CN113536227B - Maneuvering target rapid tracking method based on Kalman covariance - Google Patents

Abstract

The application discloses a maneuvering target rapid tracking method based on Kalman covariance. The application adds maneuver detection based on Kalman filtering algorithm. During maneuver detection, abnormality detection in the covariance matrix observation window is performed. When the covariance value is larger than the threshold value in the observation window, the target is considered to be maneuvering, a filtering algorithm is initialized, and the target is tracked rapidly. The method solves the problem that the estimated value is greatly deviated due to the increase of the covariance matrix in the traditional algorithm, and the tracking effect is seriously lagged. The application has great practical value in real-time tracking and filtering of maneuvering targets.

Description

Maneuvering target rapid tracking method based on Kalman covariance

Technical Field

The application 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 the situation of a target track to be monitored in real time in the situation processing process is complex and changeable due to the fact that targets in an area have mobility. In the face of a maneuvering target focused on, how to quickly adjust a tracking algorithm when maneuvering occurs, track the maneuvering target in real time, and improve situation processing timeliness, so that the method is more and more urgent.

The Kalman Filter (hereinafter referred to as Kalman algorithm) is a time domain filtering method based on the meaning of minimum variance, describes the state of the system through a state space equation, recursively estimates the state output of the system, has the advantages of small data storage amount, easy realization and the like, and is the most commonly used tracking filtering algorithm in engineering. However, the Kalman algorithm is a tracking algorithm which does not perform maneuver detection, for a maneuver-obvious target, when a motion model is inconsistent with the reality, the estimated value is greatly deviated due to the increase of an algorithm covariance matrix, and the tracking effect is seriously lagged. According to the maneuvering detection method introduced by Yaakov Bar-Shalm et al, whether the target maneuvers or not is judged by setting a threshold value based on detection statistics established by filtering news. Fan Gongqi and the like illustrate that maneuver detection based on tracking filter information cannot achieve both rapid maneuver detection performance and good maneuver detection probability due to the constraint of the filter Q effect.

Disclosure of Invention

The application aims to: when the real-time tracking and filtering are carried out on the target, for the target with obvious maneuver, when the motion model is inconsistent with the reality, the estimated value is greatly deviated due to the increase of the covariance matrix, and the tracking effect is seriously lagged. In order to avoid the influence of the Q effect on maneuver detection and quickly identify maneuver conditions, maneuver detection is added in the traditional Kalman algorithm, an average value subtraction accumulation algorithm is adopted for a covariance matrix observation window, anomaly detection is carried out on a time sequence, when the covariance value is larger than a threshold value in the observation window, a target is considered to maneuver, a filtering algorithm is initialized, and quick tracking is carried out on the target. The application has great practical value in real-time tracking and filtering of maneuvering targets.

In order to solve the technical problems, the application discloses a maneuvering target rapid tracking method based on Kalman covariance, which comprises the following steps:

step 1, selecting a constant velocity CV model as a filter of a Kalman algorithm, and performing state estimation on the filter to obtain a state vector of the filterAnd a state covariance matrix P (k|k) of the elements P of the first row and the first column of the state covariance matrix P (k|k) _k|k (1, 1) represents an 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|k Mean value m of (1, 1) _δr Standard deviation delta _δr ；

Step 3, when (P _k|k (1,1)-m _δr )＞3*δ _δr When the x-axis distance error variance P _k|k (1, 1) the change is large, the target is judged to be maneuvering, and the step 1 is executed to initialize the filter; otherwise, the tracking effect is good, and the tracking filtering is continuously carried out on the target;

and 4, outputting a filtered value of the Kalman algorithm.

In one implementation, step 1 includes the steps of:

step 1-1, setting the target motion state to be uniform (Constant Velocity, CV), sigma _v For the motion model process noise standard deviation, sigma _r To measure the noise standard deviation, T is the sampling time interval. The constant velocity CV model is chosen as a filter for the Kalman algorithm. For the dimensional consistency of matrix operations, the CV model state vector is made 4-dimensional. CV model state vector:wherein (1)>Represents constant velocity CV model state vector, k represents time, x _k-1 Coordinate value of x-axis at time k-1, < >>Velocity of x-axis at time k-1, y _k-1 Coordinate value of y-axis at time k-1, < >>The velocity of the y-axis at time k-1;

the CV model state transition matrix F is:

the error covariance matrix Q is:

the state covariance matrix P is:

step 1-2, performing one-step prediction on state estimation at the moment of k-1:

step 1-3, let H be the measurement matrix,z (k|k-1) represents the predicted value of the measurement at time k-1:

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,calculating a model innovation covariance S by the following formula _k ：

S _k ＝HP(k|k-1)H′+R；

Wherein H' represents a transpose of H;

step 1-6, calculating innovation v _k ：

Wherein Z (k) = [ x ] _k y _k ]′，x _k Coordinate value of x-axis at k time, y _k Coordinate values of a y-axis at the moment k are represented;

step 1-7, calculating gain K (K):

K(k)＝P(k|k-1)H′(S _k ) ^-1 ；

step 1-8, updating the state by a state update equation in whichState vectors representing the updated model:

step 1-9, updating the covariance of the model by the following covariance update equation:

P(k|k)＝P(k|k-1)-K(k)S _k K′(k)

where K' (K) represents the transpose of K (K).

In one implementation, step 2 includes the steps of:

in the step 2-1 of the method,

let the space observation window length be N, N E (20, 40), calculate the x-axis distance error variance P in the observation window N _k|k Mean value m of (1, 1) _δr ：

Step 2-2, calculating the variance P of the distance error of the x-axis in the observation window N _k|k Standard deviation delta of (1, 1) _δr ：

The effect of the filter on the target position is good or bad, and the effect is reflected on whether the coordinate error curve converges or not. The mean value and standard deviation of the x-axis distance variance in the observation window N are obtained through calculation, and the filtering effect of the filter can be judged through checking the convergence condition of the x-axis distance variance curve in the subsequent steps. The P is _k|k (1,1)＝cov(x _k ,x _k ) 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, performing outlier detection on the x-axis distance variance by using a statistical method, and assuming that the data obeys the normal distribution, according to a 3 x delta criterion: 99.7% of the data fall into region (P _k|k (1,1)-m _δr )≤3*δ _δr In general, it is considered that in the region (P _k|k (1,1)-m _δr )≤3*δ _δr The outer points are outliers.

When (P) _k|k (1,1)-m _δr )＞3*δ _δr When the x-axis distance error variance P _k|k (1, 1) the change is large, the target is judged to be maneuvering, and the step 1 is executed to reinitialize the filter; the maneuvering finger target deviates from the constant velocity CV model;

step 3-2, if no maneuver occurs, i.e. (P _k|k (1,1)-m _δr )≤3*δ _δr And 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 a Kalman algorithm filtering valueAs an algorithm output.

The beneficial effects are that:

the application relates to a method for quickly tracking and filtering a maneuvering target in real time in the field of situation processing, in particular to a method for quickly tracking the maneuvering target by utilizing Kalman covariance. The application uses mean value and standard deviation of x-axis distance error covariance, uses average value subtraction accumulation algorithm to detect abnormality of time sequence, judges maneuver state, and initializes filter when tracking effect is bad. The problems of large deviation of the estimated value, serious delay of the tracking effect and the like caused by the increase of the covariance matrix are avoided, the real-time performance of maneuvering target tracking is improved, and the effect of quickly tracking the real-time target track is achieved.

Drawings

The foregoing and other advantages of the application will become more apparent from the following detailed description of the application when taken in conjunction with the accompanying drawings and detailed description.

FIG. 1 is a flowchart of a fast maneuvering target tracking method based on Kalman covariance according to an embodiment of the application.

FIG. 2 is an observation trace diagram and measurement error of a Kalman algorithm before improvement for fast tracking of a maneuvering target.

FIG. 3 is an observation trace diagram and measurement error of a motorized target for rapid tracking by using the improved Kalman algorithm according to an embodiment of the present application.

FIG. 4 is a graph comparing the positional errors of a fast tracking maneuver target by the Kalman algorithm before modification and the modified Kalman algorithm used in the embodiments of the present application.

FIG. 5 is a graph of the effect of the Kalman algorithm before modification and the modified Kalman algorithm employed in an embodiment of the present application when a U-turn maneuver occurs in the target track.

Detailed Description

The application will be further described with reference to the accompanying drawings and examples.

Fig. 1 is a flowchart of a fast maneuvering target tracking method based on Kalman covariance, which is applied to an aerial target and a ground target and specifically comprises the following steps:

step 1, selecting a constant velocity CV model as a filter of a Kalman algorithm, and performing state estimation on the filter to obtain a state vector of the filterAnd a state covariance matrix P (k|k) of the elements P of the first row and the first column of the state covariance matrix P (k|k) _k|k (1, 1) represents an 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|k Mean value m of (1, 1) _δr Standard deviation delta _δr ；

Step 3, when (P _k|k (1,1)-m _δr )＞3*δ _δr When the x-axis distance error variance P _k|k (1, 1) the change is large, the target is judged to be maneuvering, and the step 1 is executed to initialize the filter; otherwise, the tracking effect is good, and the tracking filtering is continuously carried out on the target;

and 4, outputting a filtered value of the Kalman algorithm.

In this embodiment, step 1 includes the following steps: :

step 1-1, setting the target motion state to be uniform (Constant Velocity, CV). Setting target initial position (5 km,7.8 km), measuring noise as zero-mean Gaussian white noise, and standard deviation of noise as sigma _r Process noise is zero-mean gaussian white noise with standard deviation σ _v The target motion sampling interval t=10s=0.005 m/s, and the simulated target performs U-shaped motion.

A filter of the CV model Kalman algorithm is selected. CV model state vector:

the CV model state transition matrix F is:

the error covariance matrix Q is:

the state covariance matrix P is:

step 1-2, performing one-step prediction on state estimation at the moment of k-1:

step 1-3, let H be the measurement matrix,z (k|k-1) represents the predicted value of the measurement at time k-1:

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,calculating a model innovation covariance S by the following formula _k ：

S _k ＝HP(k|k-1)H′+R；

Wherein H' represents a transpose of H;

step 1-6, calculating innovation v _k ：

Wherein Z (k) = [ x ] _k y _k ]′，x _k Coordinate value of x-axis at k time, y _k Coordinate values of a y-axis at the moment k are represented;

step 1-7, calculating gain K (K):

K(k)＝P(k|k-1)H′(S _k ) ^-1 ；

step 1-8, updating the state by a state update equation in whichState vectors representing the updated model:

step 1-9, updating the covariance of the model by the following covariance update equation:

P(k|k)＝P(k|k-1)-K(k)S _k K′(k)

where K' (K) represents the transpose of K (K).

In this embodiment, step 2 performs abnormality detection on the x-axis distance error covariance by using a spatial observation window, and calculates a mean value and a standard deviation of the x-dimensional distance error covariance, including the following steps:

step 2-1, let the space observation window length be N, let N=30, calculate the x-axis distance error variance P in the observation window N _k|k Mean value m of (1, 1) _δr ：

Step 2-2, calculating the variance P of the distance error of the x-axis in the observation window N _k|k Standard deviation delta of (1, 1) _δr ：

In this embodiment, step 3 adopts an average value anomaly accumulation algorithm to perform maneuver detection, and includes the following steps:

step 3-1, using the 3. Delta. Theorem, when (P _k|k (1,1)-m _δr )＞3*δ _δr When the x-axis distance error variance P _k|k (1, 1) the change is large, the target is judged to be maneuvering, and the step 1 is executed to reinitialize the filter; the maneuvering means that the target deviates from a constant velocity CV model, if the target runs at a constant velocity, the target suddenly turns a large curve;

step 3-2, if no maneuver occurs, i.e. (P _k|k (1,1)-m _δr )≤3*δ _δr Taking the updated state vector as the state estimation of the next moment, and taking the updated covariance matrix as the next momentCovariance estimation of the score.

In this embodiment, step 4 outputs a Kalman algorithm filtered value, including:

step 4-1, outputting a Kalman algorithm filtering valueAs an algorithm output.

FIG. 2 is an observation trace diagram and measurement error of a Kalman algorithm before improvement for fast tracking of a maneuvering target. FIG. 3 is an observation trace diagram and measurement error of a motorized target for rapid tracking by using the improved Kalman algorithm according to an embodiment of the present application. Fig. 2 shows that the conventional Kalman algorithm only performs the filtering initialization at the beginning time of the filter, and even if the tracking error increases in the tracking process, the tracking error is not initialized any more, and the estimated value is greatly deviated due to the increase of the covariance matrix, so that the tracking effect is seriously lagged. Fig. 3 shows that the improved Kalman algorithm provided by the embodiment of the application can quickly identify and initialize the filter when maneuvering occurs, the obtained estimated value and the observed value have no larger deviation, the estimated value has high timeliness, and the estimated value has obvious smooth filtering effect when the covariance matrix converges. The application requirement of fast tracking real-time maneuvering targets is well met.

Further analysis of simulation results: fig. 4 is a position error comparison chart, and after calculation, the distance error average value 12.2323m of the algorithm before improvement, the standard deviation 15.5957m, the distance error average value 2.9018m of the algorithm after improvement, the standard deviation 3.5371m, and the position error is improved from 12m to 3m by the improved algorithm, so that the tracking precision is greatly improved. Fig. 5 shows that the original Kalman filter is deteriorated in tracking ability from about 550 tracking steps, i.e. the simulation time 5500s, when the U-turn maneuver occurs in the target track. The improved algorithm is very close to a real track, and quick tracking is realized.

The application provides a fast maneuvering target tracking method based on Kalman covariance, and the method and the way for realizing the technical scheme are numerous, the above description is only a preferred embodiment of the application, and it should be noted that, for a person skilled in the art, several improvements and modifications can be made, and the improvements and modifications should be regarded as the protection scope of the application. The components not explicitly described in this embodiment can be implemented by using the prior art.

Claims (2)

1. A maneuvering target rapid tracking method based on Kalman covariance is characterized by comprising the following steps:

step 1, selecting a constant velocity CV model as a filter of a Kalman algorithm, and performing state estimation on the filter to obtain a state vector of the filterAnd a state covariance matrix P (k|k) of the elements P of the first row and the first column of the state covariance matrix P (k|k) _k|k (1, 1) represents an 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|k Mean value m of (1, 1) _δr Standard deviation delta _δr ；

Step 3, when (P _k|k (1,1)-m _δr )＞3*δ _δr When the x-axis distance error variance P _k|k (1, 1) the change is large, the target is judged to be maneuvering, and the step 1 is executed to initialize the filter; otherwise, the tracking effect is good, and the tracking filtering is continuously carried out on the target;

step 4, outputting a filtering value of a Kalman algorithm;

step 1 comprises the following steps:

step 1-1, setting the target motion state as uniform velocity CV, sigma _v For the motion model process noise standard deviation, sigma _r For measuring the noise standard deviation, T is the sampling time interval; selecting constant-speed CV model as Kalman algorithm filter to make CV model state vectorThe method is characterized by 4 dimensions: />Wherein k represents time, x _k-1 Coordinate value of x-axis at time k-1, < >>Velocity of x-axis at time k-1, y _k-1 Coordinate value of y-axis at time k-1, < >>The velocity of the y-axis at time k-1;

the CV model state transition matrix F is:

the error covariance matrix Q is:

the state covariance matrix P is:

step 1-2, performing one-step prediction on state estimation at the moment of k-1:

step 1-3, let H be the measurement matrix,z (k|k-1) represents the predicted value of the measurement at time k-1:

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,calculating a model innovation covariance S by the following formula _k ：

S _k ＝HP(k|k-1)H'+R；

Wherein H' represents a transpose of H;

step 1-6, calculating innovation v _k ：

Wherein Z (k) = [ x ] _k y _k ]'，x _k Coordinate value of x-axis at k time, y _k Coordinate values of a y-axis at the moment k are represented;

step 1-7, calculating gain K (K):

K(k)＝P(k|k-1)H'(S _k ) ^-1 ；

step 1-8, updating the state by a state update equation in whichState vectors representing the updated model:

step 1-9, updating the covariance of the model by the following covariance update equation:

P(k|k)＝P(k|k-1)-K(k)S _k K'(k)

wherein K' (K) represents a transpose of K (K);

step 2 comprises the following steps:

step 2-1, making the length of the space observation window N, N E (20, 40), calculating the distance error variance P of the x-axis in the observation window N _k|k Mean value m of (1, 1) _δr ：

Step 2-2, calculating the variance P of the distance error of the x-axis in the observation window N _k|k Standard deviation delta of (1, 1) _δr ：

Step 3 comprises the following steps:

step 3-1, when (P _k|k (1,1)-m _δr )＞3*δ _δr When the x-axis distance error variance P _k|k (1, 1) the change is large, the target is judged to be maneuvering, and the step 1 is executed to reinitialize the filter; the maneuvering finger target deviates from the constant velocity CV model;

step 3-2, if no maneuver occurs, i.e. (P _k|k (1,1)-m _δr )≤3*δ _δr And 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.

2. The method according to claim 1, wherein step 4 comprises the steps of: step 4-1, outputting a Kalman algorithm filtering valueAs an algorithm output.