CN114969620A - Maximum correlation entropy filtering method for radar maneuvering target tracking - Google Patents

Maximum correlation entropy filtering method for radar maneuvering target tracking Download PDF

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CN114969620A
CN114969620A CN202210597193.8A CN202210597193A CN114969620A CN 114969620 A CN114969620 A CN 114969620A CN 202210597193 A CN202210597193 A CN 202210597193A CN 114969620 A CN114969620 A CN 114969620A
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李春霞
李明星
王恒
张德
李保卫
袁野
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Abstract

The invention relates to a radar tracking technology and provides a maximum correlation entropy filtering method for radar maneuvering target tracking. And establishing a target motion track according to the initial state parameters, obtaining a radar measurement value, and obtaining an initial filtering value of the CS + MCEKF algorithm by using a two-point initial method according to the radar measurement value. And determining the kernel bandwidth in the filtering process and a threshold value for stopping the fixed point iteration process, and recurrently obtaining a target tracking implementation step at the k +1 moment from the target state filtering value at the k moment. The method can provide a solution for the problem of difficulty in tracking the maneuvering target of the radar, thereby improving the tracking precision and stability of the maneuvering target of the radar.

Description

Maximum correlation entropy filtering method for radar maneuvering target tracking
Technical Field
The invention relates to a radar tracking technology, belongs to the field of radar signal processing, and particularly relates to a maximum correlation entropy filtering method for radar maneuvering target tracking.
Background
In recent years, with the remarkable improvement of the maneuverability of a target, the target cannot always keep a uniform-speed linear motion state or a uniform-acceleration linear motion state in the motion process, so that special motion forms such as turning, steep rising, steep falling and the like can be generated at any time in the motion process, and under the condition, the radar is increasingly difficult to effectively track the maneuvering target in real time. The difficulty is that the motion form of the target cannot be predicted in advance, so that a completely accurate model cannot be established to realize effective tracking of the target.
For the problem of maneuvering target tracking, related studies are currently mainly performed from two aspects: one is to build a model that matches the maneuver. The current maneuvering models mainly existing at home and abroad include a first-order time correlation model (Singer model), a current statistical model (CS), a Jerk model, an interactive multi-model (IMM) and the like. For the selection of the filtering algorithm, the most commonly used nonlinear filtering algorithms at present include an Extended Kalman Filter (EKF) algorithm, an Unscented Kalman Filter (UKF) algorithm, a Particle Filter (PF) algorithm, and the like.
For the above conventional nonlinear filtering algorithms, the optimization criteria adopted by them are minimum mean square error criteria (MMSE), which can only obtain the second moment information of the tracking error, so that it is difficult to ensure the target tracking accuracy when the range of motion is large.
The maximum correlation entropy criterion (MCC) can not only obtain the second-order item information of the tracking error, but also capture the high-order statistic of the tracking error, so that the tracking performance of the system can be greatly improved. Therefore, the maximum correlation entropy criterion (MCC) is applied to the radar maneuvering target tracking system, starting from the aspect of improving a filtering algorithm, and the stability and the accuracy of maneuvering target tracking are improved by combining the maximum correlation entropy extended Kalman filtering (MCEKF) algorithm with a traditional maneuvering model.
The "current" statistical model in a radar maneuvering target tracking system is first described below. The term "current" means that the acceleration of the target at the adjacent moment changes within a certain range due to the structure of the target, and the change range can only be within the field of the acceleration at the "current" moment, and based on the idea, the corrected Rayleigh distribution is adopted to describe the statistical characteristic of the acceleration. The nature of the "current" statistical model (CS) is a non-zero mean time-dependent model, and therefore the CS model uses a non-zero mean time-dependent model of the maneuvering acceleration to model the maneuvering acceleration.
The first order time-dependent model of the CS model is:
Figure BDA0003668578400000021
Figure BDA0003668578400000022
wherein the content of the first and second substances,
Figure BDA0003668578400000023
mean value representing the maneuvering acceleration, which is constant in each sampling period, a (t) colored acceleration noise representing zero mean, w (t) representing mean 0 and variance
Figure BDA0003668578400000031
And α represents a maneuvering frequency. According to formula (1) and formula (2)It is possible to obtain:
Figure BDA0003668578400000032
the discrete-time state equation under the CS model can be expressed as:
Figure BDA0003668578400000033
in the formula (I), the compound is shown in the specification,
Figure BDA0003668578400000034
respectively representing the position, velocity and acceleration of the object. F (k) is a state transition matrix, and the expression is as follows:
Figure BDA0003668578400000035
u (k) is an input control matrix, and the expression is as follows:
Figure BDA0003668578400000036
w (k) is a Gaussian white noise sequence with a covariance Q (symmetric matrix) of:
Figure BDA0003668578400000037
the specific expression is as follows:
Figure BDA0003668578400000041
from the foregoing description, the instantaneous "current" acceleration at time kT (T being the radar sampling interval) can be represented by an acceleration state vector
Figure BDA0003668578400000042
One-step prediction value of
Figure BDA0003668578400000043
Instead, then the mean value for the maneuvering acceleration can be found as:
Figure BDA0003668578400000044
the calculation mode of the maneuvering acceleration variance can be obtained through the analysis as follows:
Figure BDA0003668578400000045
the measurement equation of the discrete time system under the CS model radar polar coordinate system is as follows,
Figure BDA0003668578400000046
wherein Z (k +1) ═ r (k +1) phi (k +1)] T X (k +1) and y (k +1) are the positions of the x axis and the y axis of the target at the moment k +1 in the rectangular coordinate system, r (k +1) and phi (k +1) are the radar measurement information of the radial distance and the azimuth angle of the target at the moment k +1, V (k +1) is measurement noise and the variance is,
E(V(k+1)V T (j+1))＝R(k+1) (12)
wherein, R (k +1) is the measured noise covariance matrix at time k + 1.
Next, the maximum correlation entropy criterion (MCC) is introduced.
The maximum correlation entropy is an important argument of information that measures the similarity between two random variables X, Y ∈ R. Assuming their joint distribution function as F XY (x, y), the entropy of correlation between them is defined as,
V(X,Y)＝E[κ(X,Y)]＝∫κ(x,y)dF XY (x,y) (13)
where E represents the desired operator and κ (·,) represents the shift-invariant Mercer core. In the present invention, all the kernel functions are given by gaussian kernel functions. The expression is as follows,
Figure BDA0003668578400000051
where e-x-y, σ > 0 represents the core bandwidth.
However, in most radar tracking systems, only a limited number of data are available, so the joint probability density F between the variables XY Is typically unknown. In this case, the correlation entropy can be estimated using the sample mean. In a specific form thereof, the adhesive is,
Figure BDA0003668578400000052
where e (i) x (i) -y (i),
Figure BDA0003668578400000053
is derived from a joint probability density function F XY The N samples extracted.
The Taylor series expansion is carried out on the Gaussian kernel to obtain,
Figure BDA0003668578400000054
it can be seen that the correlation entropy is a weighted sum of all even moments of X-Y from which higher order statistics of the data can be extracted. It is noted that when the kernel bandwidth is large, the second moment will have a major effect on the correlation entropy.
Given a sequence of error data, the cost function based on the MCC criterion is:
Figure BDA0003668578400000061
disclosure of Invention
Aiming at the problems, the invention provides a maximum correlation entropy filtering method for radar maneuvering target tracking. The method can provide a solution for the problem of difficulty in tracking the maneuvering target of the radar, thereby improving the tracking precision and stability of the maneuvering target of the radar.
The invention provides the following technical scheme: a maximum correlation entropy filtering method for radar maneuvering target tracking comprises the following steps:
step S01: setting maneuvering frequency alpha and a target initial state, including an initial position and a speed of target movement, a radar sampling interval T and a radar tracking time length N;
step S02: establishing a target motion trajectory, diving or climbing according to the initial state parameters of the step S01, obtaining a radar measurement value according to the step (18),
Z(k+1)＝h(X(k+1))+V(k+1) (18)
wherein X (k +1) is a state vector of the target motion at the time k +1, Z (k +1) is a radar measurement value at the time k +1, and Z (k +1) ═ r (k +1) phi (k +1)] T R (k +1) and phi (k +1) are radar measurement information of the radial distance and azimuth angle of the target at the moment of k +1, respectively, h (-) is a nonlinear function of the target measurement, and
Figure BDA0003668578400000071
v (k +1) is the measurement noise of the target at the moment k + 1;
step S04: obtaining an initial filtering value of the CS + MCEKF algorithm by using a two-point initial method according to the radar measurement value;
step S05: determining a kernel bandwidth sigma in the filtering process and a threshold epsilon (preset as a positive threshold) for terminating the fixed point iteration process;
step S06: and (4) realizing the target tracking of the target state filtering value at the k +1 moment by recursion at the k moment through an iterative method.
In step S02, a state prior update value is obtained by the following equation according to the target motion state equation (4),
Figure BDA0003668578400000072
wherein F (k) is a state transition matrix, and U (k) is an input control matrix. According to the formula
Figure BDA0003668578400000073
Judgment of
Figure BDA0003668578400000074
Whether or not it is greater than 0, according to
Figure BDA0003668578400000075
Obtaining difference in maneuvering acceleration
Figure BDA0003668578400000076
According to
Figure BDA0003668578400000077
Obtaining a process noise covariance Q (k), wherein
Figure BDA0003668578400000081
Figure BDA0003668578400000082
Figure BDA0003668578400000083
Figure BDA0003668578400000084
Figure BDA0003668578400000085
Figure BDA0003668578400000086
Then, a one-step prediction covariance corresponding to the state prior update value is obtained according to the following formula,
Figure BDA0003668578400000087
obtaining a measurement predicted value corresponding to the prior updated value of the current state according to the formula (21), and solving a Jacobian matrix h of a nonlinear function h (-) of the target measurement X (k+1)，
Figure BDA0003668578400000088
Measuring matrix h under two-dimensional polar coordinates X The calculation method of (k +1) is as follows:
Figure BDA0003668578400000089
wherein the content of the first and second substances,
Figure BDA00036685784000000810
combining the radar system measurement equation Z (k +1) ═ h (X (k +1)) + V (k +1) and
Figure BDA00036685784000000811
constructing a CS + MCEKF nonlinear model as the following formula,
Figure BDA00036685784000000812
wherein h (-) is a nonlinear function of radar measurement, and
Figure BDA0003668578400000091
v (k +1) is the measurement noise of the target at the moment k +1, X (k +1) is the state information of the target at the moment k +1, and is the information of position, speed and acceleration, and Z (k +1) is the measurement information of the target at the moment k +1, and is the information of radial distance and azimuth angle.
The covariance matrix of θ (k +1) is,
Figure BDA0003668578400000092
wherein M (k +1) can be obtained by Cholesky decomposition of the above formula, M P (k +1| k) one-step prediction covariance matrix for target
Figure BDA0003668578400000093
Performing Cholesky decomposition to obtain a lower triangular matrix,
Figure BDA0003668578400000094
as a transpose of the lower triangular matrix, as above, M V (k +1) is a lower triangular matrix obtained by performing Cholesky decomposition on the measured covariance R (k +1),
Figure BDA0003668578400000095
r (k +1) is a measured noise covariance matrix of the radar target point trace at the moment of k +1, M is a transposed matrix of the lower triangular matrix P (k +1) and M V (k +1) is the sum of the two positive definite matrices
Figure BDA0003668578400000096
R (k +1) is obtained by Cholesky decomposition, and M (k +1) and M are obtained by mathematical transformation for convenient operation T (k +1), multiplying both sides of the formula (22) by M -1 (k +1), a nonlinear model was obtained,
D(k+1)＝B(X(k+1))+e(k+1)(25)
wherein D (k +1) is a first parameter for constructing the nonlinear model, B (k +1) is a second parameter for constructing the nonlinear model, and e (k +1) is an error parameter for constructing the nonlinear model, and respectively satisfy
Figure BDA0003668578400000101
e(k+1)＝M -1 (k+1)θ(k+1)。
In step S06, before the fixed point iteration process starts, the kernel function singular problem possibly caused by the measurement abnormality is processed. The treatment method comprises the following steps:
Figure BDA0003668578400000102
Figure BDA0003668578400000103
β(k+1)＝ψ T (k+1)ψ -1 (k+1)ψ(k+1) (28)
if | beta (k +1) | > zeta and zeta > 0, zeta is a preset positive threshold and zeta is a parameter for judging abnormal measurement before iteration, executing a prediction step, namely
Figure BDA0003668578400000104
And taking the prior updated value as a final filtering result, and if the | beta (k +1) | is less than or equal to zeta, performing a fixed-point iteration process.
Starting an iterative process, wherein t represents an iterative index, and taking the one-step predicted value of the state as an iteration initial value
Figure BDA0003668578400000105
Starting from t-1 and the initial measurement matrix is
Figure BDA0003668578400000106
(1) Constructing a Gaussian kernel function according to the formula (14) and the formula (25), constructing a diagonal matrix according to the kernel function, specifically,
Figure BDA0003668578400000107
Figure BDA0003668578400000108
Figure BDA0003668578400000111
wherein d is i (k +1) is the i-th element of D (k +1) in the nonlinear model, b i (X (t-1) (k +1)) is the ith row of B (X (k +1)),
Figure BDA0003668578400000112
is the i-th element, G, of e (k +1) in the iterative process σ In the form of a gaussian kernel function,
Figure BDA0003668578400000113
a diagonal matrix is predicted for the object motion constructed for the kernel function,
Figure BDA0003668578400000114
measuring a diagonal matrix for the target constructed by the kernel function;
(2) solving the filter value of the t-th iteration according to the following formula
Figure BDA0003668578400000115
And its corresponding covariance
Figure BDA0003668578400000116
Figure BDA0003668578400000117
Figure BDA0003668578400000118
Figure BDA0003668578400000119
Figure BDA00036685784000001110
Figure BDA00036685784000001111
(3) Comparing the estimation of the current iteration step with the iteration estimation of the previous step, ending the iteration process when the following formula is satisfied,
Figure BDA00036685784000001112
if not, repeating the steps (1) and (2) until the above formula is satisfied, ending the iterative process, and after each iterative step, needing to update the one-step prediction of the measurement value and the corresponding Jacobian matrix, thereby reconstructing B (X (k +1)) in D (k +1) ═ B (X (k +1)) + e (k +1) for use in a new iterative step;
(4) satisfy the formula
Figure BDA0003668578400000121
The temporal filtering result and its corresponding covariance are the filtering value and covariance value at the time of k +1, i.e.
Figure BDA0003668578400000122
(5) Step S06 is repeated until the filtering ends, and the filtering process ends until k +1 is equal to N.
According to the scheme, in the radar maneuvering target tracking, the radar target tracking method using the maximum correlation entropy extended Kalman filtering combined with the traditional maneuvering model can be used for solving the problems of low maneuvering target tracking precision, difficulty in tracking and poor stability of the tracking process.
Drawings
FIG. 1-flow chart of an embodiment of the present invention;
FIG. 2-schematic diagram of a target motion trajectory in a climbing form;
FIG. 3-schematic diagram of the trajectory of the target in dive form;
FIG. 4-root mean square error of filtered position for tracking algorithm in climb motion;
FIG. 5-root mean square error of the filtered velocity of the tracking algorithm in the form of a climb motion;
FIG. 6-root mean square error of filtered position of tracking algorithm in dive motion;
FIG. 7-root mean square error of the filtered velocity of the tracking algorithm in the form of dive motion;
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only one embodiment of the present invention, and not all embodiments. All other embodiments that can be derived by a person skilled in the art from the detailed description of the invention without inventive step are within the scope of the invention.
With reference to fig. 1 and 2, assuming that the target makes a climbing type maneuvering motion and a diving type maneuvering motion in a two-dimensional plane, respectively, the method comprises the following steps:
step S01: setting a maneuvering frequency alpha to 1/60, setting a target initial state to comprise an initial position and a speed of target motion (the initial position of climbing motion is (500,100) KM, the initial speed is (300,0) m/s, the initial acceleration is (0,0) m/s 2; the initial position of diving motion is (300,200) KM, the initial speed is (200,0) m/s, the initial acceleration is (0,0) m/s 2), setting a radar sampling interval T to 1s and setting a radar tracking time length N to 100;
step S02: establishing a target motion track (climbing or diving) according to the initial state parameters of the step S01, obtaining a radar measurement value according to the following formula,
Z(k+1)＝h(X(k+1))+V(k+1) (38)
wherein X (k +1) is a state vector of the target motion at the time k +1, Z (k +1) is a radar measurement value at the time k +1, and Z (k +1) ═ r (k +1) phi (k +1)] T R (k +1) and phi (k +1) are radar measurement information of the radial distance and azimuth angle of the target at the moment of k +1, respectively, and h (-) is the non-measurement of the targetA linear function, wherein V (k +1) is the measurement noise of the target at the moment k + 1;
step S04: obtaining an initial filtering value of the CS + MCEKF algorithm by using a two-point initial method according to the radar measurement value;
step S05: determining a kernel bandwidth σ (σ -10) in the filtering process, and a positive threshold ε (ε -10) that terminates the fixed-point iteration process -6 )；
Step S06: and (4) realizing the target tracking of the target state filtering value at the k +1 moment by recursion at the k moment through an iterative method.
In step S02, a state prior update value is obtained by the following equation,
Figure BDA0003668578400000146
wherein F (k) is a state transition matrix, U (k) is an input control matrix, and the expressions of F (k) and U (k) are respectively the same as those of formula (5) and formula (6).
According to the formula
Figure BDA0003668578400000141
Judgment of
Figure BDA0003668578400000142
Whether or not it is greater than 0, or not,
according to
Figure BDA0003668578400000143
Obtaining difference of maneuvering acceleration
Figure BDA0003668578400000144
According to
Figure BDA0003668578400000145
Obtaining a process noise covariance Q (k), wherein
Figure BDA0003668578400000151
Figure BDA0003668578400000152
Figure BDA0003668578400000153
Figure BDA0003668578400000154
Figure BDA0003668578400000155
Figure BDA0003668578400000156
Then, a one-step prediction covariance corresponding to the state prior update value is obtained according to the following formula,
Figure BDA0003668578400000157
obtaining a measurement predicted value corresponding to the prior updated value of the current state according to the formula (41), and solving a Jacobian matrix h of a nonlinear function h (-) of the target measurement X (k+1)，
Figure BDA0003668578400000158
Measuring matrix h under two-dimensional polar coordinates X The calculation method of (k +1) is as follows:
Figure BDA0003668578400000159
wherein the content of the first and second substances,
Figure BDA00036685784000001510
combining the radar system measurement equation Z (k +1) ═ h (X (k +1)) + V (k +1) and
Figure BDA00036685784000001511
constructing a CS + MCEKF nonlinear model as the following formula,
Figure BDA00036685784000001512
wherein h (-) is a nonlinear function of radar measurement, and
Figure BDA0003668578400000161
v (k +1) is the measurement noise of the target at time k +1, X (k +1) is the state information of the target at time k +1, typically the information of position, velocity, acceleration, etc., and Z (k +1) is the measurement information of the target at time k +1, typically the information of radial distance, azimuth, etc.
The covariance matrix of θ (k +1) is:
Figure BDA0003668578400000162
wherein M (k +1) can be obtained by Cholesky decomposition of the above formula to obtain M P (k +1) and M V (k +1) of multiplying both sides of the formula (43) by M -1 (k +1), a nonlinear model was obtained,
D(k+1)＝B(X(k+1))+e(k+1) (46)
wherein D (k +1) is a first parameter for constructing the nonlinear model, B (k +1) is a second parameter for constructing the nonlinear model, and e (k +1) is an error parameter for constructing the nonlinear model, and respectively satisfy
Figure BDA0003668578400000163
e(k+1)＝M -1 (k+1)θ(k+1)。
Before the fixed-point iteration process starts, the problem of kernel function diagonal matrix singularity possibly caused by measurement abnormality is processed. The treatment method comprises the following steps:
Figure BDA0003668578400000171
Figure BDA0003668578400000172
β(k+1)＝ψ T (k+1)η -1 (k+1)ψ(k+1) (49)
if | β (k +1) | > ζ and ζ > 0, ζ is a preset positive threshold, ζ can be taken as 100, and the predicting step is executed, namely
Figure BDA0003668578400000173
And taking the prior updated value as a final filtering result, and if the | beta (k +1) | is less than or equal to zeta, performing a fixed-point iteration process.
Starting an iterative process, wherein t represents an iterative index, and taking the one-step predicted value of the state as an iteration initial value
Figure BDA0003668578400000174
Starting from t-1 and the initial measurement matrix is
Figure BDA0003668578400000175
(1) Constructing a Gaussian kernel function, constructing a diagonal matrix according to the kernel function, specifically,
Figure BDA0003668578400000176
Figure BDA0003668578400000177
Figure BDA0003668578400000178
(2) solving the filtered value of the t iteration according to the following formula
Figure BDA0003668578400000179
And its corresponding covariance
Figure BDA00036685784000001710
Figure BDA00036685784000001711
Figure BDA00036685784000001712
Figure BDA00036685784000001713
Figure BDA00036685784000001714
Figure BDA0003668578400000181
Figure BDA0003668578400000182
(3) Comparing the estimation of the current iteration step with the iteration estimation of the previous step, ending the iteration process when the following formula is satisfied,
Figure BDA0003668578400000183
if not, repeating the steps (1) and (2) until the above formula is satisfied, ending the iteration process, and after each iteration step, needing to update the one-step prediction of the measurement value and the corresponding Jacobian matrix thereof again, thereby reconstructing B (X (k +1)) in D (k +1) ═ B (X (k +1)) + e (k +1) for use in a new iteration step;
(4) satisfaction type
Figure BDA0003668578400000184
The temporal filtering result and its corresponding covariance are the filtering value and covariance value at the time of k +1, i.e.
Figure BDA0003668578400000185
(5) Step S06 is repeated until the filtering ends, and the filtering process ends until k +1 is equal to N.
Fig. 3 to 6 are graphs showing simulation results in the above embodiment. In addition to the above-mentioned CS + MCEKF algorithm, the filtering algorithm selected in the embodiment also selects other maneuvering models to perform a comparison simulation experiment in combination with the filtering algorithms, i.e., Singer + EKF and CS + EKF algorithms. The target maneuver form and the radar initial parameter settings are shown in the following table.
TABLE 1 maneuvering target tracking simulation parameters
Figure BDA0003668578400000191
The probability of occurrence of the maximum acceleration in the above Singer model is P M 0.6, the probability of no maneuver is P 0 ＝0.2。
Fig. 3 to 6 show the position root mean square error and the velocity root mean square error of three filtering algorithms. The smaller the position root mean square error and the velocity root mean square error of the filter, the better.
As can be seen from the simulation results of fig. 3-6, when a target maneuvers during the movement process, the tracking accuracy of the position root mean square error and the speed root mean square error of the Singer + EKF and CS + EKF algorithms combined by the traditional maneuvering model and the filtering algorithm is low, and the tracking curve has poor stability and large fluctuation.
Although particular embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these particular embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (10)

1. A maximum correlation entropy filtering method for radar maneuvering target tracking is characterized by comprising the following steps:
step S01: setting maneuvering frequency alpha and a target initial state, including an initial position, a speed, a radar sampling interval T and a radar tracking time length N of target movement;
step S02: establishing a target motion track according to the initial state parameters of the step S01, obtaining a radar measurement value according to the following formula,
Z(k+1)＝h(X(k+1))+V(k+1)
wherein X (k +1) is a state vector of the target motion at the time k +1, Z (k +1) is a radar measurement value at the time k +1, and Z (k +1) ═ r (k +1) phi (k +1)] T R (k +1) and phi (k +1) are radar measurement information of the radial distance and azimuth angle of the target at the moment of k +1, respectively, h (-) is a nonlinear function of the target measurement, and
Figure FDA0003668578390000011
v (k +1) is the measurement noise of the target at the moment k + 1;
step S04: obtaining an initial filtering value of the CS + MCEKF algorithm by using a two-point initial method according to the radar measurement value;
step S05: determining a kernel bandwidth sigma in the filtering process and a threshold epsilon for terminating the fixed point iteration process;
step S06: and (4) realizing the target tracking of the target state filtering value at the k +1 moment by recursion at the k moment through an iterative method.
2. The method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 1, characterized by:
the target motion track is a climbing track or a diving track.
3. The method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 1, characterized by:
in step S02, a state prior update value is obtained by the following equation,
Figure FDA0003668578390000021
wherein F (k) is a state transition matrix, and U (k) is an input control matrix.
4. The method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 3, characterized by: according to the formula
Figure FDA0003668578390000022
Judgment of
Figure FDA0003668578390000023
Whether or not it is greater than 0, according to
Figure FDA0003668578390000024
Obtaining difference of maneuvering acceleration
Figure FDA0003668578390000025
According to
Figure FDA0003668578390000026
Obtaining a process noise covariance Q (k), wherein
Figure FDA0003668578390000027
Figure FDA0003668578390000028
Figure FDA0003668578390000029
Figure FDA00036685783900000210
Figure FDA00036685783900000211
Figure FDA00036685783900000212
Then, a one-step prediction covariance corresponding to the state prior update value is obtained according to the following formula,
Figure FDA0003668578390000031
obtaining a measurement predicted value corresponding to the prior updated value of the current state according to the following formula, and solving a Jacobian matrix h of a nonlinear function h (-) of target measurement X (k+1)，
Figure FDA0003668578390000032
5. The method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 4, characterized by:
measuring matrix h under two-dimensional polar coordinates X The calculation method of (k +1) is as follows:
Figure FDA0003668578390000033
wherein the content of the first and second substances,
Figure FDA0003668578390000034
6. the method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 5, characterized by:
combining the radar system measurement equation Z (k +1) ═ h (X (k +1)) + V (k +1) and
Figure FDA0003668578390000035
constructing a CS + MCEKF nonlinear model as follows,
Figure FDA0003668578390000036
wherein h (-) is a nonlinear function of radar measurement, and
Figure FDA0003668578390000041
v (k +1) is the measurement noise of the target at the moment k +1, X (k +1) is the state information of the target at the moment k +1, and is the information of position, speed and acceleration, and Z (k +1) is the measurement information of the target at the moment k +1, and is the information of radial distance and azimuth angle.
7. The method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 6, characterized by:
the covariance matrix of θ (k +1) is,
Figure FDA0003668578390000042
wherein M (k +1) can be obtained by Cholesky decomposition of the above formula, M P (k +1| k) one-step prediction covariance matrix for target
Figure FDA0003668578390000043
Performing Cholesky decomposition to obtain a lower triangular matrix,
Figure FDA0003668578390000044
as a transpose of the lower triangular matrix, as above, M V (k +1) is a lower triangular matrix obtained by performing Cholesky decomposition on the measured covariance R (k +1),
Figure FDA0003668578390000045
r (k +1) is a measured noise covariance matrix of the radar target point trace at the moment of k +1, M is a transposed matrix of the lower triangular matrix P (k +1) and M V (k +1) is the sum of the two positive definite matrices
Figure FDA0003668578390000046
R (k +1) is obtained by Cholesky decomposition, and M (k +1) and M are obtained by mathematical transformation for convenient operation T (k +1) left-multiplying both sides of the nonlinear model formula by M -1 (k +1), a nonlinear model was obtained,
D(k+1)＝B(X(k+1))+e(k+1)
wherein D (k +1) is a first parameter for constructing the nonlinear model, B (k +1) is a second parameter for constructing the nonlinear model, and e (k +1) is an error parameter for constructing the nonlinear model, and respectively satisfy
Figure FDA0003668578390000051
e(k+1)＝M -1 (k+1)θ(k+1)。
8. The method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 7, characterized by:
in step S06, before the fixed point iteration process starts, the problem of kernel function diagonal matrix singularity possibly caused by measurement abnormality is processed in the following manner:
Figure FDA0003668578390000052
Figure FDA0003668578390000053
β(k+1)＝ψ T (k+1)η -1 (k+1)ψ(k+1)
if | beta (k +1) | > zeta and zeta > 0, zeta is a preset positive threshold and zeta is a parameter for judging abnormal measurement before iteration, executing a prediction step, namely
Figure FDA0003668578390000054
And taking the prior updated value as a final filtering result, and if the | beta (k +1) | is less than or equal to zeta, performing a fixed-point iteration process.
9. The method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 8, characterized by:
starting an iterative process, wherein t represents an iterative index, and taking the one-step predicted value of the state as an iteration initial value
Figure FDA0003668578390000055
Starting from t-1 and the initial measurement matrix is
Figure FDA0003668578390000056
(1) Constructing a Gaussian kernel function, constructing a diagonal matrix according to the kernel function, specifically,
Figure FDA0003668578390000061
Figure FDA0003668578390000062
Figure FDA0003668578390000063
wherein d is i (k +1) is the i-th element of D (k +1) in the nonlinear model, b i (X (t-1) (k +1)) is the ith row of B (X (k +1)),
Figure FDA0003668578390000064
is the i-th element, G, of e (k +1) in the iterative process σ In the form of a gaussian kernel function,
Figure FDA0003668578390000065
a diagonal matrix is predicted for the object motion constructed for the kernel function,
Figure FDA0003668578390000066
measuring a diagonal matrix for the target constructed by the kernel function;
(2) solving the filtered value of the t iteration according to the following formula
Figure FDA0003668578390000067
And its corresponding covariance
Figure FDA0003668578390000068
Figure FDA0003668578390000069
Figure FDA00036685783900000610
Figure FDA00036685783900000611
Figure FDA00036685783900000612
Figure FDA00036685783900000613
(3) Comparing the estimation of the current iteration step with the iteration estimation of the previous step, ending the iteration process when the following formula is satisfied,
Figure FDA00036685783900000614
if not, repeating the steps (1) and (2) until the above formula is satisfied, ending the iteration process, and after each iteration step, needing to update the one-step prediction of the measurement value and the corresponding Jacobian matrix thereof again, thereby reconstructing B (X (k +1)) in D (k +1) ═ B (X (k +1)) + e (k +1) for use in a new iteration step;
(4) satisfy the formula
Figure FDA0003668578390000071
The temporal filtering result and its corresponding covariance are the filtering value and covariance value at the time of k +1, i.e.
Figure FDA0003668578390000072
(5) Step S06 is repeated until the filtering ends, and the filtering process ends until k +1 is equal to N.
10. The method of maximum correlation entropy filtering for radar maneuvering target tracking according to claim 9, characterized by:
in the step (1), when constructing the Gaussian kernel function,
the maximum correlation entropy is an important argument of information that measures the similarity between two random variables X, Y ∈ R. Assuming their joint distribution function as F XY (x, y), the entropy of correlation between them is defined as,
V(X,Y)＝E[κ(X,Y)]＝∫κ(x,y)dF XY (x,y)
where E represents the desired operator, κ (·,) represents the shift-invariant Mercer kernel, the kernel function is given by a Gaussian kernel, the expression,
Figure FDA0003668578390000073
where e-x-y, σ > 0 represents the core bandwidth.
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