CN104777465B - Random extended object shape and state estimation method based on B spline function - Google Patents
Random extended object shape and state estimation method based on B spline function Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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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
Technical Field
The invention belongs to the technical field of intelligent information processing, and relates to an estimation method for the shape and the state of an extended target. In particular to a method for estimating the shape and state of a target based on the arbitrary expansion of a B spline function, which can be used for target tracking and shape estimation in various traffic control, robot navigation, accurate guidance and other systems.
Background
In conventional detection systems such as low resolution radar, the target is treated as a single point because it is too small relative to the sensor resolution element, occupying only one resolution element. However, as the resolution of the detection devices such as modern radars and the like is continuously improved, the echo signals of the targets may be distributed in different range resolution units, the detection fields of the targets are no longer equivalent to one point, that is, a single target may generate a plurality of measurements, and such a target is referred to as an extended target in the present invention. For the tracking of the extended target, the state of a single point is difficult to fully describe the extended target, and the detection and tracking analysis need to be carried out by comprehensively considering the information such as the shape of the target.
At present, the method for estimating the shape of an extended target mainly includes: the Random substrates (RM) method and the Random Hypersurface Models (RHMs) method. The RM method uses a discrete variance matrix of an extended target measurement set as a shape parameter of a target, takes a random shape parameter matrix generated by Wishart distribution as a prior shape under a Bayesian framework, and updates the posterior shape according to measurement information at the next moment. The method has the advantages that the single-frame data is processed simply, and the method is suitable for shape estimation of the cluster target. However, the RM method can only obtain an approximate elliptical shape of the target, and if the target is not elliptical (such as star-shaped or other irregular shapes), the shape information obtained by the method will be inaccurate, and directly affect the analysis of the target state. The RHMS method is one of random set models, parameters in the set shape equation are randomly generated to serve as prior parameters, and the prior parameters are screened through a measurement set and system noise construction constraint conditions, so that the shape of a target is fitted.
Disclosure of Invention
Aiming at the problems, the invention provides a method for estimating the shape and the state of an extended target based on a B-spline function, which adopts a multi-frame statistical technology, selects a sample control point under a polar coordinate system, and uses the B-spline function to fit the shape function of the target, thereby realizing the approximate estimation of the shape of any extended target under the conditions of high noise, low measurement number and low sensor precision.
The key technology for realizing the invention is as follows: introducing a B spline technology under a polar coordinate system, performing multi-time joint estimation by adopting a Bayesian filtering frame, counting the contour length of the target at different angles, and fitting the shape of the target by using a B spline function to realize the shape estimation of any extended target.
In order to achieve the above object, the specific implementation steps are as follows:
(1) initialization parameters target State ξ0＝{x0,X0,P0,Δ0In which x0Indicating target position information, X0As shape information, P0For motion noise covariance, Δ0Is a shape noise; and assuming that Q and R respectively represent state noise covariance and measurement noise covariance; setting a parameter d,And m, wherein d is an angular division width,m is the maximum number of elements in the pseudo measurement set.
(2) When k is greater than or equal to 1, according to the measurement YkAnd state xkAnd performing Kalman filtering.
(3) With filtered position information of the targetEstablishing a polar coordinate system for the origin, recording the coordinates of the measurement relative to the origin, adding the coordinates to the pseudo measurement set to form a new pseudo measurement set Zk+1。
(4) Root of herbaceous plantAccording to the pseudo measurement set Zk+1Updating a target shape
(3a) N angles are uniformly generated between 0 and 2 pi to form a fixed and unchangeable angle setAnd count the theta passing through the origin and pointing toiA point near the ray in the angular direction; is first constructed to point at thetaiThe angle direction ray is a symmetry axis, the origin is a rectangle with the middle point of the bottom edge, the length of the bottom edge is set to be 2D, and the points in the rectangle are divided into a set Dk+1,iAnd count for Dk+1,iThe length of the pseudo measurement set profile can be approximately obtained according to the expectation of the distances from all the points to the bottom edge of the rectangle, wherein d is a prior constant;
(3b) statistics Dk+1,iAcquiring a contour set of the target at the moment k +1, performing Kalman filtering according to the contour set, and updating the shape information of the target, wherein the updated shape information is Xk+1。
(5) With Xk+1A cubic B-spline function is generated as a control vertex, and the shape of the target is estimated.
(6) If the observation information arrives at the next moment, turning to the step (2) for iteration; otherwise, the target tracking process ends.
The invention has the following advantages:
(1) the invention adopts the thought of multi-frame statistics to establish a pseudo measurement set without making any assumption on the distribution of the measurement rate, thereby accurately estimating the shape of the target under the conditions of low measurement rate and high noise.
(2) Under the extreme conditions of high noise and low measurement rate, the invention introduces the B-spline function, can carry out shape estimation on the extended target with any shape, and provides reliable information characteristics for subsequent identification, track association and the like of the target.
Drawings
FIG. 1 is an overall flow diagram of the present invention;
FIG. 2 is a diagram illustrating the effect of the method of the present invention on the shape estimation of a cross-shaped target with a pseudo-metric set;
FIG. 3 is a graph comparing the estimated shape of the method of the present invention with the true shape of the target;
FIG. 4 is a diagram illustrating the effect of the method of the present invention on the shape estimation of a pseudo-metric set of "Y" type targets;
FIG. 5 is a graph comparing the estimated shape of the method of the present invention with the true shape of the target;
FIG. 6 is a diagram of shape estimation of the first 20 frames of a cross-shaped extended target using the method of the present invention and RM method;
FIG. 7 is a metrology diagram of the first 20 frames;
FIG. 8 is a graph of the effect of average shape estimation using the method of the present invention and the RM method;
FIG. 9 is a diagram of shape estimation of the first 20 frames of a "Y" type extended object using the method of the present invention and RM method;
FIG. 10 is a metrology diagram of the first 20 frames;
FIG. 11 is a graph of the effect of the mean shape estimation of the method of the present invention and the RM method;
Detailed Description
Introduction of basic theory
1. Kalman filtering technique
Assuming that the state equation and the measurement equation of a single target are expressed as:
xk+1＝Fxk+Gwk(1)
yk＝h(xk)+vk(2) wherein x iskRepresenting the state of the target at time k, F being a one-step transition matrix, h (-) representing the observation model, wkAnd vkRespectively representing state noise and measurement noise, and the corresponding covariance is denoted as QkAnd Rk。
Assume that the state x of the target at time k is knownkSum covariance PkThe kalman filtering step is as follows:
(1) predicting a target state at a next time
xk+1|k＝Fxk+Gwk
(2) Predicting covariance matrix at next time instant
Pk+1|k＝FPkFT+GQGT
(3) Calculating gain
Kk+1＝Pk+1|k[Sk+1|k]-1
Sk+1|k＝Pk+1|k+Rk+1
(4) Performing status updates based on latest measurements
xk+1＝xk+1|k+Kk+1(yk+1-xk+1|k)
(5) Updating covariance matrix
Pk+1＝[I-Kk+1]Pk+1|k
2. Shape estimation method based on B spline function
B spline function method: a smooth curve function is formed by a limited number of control points and is adopted to fit the contour shape of the control points. If given control vertex set Uk＝[μ1,μ2,…,μn]TSubstituting the control vertex into the B spline function to obtain the B spline function with the parameter u
Wherein N isi,l(u) denotes a B-spline curve function, u denotes a form variable, l denotes the degree of the B-spline function, and is a cubic B-spline function when l is 3, and can be expressed as:
second, the invention is based on the arbitrary extended target shape and state estimation method of B spline function
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
step 1, setting the initial time k to 0, and initializing a parameter x0、P0、X0、Δ0、d、R, Q and m.
Step 2, when k is more than or equal to 1, Kalman filtering is carried out on the motion state of the target
(2.1) predicting the motion state and covariance matrix of the target at the next moment:
xk+1|k＝Fxk
Pk+1|k＝FPkFT+GQGT
(2.2) collecting Y according to the newly obtained measurementk+1Updating the target state and covariance matrix:
Pk+1＝[I-Kk+1H]Pk+1|k
wherein, | · | represents the number of elements in the set, and H is a measurement matrix;
Kk+1＝Pk+1|kH[Sk+1|k]-1
Sk+1|k＝HPk+1|kHT+R
step 3, processing the measurement set to generate a new pseudo measurement set Zk+1
(3.1) first, collect the measurement set Y at the time k +1k+1Subtracting the updated centroid coordinates from each element in the listThen incorporate ZkForming a new pseudo-metric set
(3.2) assuming that the maximum number of the pseudo measurement set elements is m, judgingWhether or not it is greater than m, ifThen orderOtherwise deleteWith intermediate time aheadAn element, reset
Step 4, according to the pseudo-measurement set Zk+1Updating a target shape
(4.1) uniformly generating n angles from 0 to 2 pi to form a fixed and unchangeable angle setAnd the pseudo measurement set is divided into subsets according to angles
Wherein d is the division width,andexpressing the coordinates of the I element in the pseudo measurement set at the moment k +1 in the x direction and the y direction of a Cartesian coordinate system;is a point zk+1,lTo the over-origin edge thetaiAngular direction line LiWherein B is1And B2Is a straight line LiTo satisfyThe parameters of (1); c (-) represents zk+1，lConstraints in the range of the positive direction of the angle;represents a through-origin and is perpendicular to LiWherein A is1And A2Is a straight lineTo satisfyThe parameter (c) of (c).
(4.2) computing the set Dk+1,iMedium element to straight lineThe expectation of distance, then the outer contour of the target can be expressed as:
zk+1,l∈Dk+1,i
and (4.3) performing Kalman filtering on the shape of the target according to the outer contour set obtained at the moment k + 1.
And (3) prediction:
Xk+1|k＝Xk
updating:
wherein,
step 5, with Xk+1Generating cubic B spline function for controlling the vertex, and estimating the shape of the target:
(5.1) mapping the point set in polar coordinates to a planar coordinate system
(5.2) orderIs Uk+1And adding an extended control vertex set of the first three elements of the set at the end of the set to generate a closed B spline function:
wherein N isi,3(u) is a cubic B-spline function
And 6, repeating the step 2, and continuing to estimate the shape and the state of the extended target.
The invention can be further illustrated by the following experimental simulations:
1. simulation conditions and parameters
Assuming that a plurality of targets do uniform motion on an x-y plane, the motion state of the targets is expressed as x ═ x, vx,y,vy]TWhere x and y are the positions of a single object in the cartesian coordinate system in the x and y directions, respectively, vxAnd vyRespectively the speed of each target in the x-direction and the y-direction. The equation of state of the target is shown in equation (1), wherein,t denotes a sampling time interval.
The measurement equation is yk＝Hxk+vkWhereinprocess noise covariance in simulation scenario isWherein sigmaw1＝σw21, measure the noise covariance asWherein sigmav1＝σv21, initial covariance of target motion state P0=diag[5,1,5,1]Initial variance vector of object shape informationThe angle set is uniformly distributed in [0, 2 pi ]]Angle n ofWhere n is 20 and the sampling interval d for each angle is 1.5. Initial pseudo metrology set Z0The pseudo measurement set is an empty set, and the maximum element number m of the pseudo measurement set is 45. The invention is compared with RM method, wherein the initial shape state X in RM method0The other state parameters are the same as those described above, namely, diag (10, 10).
2. Simulation content and result analysis
The simulation experiment, which is to compare the method of the invention with RM method for experimental analysis, is mainly carried out from the following three aspects:
experiment 1: shape estimation of pseudo-metric sets generated by different shaped targets
FIG. 2 is a diagram illustrating the effect of the method of the present invention on the shape estimation of a cross-shaped target. Therefore, the method can accurately estimate the shape of the target from the pseudo measurement set.
FIG. 3 is a graph comparing the estimated shape of the method of the present invention with the true shape of the target.
FIG. 4 is a diagram illustrating the effect of the method of the present invention on the shape estimation of a pseudo metrology set of "Y" type targets.
FIG. 5 is a graph comparing the estimated shape of the method of the present invention with the true shape of the target.
It can be seen that the method of the present invention can perform shape estimation on extended targets of different shapes.
Experiment 2: continuous estimation of cross-shaped extended target shape
FIG. 6 shows the shape estimation result of the first 20 frames of the cross-shaped extended target tracked by 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.
Fig. 7 is a metrology diagram of the first 20 frames. Comparing with fig. 6, it can be seen that, under the condition of large noise of the measurement set, the method of the present invention can estimate the correct shape, 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 achieve the shape characteristics of the target.
Experiment 3: 'Y' -shaped extended object shape continuous estimation
FIG. 9 shows the shape estimation result of the first 20 frames of the cross-shaped extended target tracked by the method of the present invention and the RM method.
Fig. 10 is a metrology diagram of the first 20 frames. As can be seen from comparison with FIG. 9, the change of the measurement shape affected by the noise does not affect the correct estimation of the method of the present invention on the shape of the extended target, and has strong anti-interference performance.
FIG. 11 is the average shape estimation result of the method of the present invention and the RM method. Therefore, the method can estimate the shape characteristics of the target more accurately.
Claims (4)
1. The method for estimating the shape and the state of the target based on the arbitrary expansion of the B spline function comprises the following steps:
(1) initialization parameters target State ξ0＝{x0,X0,P0,Δ0In which x0Indicating target position information, X0As shape information, P0For motion noise covariance, Δ0Is a shape noise; and assuming that Q and R respectively represent state noise covariance and measurement noise covariance; setting a parameter d,And m, wherein d is an angular division width,the angle set is a fixed and unchangeable angle set, and m is the maximum element number of the pseudo measurement set;
(2) when k is greater than or equal to 1, according to the measurement set YkAnd state xkPerforming Kalman filtering;
(3) with filtered position information of the targetEstablishing a polar coordinate system for the origin, recording the coordinates of the measurement relative to the origin, adding the coordinates to the pseudo measurement set to form a new pseudo measurement set Zk+1；
(4) According to the pseudo measurement set Zk+1Updating the target shape;
(5) with Xk+1Generating a cubic B spline function as a control vertex, and estimating the shape of the target;
(6) if the observation information arrives at the next moment, turning to the step (2) for iteration; otherwise, the target tracking process ends.
2. The method for estimating arbitrary extended target shape and state based on B-spline function according to claim 1, wherein the metrology set processing of step (3) generates a new pseudo metrology set Zk+1The method comprises the following steps:
(2.1) first, the measurement set Y at the time k +1 is collectedk+1Subtracting the updated centroid coordinates from each element in the listThen incorporate ZkForm a new pseudo-metric set, i.e.
(2.2) according to the maximum number m of the given pseudo measurement set elements,judgment ofWhether or not it is greater than m, ifThen orderOtherwise deleteWith intermediate time aheadAn element, reset
3. The method for arbitrarily expanding a target shape and state based on B-spline function according to claim 1, wherein the step (4) is based on a pseudo-metric set Zk+1Updating the target shape, and realizing the following steps:
(3.1) uniformly generating n angles from 0 to 2 pi to form a fixed and unchangeable angle setAnd the pseudo measurement set is divided into subsets according to the angles,
wherein d is the division width,andexpressing the coordinates of the I element in the pseudo measurement set at the moment k +1 in the x direction and the y direction of a Cartesian coordinate system;is a point zk+1,lTo the over-origin edge thetaiAngular direction line LiWherein B is1And B2Is a straight line LiTo satisfyThe parameters of (1); c (-) represents zk+1,lConstraints in the range of the positive direction of the angle;represents a through-origin and is perpendicular to LiWherein A is1And A2Is a straight lineTo satisfyThe parameters of (1);
(3.2) computing the set Dk+1,iMedium element to straight lineThe expectation of distance, then the outer contour of the target can be expressed as:
zk+1,l∈Dk+1,i
(3.3) performing Kalman filtering on the shape of the target according to the outer contour set obtained at the moment k +1,
and (3) prediction:
updating:
wherein,
4. the method for arbitrarily expanding a target shape and state based on B-spline according to claim 1, wherein the step (5) comprises the step of multiplying the target shape and state by Xk+1Generating cubic B-splines for vertex controlThe target shape is estimated and calculated according to the following method:
(4.1) mapping the point set in polar coordinates to a planar coordinate system
(4.2) orderIs Uk+1And adding an extended control vertex set of the first three elements of the set at the end of the set to generate a closed B spline function:
wherein N isi,3(u) is a cubic B-spline function.
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| CN106408594B (en) * | 2016-09-28 | 2018-10-02 | 江南大学 | Video multi-target tracking based on more Bernoulli Jacob's Eigen Covariances |
| CN106570330A (en) * | 2016-11-08 | 2017-04-19 | 河南科技大学 | Shape estimated performance evaluation method for extended target tracing |
| CN107391446A (en) * | 2017-07-24 | 2017-11-24 | 江南大学 | Irregular shape based on random matrix extends target shape and method for estimating state more |
| CN108536096B (en) * | 2018-04-11 | 2020-12-29 | 哈尔滨工业大学深圳研究生院 | Three-dimensional contour control method and device based on task polar coordinate system |
| CN112150577A (en) * | 2020-08-31 | 2020-12-29 | 北京师范大学 | Continuation method of cubic B-spline |
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