CN104777465B - Random extended object shape and state estimation method based on B spline function - Google Patents

Abstract

The invention discloses a random extended object tracking and shape estimation method based on a B spline function, and belongs to the technical field of guidance and intelligent information processing, mainly to solve the problem of carrying out tracking and shape estimation on a random extended object. According to the method, through a method of introducing multi-moment combined statistics, a pseudo measurement set of extended objects is built, object shape information is updated according to the pseudo measurement set, a B spline function is adopted for estimating object shapes, and thus, tracking and shape estimation on extended objects in random geometrical shapes can be realized, shape estimation accuracy and robustness are good, design requirements of a practical engineering system can be met, and engineering application values are good.

Description

Arbitrary extension of target shape and state estimation method based on B-spline function

technical field

The invention belongs to the technical field of intelligent information processing and relates to a method for estimating the shape and state of an extended target. Specifically, it is an arbitrarily extended target shape and state estimation method based on B-spline function, which can be used for target tracking and shape estimation in various traffic control, robot navigation and precision guidance systems.

Background technique

In traditional detection systems such as low-resolution radar, the target is treated as a single point, because it is too small compared to the resolution unit of the sensor, and only occupies one resolution unit. However, with the continuous improvement of the resolution of modern radar and other detection equipment, the echo signals of the target may be distributed in different distance resolution units, and its detection field is no longer equivalent to a point, that is, a single target may generate multiple measurements. Such objects are referred to as extended objects in the present invention. For extended target tracking, it is difficult for a single point state to fully describe the extended target, and it is necessary to comprehensively consider the target shape and other information for detection and tracking analysis.

At present, the extended object shape estimation methods mainly include: Random Matrices (RM) method and RandomHypersurface Models (RHMs) method. Among them, the RM method uses the discrete variance matrix of the extended target measurement set as the shape parameter of the target. Under the Bayesian framework, the random shape parameter matrix generated by the Wishart distribution is used as the prior shape, and according to the measurement information at the next moment Update the posterior shape. The advantage of this method is that it is relatively simple to process single-frame data and is suitable for shape estimation of cluster targets. However, the RM method can only obtain the approximate elliptical shape of the target. If the target is not elliptical (such as a star or other irregular shape), the shape information obtained by this method will be inaccurate, which will directly affect the analysis of the target state. The RHMs method is a kind of random set model. Through the set shape equation, the parameters in the equation are randomly generated as prior parameters, and the prior parameters are screened through the measurement set and system noise construction constraints to fit the target. It can be seen that this method relies too much on the prior shape of the target, and determines the shape equation of the target according to the prior shape parameters. If the parameters are unreasonable, it will directly affect the accuracy of shape estimation.

Contents of the invention

In view of the above problems, the present invention proposes an extended target shape and state estimation method based on B-spline functions, adopts multi-frame statistical technology, selects sample control points in the polar coordinate system, and uses B-spline functions to fit the shape of the target function to realize the approximate estimation of the shape of any extended target under the condition of high noise, low measurement number and low sensor accuracy.

The key technology to realize the present invention is: introduce B-spline technology under the polar coordinate system, use Bayesian filtering framework to carry out multi-moment joint estimation, count the contour length of the target on different angles, use B-spline function to fit the target shape, Enables shape estimation for arbitrarily extended objects.

To achieve the above goals, the specific steps are as follows:

(1) Initialization parameters: target state ξ ₀ ={x ₀ ,X ₀ ,P ₀ ,Δ ₀ }, where x ₀ represents target position information, X ₀ is shape information, P ₀ is motion noise covariance, Δ ₀ is the shape noise; and assume that Q and R represent the state noise covariance and measurement noise covariance respectively; set the parameters d, and m, where d is the angle division width, is a set of fixed angles, and m is the maximum number of elements in the pseudo-measurement set.

(2) When k≥1, perform Kalman filtering according to the measurement Y _k and the state x _k .

(3) Take the location information of the filtered target Establish a polar coordinate system for the origin, record the coordinates of the measurement relative to the origin, and add it to the pseudo-measurement set to form a new pseudo-measurement set Z _k+1 .

(4) Update the target shape according to the pseudo-measurement set Z _k+1

(3a) Evenly generate n angles between 0 and 2π to form a fixed set of angles And count the points near the origin and pointing to the ray in the angle direction of _θi ; first construct a rectangle with the ray pointing in the angle direction of _θi as the axis of symmetry, the origin as the midpoint of the bottom, and the length of the bottom is set to 2d, and the Points are divided into the set D _k+1,i , and the expectation of the distance from all points in D _k+1,i to the bottom of the rectangle can be calculated, then the length of the contour of the pseudo-measurement set can be obtained approximately, where d is a priori constant;

(3b) Statistically D _k+1,i obtains the contour set of the target at time k+1, performs Kalman filtering according to the contour set, and updates the shape information of the target. The updated shape information is X _k+1 .

(5) Using X _k+1 as the control vertex, generate a cubic B-spline function to estimate the shape of the target.

(6) If the observation information arrives at the next moment, go to step (2) for iteration; otherwise, the target tracking process ends.

The present invention has the following advantages:

(1) The present invention adopts the idea of multi-frame statistics to establish a pseudo-measurement set, without making any assumptions about the distribution of the measurement rate, so that the shape of the target can be accurately estimated under the condition of low measurement rate and high noise.

(2) In extreme cases of high noise and low measurement rate, the present invention introduces a B-spline function, which can estimate the shape of an extended target of any shape, and provide reliable information for subsequent target identification and track association. information features.

Description of drawings

Fig. 1 is the overall flowchart of the present invention;

Fig. 2 is the effect diagram of the shape estimation of the pseudo-measurement set as a cross-shaped target by the method of the present invention;

Fig. 3 is the comparison diagram of the shape estimated by the method of the present invention and the true shape of the target;

Fig. 4 is the effect diagram of the shape estimation of the false measurement set as "Y" type target by the method of the present invention;

Fig. 5 is a comparison diagram between the shape estimated by the method of the present invention and the true shape of the target;

Fig. 6 is the shape estimation diagram of the first 20 frames of the cross-shaped extended target by adopting the method of the present invention and the RM method;

Figure 7 is a measurement map of the first 20 frames;

Fig. 8 is the average shape estimation effect diagram adopting the method of the present invention and the RM method;

Fig. 9 is the shape estimation diagram of the first 20 frames of the "Y" type extended target using the method of the present invention and the RM method;

Figure 10 is a measurement diagram of the first 20 frames;

Fig. 11 is the average shape estimation effect diagram of the method of the present invention and the RM method;

detailed description

1. Introduction to basic theory

1. Kalman filter technology

Suppose the state equation and measurement equation of a single target are expressed as:

x _k+1 = Fx _k + Gw _k (1)

y _k ＝h(x _k )+v _k (2) Among them, x _k represents the state of the target at time k, F is a one-step transition matrix, h(·) represents the observation model, w _k and v _k represent state noise and Measurement noise, and the corresponding covariances are denoted as Q _k and R _k , respectively.

Assuming that the state x _k and covariance P _k of the target at time k are known, the Kalman filtering steps are as follows:

(1) Predict the target state at the next moment

x _k+1|k ＝Fx _k +Gw _k

(2) Predict the covariance matrix at the next moment

P _k+1|k ＝FP _k F ^T +GQG ^T

(3) Calculation gain

K _k+1 ＝P _k+1|k [S _k+1|k ] ^-1

S _k+1|k ＝P _k+1|k +R _k+1

(4) Update the status according to the latest measurement

x _k+1 ＝x _k+1|k +K _k+1 (y _k+1 -x _k+1|k )

(5) Update the covariance matrix

P _k+1 ＝[IK _k+1 ]P _k+1|k

2. Based on B-spline function shape estimation method

B-spline function method: form a smooth curve function through a limited number of control points, and use it to fit the contour shape of the control points. If the set of control vertices U _k =[μ ₁ ,μ ₂ ,…,μ _n ] ^T is given, and the control vertices are substituted into the B-spline function, the B-spline function with parameter u can be obtained

Among them, N _i,l (u) represents the B-spline curve function, u represents the formal variable, l represents the degree of the B-spline function, when l=3, it is a cubic B-spline function, and can be expressed as:

Two, the present invention is based on the arbitrarily extended target shape of B-spline function and state estimation method

With reference to Fig. 1, concrete implementation steps of the present invention are as follows:

Step 1. Let the initial moment k=0, initialize parameters x ₀ , P ₀ , X ₀ , Δ ₀ , d, , R, Q and m.

Step 2. When k≥1, perform Kalman filtering on the target motion state

(2.1) Predict the target motion state and covariance matrix at the next moment:

x _k+1|k ＝Fx _k

P _k+1|k ＝FP _k F ^T +GQG ^T

(2.2) Update the target state and covariance matrix according to the newly obtained measurement set Y _k+1 :

P _k+1 ＝[IK _k+1 H]P _k+1|k

Among them, |·| represents the number of elements in the set, and H is the measurement matrix;

K _k+1 ＝P _k+1|k H[S _k+1|k ] ^-1

S _k+1|k ＝HP _k+1|k H ^T +R

Step 3. Measurement set processing to generate a new pseudo-measurement set Z _k+1

(3.1) First subtract the updated centroid coordinates from each element in the measurement set Y _k+ 1 at time k+1 Then merge into Z _k to form a new pseudo-measurement set

(3.2) Assuming that the maximum number of elements in the pseudo-measurement set is m, judge Is it greater than m, if order otherwise delete in front of time elements, then set

Step 4. Update the target shape according to the pseudo-measurement set Z _k+1

(4.1) Evenly generate n angles from 0 to 2π to form a fixed set of angles and subset the pseudo-measurement set by angle

Among them, d is the division width, and Indicates the coordinates of the lth element in the pseudo-measurement set at time k+1 in the x-direction and y-direction of the Cartesian coordinate system; is the distance from point z _k+1,l to the straight line L _i passing through the origin along the angle direction of θ _i , where B ₁ and B ₂ satisfy the requirements on the straight line L _i Parameters; C( ) represents z _{k+1, the constraints of l} in the range of the positive direction of the angle; Indicates a straight line passing through the origin and perpendicular to L _i , where A ₁ and A ₂ are straight lines Satisfied parameters.

(4.2) Calculate the elements in the set D _{k+1, i} to the straight line The expectation of the distance, then the outer contour of the target can be expressed as:

z _k+1,l ∈D _k+1,i

(4.3) Carry out Kalman filtering on the shape of the target according to the outer contour set obtained at time k+1.

predict:

X _k+1|k ＝X _k

renew:

in,

Step 5. Using X _k+1 as the control vertex, generate a cubic B-spline function to estimate the target shape:

(5.1) Map the point set in polar coordinates to the plane coordinate system

(5.2) order Adding the extended control vertex set of the first three elements of the set to the end of the U _k+1 set can generate a closed B-spline function:

Among them, N _i,3 (u) is the cubic B-spline function

Step 6. Repeat step 2 to continue shape and state estimation for the extended target.

The present invention can be further illustrated by the following experimental simulations:

1. Simulation conditions and parameters

Assuming that multiple targets are moving at a uniform speed on the xy plane, the target motion state is expressed as x=[x,v _x ,y,v _y ] ^T , where x and y are the x direction and y of a single target in the Cartesian coordinate system The position in the y direction, v _x and v _y are the velocities of each target in the x and y directions, respectively. The state equation of the target is shown in formula (1), where, T represents the sampling time interval.

The measurement equation is y _k =Hx _k +v _k , where, The process noise covariance in the simulation scenario is Where σ _w1 ＝σ _w2 ＝1, the measurement noise covariance is Where σ _v1 ＝σ _v2 ＝1, the initial covariance of the target motion state P ₀ =diag[5,1,5,1], the initial variance vector of the target shape information The set of angles is n angles uniformly distributed on [0, 2π] Where n=20, the sampling interval d=1.5 for each angle. The initial pseudo-measurement set Z ₀ is an empty set, and the maximum number of elements in the pseudo-measurement set is m=45. The present invention is compared and analyzed with the RM method. In the RM method, the initial shape state X ₀ =diag(10,10), and other state parameters are the same as the above parameters.

2. Simulation content and result analysis

Simulation experiment, the method of the present invention and RM method are carried out comparative experiment analysis, mainly carry out experiment from following three aspects:

Experiment 1: Shape Estimation of Pseudo-measurement Sets Generated by Objects of Different Shapes

Fig. 2 is a diagram of the shape estimation effect of the method of the present invention on a cross-shaped target with a pseudo-measurement set. It can be seen that the method of the present invention can more accurately estimate the shape of the target from the pseudo-measurement set.

Fig. 3 is a comparison diagram between the shape estimated by the method of the present invention and the real shape of the target.

Fig. 4 is a diagram of the shape estimation effect of the method of the present invention for a pseudo-measurement set of a "Y"-shaped target.

Fig. 5 is a comparison diagram between the shape estimated by the method of the present invention and the real shape of the target.

It can be seen that the method of the present invention can perform shape estimation on extended objects of different shapes.

Experiment 2: Continuous Estimation of Cross-Shape Extended Object Shapes

Fig. 6 is the shape estimation result of tracking the first 20 frames of the cross-shaped extended target by using the method of the present invention and the RM method. It can be seen that the shape estimated by the method of the present invention is more accurate than the ellipse estimation result of the RM method.

Figure 7 is a measurement map of the first 20 frames. Comparing Fig. 6, it can be seen that the method of the present invention can still estimate the correct shape when the measurement set is noisy, and has strong anti-interference performance.

Fig. 8 is the average shape estimation result of the method of the present invention and the RM method. It can be seen that the method of the present invention can better obtain the shape characteristics of the target.

Experiment 3: Continuous Estimation of "Y" Shape Extended Object Shapes

Fig. 9 is the shape estimation result of tracking the first 20 frames of the cross-shaped extended target by using the method of the present invention and the RM method.

Figure 10 is the measurement map of the first 20 frames. Comparing Fig. 9, it can be seen that the change of the measurement shape affected by noise does not affect the correct estimation of the extended target shape by the method of the present invention, and has strong anti-interference performance.

Fig. 11 is the average shape estimation results of the method of the present invention and the RM method. It can be seen that the method of the present invention can estimate the shape feature of the target more accurately.

Claims (4)

1. Arbitrarily expand the target shape and state estimation method based on B-spline function, including: (1) Initialization parameters: target state ξ ₀ ={x ₀ ,X ₀ ,P ₀ ,Δ ₀ }, where x ₀ represents target position information, X ₀ is shape information, P ₀ is motion noise covariance, Δ ₀ is the shape noise; and assume that Q and R represent the state noise covariance and measurement noise covariance respectively; set the parameters d, and m, where d is the angle division width, is a fixed set of angles, m is the maximum number of elements in the pseudo-measurement set; (2) When k≥1, perform Kalman filtering according to the measurement set Y _k and state x _k ; (3) Take the location information of the filtered target Establish a polar coordinate system for the origin, record the coordinates of the measurement relative to the origin, and add it to the pseudo-measurement set to form a new pseudo-measurement set Z _k+1 ; (4) Update the target shape according to the pseudo-measurement set Z _k+1 ; (5) Using X _k+1 as the control vertex, generate a cubic B-spline function to estimate the shape of the target; (6) If the observation information arrives at the next moment, go to step (2) for iteration; otherwise, the target tracking process ends. 2. arbitrarily extended target shape and state estimation method based on B-spline function according to claim 1, wherein, the measurement set described in step (3) is processed, generates new pseudo-measurement set Z _k+1 , presses It is calculated by the following method: (2.1) First subtract the updated centroid coordinates from each element in the measurement set Y _k+ 1 at time k+1 Then incorporate into Z _k to form a new pseudo-measurement set, namely (2.2) According to the maximum number m of elements in the given pseudo-measurement set, judge Is it greater than m, if order otherwise delete in front of time elements, then set 3. arbitrarily expanding target shape and state estimation method based on B-spline function according to claim 1, wherein, the described step (4) updates target shape according to pseudo measurement set Z _k+1 , realizes by the following steps: (3.1) Evenly generate n angles from 0 to 2π to form a fixed set of angles and subset the pseudo-measurement set by angle, Among them, d is the division width, and Indicates the coordinates of the lth element in the pseudo-measurement set at time k+1 in the x-direction and y-direction of the Cartesian coordinate system; is the distance from point z _k+1,l to the straight line L _i passing through the origin along the angle direction of θ _i , where B ₁ and B ₂ satisfy the requirements on the straight line L _i Parameters; C(·) represents the constraints of z _k+1,l in the range of the positive direction of the angle; Indicates a straight line passing through the origin and perpendicular to L _i , where A ₁ and A ₂ are straight lines Satisfied parameters; (3.2) Calculate the elements in the set D _{k+1, i} to the straight line The expectation of the distance, then the outer contour of the target can be expressed as: z _k+1,l ∈D _k+1,i (3.3) Carry out Kalman filtering on the shape of the target according to the outer contour set obtained at k+1 time, predict: renew: in, 4. arbitrarily extended target shape and state estimation method based on B-spline function according to claim 1, wherein, described in step (5) is control vertex with X _k+1 , generates cubic B-spline function, estimates target shape, calculated as follows: (4.1) Map the point set in polar coordinates to the plane coordinate system (4.2) order Adding the extended control vertex set of the first three elements of the set to the end of the U _k+1 set can generate a closed B-spline function: Among them, N _i,3 (u) is a cubic B-spline function.