CN115170940A - UUV target tracking method based on generalized maximum correlation entropy Kalman filtering - Google Patents

UUV target tracking method based on generalized maximum correlation entropy Kalman filtering Download PDF

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CN115170940A
CN115170940A CN202210833026.9A CN202210833026A CN115170940A CN 115170940 A CN115170940 A CN 115170940A CN 202210833026 A CN202210833026 A CN 202210833026A CN 115170940 A CN115170940 A CN 115170940A
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高松
何嘉诚
王刚
彭倍
张堃
毛雪梅
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a UUV target tracking method based on generalized maximum correlation entropy Kalman filtering, which comprises the following steps: s1, establishing a motion equation of a UUV, wherein the UUV is an unmanned underwater vehicle; s2, establishing an observation equation of the UUV; and S3, processing the data by adopting a Kalman filtering algorithm based on weighted least squares and generalized maximum associated entropy to realize the tracking and positioning of the UUV. According to the method, the weighted least square and the generalized maximum correlation entropy Kalman filtering algorithm are applied to UUV target tracking, the process noise is processed by the weighted least square, the observation noise is processed by the generalized maximum correlation entropy, the robustness to different types of non-Gaussian noise is strong, and the excellent tracking effect can be obtained in the complex marine environment.

Description

UUV target tracking method based on generalized maximum correlation entropy Kalman filtering
Technical Field
The invention is suitable for the field of unmanned underwater vehicles, and particularly relates to a UUV target tracking method based on generalized maximum correlation entropy Kalman filtering.
Background
Unmanned Underwater Vehicles (UUV) play an important role in tasks such as Underwater detection, underwater video recording, search and reconnaissance and the like as one of research hotspots in the marine field in the present year. In order to meet the requirement of normal operation of equipment in deep sea, the accurate position information can be obtained more conveniently and accurately. Therefore, whether aiming at the remote escort of the UUV or supporting the UUV to complete a specific underwater task, tracking and positioning the moving UUV is always an extremely important subject in the ocean field. Currently, tracking and positioning for UUVs is mainly by detecting acoustic radiation of the UUV. An Ultra Short Baseline (USBL) positioning system utilizes the measured distance and the direction angle to track and position the underwater target, and is widely applied to the UUV positioning and tracking field by virtue of the advantages of high integration level and good operability.
However, since the complex marine environment (temperature, salinity, density, etc.) is dynamically changed, tracking and positioning of UUVs by using the USBL positioning system may be seriously affected by various errors, and usually Kalman Filtering (KF) is used to improve the accuracy and reliability of underwater tracking and positioning. The traditional kalman filtering is based on the linear system and gaussian assumption, and uses the minimum mean square error as the criterion. However, the marine environment cannot satisfy the assumption of gaussian noise, which results in the performance deterioration of the conventional kalman filter in the presence of non-gaussian noise, especially impulse noise interference. The main reason is that the minimum mean square error criterion can only use the second-order statistics of data, and is very sensitive to outliers in noise, which causes the robustness of the traditional kalman filtering in most practical scenes to deteriorate.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a UUV target tracking method based on generalized maximum correlation entropy Kalman filtering.
The purpose of the invention is realized by the following technical scheme: a UUV target tracking method based on generalized maximum correlation entropy Kalman filtering comprises the following steps:
s1, establishing a motion equation of the UUV:
Figure BDA0003746271990000021
in the formula, the left side of equal sign
Figure BDA0003746271990000022
Is the state of the target at time k, x k ,y k ,z k The position of the target in the coordinate system at time k,
Figure BDA0003746271990000023
the speed of the target at the moment k and T are observation time intervals for acquiring the state of the target; in the operation process, the UUV is inevitably influenced by external environment factors, and the influencing factors are regarded as process noise for modeling, so that the process noise W is added k Wherein the UUV is an unmanned underwater vehicle;
s2, establishing an observation equation of the UUV:
Figure BDA0003746271990000024
in the observation process, a USBL positioning system is adopted for observation, namely the USBL positioning system is an ultra-short baseline positioning system; the position of the target k instant obtained by the sensor is recorded
Figure BDA0003746271990000025
The observation process of the USBL positioning system is influenced by noise error, and the observation noise is defined as V k ；
S3, processing the data by adopting a Kalman filtering algorithm based on weighted least squares and generalized maximum associated entropy to realize the tracking and positioning of UUV:
s301: selecting a shape parameter alpha and a scale parameter beta, setting an initial state estimate
Figure BDA0003746271990000026
And an initial covariance matrix P 0|0 ；
S302: obtaining a predicted value, and obtaining a true value and a predicted value error covariance matrix:
Figure BDA0003746271990000027
P k|k-1 ＝A k P k-1|k-1 A k T +Q k-1
wherein A is k Is the state transition matrix of the system and,
Figure BDA0003746271990000028
is the best estimate of the state at time k-1,
Figure BDA0003746271990000029
is the predicted value of the state at time k, P k|k-1 Is an error covariance matrix of the true and predicted values at time k, i.e. a priori estimated covariance matrix, P k-1|k-1 Is an error covariance matrix, Q, of the true and estimated values at time k-1 k-1 Is a covariance matrix of the process noise at time k-1;
s303: the state at the moment k is optimized and estimated by establishing a cost function to obtain an estimated state,
Figure BDA0003746271990000031
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003746271990000032
wherein the content of the first and second substances,
Figure BDA0003746271990000033
is an estimated value of the state at the time k, and the state includes the position and the speed of the target at the current time k, so that the target tracking of UUV can be realized according to the estimated value of the state, and gamma = alpha/[ 2 beta Γ (1/alpha) ]]Is a normalization constant, exp is an exponential function with e as the base, λ =1/β α Is a nuclear parameter, C k Is the observation matrix of the k-time system, R k Is a covariance matrix of observed noise at time k;
s304: defining a filter gain matrix
Figure BDA0003746271990000034
Solving to obtain a filter gain matrix K through matrix inversion lemma on the premise of obtaining an estimation state k ；
S305: the a posteriori estimated covariance matrix is updated,
Figure BDA0003746271990000035
wherein, P k|k Is the a posteriori estimated covariance matrix at time k for the iterative update at time k + 1.
The invention has the beneficial effects that: the cost function based on the weighted least square and the generalized maximum correlation entropy is introduced into Kalman filtering, applied to a UUV target tracking and positioning algorithm, a UUV motion model and an observation model are established, and the UUV position information observed by the USBL system is filtered, so that the influence of external process noise and observation noise is avoided, and robust tracking and positioning are realized.
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FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic flow chart of a Kalman filtering method based on weighted least squares and generalized maximum entropy of correlation in an embodiment of the present invention;
FIG. 3 is a schematic of a tracking error for sampling 300 samples in an example of an embodiment of the present invention;
FIG. 4 is a schematic diagram of tracking error for sampling 300 samples when a different shape parameter α is selected in an example of an embodiment of the present invention;
fig. 5 is a schematic diagram of tracking errors for 300 samples when different shape parameter β is selected in an example of an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
As shown in fig. 1, a UUV target tracking method based on generalized maximum entropy kalman filtering includes the following steps:
s1, in order to simulate the underwater motion of a UUV, a motion equation needs to be established, namely, a motion rule of a target is modeled, the target moves at a constant speed in a three-dimensional space, and the motion equation of the target at k +1 moment under discrete time can be expressed as follows:
Figure BDA0003746271990000041
Figure BDA0003746271990000042
Figure BDA0003746271990000043
Figure BDA0003746271990000044
Figure BDA0003746271990000045
Figure BDA0003746271990000046
in the formula, x k ,y k ,z k Is the position of the target at time k,
Figure BDA0003746271990000047
the speed of the target at the moment k and the observation time interval for acquiring the state of the target T are determined, and UUV is inevitably influenced by external environment factors in the actual operation process, and the influencing factors can be regarded as process noise to carry out modeling, so the process noise W is added k 。
The above equation of motion is expressed in matrix form as follows:
Figure BDA0003746271990000048
in the formula, the left side of equal sign
Figure BDA0003746271990000049
Is the state of the target at time k
S2, establishing an observation equation, wherein the observation equation is a model hypothesis for obtaining UUV positions of the USBL system:
Figure BDA00037462719900000410
in fact, the observation process of the USBL system is affected by noise errors, which the present invention defines as V k 。
S3, introducing a cost function based on weighted least square and generalized maximum correlation entropy into Kalman filtering and applying the cost function to a target tracking and positioning algorithm of UUV, wherein the Kalman filtering method is introduced as follows:
for the kalman filter algorithm, the state space expression of the linear system is expressed as:
x k ＝A k x k-1 +w k ,
y k ＝C k x k +v k ,
where the index k represents the kth instant,
Figure BDA0003746271990000051
is the state value at the time of k,
Figure BDA0003746271990000052
is the observed value at the time of k,
Figure BDA0003746271990000053
is a matrix of state transitions that is,
Figure BDA0003746271990000054
is an observation matrix of the optical system,
Figure BDA0003746271990000055
is a result of the process noise,
Figure BDA0003746271990000056
is the observation noise. w is a k And v k Is zero mean noise, and is uncorrelated, and the covariance matrix of the two can be defined as,
Figure BDA0003746271990000057
Figure BDA0003746271990000058
due to the fact that non-Gaussian noise interference exists in practice, the performance of the Kalman filtering method based on the minimum mean square error criterion is reduced, and the noise distribution is diversified, so that the performance of the Kalman filtering method based on the maximum correlation entropy fluctuates greatly. Therefore, the invention provides a Kalman filtering method based on weighted least squares and generalized maximum correlation entropy to flexibly process different types of non-Gaussian noise in practice.
The invention provides a new cost function, which uses weighted least square to process noise and uses weighted least square and generalized maximum correlation entropy to process observation noise, and the expression is as follows:
Figure BDA0003746271990000059
wherein m, n are weight values,
Figure BDA00037462719900000510
is an estimate of the state at time k,
Figure BDA00037462719900000511
is a prediction of the state at time k, P k|k-1 Is a covariance matrix of the true and predicted values at time k, i.e. a priori estimated covariance matrix, G α,β () Is a gaussian density function, alpha is a shape parameter and beta is a scale parameter.
The optimal estimation of the current state is as follows:
Figure BDA00037462719900000512
wherein sign () is a sign function and the current state optimization estimation decision is the current cost function J L When the minimum value is obtained, the estimated state at that time
Figure BDA0003746271990000061
For optimal estimation, the specific method is a cost function J L To pair
Figure BDA0003746271990000062
Derivation is carried out, when the derivative is equal to 0, the cost function is determined to obtain the minimum value, and the above formula ensures that the estimated value obtained by the method is the optimal estimation of the true value; let n =1,m = a lambda/2, and can be obtained by simplifying the arrangement
Figure BDA0003746271990000063
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003746271990000064
let the filter gain matrix
Figure BDA0003746271990000065
Is equal to K k Is obtained by matrix inversion lemma and arrangement
Figure BDA0003746271990000066
As shown in fig. 2, the kalman filtering method provided by the present invention mainly comprises the following steps:
s301, selecting a proper shape parameter alpha and a proper scale parameter beta, and setting initial state estimation
Figure BDA0003746271990000067
And an initial covariance matrix P 0|0 。
S302. Obtain the prediction value and prediction error covariance matrix using the following equations,
Figure BDA0003746271990000068
P k|k-1 ＝A k P k-1|k-1 A k T +Q k-1
wherein A is k Is the state transition matrix of the system and,
Figure BDA0003746271990000069
is the best estimate of the state at time k-1,
Figure BDA00037462719900000610
is the predicted value of the state at time k, P k|k-1 Is an error covariance matrix of the true and predicted values at the time k, i.e. a priori estimated covariance matrix, P k-1|k-1 Is an error covariance matrix, Q, of the true and estimated values at time k-1 k-1 Is the covariance matrix of the process noise at time k-1.
S303, by establishing a cost function and carrying out optimization estimation on the current state, an estimation state can be obtained,
Figure BDA00037462719900000611
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00037462719900000612
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00037462719900000613
is an estimated value of the state at the moment k, namely the UUV target position obtained at the moment by the method, thereby realizing the target tracking of the UUV, and gamma = alpha/[ 2 beta Γ (1/alpha) ]]Is a normalization constant, exp is an exponential function with e as the base, λ =1/β α Is a nuclear parameter, C k Is the observation matrix of the k-time system, R k Is a covariance matrix of the observed noise at time k;
s304: based on the estimation states, a Kalman filter gain matrix may be defined,
Figure BDA0003746271990000071
s305. Update the a posteriori estimated covariance matrix using the following formula,
Figure BDA0003746271990000072
wherein, P k|k The method is a posterior estimation covariance matrix at the moment k, and is convenient for iterative calculation at the moment k + 1.
The performance of the UUV target tracking method based on weighted least squares and generalized maximum entropy kalman filtering in the embodiment of the present invention is evaluated by combining a specific simulation example.
In the embodiment of the present application, the constant velocity model is a common object motion model that assumes that an object moves in a straight line at a certain velocity. The weighted least square and generalized maximum correlation entropy Kalman filtering method (WGMCKF) is adopted to compare with the traditional Kalman Filtering (KF) and the maximum correlation entropy Kalman filtering (MCKF) algorithm.
The state space expression of the constant velocity model is as follows,
Figure BDA0003746271990000073
Figure BDA0003746271990000074
where T =1 represents the measurement time interval, w k And v k Is the process noise and the observation noise which are consistent with the mixed Gaussian noise, and the expression is as follows,
w i:k ～0.9N(0,0.01)+0.1N(0,1),i＝1,2,...,6
v j:k ～0.9N(0,0.01)+0.1N(0,10),j＝1,2,3
fig. 3 is a schematic diagram of tracking errors of 300 samples when the shape parameter α =1.0 and the scale parameter β =2.0 are selected in the example of the embodiment of the present invention. From qualitative comparative analysis of the tracking error trend, it can be known that: compared with the traditional Kalman filtering algorithm and the maximum correlation entropy Kalman filtering algorithm, the weighted least square and generalized maximum correlation entropy Kalman filtering method can better process the interference of non-Gaussian noise in the UUV target tracking process.
Fig. 4 is a schematic diagram of tracking errors of 300 samples sampled by respectively selecting a shape parameter α =1.0,1.5,2.0,2.5,4.0, and a scale parameter β =2.0 in an example of the embodiment of the present invention. From the analysis of the tracking steady-state error, the following results are obtained: for observation noise, the smaller the value of the shape parameter is, the better the target tracking algorithm effect is.
Fig. 5 is a schematic diagram of tracking errors of 300 samples sampled with the shape parameter α =2.0 when the scale parameter β =0.7,1.0,2.0,3.5,5.0 is respectively selected in the example of the embodiment of the present invention. From the analysis of tracking steady-state error, it can be known that: for observation noise, the smaller the scale parameter value is, the better the UUV target tracking algorithm effect is. It can be seen from fig. 4 and 5 that both the shape parameter and the scale parameter affect the performance of the algorithm of the present embodiment. When dealing with different external noise, selecting appropriate parameters may enable the algorithm to achieve the best tracking performance.
The foregoing description shows and describes a preferred embodiment of the invention, but as aforementioned, it is to be understood that the invention is not limited to the form disclosed herein, but is not to be construed as excluding other embodiments and from various other combinations, modifications, and environments and is capable of changes within the scope of the inventive concept as expressed herein, commensurate with the above teachings or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (6)

1. A UUV target tracking method based on generalized maximum correlation entropy Kalman filtering is characterized in that: the method comprises the following steps:
s1, establishing a motion equation of a UUV, wherein the UUV is an unmanned underwater vehicle;
s2, establishing an observation equation of the UUV;
and S3, processing the data by adopting a Kalman filtering algorithm based on weighted least squares and generalized maximum associated entropy to realize the tracking and positioning of the UUV.
2. The UUV target tracking method based on the generalized maximum entropy Kalman filtering is characterized in that: the motion equation in step S1 is:
Figure FDA0003746271980000011
in the formula, the left side of the equal sign
Figure FDA0003746271980000012
Is the state of the target at time k, x k ,y k ,z k The position of the target in the coordinate system at time k,
Figure FDA0003746271980000013
the speed of the target at the moment k and T are observation time intervals for acquiring the state of the target; in the operation process, the UUV is inevitably influenced by external environment factors, and the influencing factors are regarded as process noise to carry out modeling, so the process noise W is added k 。
3. The UUV target tracking method based on the generalized maximum entropy Kalman filtering is characterized in that: the observation equation in step S2 is:
Figure FDA0003746271980000014
in the observation process, a USBL positioning system is adopted for observation, namely the USBL positioning system is an ultra-short baseline positioning system; the position of the target k instant obtained by the sensor is recorded
Figure FDA0003746271980000015
The observation process of the USBL positioning system is influenced by noise error, and the observation noise is defined as V k 。
4. The UUV target tracking method based on the generalized maximum entropy Kalman filtering is characterized in that: the step S3 includes the following substeps:
s301: selecting a shape parameter alpha and a scale parameter beta, setting an initial state estimate
Figure FDA0003746271980000021
And an initial covariance matrix P 0|0 ；
S302: obtaining a predicted value, and obtaining a true value and a predicted value error covariance matrix:
Figure FDA0003746271980000022
P k|k-1 ＝A k P k-1|k-1 A k T +Q k-1
wherein A is k Is the state transition matrix of the system and,
Figure FDA0003746271980000023
is the best estimate of the state at time k-1,
Figure FDA0003746271980000024
is a prediction of the state at time k, P k|k-1 Is an error covariance matrix of the true and predicted values at time k, i.e. a priori estimated covariance matrix, P k-1|k-1 Is an error covariance matrix, Q, of the true and estimated values at time k-1 k-1 Is a covariance matrix of the process noise at time k-1;
s303: the state at the moment k is optimized and estimated by establishing a cost function to obtain an estimated state,
Figure FDA0003746271980000025
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003746271980000026
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003746271980000027
is an estimated value of the state at the time k, and since the state includes the position and velocity of the target at the current time k, the target tracking of UUV can be realized based on the estimated value of the state, γ = α/[2 β Γ (1/α)]Is a normalization constant, exp is an exponential function with e as the base, λ =1/β α Is a nuclear parameter, C k Is the observation moment of the system at time kArray, R k Is a covariance matrix of the observed noise at time k;
s304: defining a filter gain matrix
Figure FDA0003746271980000028
Solving to obtain a filter gain matrix K through matrix inversion lemma on the premise of obtaining an estimation state k ；
S305: the a posteriori estimated covariance matrix is updated,
Figure FDA0003746271980000029
wherein, P k|k Is the posterior estimated covariance matrix at time k for iterative update at time k + 1.
5. The UUV target tracking method based on the generalized maximum entropy Kalman filtering is characterized in that: the cost function established in step S303 uses weighted least squares to process noise, and uses generalized maximum correlation entropy to process observation noise, which is expressed as:
Figure FDA0003746271980000031
wherein m, n are weight values,
Figure FDA0003746271980000032
Figure FDA0003746271980000033
is an estimate of the state at time k,
Figure FDA0003746271980000034
is a prediction of the state at time k, P k|k-1 Is a covariance matrix of the true and predicted values at time k, i.e. a priori estimated covariance matrix, G α,β () Is a Gaussian densityThe function, α, is the shape parameter and β is the scale parameter.
6. The UUV target tracking method based on the generalized maximum entropy Kalman filtering is characterized in that: in step S303, when the state at time k is optimally estimated, the state optimal estimation decision is the current cost function J L When the minimum value is obtained, the estimated state at that time
Figure FDA0003746271980000035
For optimal estimation, the specific method is a cost function J L For is to
Figure FDA0003746271980000036
And (5) derivation, wherein when the derivative is equal to 0, the cost function is considered to obtain a minimum value, which is expressed as:
Figure FDA0003746271980000037
wherein sign () is a sign function, and n =1, m = α λ/2, which can be obtained by simplification
Figure FDA0003746271980000038
Wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003746271980000039
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117195946A (en) * 2023-09-08 2023-12-08 兰州理工大学 WSN maneuvering target tracking method based on extended Kalman filtering
CN117784114A (en) * 2023-12-26 2024-03-29 兰州理工大学 Irregular extended target tracking method based on mixed entropy under abnormal noise

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117195946A (en) * 2023-09-08 2023-12-08 兰州理工大学 WSN maneuvering target tracking method based on extended Kalman filtering
CN117784114A (en) * 2023-12-26 2024-03-29 兰州理工大学 Irregular extended target tracking method based on mixed entropy under abnormal noise
CN117784114B (en) * 2023-12-26 2024-05-14 兰州理工大学 Irregular extended target tracking method based on mixed entropy under abnormal noise

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