Distributed tracking method for ballistic missile free section multi-radar networking based on diffusion maximum correlation entropy

Abstract

The invention relates to the field of multi-radar networking ballistic missile free section tracking, in particular to a diffusion maximum correlation entropy-based ballistic missile free section multi-radar networking distributed tracking method, which comprises a local estimation stage and a diffusion fusion stage, in the local estimation stage, a node and a neighbor node exchange forecast estimation to obtain a consistent item for optimizing the local estimation, and the diffusion fusion stage is used for optimizing the local estimation; in order to avoid calculation of cross covariance, a reasonable error variance upper bound is constructed, a gain matrix and a local estimation and diffusion fusion stage are deduced based on a maximum correlation entropy criterion, nodes and neighbor nodes exchange local estimation, fusion is carried out by adopting a covariance cross technology and a diffusion fusion strategy, and a fusion result is obtained. According to the method, the transmission of relevant information and original measurement information between computational nodes is avoided, the advantages of consistency and diffusion are considered, and the calculation of a Jacobian matrix is avoided by adopting a volumetric criterion and a statistical linearization method, so that the method is more accurate and stable.

Description

Technical Field

[0001] The invention relates to the field of missile interception, in particular to a distributed tracking method of a ballistic missile free-segment multi-radar network based on diffusion maximum correlated entropy. Background Art

[0002] With the development of integrated electronic technology, the tracking technology of ballistic missiles is constantly developing towards multi-radar intelligence and networking. Compared with single radar tracking technology, the multi-radar system makes full use of the advantages of each radar, maximizes the utilization of information resources, and greatly improves the tracking and detection capabilities of the radar. Therefore, how to design a reasonable fusion method to obtain accurate tracking results is the focus of research. Ballistic missiles are important military weapons in modern warfare. They have the characteristics of long range, high accuracy, high speed and high lethality. As the performance of ballistic missiles continues to improve, they have also received continuous attention from various countries. According to the characteristics of their trajectory, the trajectory can be divided into active segment, free segment and reentry segment. The flight time of the active segment and the reentry segment is short and difficult to track, while the free segment accounts for about 80% of the trajectory. The trajectory is fixed and can be tracked and predicted. It is the main combat trajectory.

[0003] For the free section of ballistic missiles, its state equation and measurement equation are both nonlinear, and due to interference such as target position reflection or changes in the environment, radar detection of targets will have obvious deviations, noise no longer satisfies Gaussian distribution, and non-Gaussian flicker noise will appear. The essence of the trajectory tracking problem is a nonlinear, non-Gaussian state estimation problem. Designing a reasonable tracking method is the key to ensuring tracking performance. Usually, nonlinear estimation methods include extended Kalman filtering (EKF), unscented Kalman filtering (UKF) and cubature Kalman filtering (CKF). Compared with other algorithms, CKF does not need to calculate the Jacobian matrix, and can obtain higher accuracy with fewer sampling points, and it has more advantages in stability and calculation amount. The above-mentioned nonlinear estimation method is obtained under the Gaussian assumption, so it is necessary to design a more reasonable nonlinear non-Gaussian estimation method to accurately track the trajectory. Based on this, the present invention proposes a distributed tracking method for multi-radar networking of free section of ballistic missiles based on diffusion maximum correlated entropy. Summary of the invention

[0004] The purpose of the present invention is to provide a distributed tracking method for a ballistic missile free-stage multi-radar network based on diffusion maximum correlated entropy to solve the problems raised in the above-mentioned background technology.

[0005] To achieve the above purpose, a distributed tracking method for a ballistic missile free-stage multi-radar network based on diffusion maximum correlation entropy includes the following steps:

[0006] Step S1, local estimation, specifically calculating the prediction estimate and error covariance

[0007]

[0008] in

[0009]

[0010] in, represents the state estimation error covariance matrix at time k-1; Reason The matrix obtained by Choleskey decomposition; is the intermediate variable obtained by estimating the state at the volume point and at time k-1; represents the intermediate variable obtained by the volume point and the forecast estimate at time k, and n represents the dimension of the state vector; Represents the predicted estimated value after fusion; express Substitute into the nonlinear function f(·) for propagation; is the forecast estimate of the ith radar; is the predicted estimate of the jth radar; It is to express the intermediate variables defined for convenience; It is an intermediate variable defined for convenience; formula T represents the matrix transposition operation; Q k-1 The error variance matrix representing the process noise; yes -1 power (inverse); is an intermediate variable, which is the analytical expression of formula 21;

[0011] Computational Measurement Prediction Estimation

[0012]

[0013] in, is the new volume point obtained after the volume point is transferred through the measurement equation; h(·) is the known nonlinear transfer function; represents the forecast estimate of the measurement of radar i; Represents the error cross-covariance matrix between state and measurement; represents the error covariance matrix of the measurement; represents the measurement nominal noise variance of radar i;

[0014] Statistical Linearization

[0015]

[0016] in, represents the pseudo measurement matrix; Represents the inverse matrix of the prediction error covariance matrix, and the superscript -1 indicates the matrix inversion operation; represents the pseudo-measurement noise variance matrix obtained by statistical linearization;

[0017] Compute local state estimates and error covariance

[0018]

[0019] in, It is a variable defined for the convenience of expression; Represents the measurement information of radar i; represents the inverse matrix of the pseudo-measurement noise variance matrix obtained by statistical linearization, and the superscript -1 represents the matrix inversion operation; represents the gain matrix; represents the estimated value of radar i at time k; for The estimated error covariance matrix of n Represents the n-dimensional identity matrix;

[0020] Step S2, diffusion fusion,

[0021]

[0022] Preferably, the step S1 uses a filter designed based on the maximum correlation entropy criterion to perform local estimation calculation.

[0023] Preferably, the upper bound of the error variance is specified in the calculation of the cross-covariance matrix in step S1.

[0024] Preferably, the diffusion fusion in step S2 is performed by using covariance crossover technology and diffusion fusion strategy.

[0025] Preferably, the step S2 adopts volume criterion and statistical linearization method to perform diffusion fusion process.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] In the local estimation stage of the present invention, the node exchanges forecast estimates with neighboring nodes to obtain consistent terms for optimizing local estimates. In order to avoid the calculation of mutual covariance, a reasonable upper bound of error variance is constructed, and the gain matrix and local estimates are derived based on the maximum correlation entropy criterion. In the diffusion fusion stage, the node exchanges local estimates with neighboring nodes, and the covariance crossover technology and diffusion fusion strategy are used for fusion, which avoids the transmission of relevant information and original measurement information between computing nodes, takes into account the advantages of consistency and diffusion, and adopts the volume criterion and statistical linearization method to avoid the calculation of Jacobian matrix, which is more accurate and stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a structural diagram of the present invention;

[0029] Figure 2 A topological diagram of the radar network of the present invention;

[0030] Figure 3 The actual trajectory and estimated tracking trajectory diagram of the present invention;

[0031] Figure 4 ARMSE diagram of the present invention's position;

[0032] Figure 5 It is the ARMSE diagram of the speed of the present invention. DETAILED DESCRIPTION

[0033] 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 implementation regulations described 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.

[0034] Example

[0035] See also Figure 1 , the figure shows a preferred embodiment of the present invention, a distributed tracking method for a ballistic missile free-stage multi-radar network based on diffuse maximum correlated entropy, including local estimation and diffuse fusion, wherein the local estimation includes calculating predicted estimation and error covariance, calculating measured predicted estimation, statistical linearization and calculating local state estimation and error covariance.

[0036] Furthermore, in the free segment of the ballistic missile, only the gravitational force on the target is considered, and the target state equation is established in the geocentric inertial system, assuming that the influence of the earth's revolution is not considered; the gravitational perturbations of other celestial bodies are not considered; and the earth model adopts the standard ellipsoid model.

[0037] Select the position and velocity of the target as the state vector,

[0038]

[0039] Then the state equation is

[0040]

[0041] Among them, x, y, and z represent the position coordinates of the three coordinate axes of the target respectively. is the distance between the center of the earth and the target; R e is the equatorial radius of the Earth; J 2 is the coefficient of the second-order principal spherical harmonics; ωx ,ω y ,ω z is the measured noise, v x 、v y 、v z Represents the speed of the three coordinate axes of the target, μ=3.98604418×10 14 m 3 / s 2 represents the earth's gravitational constant; it can be discretized using the Euler formula or the Runge-Kutta pair (2) to obtain

[0042] x k =f(x k-1 )+ω k-1 (3)

[0043] x k represents the state quantity at time k, f(x k-1 ) represents the nonlinear transfer equation of the missile's state vector over time, ω k-1 Gaussian white noise with zero mean is used to represent the deviation introduced by modeling.

[0044] In this embodiment, a ground-based early warning radar is used to track the target, and the measurements include the slant distance ρ from the radar station to the target, the elevation angle γ and the azimuth angle η of the target, that is,

[0045]

[0046] Then the measurement equation is

[0047]

[0048] Among them, x L Indicates the x-direction position of the radar system; y L represents the position in the y direction of the radar system; z L represents the position in the z direction of the radar system; C is the transformation matrix from the geocentric system to the radar system; [x r y r z r ] T is the coordinate of the radar in the geocentric system, v is the measurement noise, and v is the non-Gaussian flicker noise, and its probability density function is expressed as

[0049] p(v)=(1-α)p G1 +αp G2 (7)

[0050] Where α is the flicker probability, and are two types of zero-mean Gaussian distribution noise, δ 1 <δ 2 .

[0051] Furthermore, considering a multi-radar network system, models (3) and (5) can be equivalent to the following expression:

[0052] x k =f(x k-1 )+ω k-1 (8)

[0053]

[0054] in is the missile's state vector, is the measurement information of the ith radar, f(·) and h(·) are known nonlinear transfer functions, ω k-1 and are system noise and radar measurement noise respectively, which are non-Gaussian, and their nominal noise variance matrices are Q k-1 and

[0055] The communication topology between radar networks is represented by an undirected connected graph G = (V, E, W), where V = {1, 2, ..., N}, represents the set of all links, W = [λ ij ] n×n is the weighted adjacency matrix representing the communication between two nodes, N represents the number of radars, n represents the dimension of the state vector, and m represents the dimension of the measurement vector; when λ ij > 0, indicating that nodes i and j communicate with each other and are neighbors, otherwise ij = 0, they are independent of each other, and the neighboring nodes of sensor i can be expressed as N i ={j∈V:(i,j)∈E},d i Indicates that sensor i is in N i The number of adjacent nodes in .

[0056] The structure of the present invention is as follows Figure 1 As shown, it includes two parts: local estimation and diffusion fusion. First, the node exchanges forecast estimates with its neighboring nodes, and uses a filter designed based on the maximum correlation entropy criterion to obtain local estimates. Then, the node exchanges local estimates with its neighboring nodes for diffusion fusion, thereby obtaining consistent high-precision estimates.

[0057] Furthermore, the local estimation process, for radar node i, the local filter can be expressed as the following two steps:

[0058]

[0059] Where ε is the uniform gain factor.

[0060] calculate Error

[0061]

[0062] make So there is

[0063]

[0064]

[0065] in, Represents the prediction estimation error covariance matrix at time k after fusion; The index s is used to represent the neighbor node set N of radar i. i The elements in the formula are s∈N i represents the s radars in the neighbor set of radar i; The index s is used to represent the neighbor node set N of radar i. j The elements in the formula are l∈N i represents the l radar in the neighbor set of radar i;

[0066] From (14), we can see that the calculation A large number of cross-covariance matrices need to be calculated, so a conservative upper bound will be given to avoid the calculation of cross-covariance.

[0067]

[0068] make And available

[0069]

[0070] in, It represents a number between 0 and 1, that is, express The reciprocal of (-1 power).

[0071] Pick

[0072]

[0073] beg Available

[0074]

[0075] in, for to the power of -2; Express about Seeking guidance, To find the derivative operation;

[0076] From (18), we can get

[0077]

[0078] is an intermediate variable; It means the mean The covariance is Gaussian distribution of dx k-1 Indicates x k-1 Find the integral;

[0079] Formula (21) is approximated by the volume rule: Next, the gain matrix is ​​derived based on the maximum correlation entropy criterion and the cost function is defined:

[0080]

[0081] in, is the cost function defined; G σ (·) is the Gaussian kernel function, represents the inverse matrix of the prediction covariance matrix; Represents the inverse matrix of the measurement noise variance matrix. The superscript -1 indicates the matrix inversion operation.

[0082] Statistical linearization criterion

[0083]

[0084] in

[0085]

[0086] Represents the error cross-covariance matrix between state and measurement; represents the pseudo noise obtained by statistical linearization; represents the pseudo noise variance obtained by statistical linearization; represents the error cross-covariance matrix of the measurements; represents the pseudo measurement matrix;

[0087] Substituting (23)-(26) into (22), we can obtain

[0088]

[0089] Taking the derivative of (27) and setting it to 0, we can obtain

[0090]

[0091] Pick (28) can be organized as

[0092]

[0093] so

[0094]

[0095] Fixed point iteration have so

[0096]

[0097] According to the matrix inversion formula, (32) has the following expression:

[0098]

[0099] in, is the estimated state value of radar i at time k; for The error of is the state estimation error covariance matrix of radar i at time k;

[0100] Pick

[0101]

[0102] Furthermore, in the diffusion fusion process, for the i-th radar node, the fused estimate and covariance are:

[0103]

[0104] In this embodiment, a simulation is performed on the method provided by the present invention, and the simulation parameters are sampling time T=0.1s, system noise Q=diag(10,10,10,2,2,2), and radar measurement noise R=diag[100,(1 / 57.3) 2 ×10 -6 ,(1 / 57.3) 2 ×10 -6 ], the initial position error is 100m, and the initial velocity error is 20m / s. R = 6371000m is the radius of the earth's equator. Four radars are selected to form a multi-radar system to track the trajectory. 1 =R, R 2 =0.9R 1 , R 3 =0.8R 1 and R 4 =0.7R 1 The radar measurement noise is flicker noise, that is

[0105]

[0106] The position of the radar is expressed in terms of altitude and azimuth: p =Rcosηcosγ,y p =Rcosηsinγ and z p =Rcosη. The positions of the radars are: γ 1 =130,η 1 =30,γ 2 =132,η 2 =30,γ 3 =132,η 3 =28,γ 4 =130,η 4 =28, the radar topology is as follows Figure 2 shown.

[0107] The missile state equation is solved by numerical integration method to obtain the standard flight trajectory of the missile free segment, which is used to verify the proposed tracking accuracy. The free segment flies for 330 seconds. The standard ballistic flight trajectory, the real trajectory and the tracking estimated trajectory obtained by the tracking algorithm of the present invention are shown in Figure 2. Figure 3 As shown, it can be seen from the figure that the present invention has good tracking performance.

[0108] The cumulative root mean square error (ARMSE) and mean root mean square error (MRMSE) of the position are used as performance indicators and are defined as

[0109]

[0110] Where M and are the Monte Carlo number and running time respectively. The definitions of ARMSE and MRMSE for speed are similar.

[0111] In order to verify the superiority of the present invention, the tracking accuracy of radar 1 using the maximum correlation entropy UKF (MCUKF) algorithm is compared with the tracking accuracy of the present invention (4 radars in a network), and the ARMSE of its position and speed are as follows: Figure 4 , as shown in Figure 5, it can be seen from the figure that the distributed fusion tracking scheme of the present invention makes the tracking accuracy of each radar tend to be consistent due to the information fusion between radar nodes, and is significantly better than the tracking accuracy of a single radar. The MRMSE of position and velocity are shown in Table 1. It can be seen from Table 1 that compared with the single radar system, the tracking accuracy of the present invention is improved by about 50%.

[0112] Table 1MRMSE pos and MRMSE vel

[0113]

[0114] The above content is a further detailed description of the present invention in combination with specific implementation methods. It cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, some simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the scope of protection determined by the claims submitted for the present invention.

Claims

1. A distributed tracking method for multi-radar networking of ballistic missile free segment based on diffusion maximum correlation entropy, characterized in that: The steps include: Step S1, local estimation, specifically calculating the prediction estimate and error covariance in in, represents the state estimation error covariance matrix at time k-1; Reason The matrix obtained by Choleskey decomposition; is the intermediate variable obtained by estimating the state at the volume point and at time k-1; represents the intermediate variable obtained by the volume point and the forecast estimate at time k, and n represents the dimension of the state vector; Represents the predicted estimated value after fusion; express Substitute into the nonlinear function f(·) for propagation; is the forecast estimate of the ith radar; is the predicted estimate of the jth radar; It is to express the intermediate variables defined for convenience; It is an intermediate variable defined for convenience; formula T represents the matrix transposition operation; Q k-1 The error variance matrix representing the process noise; yes to the power of -1; Computational Measurement Prediction Estimation in, It is the new volume point obtained after the volume point is transferred through the measurement equation; represents the forecast estimate of the measurement of radar i; Represents the error cross-covariance matrix between state and measurement; represents the error covariance matrix of the measurement; represents the measurement nominal noise variance of radar i; Statistical Linearization in, represents the pseudo measurement matrix; represents the inverse matrix of the state prediction error covariance matrix; represents the pseudo-measurement noise variance matrix obtained by statistical linearization; Compute local state estimates and error covariance in, It is a variable defined for the convenience of expression; is the measurement information of the i-th radar; represents the inverse matrix of the pseudo-measurement noise variance matrix obtained by statistical linearization; represents the gain matrix; represents the estimated value of radar i at time k; for The estimated error covariance matrix of n represents the n-dimensional identity matrix; Specifically, in the free phase of the ballistic missile, only the gravitational force on the target is considered, and the target state equation is established in the geocentric inertial system, assuming that the influence of the earth's revolution is not considered; the gravitational perturbation of other celestial bodies is not considered; the earth model adopts the standard ellipsoid model; Select the position and velocity of the target as the state vector, Then the state equation is Among them, x, y, and z represent the position coordinates of the three coordinate axes of the target respectively. is the distance between the center of the earth and the target; R e is the equatorial radius of the earth; J2 is the coefficient of the second-order principal spherical harmonic function; ω x ,ω y ,ω z is the measured noise, v x 、v y 、v z Represents the speed of the three coordinate axes of the target, μ=3.98604418×10 14 m 3 / s 2 represents the earth's gravitational constant; it can be discretized using the Euler formula or the Runge-Kutta pair (2) to obtain x k =f(x k-1 )+ω k-1 (3) x k represents the state quantity at time k, f(x k-1 ) represents the nonlinear transfer equation of the missile's state vector over time, ω k-1 Gaussian white noise with zero mean is used to represent the deviation caused by modeling. The ground-based early warning radar is used to track the target. The measurements include the slant range ρ from the radar station to the target, the elevation angle γ and the azimuth angle η of the target, that is, Then the measurement equation is Among them, x L Indicates the x-direction position of the radar system; y L represents the position in the y direction of the radar system; z L represents the position in the z direction of the radar system; C is the transformation matrix from the geocentric system to the radar system; [x r y r z r ] T is the coordinate of the radar in the geocentric system, v is the measurement noise, and v is the non-Gaussian flicker noise, and its probability density function is expressed as p(v)=(1-α)p G1 +αp G2 (7) Where α is the flicker probability, and They are two types of zero-mean Gaussian distribution noise, δ1<δ2; Considering a multi-radar network system, models (3) and (5) can be equivalent to the following expression: x k =f(x k-1 )+ω k-1 (8) in is the missile's state vector, is the measurement information of the ith radar, f(·) and h(·) are known nonlinear transfer functions, ω k-1 and are system noise and radar measurement noise respectively, which are non-Gaussian, and their nominal noise variance matrices are Q k-1 and The communication topology between radar networks is represented by an undirected connected graph G = (V, E, W), where V = {1, 2, ..., N}, represents the set of all links, W = [λ ij ] n×n is the weighted adjacency matrix representing the communication between two nodes, N represents the number of radars, n represents the dimension of the state vector, and m represents the dimension of the measurement vector; when λ ij > 0, indicating that nodes i and j communicate with each other and are neighbors, otherwise ij = 0, they are independent of each other, and the neighboring nodes of sensor i can be expressed as N i ={j∈V:(i,j)∈E},d i Indicates that sensor i is in N i The number of adjacent nodes in the local estimation process, for radar node i, the local filter can be expressed as the following two steps Where ε is the consistent gain coefficient; calculate Error make So there is in, is the prediction estimation error covariance matrix at time k after fusion; The index s is used to represent the neighbor node set N of radar i. i The elements in the formula s∈Ni represents the s radars in the neighbor set of radar i; The index l is used to represent the neighbor node set N of radar i j The elements in the formula are l∈N i represents the l radar in the neighbor set of radar i; From (14), we can see that the calculation A large number of cross-covariance matrices need to be calculated, so a conservative upper bound will be given to avoid the calculation of cross-covariance. make And available Pick beg Available in, for to the power of -2; From (18), we can get is an intermediate variable; It means the mean The covariance is Gaussian distribution of dx k-1 It is x k-1 Find the integral; Formula (21) is approximated by the volume rule: Next, the gain matrix is ​​derived based on the maximum correlation entropy criterion, and the cost function is defined Among them G σ (·) is the Gaussian kernel function, is the inverse matrix of the forecast error covariance matrix; is the inverse matrix of the measurement noise variance matrix, the superscript -1 indicates the inverse operation; Statistical linearization criterion in represents the cross-covariance matrix of states and measurements; represents the pseudo noise obtained by statistical linearization; represents the pseudo noise variance obtained by statistical linearization; represents the error cross-covariance matrix of the measurements; represents the pseudo measurement matrix; Substituting (23)-(26) into (22), we can obtain Taking the derivative of (27) and setting it to 0, we can obtain Pick (28) can be organized as so Fixed point iteration have so According to the matrix inversion formula, (32) has the following expression: in, is the estimated state value of radar i at time k; for The error of represents the state estimation error covariance matrix of radar i at time k; Pick Step S2, diffusion fusion, for the i-th radar node, the fused estimate and covariance are:

2. The distributed tracking method of ballistic missile free-segment multi-radar networking based on diffusion maximum correlated entropy according to claim 1 is characterized by: The step S1 uses a filter designed based on the maximum correlation entropy criterion to perform local estimation calculations.

3. The distributed tracking method of ballistic missile free-segment multi-radar networking based on diffusion maximum correlated entropy according to claim 2 is characterized by: The upper bound of the error variance is specified in the calculation of the cross-covariance matrix in step S1.

4. The distributed tracking method of ballistic missile free-stage multi-radar networking based on diffusion maximum correlation entropy according to claim 1 is characterized by: The diffusion fusion in step S2 adopts covariance crossover technology and diffusion fusion strategy for fusion.

5. The distributed tracking method of multi-radar networking of a ballistic missile free segment based on diffusion maximum correlation entropy according to claim 1 is characterized in that: The step S2 uses the volume criterion and statistical linearization method to perform the diffusion fusion process.

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