sensor network is

[0049] The advantages of the present invention compared with the prior art are:

[0050] First, the loss function and loss matrix of dual passive sensor matching are given, which fully utilizes the algebraic and geometric properties of passive sensor measurements and can effectively distinguish the correct matches.

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

[0052] Third, based on graph theory technology, a graph theory model for matching multi-sensor multi-target measurements on passive sensor networks is established, and a reasonable definition of matching is given. The computational complexity of the solution method is also low. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0055] Figure 3 This is a graph showing the minimum average matching accuracy versus noise standard deviation.

[0056] Figure 4 is a graph of the mismatch frequency versus the standard deviation of the noise.

[0057] Explanation of symbols:

[0058] A: 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 matching corresponding edges 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): matching loss matrix between passive sensor i and passive sensor l;

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

[0064] G: undirected weighted graph corresponding to the passive sensor network matching;

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

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

[0067] σ b : azimuth angle measurement noise standard deviation; σ e : Standard deviation of high and low angle measurement noise. DETAILED DESCRIPTION

[0068] The following takes a set of simulations as an example to illustrate the specific implementation of the multi-target measurement matching method based on a passive sensor network. First, the simulation scenario is introduced. In this simulation, the passive sensor network consists of 5 passive sensors, namely:

[0069]

[0070] Its network topology is as follows Figure 2 As shown. Among them, node V i Corresponding to passive sensor i, the edge E between nodes i and l i,l Corresponding to A i,l =1, that is, passive sensors i and l need to be matched. The coordinates of the six targets are:

[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, taking passive sensor i and passive sensor l as an example, the dual passive sensor matching loss matrix C(i,l) is calculated according to equations (6)-(8), and then the dual passive sensor matching loss matrix C(i,l) is solved according to equation (9). Then, based on the solved dual passive sensor matching, the graph theory model of the passive sensor network matching is established, namely the undirected weighted graph G. The weight of each edge is given by formula (10). Finally, the minimum spanning tree of the undirected weighted graph G is solved according to formula (11): Then the multi-target measurement matching of the passive sensor network is

[0073]

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

[0075] Figure 3 The figure shows the variation of the minimum average accuracy rate among all the matched dual passive sensor pairs as the noise standard deviation changes. It can be seen that the dual passive sensor matching method provided by the present invention can always ensure that all dual passive sensor matches are completely correct when the noise is small. When the noise is large, the minimum average accuracy rate can still be guaranteed to be above 90%. This shows that the method provided by the present invention can effectively complete the multi-target measurement matching between dual passive sensors, laying a reliable foundation for multi-target measurement matching based on passive sensor networks.

[0076] Figure 4 It is the maximum error matching frequency among all the dual passive sensor pairs that are matched, and the error matching frequency of the passive sensor network. It can be seen that the method provided by the present invention can ensure that no error matching occurs when the noise is small, and when the noise is large, the error matching frequency can still be guaranteed to be around 0.2. In addition, the matching of the passive sensor network obtained by the method provided by the present invention can avoid the occurrence of erroneous dual passive sensor matching, and further reduce the error matching frequency, so that even if the noise standard deviation is large, the error matching frequency does not exceed 0.05. It shows that the method provided by the present invention can effectively solve the multi-target measurement matching problem based on the passive sensor network.

[0077] In summary, the present invention aims at the problem of how to match multi-target measurements based on passive sensor networks, performs a coordinate system on the measurements of each passive sensor, proposes a matching method for dual passive sensors, and then establishes a graph theory model for passive sensor network matching, and provides a reasonable solution for matching multi-target measurements based on passive sensor networks.

Claims

1. A three-dimensional multi-target matching method based on a passive sensor network, characterized in that: Assume that in a three-dimensional scene, the coordinates of the centroid position vector of target j are T j =[x j y j z j ] T , where x j ,y j ,z j T j The components of the three coordinate axes in the public coordinate system; n is the number of targets; the coordinates of the centroid position vector of passive sensor i in the public coordinate system are S i =[x i y i z i ] T ,i=1,...,m, where x i ,y i ,z i S i The components in the three coordinate axis directions of the common coordinate system, m is the number of passive sensors; C i is the rotation matrix from the public coordinate system to the local coordinate system of passive sensor i; the label of passive sensor i to target j is φ i (j); let the adjacency matrix corresponding to the passive sensor network be A; without loss of generality, assume that the passive sensor network is connected; For three-dimensional scenes, the measurement model of passive sensors is: Among them, the azimuth measurement noise are independent and identically distributed, with a mean of 0 and a variance of and bounded random variables; high and low angular measurement noise are independent and identically distributed, with a mean of 0 and a variance of and bounded random variables, and independent; is the azimuth angle measurement value of target j in the local coordinate system of passive sensor i; is the high and low angle measurement value of target j in the local coordinate system of passive sensor i; φ i (j)∈{1,...,n} is the label of passive sensor i measuring target j; φ i (·) is a bijection from {1,...,n} to {1,...,n}, and different passive sensors have different bijections; is the Cartesian coordinate component of target i in the local coordinate system of passive sensor j, which is given by the following coordinate transformation: Based on the measurement models (1)-(2), the specific steps for matching multi-sensor multi-target measurements on a passive sensor network are as follows: Step 1: Convert the measurements of each sensor to a common coordinate system; Step 2: According to the passive sensor network topology, solve the matching of several dual passive sensors; Step 3: Establish an undirected weighted graph based on dual passive sensor matching of the passive sensor network; Step 4: Solve the multi-sensor multi-target measurement matching of passive sensor networks based on undirected weighted graphs.

2. The three-dimensional multi-target matching method based on a passive sensor network according to claim 1, characterized in that: In step 1, the passive sensor i measures the target j Corresponds to a ray in space; according to the coordinate system rotation matrix, calculate the unit vector corresponding to this ray in the common coordinate system The calculation formula is as follows:

3. The three-dimensional multi-target matching method based on a passive sensor network according to claim 2, characterized in that: In step 1, the passive sensor i measures the equivalent value of target j in the common coordinate system. Calculated by the following formula: Thus, the equivalent measurement set of passive sensor i on all targets in the common coordinate system is obtained:

4. The three-dimensional multi-target matching method based on a passive sensor network according to claim 1, characterized in that: In step 2, the adjacency matrix A of the graph corresponding to the passive sensor network means that for a network consisting of m passive sensors, the dimension of the matrix A is m×m. If the (i,l)th element of A is 1, passive sensor i and passive sensor l need to be matched. If the (i,l)th element of A is 0, passive sensor i and passive sensor l do not need to be matched.

5. The three-dimensional multi-target matching method based on a passive sensor network according to claim 4, characterized in that: According to the adjacency matrix A, the passive sensor pairs that need to be matched are matched; The equivalent measurement set of passive sensor i in the public coordinate system is And the equivalent measurement set of passive sensor l in the common coordinate system Construct the dual passive sensor matching loss matrix C(i,l), whose dimension is n×n, and its (j,k)th element [C(i,l)] j,k Equivalent measurement under public system and The matching loss function is given by: Among them, p(·) is the penalty function: and, is an auxiliary variable, given by the following formula:

6. The three-dimensional multi-target matching method based on a passive sensor network according to claim 5, characterized in that: for In the case of i j The meaning is: the measurement of passive sensor i The corresponding ray projection on the xy plane and the measurement of the passive sensor l The distance from the intersection point of the ray's projection on the xy plane to the projection of the passive sensor i on the xy plane.

7. The three-dimensional multi-target matching method based on a passive sensor network according to claim 6, characterized in that: After obtaining the loss matrix C of passive sensor i and passive sensor l, it is matched to the corresponding relationship between n groups of measurements that minimize the 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. Equation (9) is effectively solved by the KM algorithm.

8. The three-dimensional multi-target matching method based on a passive sensor network according to claim 1, characterized in that: In step 3, for a passive sensor network, passive sensor i is considered as node V i If a match is found between passive sensors i and l, then at this node V i ,V l Connect an edge E i,l , whose edge weight is the matching loss W of the two passive sensors i,l ; if A i,l =1, then the match between the two is obtained Then the weight of the edge between the two is W i,l for: Among them, C(i,l) is the matching loss matrix of passive sensor i and passive sensor l, which is composed of 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} form an undirected weighted graph G.

9. The three-dimensional multi-target matching method based on a passive sensor network according to claim 1, characterized in that: In step 4, in order to ensure that the matching on the network allows all passive sensors to reach a consensus without contradiction and is 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 a set of several dual 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: Among them, 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) is solved by Boruvka algorithm, Prim algorithm, and Kruskal algorithm; thus, the multi-sensor multi-target measurement matching on the passive sensor network is

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