CN112986977A - Method for overcoming radar extended Kalman track filtering divergence - Google Patents
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Abstract
The invention discloses a method for overcoming radar extended Kalman track filtering divergence, which comprises the following steps: carrying out system modeling according to a conventional extended Kalman filtering method; assuming that the state at the moment k of track filtering is X (k | k) and the covariance matrix is P (k | k); performing one-step prediction on the state at the moment k to obtain a prediction state and a prediction covariance matrix at the moment k + 1; carrying out anti-divergence processing on the prediction covariance matrix by adopting a correction matrix or a correction coefficient to obtain a corrected prediction covariance matrix; updating the prediction state through the measurement value of the radar detection target system at the k +1 moment, calculating an innovation vector, an innovation covariance matrix and a Kalman gain matrix, and replacing an original prediction covariance matrix with the corrected prediction covariance matrix in the calculation process; the target state and covariance matrix at time k +1 are calculated. The invention corrects the filtering output trend, improves the precision of the filtering result and effectively overcomes the divergence condition in the track filtering.
Description
Technical Field
The invention relates to the technical field of Kalman track filtering data processing, in particular to a method for overcoming radar extended Kalman track filtering divergence.
Background
The track filtering is an important component of a radar data processing algorithm, and can filter radar detection point tracks to form continuous track output, so that the detection and tracking precision of radar targets is effectively improved. The extended kalman filter is the most common track filtering algorithm, and the conventional extended kalman filter algorithm realizes the optimal estimation of the system state by establishing a system state equation and combining with the actual observation data of the system.
The problems and the disadvantages of the prior art are as follows:
1) in the field of radar air detection, particularly in military scenes, a detected target is often a high-speed and high-mobility target, and a conventional target motion model (such as a constant-speed model and a constant-acceleration model) cannot accurately describe the motion rule of the target in a long time period, so that the Kalman filtering algorithm loses optimality, and even generates large deviation in serious conditions to generate filtering divergence.
2) The precision of conventional extended kalman track filtering depends greatly on the fidelity of modeling the target motion process, and for this reason, a more complex target motion equation model is proposed, and even a more realistic motion model is established by combining different motion models. However, complex motion models are difficult to implement in engineering, and even complex motion models cannot describe all motion processes of the object completely accurately, especially when the object performs high-speed large-motor motion. This problem is exacerbated when there are multiple moving objects.
3) The conventional extended kalman filtering is modified into a square root filtering form, that is, a square root extended kalman filtering method is adopted to overcome the problem of flight path filtering divergence. However, the method is only suitable for the situation that a singular matrix possibly appears in the filtering operation process under the conditions of weak hardware computing capability and low computing precision in the prior art, and does not play any role in the problem that the system equation cannot accurately describe the real system process. Nowadays, with the improvement of hardware capability, high-precision floating point calculation is not a problem, and the use scenario of square root extended kalman filtering is further limited.
The invention self-adaptive unscented Kalman particle filtering method with publication number CN110455287A provides a partial particle filtering process and can also inhibit the problem of filtering divergence, but the application occasion is a correction means when the measured value is wrong, and the method is not suitable for the situation that the measured value is correct, the predicted value is inaccurate due to system modeling, and the flight path diverges.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problem that a target motion equation model cannot accurately describe the motion characteristics of a target for a long time in radar track filtering, so that the target filtering track is diverged, the invention provides a method for overcoming radar extended Kalman track filtering divergence, so as to correct the filtering output trend, improve the accuracy of a filtering result and overcome the divergence condition possibly occurring in track filtering.
The technical scheme is as follows: the invention relates to a method for overcoming radar extended Kalman track filtering divergence, which comprises the following steps:
(1) carrying out system modeling according to a conventional extended Kalman filtering method, and establishing a state equation and a measurement equation of a radar detection target system;
(2) assuming that the last time of the radar detection target system track filtering is k, the state of the k time is X (k | k), and the covariance matrix is P (k | k);
(3) performing one-step prediction on the state at the moment k to obtain a prediction state X (k +1| k) and a prediction covariance matrix P (k +1| k) at the moment k + 1;
(4) carrying out anti-dispersion treatment on the prediction covariance matrix by adopting a correction matrix M (k) or a correction coefficient; the correction matrix M (k) is a diagonal matrix, values on the diagonal are corresponding to correction values of each component variance in the radar detection target system, and the corrected prediction covariance matrix Pm (k +1| k) = P (k +1| k) + M (k); the specific operation of the anti-divergence processing on the prediction covariance matrix by adopting the correction coefficient is any one of the following operations: multiplying diagonal elements in the P (k +1| k) matrix by the same amplification factor, multiplying diagonal elements in the P (k +1| k) matrix by different amplification factors, multiplying all elements in the P (k +1| k) matrix by the same amplification factor, and multiplying all elements in the P (k +1| k) matrix by different amplification factors;
(5) updating the prediction state through a measured value Z (K +1) of a radar detection target system K +1 moment, calculating an innovation vector Y (K +1), an innovation matrix S (K +1) and a Kalman gain matrix K (K +1), and replacing an original prediction covariance matrix P (K +1| K) with a corrected prediction covariance matrix Pm (K +1| K) in the calculation process;
(6) the target state X (k +1| k +1) and covariance matrix P (k +1| k +1) at time k +1 are calculated.
Further perfecting the technical scheme, the radar detection target system adopts a constant acceleration model according to a formula
，
，
Obtaining: transfer matrix
Noise matrix
。
Further, the predicted state at the time k +1 in the step (3)
，
Predictive covariance matrix
，
Wherein F (k) is a transfer matrix, and Q (k) is a process excitation noise matrix, which is taken as a constant matrix.
Further, the components in the radar detection target system include target position (x, y, z), attitude angle (heading angle az, pitch angle el, roll angle ro), three-phase velocity (v)x、vx、vx) The value of the correction matrix M (k) on the diagonal
，
Wherein,
the variance correction values of the position coordinates, the attitude angles and the three-way speed are respectively.
Further, the measured value predicted in the step (5) is
H (k) is a measurement transformation matrix;
the innovation matrix is:
wherein, R (k +1) is an observation noise matrix, a diagonal matrix is adopted, and the value is the measurement error value of each component;
the innovation vector is:
；
the Kalman gain matrix is:
further, the state value calculated in the step (6) is:
the covariance matrix obtained by calculation is:
Further, in the step (5), h (k) is a jacobian matrix.
Has the advantages that: compared with the prior art, the invention has the advantages that:
1) by optimizing the traditional covariance matrix, the filtering output trend is corrected, the precision of the filtering result is improved, and the divergence condition in track filtering is effectively overcome;
2) the existing system state model of the extended Kalman filter is not required to be modified, and the system complexity is not increased;
3) the covariance matrix correction processing is inserted between one-step prediction and state updating of Kalman filtering in the core step, so that the compatibility with the original filtering process is high, and the code modification amount is small;
4) the covariance matrix correction code has low running time consumption and almost has no influence on the timeliness of the original filtering code.
Drawings
FIG. 1 is a process flow for overcoming radar extended Kalman track filter divergence in accordance with the present invention;
FIG. 2 is a diagram illustrating the results of conventional extended Kalman theory filtering;
fig. 3 is a diagram illustrating the filtering result of the present invention.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the embodiments.
The method for overcoming the divergence of the radar extended Kalman track filtering solves the divergence problem in the track filtering by correcting the covariance matrix. The Kalman recursion formula is mainly divided into a prediction part and an updating part, and in the prediction stage, the estimation value of the last state of the system is used for predicting the current system state and obtaining a predicted observation value; in the updating stage, the observed value of the current state is used for correcting the predicted value obtained in the last stage so as to obtain a new estimated value closer to the true value.
The process flow and method shown in FIG. 1:
(1) carrying out system modeling according to a conventional extended Kalman filtering method, and establishing a state equation and a measurement equation of a radar detection target system;
(2) assuming that the last time of the radar detection target system track filtering is k, the state at the time of k is X (k | k), and the state covariance matrix is P (k | k);
(3) in order to obtain a filtering state of a target k +1 moment, firstly, predicting the state of the k moment in one step to obtain a prediction state X (k +1| k) and a prediction covariance matrix P (k +1| k) of the k +1 moment;
(4) in order to overcome the divergence problem possibly occurring in the filtering process, carrying out anti-divergence treatment on the covariance matrix P (k +1| k) obtained by one-step prediction to obtain a corrected prediction covariance matrix Pm (k +1| k), wherein a simple correction method is based on a filter application scene, a correction matrix M (k) is taken as a diagonal matrix, and each element on the diagonal corresponds to the correction value of each component variance in the system state;
(5) updating the prediction state through a measured value Z (K +1) of a radar detection target system K +1 moment, calculating an innovation vector Y (K +1), an innovation matrix S (K +1) and a Kalman gain matrix K (K +1), and replacing an original prediction covariance matrix P (K +1| K) with a corrected prediction covariance matrix Pm (K +1| K) in the calculation process;
(6) the target state X (k +1| k +1) and covariance matrix P (k +1| k +1) at time k +1 are calculated.
One specific embodiment is provided below:
(1) modeling a system: performing system modeling according to a conventional extended Kalman filtering method, setting a motion equation of a radar detection target and a radar system measurement equation, wherein the system motion model adopts a constant acceleration model and is based on a formula
Obtaining: transfer matrix
Noise matrix
。
(2) And (3) state prediction: in a radar detection target system, state elements generally include position coordinates, attitude angles and three-way velocities, and assuming that a previous time of radar track filtering is k, a filtering system state at the time of k is X (k | k), a covariance matrix is P (k | k), and a state transfer function is F (k), a state predicted value X (k +1| k) at the time of k +1 can be obtained, that is, a radar detection target system is provided with a
(3) And (3) covariance prediction: since the system is in transition, the covariance is predicted to obtain the covariance matrix P (k +1| k), i.e., the covariance matrix P (k +1| k)
Where Q (k) is a process excitation noise matrix, it may be a constant matrix.
(4) And (3) covariance correction: in order to solve the divergence problem possibly occurring in the filtering process, the state covariance matrix P (k +1| k) obtained by one-step prediction is subjected to divergence prevention treatment between one-step prediction and state updating, and the obtained modified matrix is Pm (k +1| k), namely Pm (k +1| k) = P (k +1| k) + M (k)
It is generally assumed that the dimensions of the system state are independent of each other, and therefore, the modification matrix m (k) is set as a diagonal matrix, and the size of the diagonal element directly affects the filtering effect. The radar track filtering mainly aims at target position (x, y, z), attitude angle (course angle az and pitch angle)el, roll angle ro), three-phase velocity (v)x、vx、vx) The prediction is performed so that the diagonal of the correction matrix M (k) of the present invention takes the value of the correction for each element corresponding to each component variance in the system state, i.e., the correction value
(5) And (3) gain matrix calculation: the final filtering result of kalman filtering is synthesized by weighting of prediction and observation, so that it is necessary to calculate the innovation matrix S (K +1) and the kalman gain matrix K (K +1),
predicted measurements:
，
for most radars, the nonlinear relation exists due to the fact that the state of a target is different from an observation coordinate system, so that nonlinear deviation may exist in calculation of the H matrix, therefore, firstly, the nonlinear system is subjected to linearization processing, the H matrix is obtained in a nonlinear mode, and a nonlinear tool used by the method is a Jacobian matrix;
an innovation matrix:
，
wherein, R (k +1) represents an observation noise matrix, which is taken as a diagonal matrix in the system and is a measurement error value (standard deviation) of each component and represented by variance;
innovation vector:
；
kalman gain matrix:
1) and (3) filtering estimation calculation: the filtered estimate is the state value X (k +1| k +1) of the kalman filter output,
2) and (3) filtering estimation covariance calculation: after the state value is updated, the covariance matrix needs to be updated to obtain P (k +1| k +1) for the next recursion process, where I is the identity matrix, i.e. the unit matrix
The main difference between the other embodiment and the method of anti-divergence processing in step 4, which is known as m (k) diagonal matrix from step 4, is that the influence on the P (k +1| k) matrix is mainly the magnitude of the diagonal element value. Therefore, we can multiply the diagonal elements (or all elements) of the P (k +1| k) matrix by a certain amplification factor (or different amplification factors) to improve the uncertainty corresponding to one-step prediction without superimposing the correction matrix m (k), and the specific mode can be selected according to different application scenarios.
As shown in fig. 2, a schematic diagram of a filtering result of the conventional extended kalman theory is adopted, a straight line is a real track, a fluctuation line is a filtering track, and a motion model shown in the diagram cannot completely reflect the motion characteristic of a target, so that the filtering result is diverged.
As shown in fig. 3, the filtering result obtained by the method of the present invention is schematically shown, where the straight line is the real track and the fluctuating line is the filtering track. As can be seen from the comparison of FIG. 2 and FIG. 3, the invention corrects the filtering output trend, improves the accuracy of the filtering result, and effectively overcomes the divergence condition which may occur in the track filtering.
As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. A method for overcoming radar extended Kalman track filtering divergence comprises the following steps:
(1) carrying out system modeling according to a conventional extended Kalman filtering method, and establishing a state equation and a measurement equation of a radar detection target system;
(2) assuming that the last time of the radar detection target system track filtering is k, the state of the k time is X (k | k), and the covariance matrix is P (k | k);
(3) performing one-step prediction on the state at the moment k to obtain a prediction state X (k +1| k) and a prediction covariance matrix P (k +1| k) at the moment k + 1;
(4) carrying out anti-divergence processing on the prediction covariance matrix P (k +1| k) to obtain a corrected prediction covariance matrix Pm (k +1| k);
(5) updating the prediction state through a measured value Z (K +1) of a radar detection target system K +1 moment, calculating an innovation vector Y (K +1), an innovation matrix S (K +1) and a Kalman gain matrix K (K +1), and replacing an original prediction covariance matrix P (K +1| K) with a corrected prediction covariance matrix Pm (K +1| K) in the calculation process;
(6) calculating a target state X (k +1| k +1) and a covariance matrix P (k +1| k +1) at the moment k + 1;
the method is characterized in that: in the step (4), a correction matrix M (k) or a correction coefficient is adopted to perform anti-divergence processing on the prediction covariance matrix; the correction matrix M (k) is a diagonal matrix, values on the diagonal are corresponding to correction values of each component variance in the radar detection target system, and the corrected prediction covariance matrix Pm (k +1| k) = P (k +1| k) + M (k); the specific operation of the anti-divergence processing on the prediction covariance matrix by adopting the correction coefficient is any one of the following operations: multiplying diagonal elements in the P (k +1| k) matrix by the same amplification factor, multiplying diagonal elements in the P (k +1| k) matrix by different amplification factors, multiplying all elements in the P (k +1| k) matrix by the same amplification factor, and multiplying all elements in the P (k +1| k) matrix by different amplification factors.
2. The method for overcoming radar extended kalman path filter divergence according to claim 1, wherein: the radar target detection system adopts a constant acceleration model according to a formula
，
，
Obtaining: transfer matrix
Noise matrix
。
3. The method for overcoming radar extended kalman path filter divergence according to claim 2, wherein:
the predicted state at the time k +1 in the step (3)
，
Predictive covariance matrix
，
Wherein F (k) is a transfer matrix, and Q (k) is a process excitation noise matrix, which is taken as a constant matrix.
4. The method for overcoming radar extended kalman path filter divergence according to claim 3, wherein: the components in the radar detected target system include target position (x, y, z)Attitude angle (course angle az, pitch angle el, roll angle ro), three-phase velocity (v)x、vx、vx) The values on the diagonal of the correction matrix M (k) correspond to the correction values of each component variance in the system state,
wherein,
the variance correction values of the position coordinates, the attitude angles and the three-way speed are respectively.
5. The method for overcoming radar extended kalman path filter divergence according to claim 4, wherein: the measured value predicted in the step (5) is
H (k) is a measurement transformation matrix;
the innovation matrix is:
wherein, R (k +1) is an observation noise matrix, a diagonal matrix is adopted, and the value is the measurement error value of each component;
the innovation vector is:
；
the Kalman gain matrix is:
。
6. the method for overcoming radar extended kalman path filter divergence according to claim 5, wherein: the state value calculated in the step (6)Comprises the following steps:
；
the covariance matrix obtained by calculation is:
and I is an identity matrix.
7. The method for overcoming radar extended kalman path filter divergence according to claim 5, wherein: in the step (5), H (k) is a Jacobian matrix.
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