CN113536227A - Maneuvering target rapid tracking method based on Kalman covariance - Google Patents

Maneuvering target rapid tracking method based on Kalman covariance Download PDF

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CN113536227A
CN113536227A CN202110850254.2A CN202110850254A CN113536227A CN 113536227 A CN113536227 A CN 113536227A CN 202110850254 A CN202110850254 A CN 202110850254A CN 113536227 A CN113536227 A CN 113536227A
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曹静
车德朝
于志伟
王聪琳
杨增
闫柯
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CETC 28 Research Institute
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Abstract

The invention discloses a maneuvering target rapid tracking method based on Kalman covariance. The invention adds maneuvering detection on the basis of Kalman filtering algorithm. And (3) carrying out abnormal detection in the covariance matrix observation window during the dynamic detection. When the covariance value is larger than the threshold value in the observation window, the target is considered to be mobile, and a filtering algorithm is initialized to quickly track the target. The method solves the problems that the estimation value is greatly deviated due to the increase of the covariance matrix in the traditional algorithm, and the tracking effect is seriously lagged. The invention has great practical value in real-time tracking and filtering of the moving target.

Description

Maneuvering target rapid tracking method based on Kalman covariance
Technical Field
The invention belongs to the field of situation processing, and particularly relates to a maneuvering target rapid tracking method based on Kalman covariance.
Background
Modern situation processing is increasingly complex, and due to the fact that multiple targets exist in an area, target track conditions to be monitored in real time in the situation processing process are complex and changeable. In the face of a maneuvering target which is focused on, how to quickly adjust a tracking algorithm when maneuvering occurs to track the track in real time and improve situation handling timeliness is more and more urgent.
A Kalman Filter (Kalman algorithm for short) is a time-domain filtering method based on the minimum variance, describes the system state through a state-space equation, estimates the system state output by recursion, has the advantages of small data storage capacity, easy realization and the like, and is the most common tracking filtering algorithm in engineering. However, for a target with obvious maneuvering, when the motion model is inconsistent with the actual target, the estimated value is greatly deviated due to the increase of the covariance matrix of the algorithm, and the tracking effect is seriously delayed. The maneuver detection method introduced by Yaakov Bar-Shalom and the like judges whether a target maneuvers by setting a threshold value according to detection statistics established by filtering innovation. Analysis such as the fang hong flag shows that due to the constraint of the Q effect of the filter, the maneuvering detection based on the information of the tracking filter cannot simultaneously obtain the quick maneuvering detection performance and the good maneuvering detection probability.
Disclosure of Invention
The purpose of the invention is as follows: when the real-time tracking filtering is performed on the target, for the target with obvious maneuvering, when the motion model is inconsistent with the actual motion model, the estimated value is greatly deviated due to the increase of the covariance matrix, and the tracking effect is seriously delayed. In order to avoid the influence of Q effect on maneuvering detection and quickly identify the maneuvering situation, the maneuvering detection is added to the traditional Kalman algorithm, the mean subtraction accumulation algorithm is adopted for a covariance matrix observation window, the time sequence is subjected to abnormal detection, when the covariance value is larger than the threshold value in the observation window, the target is considered to be maneuvered, a filtering algorithm is initialized, and the target is quickly tracked. The invention has great practical value in real-time tracking and filtering of the moving target.
In order to solve the technical problem, the invention discloses a maneuvering target rapid tracking method based on Kalman covariance, which comprises the following steps:
step 1, selecting a uniform velocity CV model as a Kalman algorithm filter,performing state estimation on the filter to obtain a state vector of the filter
Figure BDA0003182173280000011
And a state covariance matrix P (k | k) having elements P of a first row and a first columnk|k(1,1) represents the x-axis distance error variance;
step 2, calculating the x-axis distance error variance P in the observation window of the state covariance matrix P (k | k)k|kAverage value m of (1,1)δrStandard deviation of deltaδr；
Step 3, when (P)k|k(1,1)-mδr)＞3*δδrTime, x-axis distance error variance Pk|k(1,1) judging that the target is maneuvering when the change is large, and executing the step 1 to initialize the filter; otherwise, the tracking effect is good, and the target is continuously tracked and filtered;
and 4, outputting the filtering value of the Kalman algorithm.
In one implementation, step 1 includes the steps of:
step 1-1, setting the target motion state as Constant Velocity (CV), sigmavFor the process noise standard deviation, σ, of the motion modelrTo measure the noise standard deviation, T is the sampling time interval. And selecting the constant-speed CV model as a filter of a Kalman algorithm. For consistent dimensionality of the matrix operations, let the CV model state vector be 4-dimensional. CV model state vector:
Figure BDA0003182173280000021
wherein the content of the first and second substances,
Figure BDA0003182173280000022
representing the state vector of the uniform velocity CV model, k representing the time, xk-1Is the coordinate value of the x-axis at time k-1,
Figure BDA0003182173280000023
speed of x-axis at time k-1, yk-1Is the coordinate value of the y-axis at time k-1,
Figure BDA0003182173280000024
the speed of the y-axis at time k-1;
the CV model state transition matrix F is:
Figure BDA0003182173280000025
the error covariance matrix Q is:
Figure BDA0003182173280000026
the state covariance matrix P is:
Figure BDA0003182173280000031
step 1-2, performing one-step prediction on the state estimation at the moment k-1:
Figure BDA0003182173280000032
step 1-3, let H be the measurement matrix,
Figure BDA0003182173280000033
z (k | k-1) represents the predicted value of the measurement at time k-1:
Figure BDA0003182173280000034
step 1-4, one-step prediction of state covariance is as follows:
P(k|k-1)＝F*P(k-1|k-1)*F′+Q；
wherein F' represents a transpose of F;
step 1-5, let R be the noise covariance matrix,
Figure BDA0003182173280000035
the model innovation covariance S is calculated by the following formulak：
Sk＝HP(k|k-1)H′+R；
Wherein H' represents the transpose of H;
step 1-6, calculating innovation vk：
Figure BDA0003182173280000036
Wherein Z (k) ═ xk yk]′，xkCoordinate value, y, representing the x-axis at time kkA coordinate value representing the y-axis at time k;
step 1-7, calculating gain k (k):
K(k)＝P(k|k-1)H′(Sk)-1；
step 1-8, updating the state by a state update equation wherein
Figure BDA0003182173280000041
State vector representing the updated model:
Figure BDA0003182173280000042
step 1-9, the covariance of the model is updated by the covariance update equation:
P(k|k)＝P(k|k-1)-K(k)SkK′(k)
where K' (K) denotes the transpose of K (K).
In one implementation, step 2 includes the steps of:
in the step 2-1, the step of the method,
let the length of the space observation window be N, N belongs to (20,40), calculate the error variance P of the x-axis distance in the observation window Nk|kAverage value m of (1,1)δr：
Figure BDA0003182173280000043
Step 2-2, calculating the x-axis distance in the observation window NError variance Pk|kStandard deviation δ of (1,1)δr：
Figure BDA0003182173280000044
The filter has good and bad effect of filtering the target position, and is reflected on whether the coordinate error curve is converged or not. The mean value and the standard deviation of the x-axis distance variance in the observation window N are obtained through calculation, so that the filtering effect of the filter can be judged by checking the convergence condition of the x-axis distance variance curve in the subsequent steps. The P isk|k(1,1)＝cov(xk,xk) Is an x-axis distance convolution, i.e., an x-axis distance variance.
In one implementation, step 3 includes the steps of:
step 3-1, carrying out outlier detection on the x-axis distance variance by using a statistical method, assuming that data are subject to positive distribution, and according to a 3 × δ criterion: 99.7% of the data will fall into region (P)k|k(1,1)-mδr)≤3*δδrIn general, the region (P) is considered to bek|k(1,1)-mδr)≤3*δδrThe outer points are outliers.
When (P)k|k(1,1)-mδr)＞3*δδrTime, x-axis distance error variance Pk|k(1,1) when the change is large, judging that the target is maneuvering, and executing step 1 to reinitialize the filter; the maneuvering index target deviates from the uniform CV model;
step 3-2, if no maneuver has taken place, i.e. (P)k|k(1,1)-mδr)≤3*δδrAnd taking the updated state vector as the state estimation of the next moment, and taking the updated covariance matrix as the covariance estimation of the next moment.
In one implementation, step 4 includes the steps of:
step 4-1, outputting Kalman algorithm filtering value
Figure BDA0003182173280000051
As the algorithm output.
Has the advantages that:
the invention relates to a method for quickly tracking and filtering a real-time maneuvering target in the field of situation processing, in particular to a maneuvering target quick tracking method by utilizing Kalman covariance. The method utilizes the mean value and the standard deviation of the covariance of the x-axis distance error, adopts a mean value subtraction accumulation algorithm, performs abnormity detection on a time sequence, judges the maneuvering state, and initializes a filter when the tracking effect is poor. The problems that large deviation of an estimated value is caused due to the fact that a covariance matrix is increased, the tracking effect is seriously delayed and the like are solved, the real-time performance of the maneuvering target tracking is improved, and the effect of quickly tracking the real-time target track is achieved.
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The foregoing and other advantages of the invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
FIG. 1 is a flowchart of a method for quickly tracking a maneuvering target based on Kalman covariance according to an embodiment of the present application.
FIG. 2 is an observation trajectory graph and measurement errors of a Kalman algorithm before improvement for fast tracking of a maneuvering target.
Fig. 3 is an observation trajectory diagram and measurement errors of the modified Kalman algorithm used in the embodiment of the present application for fast tracking of a maneuvering target.
Fig. 4 is a comparison diagram of position errors of the Kalman algorithm before the improvement and the Kalman algorithm after the improvement adopted in the embodiment of the present application for the quick tracking of the maneuvering target.
FIG. 5 is a graph of the effect of the Kalman algorithm before improvement and the improved Kalman algorithm adopted in the embodiment of the application when U-shaped turning maneuver occurs on the target track.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Fig. 1 is a flowchart of a method for quickly tracking a maneuvering target based on Kalman covariance in an embodiment of the present application, which is applied to an aerial target and a ground target, and includes the following specific contents:
step 1, selecting a uniform velocity CV model as filtering of Kalman algorithmA state estimator for estimating the state of the filter to obtain the state vector of the filter
Figure BDA0003182173280000061
And a state covariance matrix P (k | k) having elements P of a first row and a first columnk|k(1,1) represents the x-axis distance error variance;
step 2, calculating the x-axis distance error variance P in the observation window of the state covariance matrix P (k | k)k|kAverage value m of (1,1)δrStandard deviation of deltaδr；
Step 3, when (P)k|k(1,1)-mδr)＞3*δδrTime, x-axis distance error variance Pk|k(1,1) judging that the target is maneuvering when the change is large, and executing the step 1 to initialize the filter; otherwise, the tracking effect is good, and the target is continuously tracked and filtered;
and 4, outputting the filtering value of the Kalman algorithm.
In this embodiment, step 1 includes the following steps: :
step 1-1, setting the target motion state as Constant Velocity (CV). Setting target initial position (5km, 7.8km), measuring noise is white Gaussian noise with zero mean value, and standard deviation of noise is sigmar100m, the process noise is white gaussian with zero mean and the noise standard deviation is σvAnd (4) simulating the U-shaped motion of the target at the target motion sampling interval T of 0.005m/s and 10 s.
The filter of the CV model Kalman algorithm is selected. CV model state vector:
Figure BDA0003182173280000062
the CV model state transition matrix F is:
Figure BDA0003182173280000063
the error covariance matrix Q is:
Figure BDA0003182173280000064
the state covariance matrix P is:
Figure BDA0003182173280000071
step 1-2, performing one-step prediction on the state estimation at the moment k-1:
Figure BDA0003182173280000072
step 1-3, let H be the measurement matrix,
Figure BDA0003182173280000073
z (k | k-1) represents the predicted value of the measurement at time k-1:
Figure BDA0003182173280000074
step 1-4, one-step prediction of state covariance is as follows:
P(k|k-1)＝F*P(k-1|k-1)*F′+Q；
wherein F' represents a transpose of F;
step 1-5, let R be the noise covariance matrix,
Figure BDA0003182173280000075
the model innovation covariance S is calculated by the following formulak：
Sk＝HP(k|k-1)H′+R；
Wherein H' represents the transpose of H;
step 1-6, calculating innovation vk：
Figure BDA0003182173280000076
Wherein Z (k) ═ xk yk]′，xkCoordinate value, y, representing the x-axis at time kkA coordinate value representing the y-axis at time k;
step 1-7, calculating gain k (k):
K(k)＝P(k|k-1)H′(Sk)-1；
step 1-8, updating the state by a state update equation wherein
Figure BDA0003182173280000081
State vector representing the updated model:
Figure BDA0003182173280000082
step 1-9, the covariance of the model is updated by the covariance update equation:
P(k|k)＝P(k|k-1)-K(k)SkK′(k)
where K' (K) denotes the transpose of K (K).
In this embodiment, the step 2 of performing x-axis distance error covariance abnormality detection by using the spatial observation window to calculate the mean and standard deviation of the x-dimensional distance error covariance includes the following steps:
step 2-1, making the length of the space observation window N, making N equal to 30, and calculating the x-axis distance error variance P in the observation window Nk|kAverage value m of (1,1)δr：
Figure BDA0003182173280000083
Step 2-2, calculating the x-axis distance error variance P in the observation window Nk|kStandard deviation δ of (1,1)δr：
Figure BDA0003182173280000084
In this embodiment, step 3 adopts an average anomaly accumulation algorithm to perform maneuver detection, and includes the following steps:
step 3-1, using the theorem of 3 x δ, when (P)k|k(1,1)-mδr)＞3*δδrTime, x-axis distance error variance Pk|k(1,1) when the change is large, judging that the target is maneuvering, and executing step 1 to reinitialize the filter; the maneuvering finger target deviates from the constant speed CV model and turns a big bend suddenly if the target runs at a constant speed;
step 3-2, if no maneuver has taken place, i.e. (P)k|k(1,1)-mδr)≤3*δδrAnd taking the updated state vector as the state estimation of the next moment, and taking the updated covariance matrix as the covariance estimation of the next moment.
In this embodiment, the step 4 of outputting the Kalman algorithm filter value includes:
step 4-1, outputting Kalman algorithm filtering value
Figure BDA0003182173280000085
As the algorithm output.
FIG. 2 is an observation trajectory graph and measurement errors of a Kalman algorithm before improvement for fast tracking of a maneuvering target. Fig. 3 is an observation trajectory diagram and measurement errors of the modified Kalman algorithm used in the embodiment of the present application for fast tracking of a maneuvering target. Fig. 2 shows that the conventional Kalman algorithm only performs filter initialization at the start time of the filter, and the filter is not initialized again even if the tracking error increases during the tracking process, so that the estimated value has large deviation due to the increase of the covariance matrix, and the tracking effect is delayed seriously. Fig. 3 shows that the improved Kalman algorithm provided by the embodiment of the present application can quickly identify and initialize the filter when a maneuver occurs, the obtained estimated value does not have a large deviation from the observed value, the estimated value has high timeliness, and meanwhile, the estimated value also has an obvious smoothing filtering effect when the covariance matrix is converged. The application requirement of quickly tracking the real-time maneuvering target is better met.
Further analysis of the simulation results: FIG. 4 is a position error comparison diagram, which is calculated to obtain an algorithm distance error mean value 12.2323m and a standard deviation 15.5957m before improvement, an algorithm distance error mean value 2.9018m and a standard deviation 3.5371m after improvement, wherein the improved algorithm increases the position error from 12m to within 3m, and the tracking accuracy is greatly improved. Fig. 5 shows that when a U-shaped turning maneuver occurs on a target track, the tracking capability of the original Kalman filter deteriorates from about 550 tracking steps, i.e., from 5500s of simulation time. The improved algorithm is very close to the real track, and the rapid tracking is realized.
The present invention provides a method for quickly tracking a maneuvering target based on Kalman covariance, and a plurality of methods and approaches for implementing the technical solution, and the above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, a plurality of improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (5)

1. A maneuvering target fast tracking method based on Kalman covariance is characterized by comprising the following steps:
step 1, selecting a uniform velocity CV model as a filter of a Kalman algorithm, and performing state estimation on the filter to obtain a state vector of the filter
Figure FDA0003182173270000011
And a state covariance matrix P (k | k) having elements P of a first row and a first columnk|k(1,1) represents the x-axis distance error variance;
step 2, calculating the x-axis distance error variance P in the observation window of the state covariance matrix P (k | k)k|kAverage value m of (1,1)δrStandard deviation of deltaδr；
Step 3, when (P)k|k(1，1)-mδr)＞3*δδrTime, x-axis distance error variance Pk|k(1,1) if the change is large, judging that the target is maneuvering, and executing the step 1 to initialize the filter; otherwise, the tracking effect is good, and the target is continuously tracked and filtered;
and 4, outputting the filtering value of the Kalman algorithm.
2. The method of claim 1, wherein step 1 comprises the steps of:
step 1-1, setting the target motion state as uniform CV, sigmavFor the process noise standard deviation, σ, of the motion modelrFor measuring the noise standard deviation, T is the sampling time interval; selecting a uniform velocity CV model as a filter of a Kalman algorithm to enable the CV model to be in a state vector
Figure FDA0003182173270000012
Is in 4 dimensions:
Figure FDA0003182173270000013
where k denotes time, xk-1Is the coordinate value of the x-axis at time k-1,
Figure FDA0003182173270000014
speed of x-axis at time k-1, yk-1Is the coordinate value of the y-axis at time k-1,
Figure FDA0003182173270000015
the speed of the y-axis at time k-1;
the CV model state transition matrix F is:
Figure FDA0003182173270000016
the error covariance matrix Q is:
Figure FDA0003182173270000021
the state covariance matrix P is:
Figure FDA0003182173270000022
step 1-2, performing one-step prediction on the state estimation at the moment k-1:
Figure FDA0003182173270000023
step 1-3, let H be the measurement matrix,
Figure FDA0003182173270000024
z (k | k-1) represents the predicted value of the measurement at time k-1:
Figure FDA0003182173270000025
step 1-4, one-step prediction of state covariance is as follows:
P(k|k-1)＝F*P(k-1|k-1)*F′+Q；
wherein F' represents a transpose of F;
step 1-5, let R be the noise covariance matrix,
Figure FDA0003182173270000026
the model innovation covariance S is calculated by the following formulak：
Sk＝HP(k|k-1)H+R；
Wherein H' represents the transpose of H;
step 1-6, calculating innovation vk：
Figure FDA0003182173270000031
Wherein Z (k) ═ xk yk]′，xkCoordinate value, y, representing the x-axis at time kkA coordinate value representing the y-axis at time k;
step 1-7, calculating gain k (k):
K(k)＝P(k|k-1)H′(Sk)-1；
step 1-8, the state is updated by the following state update equation, where X (k | k) represents the state vector of the updated model:
Figure FDA0003182173270000032
step 1-9, the covariance of the model is updated by the covariance update equation:
P(k|k)＝P(k|k-1)-K(k)SkK′(k)
where K' (K) denotes the transpose of K (K).
3. The method of claim 2, wherein step 2 comprises the steps of:
step 2-1, making the length of the space observation window N, N belongs to (20,40), and calculating the error variance P of the x-axis distance in the observation window Nk|kAverage value m of (1,1)δr：
Figure FDA0003182173270000033
Step 2-2, calculating the x-axis distance error variance P in the observation window Nk|kStandard deviation δ of (1,1)δr：
Figure FDA0003182173270000034
4. A method according to claim 3, characterized in that step 3 comprises the steps of:
step 3-1, when (P)k|k(1，1)-mδr)＞3*δδrTime, x-axis distance error variance Pk|k(1,1) when the change is large, judging that the target is maneuvering, and executing step 1 to reinitialize the filter; the maneuvering index target deviates from the uniform CV model;
step 3-2, if no maneuver has taken place, i.e. (P)k|k(1，1)-mδr)≤3*δδrTaking the updated state vector as the state estimation of the next momentAnd calculating the updated covariance matrix as the covariance estimation of the next moment.
5. The method of claim 4, wherein step 4 comprises the steps of:
and 4-1, outputting the Kalman algorithm filtering value X (k | k) as algorithm output.
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