Target fusion method based on average field belief propagation under unknown time-varying parameter condition

Abstract

The invention discloses a target fusion method based on average field belief propagation under an unknown time-varying parameter condition, and belongs to the technical field of radar target fusion tracking. The method aims at solving the problem that an existing target fusion algorithm cannot achieve target fusion under the condition of unknown time-varying parameters. Comprising the steps of calculating a marginal probability of a target existence probability based on a Markov law; setting an associated data set and determining constraint conditions that the associated data of each sensor comes from a target and clutter; calculating prior probability distribution; calculating a joint posterior probability density function based on the conditional probability; establishing a factor graph model based on average field-belief propagation, reconstructing a joint posterior probability density function and calculating a belief value; solving a target motion state, a target existence probability, a measurement noise covariance and a correlation variable; and iteratively solving until the difference value of the target motion states in two adjacent calculations is smaller than a preset threshold value, and taking the current target motion state as a final target fusion state. The method is used for target fusion under the unknown time-varying parameter condition.

Description

Technical Field

[0001] The invention relates to a target fusion method under unknown time-varying parameter conditions based on mean field belief propagation, and belongs to the technical field of radar target fusion tracking. Background Art

[0002] Radar target fusion tracking technology is a key technology in modern radar systems. Its accuracy and reliability directly affect subsequent decision-making and control. The information obtained by a single sensor often has problems such as noise interference and data loss, resulting in insufficient tracking accuracy. Through multi-source data fusion, the limitations of a single sensor are overcome, the probability of target detection is increased, the stability and continuity of target tracking are improved, and the target tracking accuracy is improved.

[0003] Tianfa ship-borne high-frequency radar combines the characteristics of sky wave over-the-horizon radar and ground wave over-the-horizon radar. It has the advantages of long sky wave action range, large coverage, anti-stealth, anti-anti-radiation missile and stable ground wave propagation. At the same time, since its radar transmitter is generally located in inland areas and the receiver is located on the ship, the ship can obtain electromagnetic support under radio silence conditions, which is of great tactical significance in ocean voyages.

[0004] Regarding the target fusion algorithm of the Tianfa ship-receiving high-frequency radar, most existing models perform target fusion under known parameter conditions. However, in actual detection situations, there are situations where the parameters are unknown, and the existing algorithms cannot achieve target fusion. Therefore, the existing methods cannot achieve target tracking under the condition of unknown time-varying parameters. Summary of the invention

[0005] Aiming at the problem that the existing target fusion algorithm cannot realize target fusion under the condition of unknown time-varying parameters, the present invention provides a target fusion method under the condition of unknown time-varying parameters based on mean field belief propagation.

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

[0007] Set the existence probability of target i at time k to e i,k , based on Markov's law, calculate the existence probability e of target i at time k+1 i,k+1 The marginal probability of

[0008] Assume that the associated data set of the multipath data of the s-th shipborne platform sensor at time k is Determine the constraints on the target and clutter from which the associated data for each sensor is derived;

[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-belief propagation principle, a factor graph model based on mean field-belief propagation is established;

[0011] According to the factor graph model, the joint posterior probability density function is reconstructed and the belief value is calculated; the target motion state, target existence probability, measurement noise covariance and associated variables are solved at the same time; 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 under unknown time-varying parameters based on mean field belief propagation of the present invention, the existence probability e of target i at time k+1 is i,k+1 The marginal probability is denoted as Pr:

[0013]

[0014] Where Pr(e i,k+1 =0) means e i,k+1 The marginal probability of

[0015] Where T i,e is the transition probability matrix:

[0016]

[0017] Where Pr(e i,k+1 =1|e i,k =1) indicates e i,k+1 Based on e i,k The conditional probability of .

[0018] According to the target fusion method under unknown time-varying parameters based on mean field belief propagation of the present invention, the number of shipborne platform sensors is set to The network path for each sensor to receive target data is , the target is x, associative array The target associated variable in is The clutter correlation variable is The constraints are established as:

[0019]

[0020] In the formula is the total number of target associated variables.

[0021] According to the target fusion method under unknown time-varying parameter conditions based on mean field belief propagation of the present invention, based on the existence probability e i,kand associative arrays Calculate the prior probability distribution between the target visibility state and the associated data

[0022] Where E k ={e i,k} i＝1,...,χ ,λ s is the clutter density of the s-th shipborne platform sensor, is the gate volume of the s-th shipborne platform sensor at time k, is the clutter point trace associated at time k, is the detection probability of the τth path of the sth shipborne platform sensor, is the target detection probability, ε is the target detection probability constant, is the target detection function,

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

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

[0025] Where K is the upper limit of time, X 1:K is the target motion state array from time 1 to time K, A 1:K is an associative array from time 1 to time K, R 1:K is the target measurement noise covariance array from time 1 to time K;

[0026] In the optimal Bayesian framework, Z 1:K Represents the measured value and calculates the joint posterior probability density function

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

[0028]

[0029] Where p(x i,k+1 |x i,k ) is the conditional probability, x i,k is the target motion state of the i-th target at time k, is the measurement noise covariance of target i of the s-th sensor at time k;

[0030]

[0031] In the formula is the jth measurement value of the sth sensor at time k, is the measurement noise covariance matrix;

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

[0033]

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

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

[0036]

[0037] Where MF represents the mean field propagation part, and BP represents the back propagation part;

[0038] is the target motion state variable node in the factor graph model, is the measurement variable node in the factor graph model, is the target measurement noise covariance variable node in the factor graph model, There are probability variable nodes in the factor graph model. To mark the variable node:

[0039]

[0040] According to the reconstruction of the joint posterior probability density function Calculate Beliefs:

[0041]

[0042] Where 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 association array;

[0043] Where b X is the target state belief, α represents the factor graph model node, represents the mean field propagation part MF, represents the amount of conversion from node α to the node in X, b E is the probability belief of the target existence, represents the back propagation part BP, b R is the measurement noise covariance belief, b A is the associated variable belief.

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

[0045]

[0046] Combined with the information propagation rule update method, we get:

[0047]

[0048] is the information of the i-th target state at time k-1, is the noise covariance information of the i-th target measurement received by the s-th sensor at time k, is the associated variable information of the sth sensor at time k;

[0049]

[0050] Further we get:

[0051]

[0052] Where N is the Gaussian distribution function, F k is the target state transfer matrix, is the estimated value of the motion state of the i-th target at time k-1, P i,k-1 is the i-th target covariance matrix at time k-1, Q k is the process noise covariance matrix, is the estimate of the measurement noise covariance taking into account the ionospheric height error, Estimate values ​​for target associated variables;

[0053] Simplifying the above formula, we get:

[0054]

[0055] is the fusion measurement value, h k is the measurement transfer function, is the fused measurement noise covariance,

[0056]

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

[0058]

[0059] Fusion of measurements from different shipborne platforms to achieve measurement-level fusion:

[0060]

[0061] Where z i,k is the measurement value fusion value;

[0062] The target motion state estimate and target covariance matrix are calculated:

[0063]

[0064] Where E is the mathematical expectation.

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

[0066] Verification experiments show that under all detection probabilities, the track maintenance length of the method proposed in the present invention is basically unchanged compared with the traditional MF-BP method, and the distance and speed accuracy can be improved by more than 20%. The traditional MF-BP method realizes target association and state estimation by iteration in the factor graph, and can obtain the ionospheric height value at the same time. However, under the background of the Tianfa ship-receiver high-frequency radar, due to the influence of sea clutter and the movement of the ship platform, the target echo signal-to-clutter ratio is unstable. At the same time, this error is coupled with the ionospheric error, which makes it difficult for the traditional MF-BP method to directly solve the ionospheric height value, affecting target prediction, association and state estimation. The MF-VB-BP method proposed in the present invention can effectively consider the unknown parameters in this coupling situation and improve the accuracy of target state estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flow chart of the target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to the present invention;

[0068] Figure 2 It is a schematic diagram of the MF-BP tracking results of 100 Monte Carlo results in the verification experiment; in the figure, the horizontal axis X represents the length of the motion area set in the experiment in the X-axis direction, the vertical axis Y represents the length of the motion area set in the experiment 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 3It is a schematic diagram of the MP-VR-OTHRs tracking results of 100 Monte Carlo results in the verification experiment; in the figure, MP-VR-OTHRs represents the tracking method of the present invention under the sky-transmitting-ship-receiving system;

[0070] Figure 4 It is a schematic diagram of RMSE of non-crossing target distance 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, and MF-BP T1 represents the tracking result of target 1 under the tracking method of the present invention; T1 to T4 represent targets 1 to 4;

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

[0072] Figure 6 is a schematic diagram of the cross-target distance RMSE; T5 represents target 5, and T6 represents target 6;

[0073] Figure 7 It is a schematic diagram of the cross-target speed RMSE;

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

[0075] Fig. 9 It is a schematic diagram of the average root mean square error ARMSE of the speed of five targets;

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

[0077] Fig.11 This is a schematic diagram of the factor graph model based on mean field-belief propagation; in the figure, η is equivalent to In the picture Indicates a target-related variable with a target of 0 and a measurement of 1. Indicates that the target is 0 and the measurement is The target associated variable, The target is χ and the path is Measured as The target associated variable. DETAILED DESCRIPTION

[0078] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0079] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0080] The present invention will be further described below in conjunction with the accompanying drawings, but is not intended to be a limitation of the present invention.

[0081] Specific implementation method 1. Combination Figure 1 As shown, the present invention provides a target fusion method under unknown time-varying parameter conditions based on mean field belief propagation, comprising:

[0082] Set the existence probability of target i at time k to e i,k , based on Markov's law, calculate the existence probability e of target i at time k+1 i,k+1 The marginal probability of

[0083] Assume that the associated data set of the multipath data of the s-th shipborne platform sensor at time k is Determine the constraints on the target and clutter from which the associated data for each sensor is derived;

[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-belief propagation principle, a factor graph model based on mean field-belief propagation is established;

[0086] According to the factor graph model, the joint posterior probability density function is reconstructed and the belief value is calculated; the target motion state, target existence probability, measurement noise covariance and associated variables are solved at the same time; 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] In this implementation, the measurement model and the target and ship motion models are first established based on the satellite-send-ship-receive radar system. Each shipborne platform in the network sends the measurement value to the fusion center, and the fusion center processes all the measurements, that is, measurement-level fusion is performed. i,k When it is 1, target i exists, e i,kWhen it is 0, target i does not exist, and its marginal probability conforms to Markov's law.

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

[0089]

[0090] Where Pr(e i,k+1 =0) means e i,k+1 The marginal probability of

[0091] Where T i,e is the transition probability matrix:

[0092]

[0093] Where Pr(e i,k+1 =1|e i,k =1) indicates e i,k+1 Based on e i,k The conditional probability of .

[0094] For the convenience of discussion, the ionosphere is divided into E layer and F layer, and the maximum number of paths is 2. represents an associative array. Assuming that each shipborne platform operates independently, the multipath measurements of different shipborne platforms are locally and individually associated with the target. It is represented by the measurement of the sth sensor at time k. When it is 1, it means the τth path from target i is measured at j. When the representative measurement j comes from clutter, two assumptions are made about the correlation:

[0095] 1) At each moment, a measurement comes from the target or from clutter;

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

[0097] Set the number of onboard platform sensors to The network path for each sensor to receive target data is , the target is x, associative array The target associated variable in is The clutter correlation variable is The constraints are established as:

[0098]

[0099] In the formula is the total number of target associated variables.

[0100] Introducing logo is the set of all feasible joint multipath data association events, when The redundant variable is 1 when , 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 the associated data

[0102]

[0103] Where E k ={e i,k} i＝1,…,χ ,λ s is the clutter density of the s-th shipborne platform sensor, is the gate volume of the s-th shipborne platform sensor at time k, is the clutter point trace associated at time k, is the detection probability of the τth path of the sth shipborne platform sensor, is the target detection probability, ε is the target detection probability constant, is the target detection function,

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

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

[0106] Where K is the upper limit of time, X 1:K is the target motion state array from time 1 to time K, A 1:K is an associative array from time 1 to time K, R 1:K is the target measurement noise covariance array from time 1 to time K;

[0107] In the optimal Bayesian framework, Z 1:K Represents the measured value and calculates the joint posterior probability density function

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

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

[0110]

[0111] Where p(x i,k+1 |x i,k ) is the conditional probability, x i,k is the target motion state of the i-th target at time k, is the measurement noise covariance of target i of the s-th sensor at time k;

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

[0113]

[0114] In the formula is the jth measurement value of the sth sensor at time k, is the measurement noise covariance matrix;

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

[0116]

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

[0118] Establish a factor graph model based on mean field-belief propagation, A, I, N represent sets, the cardinality of set I is represented by |I|, if i∈I, it is written as I\{i}, with Ι I Indicates the relationship between i and I, if i∈I then Ι I is 1, X represents a discrete random variable with a finite number of realizations, and its probability mass function p X , with x representing a variable in X, and x=(x|i∈I) T vector, In addition to X i All possible X, with p X The probability mass function representing the vector X can be expressed as;

[0119]

[0120] in at the same time It is not a general assumption Then N(a) is the set of all variable nodes a∈A connected to a factor node, N(i) represents the set of all factor nodes i∈I connected to the variable node, and by For the BP part, The MF part. Define region R to include all A R ∈A, given a count c for each region R R , for a group It can be expressed as:

[0121]

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

[0123] 1) MF area:

[0124] 2) Small area:

[0125] 3) Large area:

[0126] Then the entire area can be expressed as:

[0127]

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

[0129]

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

[0131]

[0132] And the marginalization constraints:

[0133]

[0134] The constraints are restricted by Lagrangian, then:

[0135]

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

[0137]

[0138] The belief update can be expressed as:

[0139]

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

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

[0142] Where MF represents the mean field propagation part, and BP represents the back propagation part;

[0143] is the target motion state variable node in the factor graph model, is the measurement variable node in the factor graph model, is the target measurement noise covariance variable node in the factor graph model, There are probability variable nodes in the factor graph model. To mark the node variable point:

[0144]

[0145] as well as in and is a pair of redundant variables, so as to facilitate the derivation of belief propagation. According to the factor graph constructed by the present invention, it can be restated as

[0146] According to the reconstruction of the joint posterior probability density function Calculate Beliefs:

[0147]

[0148] Where 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 association array;

[0149] Where b X is the target state belief, α represents the factor graph model node, represents the mean field propagation part MF, represents the amount of conversion from node α to the node in X, b Eis the probability belief of the target existence, represents the back propagation part BP, b R is the measurement noise covariance belief, b A is the associated variable belief.

[0150] Going further, the following iterative calculation of the fusion state is performed:

[0151] Solve the target state b X (X 1:K ), the target motion state X can be independently moved by each target, and each moment conforms to the first-order Markov, and the motion state belief of all targets is decomposed as follows:

[0152] Decomposition X (X 1:K ):

[0153]

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

[0155]

[0156] Combined with the information propagation rule update method, we get:

[0157]

[0158] is the information of the i-th target state at time k-1, is the noise covariance information of the i-th target measurement received by the s-th sensor at time k, is the associated variable information of the sth sensor at time k;

[0159]

[0160] Further we get:

[0161]

[0162] Where N is the Gaussian distribution function, F k is the target state transfer matrix, is the estimated value of the motion state of the i-th target at time k-1, P i,k-1 is the i-th target covariance matrix at time k-1, Q k is the process noise covariance matrix, is the estimate of the measurement noise covariance taking into account the ionospheric height error, Estimate values ​​for target associated variables;

[0163] It should be noted that is the estimated value of the measurement noise covariance taking into account the ionospheric height error. Simplifying the above formula, we get:

[0164]

[0165] is the fusion measurement value, h k is the measurement transfer function, is the fusion measurement noise covariance, then we get:

[0166]

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

[0168]

[0169] Fusion of measurements from different shipborne platforms to achieve measurement-level fusion:

[0170]

[0171] Where z i,k is the measurement value fusion value;

[0172] The target motion state estimate and target covariance matrix are calculated:

[0173]

[0174] Where E is the mathematical expectation.

[0175] The method to solve the probability of target existence is:

[0176] Solve for the target existence probability b E (E 1:K ), similar to the target motion state X, the target existence probability is also independent among targets and conforms to the first-order Markov chain;

[0177]

[0178] For the existence probability e i,k , the variable domain is represented by 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 For the intermediate variable:

[0186]

[0187] Then the target existence probability at time 1:K is briefly described as:

[0188]

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

[0190] According to the above formula, the probability of target existence conforms to the hidden Markov model, where π i,e is the initial value, and the observed value is ξ k (e i,k ), the forward-backward algorithm can be used to solve the probability of target existence and thus realize track management. At the same time, 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 to affect the target detection probability through the target existence probability.

[0191] The measurement noise covariance is calculated as:

[0192] Solve for the measurement noise covariance belief b R (R 1:K ), the target measurement noise R after the ionospheric height is introduced is different due to the target echo signal-to-noise ratio and the target location. Assuming that the target measurement noise covariance R is independent of each other:

[0193]

[0194] Will The variable domain is represented as Then the belief can be calculated as:

[0195]

[0196] Integrating the above formula, we get:

[0197]

[0198] ρ is the forgetting factor;

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

[0200] get:

[0201] The belief is calculated as:

[0202]

[0203] In the formula is the fusion measurement value A collection of;

[0204] According to the above formula, it can be seen In line with the given and The Gaussian distribution of It is difficult to solve directly, so the inverse gamma distribution is used as the conjugate prior distribution of the Gaussian distribution variance, and we get The probability distribution function of constitute:

[0205]

[0206] Where Inv-Gamma represents the inverse gamma distribution, is the intermediate variable, is the intermediate variable, δ is the shape parameter of the inverse gamma distribution, g is the scale parameter of the inverse gamma distribution,

[0207] Will Depend on Measured as Where E is the mathematical expectation:

[0208]

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

[0210] The method to solve for the associated variable is:

[0211] Assuming that the local multipath data association is independent under different shipborne platforms, the confidence of multipath data association is decomposed into:

[0212]

[0213] In the formula is the associated variable of the sth sensor at time k;

[0214] against The variable domain is represented as

[0215] is the point trace association variable, is the track-related variable;

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

[0217]

[0218] in For the BP area, according to the two situations that each path has only two conditions: generating measurement or not generating measurement, and Constraints are made, so it can be expressed as:

[0219]

[0220] Infer the estimated value of the target associated variable based on the above belief

[0221]

[0222] in and for:

[0223]

[0224] Repeat the above process of solving the target motion state, target existence probability, measurement noise covariance and associated variables until E is calculated 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 used as the final target fusion state.

[0225] Verification experiment:

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

[0227] Single target tracking results, such as Figure 2 and Figure 3 As shown in the figure, when the target is a non-intersecting target, the RMSE simulation results of the target's speed and distance are as follows: Figure 4 and Figure 5 As shown in the figure, when the target is a cross target, the RMSE simulation results of the target's speed and distance are as follows: Figure 6 and Figure 7 100 Monte Carlo simulations were performed under different detection probabilities. The ARMSE results and track maintenance length results of the five targets after convergence are shown in Figures 8 to 10 shown.

[0228] contrast Figures 8 to 10The error results of the two methods show that under all detection probabilities, the track maintenance length of the method of the present invention remains basically unchanged compared with the MF-BP method, and the distance and speed accuracy can be improved by more than 20%. The MF-BP method realizes target association and state estimation by iteration in the factor graph, and can obtain the ionospheric height value at the same time. However, under the background of the high-frequency radar of the Tianfa ship, due to the influence of sea clutter and the movement of the ship platform, the signal-to-clutter ratio of the target echo is unstable. At the same time, this error is coupled with the ionospheric error, which makes it difficult for the MF-BP method to directly solve the ionospheric height value, affecting the target prediction, association and state estimation. The method of the present invention-the MF-VB-BP method can effectively consider the unknown parameters in this coupling situation and improve the accuracy of target state estimation.

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

[0230] 1) According to the sky-send-ship-receive radar system, the measurement model and the target and ship motion model are established. Each shipborne platform in the network sends the measurement value to the fusion center, which processes all the measurements. The existence probability of target i 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 the target can be obtained through formula (1) and formula (2);

[0231] 2) The ionosphere is divided into E layer and F layer, then the maximum number of paths is 2, represents an associative array. Assuming that each shipborne platform operates independently, the multipath measurements of different shipborne platforms are locally and individually associated with the target. Two assumptions are made for the association: 1) at each moment, a measurement comes from the target or from the clutter; 2) each path to each target produces at most one measurement. The association variables can be constrained by formula (3);

[0232] 3) The prior probability distribution between the target visibility state and the multipath data association variable is obtained through formula (4);

[0233] 4) Further considering the coupling of 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, express the probability mass function of vector X by formula (8), the entire region can be expressed by formula (10), the free energy of the entire region can be expressed by formula (11), and the belief value can be solved by formula (16);

[0235] 6) The factor graph constructed according to the present invention can re-describe 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 through formula (19), and for factor node x i,k , the information can be calculated by formula (20), the measurement noise covariance estimate considering the ionospheric height error can be obtained by formula (25), the measurements from different shipborne platforms are fused again to achieve measurement level fusion, and the target state and error covariance can be obtained by formula (29);

[0237] 8) Decompose all target existence probabilities using formula (30) for factor node e i,k , information can be calculated by formula (31), and formula (35) can be used to obtain 1: the probability of target existence at time K;

[0238] 9) After the target measurement noise R is introduced into the ionospheric height, assuming that the target measurement noise covariance R is independent of each other, the measurement noise covariance can be decomposed by formula (36) to obtain the factor node The information can be calculated by formula (37), and the measurement noise covariance can be obtained by formula (43). The inverse gamma distribution is taken as the conjugate prior distribution of the Gaussian distribution variance. At this time, the probability distribution function of the measurement noise covariance is given by The composition can be obtained by formula (45)

[0239] 10) Assuming that the local multipath data associations are independent under different motion platforms, the confidence of the multipath data association can be decomposed by formula (46) for the factor nodes The information node can be divided into MF area and BP area. The MF area can be obtained by formula (47) and formula (48), the BP area can be obtained by formula (49) and formula (50), and the associated variable can be obtained by formula (51);

[0240] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A target fusion method under unknown time-varying parameters based on mean field belief propagation, characterized in that: include: Set the existence probability of target i at time k to e i,k , based on Markov's law, calculate the existence probability e of target i at time k+1 i,k+1 The marginal probability of Assume that the associated data set of the multipath data of the s-th shipborne platform sensor at time k is Determine the constraints on the target and clutter from which the associated data for each sensor is derived; 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; Based on the mean field-belief propagation principle, a factor graph model based on mean field-belief propagation is established; According to the factor graph model, the joint posterior probability density function is reconstructed and the belief value is calculated; the target motion state, target existence probability, measurement noise covariance and associated variables are solved at the same time; 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.

2. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 1 is characterized in that: The existence probability of target i at time k+1 is e i,k+1 The marginal probability is denoted as Pr: Where Pr(e i,k+1 =0) means e i,k+1 The marginal probability of Where T i,e is the transition probability matrix: Where Pr(e i,k+1 =1|e i,k =1) indicates e i,k+1 Based on e i,k The conditional probability of .

3. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 2 is characterized in that: Set the number of onboard platform sensors to The network path for each sensor to receive target data is , the target is x, associative array The target associated variable in is The clutter correlation variable is The constraints are established as: In the formula is the total number of target associated variables.

4. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 2 is characterized in that: 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 Where E k ={e i,k } i＝1,...,χ ,λ s is the clutter density of the s-th shipborne platform sensor, is the gate volume of the s-th shipborne platform sensor at time k, is the clutter point trace associated at time k, is the detection probability of the τth path of the sth shipborne platform sensor, is the target detection probability, ε is the target detection probability constant, is the target detection function, 5. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 4 is characterized in that: Define the conditional probability Θ 1:K for: I 1:K ={E 1:K ,X 1:K ,A 1:K ,R 1:K }, Where K is the upper limit of time, X 1:K is the target motion state array from time 1 to time K, A 1:K is an associative array from time 1 to time K, R 1:K is the target measurement noise covariance array from time 1 to time K; In the optimal Bayesian framework, Z 1:K Represents the measured value and calculates the joint posterior probability density function Where p(Θ 1:K |Z 1:K ) is the posterior probability function; Where p(x i,k+1 |x i,k ) is the conditional probability, x i,k is the target motion state of the i-th target at time k, is the measurement noise covariance of target i of the s-th sensor at time k; In the formula is the jth measurement value of the sth sensor at time k, is the measurement noise covariance matrix; Then the joint posterior probability density function is Described as: In the formula To introduce the logo, is the set of all feasible joint multipath data association events, when is 1 if the value is true, otherwise it is 0.

6. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 5 is characterized in that: According to the factor graph model, the joint posterior probability density function is reconstructed Where MF represents the mean field propagation part, and BP represents the back propagation part; is the target motion state variable node in the factor graph model, is the measurement variable node in the factor graph model, is the target measurement noise covariance variable node in the factor graph model, There are probability variable nodes in the factor graph model. To mark the variable node: According to the reconstruction of the joint posterior probability density function Calculate Beliefs: Where 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 association array; Where b X is the target state belief, α represents the factor graph model node, represents the mean field propagation part MF, represents the amount of conversion from node α to the node in X, b E is the probability belief of the target existence, represents the back propagation part BP, b R is the measurement noise covariance belief, b A is the associated variable belief.

7. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 6 is characterized in that: Decomposition X (X 1:K ): Combined with the information propagation rule update method, we get: is the information of the i-th target state at time k-1, is the noise covariance information of the i-th target measurement received by the s-th sensor at time k, is the associated variable information of the sth sensor at time k; Further we get: Where N is the Gaussian distribution function, F k is the target state transfer matrix, is the estimated value of the motion state of the i-th target at time k-1, P i,k-1 is the i-th target covariance matrix at time k-1, Q k is the process noise covariance matrix, is the estimate of the measurement noise covariance taking into account the ionospheric height error, Estimate values ​​for target associated variables; Simplifying the above formula, we get: is the fusion measurement value, h k is the measurement transfer function, is the fused measurement noise covariance, Restatement b X (x i,k )for: Fusion of measurements from different shipborne platforms to achieve measurement-level fusion: Where z i,k is the measurement value fusion value; The target motion state estimate and target covariance matrix are calculated: Where E is the mathematical expectation.

8. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 7, characterized in that: The method to solve the probability of target existence is: For the existence probability e i,k , the variable domain is represented by get: in: for e i,k-1 Node to Information between nodes; Simplifying, we get: b E (e i,k )=T i,e b E (e i,k -1)ξ k (e i,k ), ξ k For the intermediate variable: Then the target existence probability at time 1:K is briefly described as: π i,e is the initial probability, π i,e =[Pr(e i,k =1), Pr(e i,k =0)].

9. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 8, characterized in that: The measurement noise covariance is calculated as: Will The variable domain is represented as but: ρ is the forgetting factor; Rewrite the above formula as follows: get: In the formula is the fusion measurement value A collection of; Using the inverse gamma distribution as the conjugate prior distribution of the Gaussian distribution variance, we get The probability distribution function of constitute: Inv-Gamma represents the inverse gamma distribution. is the intermediate variable, is the intermediate variable, δ is the shape parameter of the inverse gamma distribution, g is the scale parameter of the inverse gamma distribution, Will Depend on Measured as Where E is the mathematical expectation: h' k h k The transpose of .

10. The target fusion method under unknown time-varying parameter conditions based on mean field belief propagation according to claim 9, characterized in that: The method to solve for the associated variable is: Assuming that the local multipath data association is independent under different shipborne platforms, the confidence of multipath data association is decomposed into: In the formula is the associated variable of the sth sensor at time k; against Denote the variable domain as is the point trace association variable, is the track-related variable; Divide the nodes in the factor graph model into MF regions With BP region For MF area: in For BP area: Infer target associated variable estimates in and for: Repeat the above process of solving the target motion state, target existence probability, measurement noise covariance and associated variables until E is calculated 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 used as the final target fusion state.

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