A message passing based distributed space-based radar networked tracking method

Abstract

The application discloses a kind of distributed space-based radar networking tracking methods based on message passing, based on the distributed space-based radar networking of multiple satellite platforms, antenna array, transmitting system, receiving system, radar power etc., the method comprises: the sequence of first target motion state, target visible state, data association and latent variable in joint observation variable are described using factor graph;Based on the connection relationship of variable node and factor node in factor graph, the approximate solution of joint posterior probability density is solved using BP-MF combined approximation method;According to the approximate solution of joint probability density, the target is tracked.The present application is based on the distributed space-based radar networking, combines factor graph and uses BP-MF combined approximation method to convert the solution of high-dimensional posterior probability density fitting into the solution of low-dimensional posterior probability density product, solves the problem of cumulative propagation of estimation error and identification risk in the case of guaranteeing networking performance using distributed networking tracking method, avoids.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of target tracking, and relates to a message passing based distributed space-based radar network tracking method. BACKGROUND

[0002] The space-based radar is a radar with a satellite as a load platform. The working height of the space-based radar enables it to have a farther field of view range than general air-based, land-based and ship-borne radars, can cover areas that air-based radars cannot enter, and will not be interfered and threatened by anti-radiation unmanned aerial vehicles, anti-radiation missiles and other weapons. Meanwhile, as the space-based radar runs on an orbit outside the earth, it can work all the time without being affected by the outside environment, greatly overcoming the working time limit of the air-based radar. With the development of radar technology and the reduction of launch cost, the space-based radar will become an object that countries compete to develop in the future.

[0003] The tracking effect of the space-based radar is difficult to perform outstandingly because it is in the extraterrestrial space and is subject to various disturbances during operation, and there is a series of complex coordinate conversion between the target motion coordinate system. In order to improve the tracking quality, the space-based radar network tracking is of great significance. The current theoretical method mainly has the following problems: ①The target tracking task needs to process state estimation, target detection and data association tasks at the same time, these tasks are highly related and deeply coupled, the current method adopts a functional module combination and a sequential open-loop structure, and is easy to cause estimation error and identification risk cumulative propagation. ②The current radar network fusion mainly considers centralized fusion, which has great requirements for performance due to the performance of the space-based radar, and there are few researches on distributed fusion based on the space-based radar.

[0004] Therefore, the technical problems in the prior art still need to be solved. SUMMARY

[0005] The purpose of the application is to provide a message passing based distributed space-based radar network tracking method, so as to solve the problem of avoiding estimation error and identification risk cumulative propagation by using the distributed network tracking method while ensuring the network performance.

[0006] The application adopts the following technical scheme:

[0007] The application provides a message passing based distributed space-based radar network tracking method, which is based on a distributed space-based radar network composed of multiple satellite platforms, antenna arrays, transmission systems, receiving systems, radar power supplies and the like. The method implementation steps include:

[0008] Obtaining a first target motion state, a target visible state, data association and a joint observation variable from an initial time to time K; the joint observation variable is a radar measurement from the initial time to time K;

[0009] The first target motion state, the target visible state, the sequence of data association, and the latent variable in the joint observation variable are described by a factor graph, the factor graph taking the first target motion state conditional probability function, the target visible state conditional probability function, the data association conditional probability function, and the joint observation variable conditional probability function as factor nodes, and taking the first target motion state variable, the target visible state variable, and the data association variable as variable nodes;

[0010] Based on the connection relationship between the variable nodes and the factor nodes in the factor graph, an approximate solution of the joint posterior probability density is solved by using a BP-MF combined approximation method, and the approximate solution is the product of the first target motion state posterior probability density, the target visible state posterior probability density, and the data association posterior probability density.

[0011] According to the approximate solution of the joint probability density, the target is tracked.

[0012] Optionally, the radar measurement generation method comprises:

[0013] The first target motion state is coordinate-converted by a measurement function;

[0014] The first target motion state after coordinate conversion is added with Gaussian white noise to generate a radar measurement.

[0015] Optionally, the coordinate conversion of the first target motion state by the measurement function comprises:

[0016] The first target motion state is converted from the Earth-Centered, Earth-Fixed coordinate system to the Earth-Centered, second orbit coordinate system by a first coordinate conversion factor to generate a second target motion state;

[0017] The second target motion state in the second orbit coordinate system is converted to the antenna array coordinate system by a second coordinate conversion factor to generate a third target motion state;

[0018] The third target motion state in the antenna array coordinate system is converted to the antenna array measurement coordinate system by a third coordinate conversion factor.

[0019] Optionally, the solving process of the first target motion state posterior probability density comprises: according to the factor nodes of the first target motion state, a MF approximation method is used to solve the first target motion state transmission message, the joint observation variable transmission message, and the coupling transmission message;

[0020] The first target motion state posterior probability density is approximately solved according to the first target motion state transmission message, the joint observation variable transmission message, and the coupling transmission message.

[0021] Optionally, the solving process of the target visible state posterior probability density comprises:

[0022] According to the factor node of the target visible state, a BP-MF combined approximation method is used to solve the target visible state transmission message and the event correlation transmission message.

[0023] According to the target visible state transmission message and the event correlation transmission message, a first target motion state posterior probability density is approximately solved.

[0024] Optionally, the solving process of the data association posterior probability density comprises:

[0025] According to the factor node of the data association, a BP-MF combined approximation method is used to solve the target event correlation transmission message, the target visible state transmission message, the measurement constraint factor and the target constraint factor.

[0026] According to the target event correlation transmission message, the target visible state transmission message, the measurement constraint factor and the target constraint factor, a data association posterior probability density is approximately solved.

[0027] The application further provides a distributed space-based radar network tracking device based on transmission message transmission, comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, characterized in that the processor implements a distributed space-based radar network tracking method based on transmission message transmission when executing the computer program.

[0028] The application has the beneficial effects that the first target motion state, the target visible state, the sequence of data association and the latent variable in the joint observation variable are described by using a factor graph, the connection between each node of the distributed space-based radar network is described by using the form of the factor graph, and the joint optimization problem is described.

[0029] Based on the factor graph, a BP-MF combined approximation method is used to divide the factor graph into a BP region and a MF region, based on the BP attribute or the MF attribute of each factor, an approximate solution of the joint posterior probability density is solved, and the problem is solved more simply and intuitively.

[0030] Finally, each target is tracked based on the approximate solution of the solved joint probability density, the accumulation of the estimation error and the identification risk generated in the traditional control method is avoided, and the stability of the system performance is ensured. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 It is a non-directional graph schematic diagram of the radar distributed data fusion model based on the application;

[0032] Figure 2 It is a factorization of the space-based radar network tracking problem based on the application in a factor graph model;

[0033] It is a factorization of the space-based radar network tracking problem based on the application in a factor graph model;Figure 3 For Figure 2 Target motion state Subgraph of local area;

[0034] Figure 4 For Figure 2 Target visibility state Subgraph of local area;

[0035] Figure 5 For Figure 2 Data association Subgraph of local area;

[0036] Figure 6 It is a schematic diagram of a message passing based distributed space-based radar network tracking device of the present application;

[0037] Figure 7 It is a simulation graph of the average position of the algorithm of the present application and the centralized fusion algorithm and the average position without fusion;

[0038] Figure 8 It is a simulation graph of the average speed of the algorithm of the present application and the centralized fusion algorithm and the average speed without fusion;

[0039] Figure 9 It is a simulation graph of the average OSPA of the algorithm of the present application and the centralized fusion algorithm and the average OSPA without fusion. DETAILED DESCRIPTION

[0040] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0041] The design idea of the technical solution of the present application is:

[0042] Step one, description of the problem of distributed space-based radar network tracking;

[0043] Step two, the problem defined in step one is expressed in the form of a factor graph, and different areas are divided in the factor graph according to the nature of the problem;

[0044] Step three, use the message passing method to solve the problems in different areas.

[0045] Based on the above design idea, the present application provides a message passing based distributed space-based radar network tracking method, which is based on a distributed space-based radar network composed of multiple satellite platforms, antenna arrays, transmitting systems, receiving systems, radar power supplies, etc. The method includes the following steps:

[0046] (1) Obtain the first target motion state, target visibility state, data association and joint observation variable from the initial time to time K; the joint observation variable is all radar measurements from the initial time to time K.

[0047] In one embodiment, the first target motion state, target visibility state, data association, and joint observation variables from the initial time to time K are obtained by establishing a target kinematic state model, a visibility state model, a data association model, and a measurement model. The specific modeling process is as follows:

[0048] S1.1 Establish the target kinematic state model and visibility state model

[0049] The motion states of all first targets at time k are determined by... It means that among them It is the maximum number of targets in the overlapping region at time k. Given the number of radars, the target's motion state varies independently and is generally a near-uniform linear motion. The target dynamics equation is given by the following formula:

[0050]

[0051] Here is the state transition matrix. With a mean of 0 and a variance of Gaussian white noise.

[0052] From the above formula, we can know that under a given... Target dynamic state under the condition The distribution is

[0053] All targets are detected by the sensor at time k. s The joint target visibility status observed is binary variable Let represent the visibility of target i at time k. If target i is visible at time k, then... If target i is not visible at time k, then we have For binary variables have and The detection probability of the target's visibility state.

[0054] Visible state The evolution follows a discrete-time homogeneous Markov chain, that is:

[0055]

[0056] The transition matrix The specific form is as follows:

[0057]

[0058] The initial probability is

[0059] S1.2 Establishing a Measurement Model

[0060] All radar measurements at time k are provided by express, The meaning is the measurement set of the s-th radar at time k. Let be the number of measurements, and let be the coordinate system of the antenna array measurement coordinate system. For radar s, each measurement at time k is . in These are the radial distance, azimuth angle, and elevation angle, respectively. Due to the presence of clutter, the measurement equation for radar s is:

[0061]

[0062] Where h(·) is the measurement function. The mean is 0, and the equation is: Gaussian white noise. Assume x i,k and They are independent of each other. Assume clutter. Uniformly distributed in a volume of Within the radar observation area, i.e. The amount of clutter follows a parameter λ. s The Poisson distribution.

[0063] S1.3 Establishing a data association model

[0064] Assuming the radars operate independently, the data correlation of all radars at time k is determined by... This means that radar measurements are correlated with the target locally and independently. remember For radar s Data association events at time k. Binary variable. This indicates the associated event between the target and the measurement.

[0065] All feasible data association events are constructed based on the following two assumptions: (a) at time t, a measurement either originates from a target or is clutter; (b) at time t, the target produces at most one measurement. Based on these two assumptions, the association variables... The following two constraints must be met:

[0066]

[0067]

[0068] A reasonable joint related event The constraints of formulas (5) and (6) should be satisfied. An indicator function is introduced. To represent constraints. Let k be the set of all reasonable joint correlation events for radar s at time k. For data correlation events... If then there is otherwise there is not

[0069] Given targets and measurements, the prior probability density of the data association event conditioned on the target visible state is:

[0070] where

[0071] is the target detection indicator, is the number of unassociated measurements in .

[0072] It should be noted that the present application processing to establish the steps S1.1-S1.3 above also includes S1.4.

[0073] S1.4 establish distributed data fusion model

[0074] The radar is regarded as a node, and the radars which can communicate with each other are regarded as two corresponding nodes connected by an edge. Then the communication relationship between the radar networking can be described by an undirected graph , where is the node set, and ε is the edge set. In order to facilitate derivation, the mutual communication between nodes is considered to be error-free. Figure 1 A simple example of the graph model is given, Figure 1 the node set in which is The edge set is ε={{1,2},{2,3},{3,4},{3,5}}. Referring to Figure 1 and the set , it can be seen that node 1 and node 2 can communicate with each other, node 2 and node 1 and node 3 can communicate with each other, node 3 and node 2, node 4 and node 5 can communicate with each other, and node 4 and node 5 can only communicate with node 3.

[0075] For the distributed algorithm, the most important problem is how to do information fusion. Introducing the coupling transmission message node g k,st to represent the relationship between the two local first target motion state variables and at time k:

[0076]

[0077] is the neighbor node set of node s, and β is the coupling parameter and β>0.

[0078] ​the first target motion state the target visible state data association and joint observation variable

[0079] Through the modeling process of S1.1-S1.4, the first target motion state, the target visible state, the data association, and the joint observation variable can be obtained based on the distributed space-based radar network, and a problem of solving the joint probability density is established according to these data.

[0080] (2) the mutual relationship among the first target motion state, the target visible state, the data association, and the joint observation variable is described by using a factor graph, the factor graph takes the first target motion state conditional probability function, the target visible state conditional probability function, the data association conditional probability function, and the joint observation variable conditional probability function as factor nodes, and takes the first target motion state variable, the target visible state variable, and the data association variable as variable nodes.

[0081] In an embodiment, the step describes the defined problem of solving the joint probability density in the form of a factor graph.

[0082] First, the above to-be-solved joint probability density problem is factorized, denoted as Θ 1:K ={E 1:K ,X 1:K ,A 1:K} as the sequence of the first target motion state, the visible state, and the data association from the initial time to time K, the joint observation variable Y 1:K is all radar measurement sequences from the initial time to time K. The multi-target tracking task of the space-based radar network is to simultaneously perform data association A 1:K , target detection E 1:K , and target tracking X 1:K under the condition of Y 1:K . In the Bayesian framework, the joint posterior probability density needs to be solved, and then the posterior probability density of the latent variable is obtained by marginalizing it. The factorization is based on the mutual relationship among the first target motion state, the target visible state, the data association, and the joint observation variable, as shown in (A1)-(A7):

[0083] (A1) the local latent variable (related to the local radar) includes the target visible state the first target motion state data association where the data association is independent over time, while the target visible state and the first target motion state It evolves using a first-order Markov process;

[0084] (A2) Given X k and A k Measurement Y k Conditions are independent under different radar s;

[0085] (A3)A k With the target visible state E k Related;

[0086] (A4) Given A k X k Conditions independent of E k In other words, we use a visibility model to handle the number of changing and unknown targets. Visibility models are typically used in variational algorithms, assuming that the first target's motion state has the same posterior probability density in both visible and invisible situations.

[0087] (A5) Local latent variables and Factorization can be performed at the target level (i.e., assuming that the targets are independent of each other);

[0088] (A6) Local latent variables and Factorization can be performed at the radar level (i.e., assuming that the measurement sets obtained by the radar are independent of each other).

[0089] (A7) Local latent variables in a distributed fusion framework With latent variables It is relevant, given a set of latent variables from neighbors. In this case, It can operate independently at the level of neighboring nodes.

[0090] By using (A1), (A3), (A5), (A6), and (A7), the high-dimensional joint probability density can be obtained. Using the conditional probability p(X) of the first target motion state 1:K ), the conditional probability of the target's visible state p(E) 1:K ), and the data association conditional probability p(A) 1:K The result of a series of conditional probability products is represented. Among them,

[0091]

[0092]

[0093]

[0094] By using (A2) and (A4), and considering that the measurements are independent of each other, the joint observation variable conditional probability p(Y k |X k ,A k ) can be written as:

[0095]

[0096] Based on the above factorization, the joint probability density can be written as:

[0097]

[0098] By observing the high-dimensional joint posterior probability in equation (13), it can be seen that includes both continuous latent variables X 1:K and discrete continuous variables (E 1:K ,A 1:K ). It is very difficult to obtain the marginal distribution of a certain variable by marginalizing . Due to the nonlinear transformation between the target state and the measurement, the integral of X 1:K may not have a closed-form analytical solution, and the sum of (E 1:K ,A 1:K ) is also difficult to solve due to complex data association. In this case, it is reasonable to approximate the result to avoid the high cost of direct solution. At the same time, the target state (X 1:K E 1:K ,) and the environmental parameter A 1:K are not independent of each other, and the collaborative estimation of them helps to improve the estimation result of each parameter, so a joint solution framework is very important. In summary, it is difficult and impractical to solve the optimal solution of the problem, and an iterative optimization method should be used to approximate the optimal result.

[0099] After the above factorization of the high-dimensional joint probability density, as shown in equation (13), the problem is further described by a factor graph, as shown in Figure 2 . Among them, the variable node is represented by a circle, and represent the target dynamics state, the target visible state, and the data association latent variable of the SBR s at time k, respectively; the factor node is represented by a square, is the first target motion state conditional probability function, is the target visible state conditional probability function, is the joint observation variable conditional probability function, is the data association conditional probability function, and to couple the conditional probability functions, representing the corresponding factor nodes; and representing the frame constraint factor node.

[0100] (3) Based on the connection relationship between the variable nodes and the factor nodes in the factor graph, the BP-MF combined approximation method is used to solve the approximate solution of the joint posterior probability density, which is the product of the first target state posterior probability density, the target visible state posterior probability density and the data association posterior probability density.

[0101] In an embodiment, based on the transmission of messages between the factor nodes related to the variable nodes in the factor graph at different times and the properties of the nodes, the factor graph can be divided into different regions to solve the joint posterior probability density respectively, wherein the factor nodes have the above and

[0102] Because the MF approximation method is more suitable for models in the form of conjugate exponent, and the BP approximation method is better for hard constraints, the factor graph is divided into MF regions and BP regions representing the variable nodes, representing the factor nodes, then:

[0103]

[0104] Then the joint posterior probability density can be written as:

[0105]

[0106] The posterior probability density of the variable in the middle can be calculated approximately as:

[0107]

[0108]

[0109]

[0110] The BP-MF combined approximation method is based on the free energy of the region, and provides an iterative optimization method using the message passing algorithm on the factor graph. This combined method can solve problems that contain both continuous variables and discrete variables, and meets the properties of the above proposed problem.

[0111] (4) According to the approximate solution of the joint probability density, each target is tracked.

[0112] In an embodiment, in order to obtain the tracking result after receiving the measurement at time k, the joint posterior distribution p(Θ k |Y k ) is solved, and the approximate distribution of each variable is finally obtained according to the derivation steps described above, wherein the distribution of the first target state is the tracking result of the target at this time.

[0113] The present application defines the target tracking problem in the Bayesian framework, and factors the high-dimensional coupled hidden variables such as the first target motion state, target visibility and data association. The present application research adopts the message passing method to solve the problem, and solves the problem by using the BP method and the MF method according to the nature of the factored problem, effectively solving the problem of high-dimensional coupled hidden variables that are difficult to solve directly. The present application research aims at the space-based radar network fusion problem, considers the performance constraints of space-based radars, and adopts distributed fusion to solve the fusion problem in the network, that is, the demand for tracking quality is met and the performance constraints are met.

[0114] Optionally, the radar measurement generation method comprises:

[0115] The first target motion state is converted through a measurement function;

[0116] The first target motion state converted through the measurement function is added with Gaussian white noise to generate the radar measurement.

[0117] Optionally, the first target motion state is converted through the measurement function, comprising:

[0118] The first target motion state is converted from the ECEF coordinate system to the GSOF coordinate system through a first coordinate conversion factor to generate a second target motion state;

[0119] The second target motion state in the GSOF coordinate system is converted to the antenna array coordinate system through a second coordinate conversion factor to generate a third target motion state;

[0120] The third target motion state in the antenna array coordinate system is converted to the antenna array measurement coordinate system through a third coordinate conversion factor.

[0121] In an embodiment, in step S1.2, since the measurement of the space-based radar is obtained in the antenna array measurement coordinate system, and the target moves in the ECEF coordinate system, a suitable measurement function h(g) is needed to convert the first target motion state. The specific derivation is as follows: first, the target coordinate system ECEF is converted to the GSOF coordinate system:

[0122]

[0123]

[0124] S0 is the Greenwich Sidereal Time angle at initial time t0, ω e is the rotation speed of the earth 7.292155e-5 rad\s, t is the time span between the current time and the time t0, o is the right ascension of the ascending node, g is the orbit inclination, ω is the argument of perigee, the subscript z represents rotation around the z axis of the coordinate system, x ECEF is the first target motion state, x GSOF is the second target motion state in the coordinate system of the earth-centered earth-fixed coordinate system, is the first coordinate conversion factor.

[0125] The second coordinate transformation is from the earth-centered second orbit coordinate system to the antenna array face coordinate system (AAF),

[0126]

[0127]

[0128] where f is the true anomaly at time t, R0 is the distance between the earth center and the satellite, the subscript b represents the satellite body coordinate system, and the subscript a represents the antenna array face coordinate system, is the second coordinate conversion factor, x AAF is the third target motion state.

[0129] The third coordinate transformation is from the antenna array face coordinate system to the antenna array measurement coordinate system. This step of transformation is a nonlinear transformation from the Cartesian coordinate system to the spherical coordinate system, and the third coordinate conversion factor is denoted as According to the third coordinate conversion factor, the first target motion state coordinate conversion is as follows:

[0130]

[0131] In summary, the measurement equation h(x i,k ) in step S1.2 is as follows:

[0132]

[0133] Therefore, due to the existence of clutter, the measurement equation of the radar s is as follows:

[0134]

[0135] where h(g) is the measurement function, is a Gaussian white noise with a mean of 0 and a variance of It is assumed that x i,k and are independent of each other. It is assumed that the clutter are uniformly distributed in a volume of the radar observation region, i.e. The number of clutters obeys a Poisson distribution with parameter s .

[0136] Optionally, the solving process of the first target motion state posterior probability density comprises:

[0137] solving the first target motion state passing message, the joint observation variable passing message and the coupling passing message according to the first target motion state factor node by using the MF approximation method;

[0138] approximate solving the first target motion state conditional probability function according to the first target motion state passing message, the joint observation variable passing message and the coupling passing message.

[0139] In an embodiment, the posterior probability density of the first target motion state X 1:K is approximate solved in the following process:

[0140] Assuming that the motions among targets are independent, the belief of all target joint motion states is factorized as:

[0141]

[0142] To illustrate the passing message passing in Figure 2 and better derive b X (X 1:K ), Figure 3 more details are shown for the part of the variable node in Figure 2 . For each variable node , the factor node set connected with it is , and the variable node sets connected with the factor nodes in the factor node set are and Then the posterior probability density of the first target motion state X 1:K can be calculated as:

[0143]

[0144] where is the first target motion state passing message, is the joint observation variable passing message and is the coupling passing message.

[0145] According to the passing message, each term in can be calculated as:

[0146] ​

[0147]

[0148]

[0149] Furthermore, in each item:

[0150]

[0151]

[0152]

[0153] Substituting equation (24) into equations (21), (22), and (23), we obtain:

[0154]

[0155]

[0156]

[0157] in,

[0158]

[0159] Therefore, the first target motion state X 1:K posterior probability density It can be approximated as:

[0160]

[0161] Optionally, the process of solving the posterior probability density of the target's visible state includes:

[0162] Based on the target visible state factor nodes, the BP-MF combined approximation method is used to solve the target visible state transmission message and data association transmission message;

[0163] The posterior probability density of the target's visible state is approximately solved by passing messages based on the target's visible state and data association.

[0164] In one embodiment, the target visibility state E 1:K The approximate solution process for the posterior probability density is as follows:

[0165] Similar to the target dynamics, the appearance and disappearance of a target are directly independent, and the states of targets are independent of each other. The results estimated by the sensors are also independent of each other. Therefore, the visible state of a target can be factorized as follows:

[0166]

[0167] and Figure 3 The definition is similar. Figure 4 The target's visibility status was displayed. The corresponding subgraph. For each variable node The connected set of factor nodes is With factor node set The sets of variable nodes connected to the factor nodes in the table are respectively and Referring to equation (17), the target's visible state E 1:K posterior probability density It can be calculated as:

[0168]

[0169] So The message passed from the factor node to the variable node can be calculated as follows:

[0170]

[0171]

[0172] Substituting equations (31) and (32) into equation (30), the target's visible state E 1:K posterior probability density It can be approximated as:

[0173]

[0174] in,

[0175]

[0176] Optionally, the process of solving the posterior probability density of the data association includes:

[0177] Based on the data association factor nodes, the BP-MF combined approximation method is used to solve for the target event association transmission message, the target visibility state transmission message, the measurement constraint factor, and the target constraint factor.

[0178] The posterior probability density of the data association is approximately solved by considering the target event associated message, the target visibility state message, the measurement constraint factor, and the target constraint factor.

[0179] In one embodiment, data association A 1:K The approximate solution process for the posterior probability density is as follows:

[0180] Assuming that data associations are independent across different SBRs and at different times, then data association A 1:K It can be factorized as:

[0181]

[0182] Figure 5 The data association corresponding to the event is represented by a subgraph, where the variable nodes are connected to the factor nodes representing the measurement constraints at the measurement level and representing the target constraints at the target level. The set of variable nodes connected to the factor nodes in the set of factor nodes is denoted by For simplicity, we denote The posterior probability density of the data association A 1:K can be computed as:

[0183]

[0184] The message passing rule is used to update the messages in the MF region, which can be computed as:

[0185]

[0186]

[0187] where is the target event associated message, is the target visible state associated message.

[0188] By using the Gaussian approximation, the message in (38) can be computed as:

[0189]

[0190] where is the Jacobian matrix, D y is the dimension of the measurement.

[0191] The message passing rule is used to update the messages in the BP region, which can be computed as:

[0192]

[0193] From the measurement constraints, at time k, the measurement j produced by the radar s is either from the target i or a clutter. If there is then there is correspondingly. Therefore, the above equation can be computed as: ​​​​

[0194]

[0195] Similarly, the passing message may be calculated as:

[0196]

[0197] wherein, is the passing message of the measurement constraint factor, is the passing message of the target constraint factor.

[0198] Because the associated variable is a binary function, it is expected to be more applicable, and the expectation is calculated as follows:

[0199]

[0200] The temporary variable in the above formula is specifically:

[0201]

[0202]

[0203]

[0204]

[0205] The passing message passed by the variable node to the factor node in formulas (46) and (47) can be calculated as:

[0206]

[0207]

[0208] Then, by combining formulas (46)-(51), the final result of the temporary variable is:

[0209]

[0210]

[0211] The application also provides a message passing based distributed space-based radar network tracking device 600, as shown in the figure, the device 600 includes a memory 601, a processor 602 and a computer program 603 stored in the memory and executable on the processor, when the processor 602 executes the computer program 603, a message passing based distributed space-based radar network tracking method as any one of the above embodiments is implemented. Figure 6

[0212] ​It should be noted that the message-passing-based distributed space-based radar network tracking method that this device can execute is consistent with the implementation method of the above-described method embodiments, and will not be repeated here.

[0213] The present invention also provides experimental simulation results of a distributed space-based radar network tracking method based on message passing.

[0214] Example 1

[0215] Example 1 considers a simulation scenario of four space-based radars networked together for multi-target tracking, with a total of 10 targets moving within the overlapping observation area of ​​the radars. Specific radar satellite orbital parameters are shown in Table 1. The attitude angles of the radar antenna array coordinate system and the satellite attitudes are both 0°, and satellite 1 and satellite 2 are in the same orbital plane. It is assumed that all sea surface targets move at a uniform linear velocity. In this simulation, the radar measurement errors are consistent, with standard deviations of 0.114 km for radial distance, 0.03 rad for azimuth, and 0.006 rad for elevation. The sampling time T is 10 s, and the clutter density is 1e⁻⁶.

[0216] Table 1 Parameters of the four radar satellites

[0217]

[0218]

[0219] Simulation results can be found in the figure. Figure 7-9 ,pass Figure 7 It is evident that the average position based on the tracking method of this invention is significantly better than the average position without fusion, and is close to the average position of the optimal centralized fusion method; through Figure 8 It is evident that the average speed of the tracking method based on this invention is significantly better than the average position without fusion, and approaches the average speed of optimal centralized fusion; through Figure 9 It is evident that the average OSPA based on the tracking method of this invention almost overlaps with the average OSPA without fusion and the average OSPA of optimal centralized fusion.

[0220] The above analysis shows that the message-passing-based distributed space-based radar network tracking method provided by this invention converges to the centralized fusion method and is superior to the non-fusion method. Simulation results also prove the effectiveness of the algorithm of this invention.

[0221] Table 2 shows the average values ​​of the following three indicators. According to the data, the improvement in tracking accuracy is very significant, especially the average position RMSE. Compared with the non-fusion algorithm, the algorithm of this invention has improved by about 32.11%. The average speed RMSE and average OSPA have also been improved.

[0222] Table 2 Tracking accuracy index results

[0223]

[0224] The above merely provides the preferred embodiment of the present application and not intended to limit the present application. Accordingly, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall fall within the protection scope of the present application.

Claims

1. A message passing based distributed space-based radar networked tracking method, characterized in that, The method is implemented by steps including: obtaining a first target motion state, a target visibility state, data association and joint observation variables from an initial time to a time t; describing the interrelation of the first target motion state, the target visibility state, the data association and the joint observation variables by a factor graph, the factor graph taking a first target motion state conditional probability function, a target visibility state conditional probability function, a data association conditional probability function and a joint observation variable conditional probability function as factor nodes, and taking a first target motion state variable, a target visibility state variable and a data association variable as variable nodes; solving an approximate solution of a joint posterior probability density by a BP-MF combined approximation method based on the connection relationship between the variable nodes and the factor nodes in the factor graph, the approximate solution being a product of a first target motion state posterior probability density, a target visibility state posterior probability density and a data association posterior probability density; tracking a target according to the approximate solution of the joint posterior probability density; the solving process of the first target motion state posterior probability density includes: solving a first target motion state transmission message, a joint observation variable transmission message and a coupling transmission message by an MF approximation method according to a factor node of the first target motion state; approximately solving the first target motion state posterior probability density according to the first target motion state transmission message, the joint observation variable transmission message and the coupling transmission message.

2. The message-passing based distributed space-based radar netted tracking method according to claim 1, wherein, the generation method of the radar measurement includes: performing coordinate conversion on the first target motion state by a measurement function; generating the radar measurement by adding the first target motion state after coordinate conversion to a Gaussian white noise.

3. The message passing based distributed space-based radar netted tracking method according to claim 2, wherein, the coordinate conversion on the first target motion state by the measurement function includes: converting the first target motion state from a geocentric geodetic coordinate system to a geocentric second orbital coordinate system by a first coordinate conversion factor to generate a second target motion state; converting the second target motion state in the second orbital coordinate system to an antenna array plane coordinate system by a second coordinate conversion factor to generate a third target motion state; converting the third target motion state in the antenna array plane coordinate system to an antenna array plane measurement coordinate system by a third coordinate conversion factor.

4. The message-passing based distributed space-based radar netted tracking method according to claim 1, wherein, the solving process of the target visibility state posterior probability density includes: solving a target visibility state transmission message and a data association transmission message by the BP-MF combined approximation method according to a factor node of the target visibility state; approximately solving the target visibility state posterior probability density according to the target visibility state transmission message and the event association transmission message.

5. The message passing based distributed space-based radar netted tracking method according to claim 1, wherein, the solving process of the data association posterior probability density includes: solving a target event association transmission message, a target visibility state transmission message, a measurement constraint factor and a target constraint factor by the BP-MF combined approximation method according to a factor node of the data association; The data association posterior probability density is approximately solved according to the target event association delivery message, the target visibility state delivery message, the measurement constraint factor and the target constraint factor.

6. A message passing based distributed space-based radar netted tracking apparatus, characterized in that, The computer program product comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the message passing based distributed space-based radar networked tracking method according to any one of claims 1-5 when executing the computer program.

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