CN112800889A - Target tracking method based on distributed matrix weighting and Gaussian filtering fusion - Google Patents
Target tracking method based on distributed matrix weighting and Gaussian filtering fusion Download PDFInfo
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Abstract
A target tracking method based on distributed matrix weighting fusion Gaussian filtering is characterized in that Gaussian filtering is used for local state estimation, then statistical linear regression is used for approximating error cross covariance between local estimation, finally, an optimization parameter under a maximum likelihood criterion is obtained by solving an optimization problem, and an error cross covariance matrix is adjusted. The invention reduces the performance loss caused by the linearization error in the statistical linear regression and improves the target tracking precision.
Description
Technical Field
The invention belongs to the field of moving target tracking, and particularly relates to a target tracking method based on distributed matrix weighting and Gaussian filtering.
Background
The target tracking is a basic problem in the fields of military and civil use, and plays an important role in the fields of military national defense, urban traffic, family service and the like. In recent years, communication technology and microelectronic technology are rapidly developed, wireless sensor networks are widely applied to positioning and tracking of moving targets, and the requirement of people on target tracking accuracy is higher and higher.
In moving object tracking, nonlinear filtering problems are often involved. Gaussian filtering is a kind of nonlinear filtering method, and is widely used in practical systems. However, only a single sensor is considered in gaussian filtering, and the estimation accuracy often cannot meet the requirement, so that data of a plurality of sensors needs to be fused to obtain estimation with higher accuracy. Although the global optimal estimation can be achieved by centralized fusion, the robustness and reliability are poor compared with distributed fusion due to the error of sensor information and the complexity of calculation. The matrix weighted fusion is an optimal weighted fusion criterion in the sense of minimum mean square error, but it needs to know the cross covariance between local filters, and in the case of a linear system, the cross covariance can be deduced as an analytic solution by using Kalman filtering. However, in a nonlinear system, the state of the system and the measurement equation are complicated, the error cross-covariance between local filters cannot be obtained, and the classical fusion criterion is not applicable.
Disclosure of Invention
In order to solve the problem that the error covariance between local filters cannot be obtained when the existing nonlinear moving target tracking method is fused, the invention provides a target tracking method based on distributed matrix weighting fusion Gaussian filtering, and the target tracking precision and robustness are improved.
In order to achieve the purpose, the invention provides the following technical scheme:
a target tracking method based on a distributed matrix weighting fusion Gaussian filter comprises the following steps:
step 1: establishing a nonlinear system state space model and a measurement model, wherein the process comprises the following steps:
1.1 establishing a System State model
xk+1=f(xk)+wk (1)
Wherein xkSystem state at time k, f (x)k)∈RnIs an arbitrary non-linear vector function, wkAs covariance of QkWhite gaussian noise of (1);
1.2 building a system measurement model
Where i is the observation station number,the measured value of the observation station i at the moment k +1,for any non-linear function of the vector,is covariance ofWhite gaussian noise of (1);
step 2: calculating local Gaussian filter estimation and covariance by the following process:
2.1 initialization x0|0And P0|0,k=0;
2.2 definition
Where g (x) is an arbitrary non-linear function,is mean value ofNormal distribution with covariance P, L system state dimension, S Chislesky decomposition with P, ej∈RL×1Row 1 for j and row 0 for other row;
Wherein
And step 3: calculating the local estimation cross covariance and the fusion estimation, and the process is as follows:
wherein
Wherein the optimized parameter lambda is based on the maximum likelihood criterion of the measurementkThe optimization problem is solved and obtained;
first, define
Solving for
In the step 3, the error cross covariance between the local estimates is approximated by using a statistical linear regression method, the optimization parameters under the maximum likelihood criterion are obtained by solving the optimization problem, and the error cross covariance matrix is adjusted, so that the performance loss caused by the linearization error in the statistical linear regression is reduced.
The invention has the following beneficial effects: the invention provides a target tracking method based on distributed matrix weighting fusion Gaussian filtering. The method first uses Gaussian filtering to estimate the local state, and then uses a statistical linear regression method to approximate the error cross covariance between the local estimates. And finally, obtaining an optimized parameter under a maximum likelihood criterion by solving an optimization problem, adjusting an error cross covariance matrix, reducing performance loss caused by a linearization error in statistical linear regression, and improving target tracking precision.
Drawings
Fig. 1 is a schematic diagram of a robot target tracking system.
FIG. 2 is a control flow chart of the present invention.
Fig. 3 is a trajectory and tracking estimation of a mobile robot.
Fig. 4 is a diagram illustrating accumulated errors.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 4, a target tracking method based on a distributed matrix weighted fusion gaussian filter includes the following steps:
step 1: establishing a nonlinear system state space model and a measurement model, wherein the process comprises the following steps:
1.1 establishing a System State model
xk+1=f(xk)+wk (1)
Wherein xkSystem state at time k, f (x)k)∈RnIs an arbitrary non-linear vector function, wkAs covariance of QkWhite gaussian noise of (1);
1.2 building a system measurement model
Where i is the observation station number,the measured value of the observation station i at the moment k +1,for any non-linear function of the vector,is covariance ofWhite gaussian noise of (1);
step 2: calculating local Gaussian filter estimation and covariance by the following process:
2.1 initialization x0|0And P0|0,k=0;
2.2 definition
Where g (x) is an arbitrary non-linear function,is mean value ofNormal distribution with covariance P, L system state dimension, S Chislesky decomposition with P, ejRow 1 for j and row 0 for other row;
Wherein
And step 3: calculating the local estimation cross covariance and the fusion estimation, and the process is as follows:
wherein
Wherein the optimized parameter lambda is based on the maximum likelihood criterion of the measurementkThe optimization problem is solved and obtained;
first, define
Solving for
To verify the effectiveness of the method designed by the present invention, the following example was used for verification.
As shown in fig. 1, the robot is in a wireless sensor network, and the robot is tracked by a distributed fusion estimation method, and a motion model of the robot is shown as (19):
wherein s isx,k,sy,kIs the position coordinate of the robot at time k, thetakIs the direction of the robot at time k, vl,k,vr,kThe speed of the left and right wheels of the robot, and d is the distance from the left and right wheels to the center of the robot;
considering the system process noise, the model is rewritten as:
The measurement equation of the system is shown in equation (21):
wherein (a)i,bi) Is the sensor location.
The target tracking algorithm of the present invention is simulated as follows, and the parameters are set as follows: Δ t ═ 0.5, Qk=diag(0.01,0.01,(π/180)2),uv=5, uw=0.125,(a1,b1)=(0,0),(a2,b2)=(200,0),(a3,b3)=(200,200), (a4,b4)=(0,200)。
Defining the accumulated error of the system as shown in equation (22)
The results are shown in fig. 3-4, fig. 3 is a track and tracking estimation of the mobile robot, and fig. 4 is a schematic diagram of accumulated errors, which shows that the method provided by the present invention has a good tracking estimation effect.
While the foregoing has described a preferred embodiment of the invention, it will be appreciated that the invention is not limited to the embodiment described, but is capable of numerous modifications without departing from the basic spirit and scope of the invention as set out in the appended claims.
Claims (2)
1. A target tracking method based on distributed matrix weighting and Gaussian filtering is characterized by comprising the following steps:
step 1: establishing a nonlinear system state space model and a measurement model, wherein the process comprises the following steps:
1.1 establishing a System State model
xk+1=f(xk)+wk (1)
Wherein xkSystem state at time k, f (x)k)∈RnIs an arbitrary non-linear vector function, wkAs covariance of QkWhite gaussian noise of (1);
1.2 building a system measurement model
Where i is the observation station number,the measured value of the observation station i at the moment k +1,for any non-linear function of the vector,is covariance ofWhite gaussian noise of (1);
step 2: calculating local Gaussian filter estimation and covariance by the following process:
2.1 initialization x0|0And P0|0,k=0;
2.2 definition
Where g (x) is an arbitrary non-linear function,is mean value ofNormal distribution with covariance P, L system state dimension, S Chislesky decomposition with P, ej∈RL×1Row 1 for j and row 0 for other row;
Wherein
And step 3: calculating the local estimation cross covariance and the fusion estimation, and the process is as follows:
wherein
Wherein the optimized parameter lambda is based on the maximum likelihood criterion of the measurementkThe optimization problem is solved and obtained;
first, define
Solving for
2. The method as claimed in claim 1, wherein in step 3, the error cross-covariance between local estimates is approximated by a statistical linear regression method, and the optimization parameters under the maximum likelihood criterion are obtained by solving the optimization problem, and the error cross-covariance matrix is adjusted to reduce the performance loss caused by the linearization error in the statistical linear regression.
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CN113334388A (en) * | 2021-07-08 | 2021-09-03 | 清华大学 | Robot kinematics calibration method and calibration device based on local linear regression |
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CN106950562A (en) * | 2017-03-30 | 2017-07-14 | 电子科技大学 | A kind of state fusion method for tracking target based on predicted value measurement conversion |
CN107390199A (en) * | 2017-09-20 | 2017-11-24 | 哈尔滨工业大学(威海) | A kind of radar maneuvering target tracking waveform design method |
CN108983215A (en) * | 2018-05-25 | 2018-12-11 | 哈尔滨工程大学 | A kind of method for tracking target based on maximum cross-correlation entropy adaptively without mark particle filter |
CN110426689A (en) * | 2019-07-02 | 2019-11-08 | 中国航空工业集团公司雷华电子技术研究所 | A kind of airborne multi-platform Multi-sensor systematic error registration Algorithm based on EM-CKS |
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CN106950562A (en) * | 2017-03-30 | 2017-07-14 | 电子科技大学 | A kind of state fusion method for tracking target based on predicted value measurement conversion |
CN107390199A (en) * | 2017-09-20 | 2017-11-24 | 哈尔滨工业大学(威海) | A kind of radar maneuvering target tracking waveform design method |
CN108983215A (en) * | 2018-05-25 | 2018-12-11 | 哈尔滨工程大学 | A kind of method for tracking target based on maximum cross-correlation entropy adaptively without mark particle filter |
CN110426689A (en) * | 2019-07-02 | 2019-11-08 | 中国航空工业集团公司雷华电子技术研究所 | A kind of airborne multi-platform Multi-sensor systematic error registration Algorithm based on EM-CKS |
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CN113334388A (en) * | 2021-07-08 | 2021-09-03 | 清华大学 | Robot kinematics calibration method and calibration device based on local linear regression |
CN113334388B (en) * | 2021-07-08 | 2022-12-02 | 清华大学 | Robot kinematics calibration method and calibration device based on local linear regression |
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