Target fusion method under unknown time-varying parameters based on mean field belief propagation

Abstract

The application discloses a target fusion method based on mean field belief propagation under unknown time-varying parameter condition, and belongs to the technical field of radar target fusion tracking.The application aims at the problem that the existing target fusion algorithm cannot realize target fusion under unknown time-varying parameter condition.The application comprises the following steps: calculating marginal probability based on Markov law; setting an association data group and determining the constraint condition that the association data of each sensor is derived from a target and clutter; calculating prior probability distribution; calculating joint posterior probability density function based on conditional probability; establishing a factor graph model based on mean field-belief propagation, reconstructing the joint posterior probability density function and calculating belief value; solving target motion state, target existence probability, measurement noise covariance and association variable; iteratively solving until the difference between target motion states in adjacent two times is less than a preset threshold value, and taking the current target motion state as a final target fusion state.The application is used for target fusion under unknown time-varying parameter condition.

Description

Technical Field

[0001] This invention relates to a target fusion method under unknown time-varying parameter conditions based on mean field confidence propagation, and belongs to the field of radar target fusion and tracking technology. Background Technology

[0002] Radar target fusion tracking technology is a key technology in modern radar systems, and its accuracy and reliability directly affect subsequent decision-making and control. Information acquired by a single sensor often suffers from noise interference and data gaps, resulting in insufficient tracking accuracy. By fusing data from multiple information sources, the limitations of single sensors are overcome, improving the target detection probability, enhancing the stability and continuity of target tracking, and increasing target tracking accuracy.

[0003] The Tianfa shipborne high-frequency radar combines the characteristics of skywave and groundwave over-the-horizon radars. It has the advantages of long-range operation, wide coverage, anti-stealth, and anti-anti-radiation missiles, as well as stable propagation of ground waves. At the same time, since its radar transmitter is generally located inland and the receiver is located on the ship, the ship can obtain electromagnetic support under radio silence conditions, which has great tactical significance in ocean voyages.

[0004] Regarding target fusion algorithms for Tianfa shipborne high-frequency radar, existing models mostly perform target fusion under known parameter conditions. However, in actual detection scenarios, there are situations where the parameters are unknown, and in such cases, existing algorithms cannot achieve target fusion. Therefore, existing methods cannot achieve target tracking under conditions of unknown time-varying parameters. Summary of the Invention

[0005] To address the problem that existing target fusion algorithms cannot achieve target fusion under unknown time-varying parameters, this invention provides a target fusion method based on mean-field confidence propagation under unknown time-varying parameters.

[0006] The present invention provides a target fusion method based on mean-field confidence propagation under unknown time-varying parameter conditions, comprising:

[0007] Let the probability of the existence of target i at time k be e. i,k The probability e of the existence of target i at time k+1 is calculated based on Markov's law. i,k+1 The marginal probability;

[0008] Set the associated data group of the multipath data of the s-th shipborne platform sensor at time k as follows: Determine the source of the associated data for each sensor from the constraints of the target and clutter;

[0009] Based on the existence probability e i,k and associative arrays Calculate the prior probability distribution between the target visibility state and the associated data; then define the conditional probability and calculate the joint posterior probability density function;

[0010] Based on the mean-field confidence propagation principle, a factor graph model based on mean-field confidence propagation is established;

[0011] Based on the factor graph model, the joint posterior probability density function is reconstructed, and the belief value is calculated. At the same time, the target motion state, the target existence probability, the measurement noise covariance, and the associated variables are solved. The solution is iterated until the difference between the target motion states in two adjacent calculations is less than a preset threshold, and the current target motion state is taken as the final target fusion state.

[0012] According to the target fusion method based on mean-field confidence propagation under unknown time-varying parameters of the present invention, the existence probability e of target i at time k+1 is... i,k+1 The marginal probability is expressed as Pr:

[0013]

[0014] In the formula Pr(e i,k+1 =0) means e i,k+1 The marginal probability;

[0015] In the formula T i,e Here is the transition probability matrix:

[0016]

[0017] In the formula Pr(e i,k+1 =1|e i,k =1) represents e i,k+1 Based on e i,k The conditional probability.

[0018] According to the target fusion method based on mean-field confidence propagation under unknown time-varying parameters of the present invention, the number of shipborne platform sensors is set to be... There are [number] sensors, and the network path for each sensor to receive target data is [path]. 1, target is χ, associative array The target correlation variable in the data is Clutter correlation variables are The constraints are established as follows:

[0019]

[0020] In the formula The total number of the target related variables.

[0021] The target fusion method based on mean-field confidence propagation under unknown time-varying parameters according to the present invention is based on the existence probability e i,kand associative arrays Calculate the prior probability distribution between the target visibility state and associated data.

[0022] In the formula E k ={e i,k} i＝1,...,χ , λ s Let be the clutter density of the s-th shipborne platform sensor. Let be the gate volume of the s-th shipborne platform sensor at time k. The clutter trace associated at time k, Let be the detection probability of the t-th path by the s-th shipborne platform sensor. Let ε be the target detection probability, and ε be the target detection probability constant. It is an object detection function.

[0023] According to the target fusion method based on mean-field confidence propagation under unknown time-varying parameters of the present invention, the conditional probability Θ is defined. 1:K for:

[0024] Θ 1:K ={E 1:K ,X 1:K A 1:K ,R 1:K},

[0025] In the formula, K is the upper limit of time, and X 1:K Let A be the target motion state array from time 1 to time K. 1:K R is an associative array from time 1 to time K. 1:K The target measurement noise covariance array from time 1 to time K;

[0026] Under the optimal Bayesian framework, with Z 1:K Represent the measured values ​​and calculate the joint posterior probability density function.

[0027] In the formula p(Θ) 1:K |Z 1:K ) is the posterior probability function;

[0028]

[0029] In the formula p(x i,k+1 |x i,k ) represents the conditional probability, x i,k Let i be the target motion state of the i-th target at time k. Let be the measurement noise covariance of the target i of the s-th sensor at time k;

[0030]

[0031] In the formula Let j be the j-th measurement value of the s-th sensor at time k. The measurement noise covariance matrix;

[0032] Then the joint posterior probability density function Described as:

[0033]

[0034] In the formula To introduce a mark, For the set of all feasible joint multipath data association events, when It is 1 if it is true, otherwise it is 0.

[0035] According to the target fusion method based on mean-field confidence propagation under unknown time-varying parameters of the present invention, the joint posterior probability density function is reconstructed based on the factor graph model.

[0036]

[0037] In the formula, MF represents the mean-field propagation part, and BP represents the back-propagation part;

[0038] These are the nodes representing the target motion state variables in the factor graph model. For the measurement variable nodes in the factor graph model, For nodes in the target measurement noise covariance variable in the factor graph model, For the presence of probability variable nodes in the factor graph model, To mark the variable node:

[0039]

[0040] Based on the reconstructed joint posterior probability density function Calculation of beliefs:

[0041]

[0042] In the formula, X represents the target motion state array, E represents the existence probability array, R represents the target measurement noise covariance array, and A represents the correlation array;

[0043] In the formula b X For the goal state belief, α represents a node in the factor graph model. This represents the mean-field propagation portion MF. b represents the transformation amount from node α to a node in X. E There is a probabilistic belief in the existence of a goal. This represents the backpropagation portion of BP, b R To measure the belief in noise covariance, b A Beliefs are related variables.

[0044] According to the target fusion method based on mean-field confidence propagation under unknown time-varying parameters of the present invention, b is decomposed X (X 1:K ):

[0045]

[0046] Combining the information dissemination rule update method, we get:

[0047]

[0048] This provides information about the i-th target state at time k-1. Let be the noise covariance information of the i-th target measurement received by the s-th sensor at time k. The associated variable information of the s-th sensor at time k;

[0049]

[0050] Further results were obtained:

[0051]

[0052] In the formula, N is the Gaussian distribution function, F k Let be the target state transition matrix. Let P be the estimated motion state of the i-th target at time k-1. i,k-1 Let Q be the covariance matrix of the i-th target at time k-1. k The process noise covariance matrix is... To estimate the measurement noise covariance considering ionospheric height error, Estimate the target related variables;

[0053] Simplifying the above equation, we get:

[0054]

[0055] To fuse the measurement values, h k For measurement conversion function, To integrate measurement noise covariance,

[0056]

[0057] restate b X (x i,k )for:

[0058]

[0059] Measurement-level fusion is achieved by fusing measurements from different shipboard platforms:

[0060]

[0061] In the formula z i,k This is a fusion of measured values;

[0062] The estimated value of the target's motion state and the target covariance matrix are calculated as follows:

[0063]

[0064] In the formula, E represents the mathematical expectation.

[0065] The beneficial effects of the present invention are as follows: The method of the present invention starts with centralized target fusion tracking and solves the target fusion tracking problem under unknown time-varying parameters.

[0066] Verification experiments show that, under all detection probabilities, the proposed method maintains a relatively constant track length compared to the traditional MF-BP method, while improving range and velocity accuracy by more than 20%. The traditional MF-BP method achieves target association and state estimation through iterative calculation of the factor graph, and can also obtain the ionospheric height value. However, in the context of high-frequency radar from a satellite to a ship, the influence of sea clutter and the motion of the ship platform leads to unstable target echo signal-to-clutter ratio. Furthermore, this error is coupled with the ionospheric error, making it difficult for the traditional MF-BP method to directly solve for the ionospheric height value, thus affecting target prediction, association, and state estimation. The proposed MF-VB-BP method effectively considers the unknown parameters under such coupled conditions, improving the accuracy of target state estimation. Attached Figure Description

[0067] Figure 1 This is a flowchart illustrating the target fusion method based on mean-field confidence propagation under unknown time-varying parameters as described in this invention.

[0068] Figure 2 This is a schematic diagram of the MF-BP tracking results of 100 Monte Carlo simulations in the verification experiment; the horizontal axis X represents the length of the experimentally set motion area in the X-axis direction, the vertical axis Y represents the length of the experimentally set motion area in the Y-axis direction, Shipborne represents the shipborne track, Target represents the target track, and MF-BP represents the traditional MF-BP tracking method.

[0069] Figure 3This is a schematic diagram of the MP-VR-OTHRs tracking results from 100 Monte Carlo runs in the verification experiment; MP-VR-OTHRs in the figure represent the tracking method of the present invention under the Tianfa ship-receiving system.

[0070] Figure 4 This is a schematic diagram of the RMSE distance between non-crossing targets in the verification experiment; in the figure, the horizontal axis CIT represents the number of tracking frames, the vertical axis RMSE represents the root mean square error, MF-R-BP T1 represents the tracking result of target 1 under the traditional MF-BP tracking method, MF-BP T1 represents the tracking result of target 1 under the tracking method of this invention; T1 to T4 represent target 1 to target 4.

[0071] Figure 5 This is a schematic diagram of the RMSE of non-intersecting target velocities in the verification experiment;

[0072] Figure 6 This is a diagram illustrating the RMSE (Reference Range Between Targets) at intersection; T5 represents target 5, and T6 represents target 6.

[0073] Figure 7 This is a diagram illustrating the RMSE (Mean Exchange Rate) of intersecting targets.

[0074] Figure 8 This is a schematic diagram of the average root mean square error (ARMSE) of the distances to five targets;

[0075] Figure 9 This is a schematic diagram of the root mean square error (ARMSE) of the velocity of five targets;

[0076] Figure 10 This is a schematic diagram of the track maintenance length; the horizontal axis Pd represents the detection probability, and the vertical axis Length represents the track maintenance length.

[0077] Figure 11 This is a schematic diagram of a factor graph model based on mean-field confidence propagation; in the diagram, η is equivalent to... In the picture This represents a target-related variable with a target value of 0 and a measurement value of 1. This indicates that the target is 0, and the measurement is... The target related variable, Let the target be χ and the path be χ. Measurement The target related variable. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0080] The present invention will be further described below with reference to the accompanying drawings, but this should not be construed as limiting the invention.

[0081] Specific Implementation Method 1: Combination Figure 1 As shown, this invention provides a target fusion method based on mean-field confidence propagation under unknown time-varying parameters, comprising:

[0082] Let the probability of the existence of target i at time k be e. i,k The probability e of the existence of target i at time k+1 is calculated based on Markov's law. i,k+1 The marginal probability;

[0083] Set the associated data group of the multipath data of the s-th shipborne platform sensor at time k as follows: Determine the source of the associated data for each sensor from the constraints of the target and clutter;

[0084] Based on the existence probability e i,k and associative arrays Calculate the prior probability distribution between the target visibility state and the associated data; then define the conditional probability and calculate the joint posterior probability density function;

[0085] Based on the mean-field confidence propagation principle, a factor graph model based on mean-field confidence propagation is established;

[0086] Based on the factor graph model, the joint posterior probability density function is reconstructed, and the belief value is calculated. At the same time, the target motion state, the target existence probability, the measurement noise covariance, and the associated variables are solved. The solution is iterated until the difference between the target motion states in two adjacent calculations is less than a preset threshold, and the current target motion state is taken as the final target fusion state.

[0087] This implementation first establishes a measurement model and a target / ship motion model based on the Tianfa shipborne radar system. Each shipborne platform in the network sends its measurements to the fusion center, where all measurements are processed—that is, measurement-level fusion is performed. When e i,k If e is 1, then target i exists. i,kWhen the value is 0, target i does not exist, and its marginal probability conforms to Markov's law.

[0088] Furthermore, let e be the probability of the existence of target i at time k+1. i,k+1 The marginal probability is expressed as Pr:

[0089]

[0090] In the formula Pr(e i,k+1 =0) means e i,k+1 The marginal probability;

[0091] In the formula T i,e Here is the transition probability matrix:

[0092]

[0093] In the formula Pr(e i,k+1 =1|e i,k =1) represents e i,k+1 Based on e i,k The conditional probability.

[0094] For ease of discussion, the ionospheric height is divided into the E layer and the F layer, then the maximum path length is 2. Let represent the associative array. Assuming each shipborne platform operates independently, and the multipath measurements of different shipborne platforms are associated locally and individually with the target, then... Let the measurement of the s-th sensor at time k be denoted as , when A value of 1 indicates that measurement j originates from the τth path of target i. The representative's measurement j originates from clutter. Two assumptions are made regarding the correlation:

[0095] 1) At any given moment, a measurement originates from the target or from clutter;

[0096] 2) Each path for each target generates at most one measurement.

[0097] The number of sensors on the shipboard platform is set to There are [number] sensors, and the network path for each sensor to receive target data is [path]. 1, target is χ, associative array The target correlation variable in the data is Clutter correlation variables are The constraints are established as follows:

[0098]

[0099] In the formula The total number of the target related variables.

[0100] Introduction of markers It is the set of all feasible joint multipath data association events, when When the condition is met, the redundant variable is 1; otherwise, it is 0.

[0101] Based on the existence probability e i,k and associative arrays Calculate the prior probability distribution between the target visibility state and associated data.

[0102]

[0103] In the formula E k ={e i,k} i＝1,…,χ , λ s Let be the clutter density of the s-th shipborne platform sensor. Let be the gate volume of the s-th shipborne platform sensor at time k. The clutter trace associated at time k, Let be the detection probability of the t-th path by the s-th shipborne platform sensor. Let ε be the target detection probability, and ε be the target detection probability constant. It is an object detection function.

[0104] Further considering the coupling between time-varying ionospheric height error and measurement error, the measurement noise covariance matrix is ​​defined as follows: Define conditional probability Θ 1:K for:

[0105] Θ 1:K ={E 1:K ,X 1:K A 1:K ,R 1:K},

[0106] In the formula, K is the upper limit of time, and X 1:K Let A be the target motion state array from time 1 to time K. 1:K R is an associative array from time 1 to time K. 1:K The target measurement noise covariance array from time 1 to time K;

[0107] Under the optimal Bayesian framework, with Z 1:K Represent the measured values ​​and calculate the joint posterior probability density function.

[0108] In the formula p(Θ) 1:K |Z 1:K ) is the posterior probability function;

[0109] Since the target state, the probability of target existence, and the measurement error covariance matrix follow a first-order Markov model, then:

[0110]

[0111] In the formula p(x i,k+1 |x i,k ) represents the conditional probability, x i,k Let i be the target motion state of the i-th target at time k. Let be the measurement noise covariance of the target i of the s-th sensor at time k;

[0112] A 1:K Based on E 1:K Z 1:K Based on R 1:K A 1:K and X 1:K ;

[0113]

[0114] In the formula Let j be the j-th measurement value of the s-th sensor at time k. The measurement noise covariance matrix;

[0115] Then the joint posterior probability density function Described as:

[0116]

[0117] In the formula To introduce a mark, For the set of all feasible joint multipath data association events, when It is 1 if it is true, otherwise it is 0.

[0118] A factor graph model based on mean-field confidence propagation is established, where A, I, N represent sets, and the cardinality of set I is denoted as |I|, where i ∈ I is written as I\{i}, and I is the cardinality of set I. I Indicates the relationship between i and I, if i∈I then I I Let X be a discrete random variable with a finite number of realizations and its probability mass function p. X Let x represent a variable in X, and let x = (x|i∈I) T vector, Represents, except for X i All possible X, in p X The probability mass function representing vector X can then be expressed as:

[0119]

[0120] in at the same time Not generally hypothetical Then N(a) is the set of all variable nodes a∈A connected to a certain factor node, and N(i) represents the set of all factor nodes i∈I connected to a variable node. by For the BP part, This is the MF part. Define region R to contain all... A R ∈A, for each region R, a count c is given. R For a group It can be represented as:

[0121]

[0122] The factor graph described above can then be represented as the union of three regions:

[0123] 1) MF region:

[0124] 2) Small area:

[0125] 3) Large regions:

[0126] The entire region can then be represented as:

[0127]

[0128] The free energy of the entire region is:

[0129]

[0130] in Then belief b i and b a Normalization constraints must be satisfied:

[0131]

[0132] And marginalization constraints:

[0133]

[0134] If the constraints are imposed using Lagrange multiplication, then:

[0135]

[0136] By setting the derivative with respect to belief and the Lagrange multipliers to zero, we can obtain the stable point of the Lagrange multiplier, and then solve for the belief value:

[0137]

[0138] The renewal of beliefs can be represented as:

[0139]

[0140] Where n i→a (x i ) represents the message sent from variable node i to factor node a, m a→i This represents the node from factor node a to variable node i.

[0141] According to the factor graph model, such as Figure 11 As shown, the joint posterior probability density function is reconstructed.

[0142] In the formula, MF represents the mean-field propagation part, and BP represents the back-propagation part;

[0143] These are the nodes representing the target motion state variables in the factor graph model. For the measurement variable nodes in the factor graph model, For nodes in the target measurement noise covariance variable in the factor graph model, For the presence of probability variable nodes in the factor graph model, For the marker node variable point:

[0144]

[0145] as well as in and As a pair of redundant variables to facilitate the derivation of confidence propagation, the factor graph constructed according to this invention can be restated.

[0146] Based on the reconstructed joint posterior probability density function Calculation of beliefs:

[0147]

[0148] In the formula, X represents the target motion state array, E represents the existence probability array, R represents the target measurement noise covariance array, and A represents the correlation array;

[0149] In the formula b X For the goal state belief, α represents a node in the factor graph model. This represents the mean-field propagation portion MF. b represents the transformation amount from node α to a node in X. EThere is a probabilistic belief in the existence of a goal. This represents the backpropagation portion of BP, b R To measure the belief in noise covariance, b A Beliefs are related variables.

[0150] Next, we will perform iterative calculations of the fusion state:

[0151] Solve for the target state b X (X 1:K The motion state X of the target can be obtained through the independent motion of each target, and each time step conforms to a first-order Markov law. The motion state beliefs of all targets can be decomposed as follows:

[0152] Decompose b X (X 1:K ):

[0153]

[0154] For factor node x i,k Its variable domain can be represented as The information can then be calculated as:

[0155]

[0156] Combining the information dissemination rule update method, we get:

[0157]

[0158] This provides information about the i-th target state at time k-1. Let be the noise covariance information of the i-th target measurement received by the s-th sensor at time k. The associated variable information of the s-th sensor at time k;

[0159]

[0160] Further results were obtained:

[0161]

[0162] In the formula, N is the Gaussian distribution function, F k Let be the target state transition matrix. Let P be the estimated motion state of the i-th target at time k-1. i,k-1 Let Q be the covariance matrix of the i-th target at time k-1. k The process noise covariance matrix is... To estimate the measurement noise covariance considering ionospheric height error, Estimate the target related variables;

[0163] It is important to note that here... This is an estimate of the measurement noise covariance that takes into account the error in ionospheric height. Simplifying the above formula, we get:

[0164]

[0165] To fuse the measurement values, h k For measurement conversion function, To fuse the measurement noise covariance, we obtain:

[0166]

[0167] restate b X (x i,k )for:

[0168]

[0169] Measurement-level fusion is achieved by fusing measurements from different shipboard platforms:

[0170]

[0171] In the formula z i,k This is a fusion of measured values;

[0172] The estimated value of the target's motion state and the target covariance matrix are calculated as follows:

[0173]

[0174] In the formula, E represents the mathematical expectation.

[0175] The method for determining the probability of the existence of the target is as follows:

[0176] Solve for the probability b of the existence of the target. E (E 1:K Similar to the target's motion state X, the probability of the target's existence is also independent among the targets and conforms to a first-order Markov chain.

[0177]

[0178] Regarding the probability of existence e i,k The variable domain is represented as get:

[0179]

[0180] in:

[0181]

[0182] For ei,k-1 Node to Information between nodes;

[0183] Simplifying, we get:

[0184] b E (e i,k ) = T i,e b E (e i,k -1)ξ k (e i,k (33),

[0185] ξ k As an intermediate variable:

[0186]

[0187] Therefore, the probability of the target's existence at time 1:K can be simplified as follows:

[0188]

[0189] π i,e Let π be the initial probability. i,e =[Pr(e i,k =1), Pr(e i,k =0).

[0190] As can be seen from the above formula, the probability of the target's existence conforms to a Hidden Markov Model, where π... i,e Let ξ be the initial value and the observed value be ξ. k (e i,k If the probability of target existence can be calculated using a forward-backward algorithm, then trajectory management can be achieved. Furthermore, the detection probability in the above formula is related to the probability of target existence. If e i,k =1 If e i,k =0 ι is a very small value that affects the target detection probability by passing the probability of the target's existence.

[0191] The method for calculating the measurement noise covariance is as follows:

[0192] Solving for the measurement noise covariance belief b R (R 1:K The target measurement noise R after introducing ionospheric height varies depending on the target echo signal-to-noise ratio and the target's location. Assume the target measurement noise covariance R is independent:

[0193]

[0194] Will The variable field is represented as The belief can then be calculated as:

[0195]

[0196] Combining the above equations, we get:

[0197]

[0198] ρ is the forgetting factor;

[0199] The above equation can be further rewritten as:

[0200] get:

[0201] Beliefs are calculated as follows:

[0202]

[0203] In the formula For fusion measurement values A set;

[0204] According to the above formula, it can be seen that... Conforms to the given and The Gaussian distribution, its covariance Because it is difficult to solve directly, the inverse gamma distribution is used as the conjugate prior distribution of the Gaussian distribution variance, resulting in... The probability distribution function is derived from constitute:

[0205]

[0206] In the formula, Inv-Gamma represents the inverse gamma distribution. As an intermediate variable, Let δ be the shape parameter of the inverse gamma distribution and g be the scale parameter of the inverse gamma distribution.

[0207] Will Depend on Measured as In the formula, E represents the mathematical expectation:

[0208]

[0209] h' k for h k The transpose of .

[0210] The method for solving correlation variables is as follows:

[0211] Assuming that local multipath data associations are independent across different shipboard platforms, the confidence level of multipath data associations can be decomposed into:

[0212]

[0213] In the formula Let be the correlation variable of the s-th sensor at time k;

[0214] against Represent the variable domain as

[0215] For the correlation variable of the dots, For trajectory-related variables;

[0216] Divide the nodes in the factor graph model into MF regions. With BP region For the MF region:

[0217]

[0218] in For the BP region, based on the fact that each path only has two possibilities—generating measurements and not generating measurements—it is possible to... and By applying constraints, it can therefore be expressed as:

[0219]

[0220] Based on the above beliefs, infer the estimated values ​​of the target-related variables.

[0221]

[0222] in and for:

[0223]

[0224] Repeat the above process of solving for the target motion state, target existence probability, measurement noise covariance, and related variables until E is found in two consecutive iterations. k+1 With E k If the difference is less than the threshold ξ, the current target motion state array X is taken as the final target fusion state.

[0225] Verification experiment:

[0226] Radar coordinate registration simulation parameter configuration: Shipborne platform 1 is set to [20km, 0m / s, 1000km, 4m / s], shipborne platform 2 is set to [-20km, 0m / s, 1000km, 4m / s], generating 5 targets: Target 1 is [40km, 6m / s, 1100km, -3km], Target 2 is [60km, 0m / s, 1050km, 3m / s], Target 3 is [-70km, 5m / s, 1060km, -4m / s], and Target 4 is [-70km, 5m / s]. / s, 1060km, 4m / s], target 5 is [-30km, 7m / s, 1100km, 0m / s], ionospheric height E layer is set to 100km, F layer is set to 260km, E layer measurement error is 10km, F layer measurement error is 40km, detection area is x=[-100km, 100km], y=[1000km, 1200km], detection probability is 0.6, sampling period is 40 seconds, 80 coherent accumulation times (CIT) are generated, process noise is 0.001m / s 2 The range measurement error was set to 2 km, the Doppler velocity measurement error to 0.1 m / s, the azimuth measurement error for shipborne platform 1 was set to 0.025 rad, and the azimuth measurement error for shipborne platform 2 was set to 0.035 rad. The results of 100 Monte Carlo simulations are as follows: Figure 2 and Figure 3 As shown.

[0227] Single target tracking results, such as Figure 2 and Figure 3 As shown, when the target is a non-intersecting target, the RMSE simulation results of the target's velocity and distance are as follows: Figure 4 and Figure 5 As shown, when the target is an intersecting target, the RMSE simulation results of the target's velocity and distance are as follows: Figure 6 and Figure 7 As shown. After 100 Monte Carlo simulations with different detection probabilities, the ARMSE results and track maintenance lengths for the five targets after convergence are as follows. Figures 8 to 10 As shown.

[0228] contrast Figures 8 to 10Compared to the MF-BP method, the proposed method maintains a relatively constant track length and improves range and velocity accuracy by over 20% across all detection probabilities. The MF-BP method achieves target association and state estimation through iterative calculation of the factor graph, and can also obtain the ionospheric height value. However, in the context of high-frequency radar from a satellite to a ship, the target echo signal-to-clutter ratio is unstable due to sea clutter and the motion of the ship platform. Furthermore, this error is coupled with the ionospheric error, making it difficult for the MF-BP method to directly solve for the ionospheric height value, thus affecting target prediction, association, and state estimation. The proposed method—MF-VB-BP—effectively considers the unknown parameters under this coupled condition, improving the accuracy of target state estimation.

[0229] The specific implementation process of the method of the present invention includes the following steps:

[0230] 1) Based on the shipborne radar system, a measurement model and target / ship motion model are established. Each shipborne platform in the network sends its measurements to the fusion center, where all measurements are processed. The probability of target i existing at time k is e. i,k The array of all targets is E. k ={e i,k} i＝1,...,χ χ represents all targets, and the marginal probability of a target can be obtained through formulas (1) and (2).

[0231] 2) Dividing the ionospheric height into E and F layers, the maximum path length is 2. Let represent the correlation array. Assuming that each shipborne platform operates independently, the multipath measurements of different shipborne platforms are correlated with the target locally and individually. Two assumptions are made regarding the correlation: 1) At any given time, a measurement originates from the target or from clutter; 2) Each path of each target generates at most one measurement. The correlation variables can be constrained by formula (3).

[0232] 3) Obtain the prior probability distribution between the target visibility state and the multipath data association variables through formula (4);

[0233] 4) Further considering the coupling between time-varying ionospheric height error and measurement error, under the optimal Bayesian framework, the target state, target existence probability, and measurement error covariance matrix can be obtained by formula (5), and the joint probability distribution can be obtained by formula (7).

[0234] 5) Establish a factor graph model based on mean field-belief propagation. The probability mass function of vector X is represented by formula (8). The entire region can be represented by formula (10). The free energy of the entire region can be represented by formula (11). The belief value can be solved by formula (16).

[0235] 6) The factor graph constructed according to the present invention can be used to redescribe the joint probability distribution through formula (17), and then each belief can be obtained through formula (18);

[0236] 7) Decompose the motion state beliefs of all targets using formula (19), for factor node x i,k Information can be calculated using formula (20). Considering the measurement noise covariance estimate of the ionospheric height error, the target state can be obtained using formula (25). Measurements from different shipborne platforms are fused again to achieve measurement-level fusion. The target state and error covariance can be obtained using formula (29).

[0237] 8) Decompose the existence probability of all targets using formula (30), and for factor node e i,k The information can be calculated using formula (31), and the probability of the target's existence at time 1:K can be obtained using formula (35).

[0238] 9) Introducing the target measurement noise R after the ionospheric height, assuming that the target measurement noise covariance R is independent, the measurement noise covariance can be decomposed using formula (36) for the factor nodes. Information can be calculated using formula (37), and the measurement noise covariance can be obtained using formula (43). The inverse gamma distribution is used as the conjugate prior distribution of the Gaussian distribution variance. At this point, the probability distribution function of the measurement noise covariance is derived from... The composition can be obtained using formula (45).

[0239] 10) Assuming that the local multipath data association is independent under different motion platforms, the confidence of the multipath data association can be decomposed using formula (46) for factor nodes. Information nodes can be divided into MF regions and BP regions. The MF region can be obtained through formulas (47) and (48), the BP region can be obtained through formulas (49) and (50), and the associated variables can be obtained through formula (51).

[0240] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A target fusion method based on mean-field confidence propagation under unknown time-varying parameters, characterized in that, include: Let the probability of the existence of target i at time k be... Calculate the existence probability of target i at time k+1 based on Markov's law. The marginal probability; Set the associated data group of the multipath data of the s-th shipborne platform sensor at time k as follows: The associated data of each sensor is determined to originate from the constraints of the target and clutter. Based on the probability of existence and associative arrays Calculate the prior probability distribution between the target visibility state and associated data; then define the conditional probability and calculate the joint posterior probability density function; Based on the mean-field confidence propagation principle, a factor graph model based on mean-field confidence propagation is established; Based on the factor graph model, the joint posterior probability density function is reconstructed, and the belief value is calculated. At the same time, the target motion state, the target existence probability, the measurement noise covariance, and the associated variables are solved. The solution is iterated until the difference between the target motion states in two adjacent calculations is less than a preset threshold, and the current target motion state is taken as the final target fusion state. The probability of the existence of target i at time k+1 The marginal probability is expressed as : ， In the formula express The marginal probability; In the formula Here is the transition probability matrix: ， In the formula express based on The conditional probability; The number of sensors on the shipboard platform is set to There are [number] sensors, and the network path for each sensor to receive target data is [path]. One, the target is One, associative array The target correlation variable in the data is The clutter correlation variable is Establish the following constraints: ， In the formula The total number of target related variables; Based on the probability of existence and associative arrays Calculate the prior probability distribution between the target visibility state and associated data. : ， In the formula , Let be the clutter density of the s-th shipborne platform sensor. Let be the gate volume of the s-th shipborne platform sensor at time k. The clutter trace associated at time k, For the s-th shipborne platform sensor The detection probability of each path, , The probability of target detection. Let be the target detection probability constant. It is an object detection function. ; Define conditional probability for: ， In the formula The upper limit of time, This is the target motion state array from time 1 to time K. This is an associative array from time 1 to time K. The target measurement noise covariance array from time 1 to time K; Under the optimal Bayesian framework, with Represent the measured values ​​and calculate the joint posterior probability density function. : ， In the formula Let be the posterior probability function; ， In the formula For conditional probability, Let i be the target motion state of the i-th target at time k. Let be the measurement noise covariance of the target i of the s-th sensor at time k; ， In the formula Let j be the j-th measurement value of the s-th sensor at time k. The measurement noise covariance matrix; Then the joint posterior probability density function Described as: In the formula To introduce a mark, For the set of all feasible joint multipath data association events, when , It is 1 if it is true, otherwise it is 0; Based on the factor graph model, reconstruct the joint posterior probability density function. : ， In the formula, MF represents the mean-field propagation part, and BP represents the back-propagation part; These are the nodes representing the target motion state variables in the factor graph model. For the measurement variable nodes in the factor graph model, For nodes in the target measurement noise covariance variable in the factor graph model, For the presence of probability variable nodes in the factor graph model, To mark the variable node: ， ， ， ， ； Based on the reconstructed joint posterior probability density function Calculation of beliefs: ， In the formula Represents the target motion state array. This indicates the existence of a probability array. This represents the target measurement noise covariance array. Represents an associative array; In the formula For the goal state belief, Represents nodes in a factor graph model. This represents the mean-field propagation portion MF. Indicates that by node arrive The amount of conversion at the middle node, There is a probabilistic belief in the existence of a goal. This represents the backpropagation portion of BP. To measure the belief in noise covariance, Beliefs are associated variables; break down : ； ， Combining the information dissemination rule update method, we get: ， ， This provides information about the i-th target state at time k-1. Let be the noise covariance information of the i-th target measurement received by the s-th sensor at time k. The associated variable information of the s-th sensor at time k; ； Further results were obtained: ， In the formula The function is a Gaussian distribution. Let be the target state transition matrix. This is the estimated motion state of the i-th target at time k-1. Let be the covariance matrix of the i-th target at time k-1. The process noise covariance matrix is... To estimate the measurement noise covariance considering ionospheric height error, Estimate the target related variables; Simplifying the above equation, we get: ， To integrate the measurement values, For measurement conversion function, To integrate measurement noise covariance, ； restate for: ， Measurement-level fusion is achieved by fusing measurements from different shipboard platforms: ， In the formula This is a fusion of measured values; The estimated value of the target's motion state and the target covariance matrix are calculated as follows: ， In the formula, E is the expected value. The method for determining the probability of the existence of the target is as follows: ， Regarding the probability of existence The variable domain is represented as ,get: ， in: for Node to Information between nodes; Simplifying, we get: ， As an intermediate variable: ， Therefore, the probability of the target's existence at time 1:K can be simplified as follows: ， The initial probability, ; The method for calculating the measurement noise covariance is as follows: ， Will The variable field is represented as ,but: ， ， ， ， Forgetting factor; The above equation can be rewritten as: ,get: ， ， In the formula For fusion measurement values A set; Using the inverse gamma distribution as the conjugate prior distribution of the Gaussian distribution variance, we obtain... The probability distribution function is derived from constitute: ， In the formula Indicates the inverse gamma distribution. As an intermediate variable, As an intermediate variable, The shape parameter of the inverse gamma distribution. is the scaling parameter of the inverse gamma distribution. Will Depend on Measured as In the formula For mathematical expectation: ， for transpose; Repeat the above process of solving for the target motion state, target existence probability, measurement noise covariance, and related variables until the results of two consecutive iterations are obtained. and The difference is less than the threshold , the current target motion state array The ultimate goal is to achieve a state of fusion.

2. The target fusion method based on mean-field confidence propagation under unknown time-varying parameters as described in claim 1, characterized in that, The method for solving correlation variables is as follows: Assuming that local multipath data associations are independent across different shipboard platforms, the confidence level of multipath data associations can be decomposed into: ， In the formula Let be the correlation variable of the s-th sensor at time k; against Representing the variable domain as , For the correlation variable of the dots, For trajectory-related variables; Divide the nodes in the factor graph model into MF regions. With BP region : For the MF region: ， ， in ; For the BP region: ， ， Inferring the estimated values ​​of the target related variables : ， in and for: 。

Images