An extended target tracking method based on deformed super-ellipse

Abstract

The present application belongs to the technical field of extended object tracking, and particularly relates to an extended object tracking method based on a deformed superellipse. The present application uses a deformed superellipse to simulate the shape of an extended object, and the motion state of the extended object is represented by two groups of parameters. The first group is the position coordinates of the center of the superellipse before nonlinear transformation, and the second group is the speed of the center in each direction. In order to describe the measurement generated uniformly on the contour and inside of the deformed superellipse, the present application proposes a new measurement likelihood model, on the basis of which the posterior probability of the measurement can be calculated. The particle filter is used to estimate the shape parameters of the extended object and obtain the measurement information of the first group of motion states, and then the Kalman filter is combined to estimate the second group of parameters of the motion state of the extended object and correct the center coordinates estimated by the particle filter.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of extended object tracking, and particularly relates to an extended object tracking method based on a deformed superellipse. BACKGROUND

[0002] With the development of tracking devices, a tracking target occupies multiple resolution units at high sensor resolution, instead of being approximated as a traditional point target, and in the past few years, extended object tracking methods have been extensively researched and applied. Compared with traditional point target tracking, extended objects also need to be estimated in morphology.

[0003] A conventional method is a random matrix method, which uses an ellipse to model the shape, and in the earliest time, an inverse Wishart distribution is used to approximate the prior of the shape parameter, and then a variational Bayesian method uses a variational approximation method to approximate the prior and performs iterative estimation, so that the estimation accuracy of the shape parameter is improved at the cost of higher computational complexity. The use of an ellipse model can solve the extended object tracking problem in some scenarios, such as tracking of ships and cars, but cannot be applied to irregularly shaped extended object tracking.

[0004] Deformed superellipse is a very flexible shape model, which introduces two new parameters to change the sharpness and bending degree of the superellipse. After introducing the two nonlinear transformations, the deformed superellipse can describe the contour that does not have simple symmetry and is applied in many fields, for example, in the medical field, the deformed superellipse can be used to fit various prostate shapes, and in the tracking field, the deformed superellipse can also be used to describe more flexible extended objects such as flexible unmanned aerial vehicle groups. SUMMARY

[0005] In view of the above problems, the application provides an extended object tracking algorithm based on a deformed superellipse.

[0006] Let (x, y) represent the two-dimensional space coordinates before transformation, and (x', y') represent the coordinates after transformation, and then the transformation and inverse transformation formulas related to the deformed superellipse are given for subsequent use. The deformed superellipse is described by eight parameters S=(lx, ly, a x ,a y ,r,ε,ta,b), wherein {a x ,a y ,r,ε} are used to describe the superellipse:

[0007]

[0008] On this basis, parameters {ta, b} (-1≤ta≤1, -1≤b≤1) are introduced to sharpen and twist the superellipse:

[0009]

[0010]

[0011] wherein:

[0012] γ = x / (a y / b-y)

[0013] {lx,ly,r} are used to describe the center position (translation) and rotation of the deformed super-ellipse:

[0014]

[0015]

[0016] The technical scheme adopted by the present application is:

[0017] The present application uses a deformed super-ellipse to simulate the shape of an extended target, the motion state of the extended target being represented by two groups of parameters, the first group being the position coordinates of the center of the super-ellipse before nonlinear transformation, and the second group being the velocity of the center in each direction. In order to describe the measurements generated uniformly on the contour and inside of the deformed super-ellipse, the present application proposes a new measurement likelihood model, on the basis of which the posterior probability of the measurement can be calculated. The particle filter is used to estimate the shape parameters of the extended target and obtain the measurement information of the first group of motion states, and the Kalman filter is used to estimate the second group of parameters of the motion state of the extended target and correct the center coordinates estimated by the particle filter. The algorithm steps are as follows:

[0018] S1, establish the motion and measurement model:

[0019] The measurement set at time t is defined as The number of measurements M obeys a Poisson distribution, and the measurements are generated uniformly on the contour and inside of the deformed super-ellipse. The shape parameters of the deformed super-ellipse are described by the eight parameters given above, and are defined as S(t) = (lx t ,ly t ,a x t ,a y t ,r t ,ε t ,ta t ,b t ). Wherein, {a x t ,a y t ,r t ,ε t ,ta t ,b tlx, ly, θ, a, b, r, ε, ta, tb, respectively, represent the long and short semi-axes, the rotation angle, the squareness, the thinness and the twist degree, and the center thereof is defined as its translation parameter t , ly t ) T , and the remaining parameters S p (t) = (a x t ,a y t ,r t ,ε t ,ta t ,b t ) :

[0020] S p (t+1) = F p (t)S p (t) + v p (t)

[0021] where F p (t) is the state transition matrix of the state parameters, v p (t) is its process noise and obeys the mean of 0 and the covariance matrix of Q p (t). The motion state x(t) of the center is composed of two-dimensional position coordinates and velocities The state equation of the deformed super-elliptical center is as follows:

[0022] x(t+1) = F(t)x(t) + v(t)

[0023] where v(t) represents white noise with a mean of 0, and Q(t) represents its covariance matrix. F(t) represents the state transition matrix, and △t represents the sampling interval:

[0024]

[0025] S2, particle initialization:

[0026] At the t-th moment, N groups of particles form an 8xN matrix Par t , and the j-th column element of the matrix represents a group of particles Par t (j) (1≤j≤N), each group of particles corresponds to the eight shape parameters of S(t) one by one, and the N groups of particles are used for subsequent particle filtering.

[0027] S3, calculate the diameter:

[0028] At the t-th moment, the measurement and the particle Par t (j) are calculated according to the given inverse transformation formula and the particle parameters ​First, the inverse transformation of rotation and translation is performed to obtain the coordinates Two step vectors are set (the vector direction is consistent with the direction of the particle parameter) and The search method is used to obtain the radius length in the direction of the center

[0029] (1) The particle parameter is inversely transformed to obtain and the result of is calculated.

[0030] (2) According to the result, it is judged whether it is inside the deformation hyperellipse. If not, return to otherwise, proceed to (3).

[0031] (3) Repeat (1), and according to the result of it is judged whether it is inside the deformation hyperellipse. If yes, repeat (3), otherwise proceed to (4).

[0032] (4) Repeat (1), and according to the result of it is judged whether it is inside the deformation hyperellipse. If yes, record the coordinates and proceed to (5), otherwise repeat (4).

[0033] (5) Repeat (1), and according to the result of it is judged whether it is inside the deformation hyperellipse. If yes, repeat (5), otherwise proceed to (6).

[0034] (6) Repeat (1), and according to the result of it is judged whether it is inside the deformation hyperellipse. If yes, record the coordinates and return to otherwise, repeat (6).

[0035] S4, calculate the posterior probability:

[0036] Because the measurements are uniformly distributed inside the deformation hyperellipse, the following measurement equation can be written:

[0037]

[0038]

[0039] where w p (t) represents the measurement noise of the measurement, and the covariance is R p ​(t), where L is a random variable following a uniform distribution: This uniform distribution can be approximated as a Gaussian distribution with mean 0 and variance 1 / 4: Substituting this into the above equation, we can obtain the posterior probability of the measurement set Z(t):

[0040]

[0041]

[0042]

[0043] where eps is a fixed small value.

[0044] S5, Particle Filter:

[0045] At the beginning of time t, update The measurement mean is:

[0046]

[0047]

[0048] Iterate the measurement set Z(t) and Par t The posterior probability can be calculated by the method given in S4, and the particle weight after normalization can be obtained to estimate the shape parameter of the deformed super-ellipse S t|t The updated particles are used for iteration at the next time. It is worth noting that in order to prevent overestimation of the shape, here we take the method of dividing the particle weight p(Z(t)|Par t (j)) by the area of the deformed super-ellipse (here the area of the super-ellipse is used for approximation) to reduce the particle weight with large area parameters:

[0049]

[0050] S6, Kalman Filter:

[0051] The measurement point of the center of the deformed super-ellipse after particle filtering is lz m (t) = (lx t , ly t ) T Let be the estimated covariance matrix of the motion state at time t, be the estimated covariance matrix of the particle filter about the center position at time t, which can be regarded as the measurement error of the center coordinates introduced by the particle filter in the Kalman filter stage (which itself also contains measurement error):

[0052]

[0053] After Kalman filtering, the motion state estimation x t|t and the center position estimation lz t|t :

[0054]

[0055] lz t|t = H (t) x t|t

[0056]

[0057]

[0058] The estimation of the shape parameters {a x t ,a y t ,r t ,ε t ,ta t ,b t}, the motion state x (t) and the center position lz (t) at time t is completed, and the iterative estimation at the next time is performed.

[0059] The beneficial effects of the present application are:

[0060] The present application proposes a new extended object tracking algorithm, and the extended object is modeled by a deformed super-ellipse. The algorithm completes the estimation of the shape parameters and the motion state through particle filtering and Kalman filtering, and realizes the effective tracking of the extended object under the modeling of the deformed super-ellipse. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 is a simulation effect diagram of the extended object tracking algorithm.

[0062] Figure 2 is an estimation error diagram of the shape parameters of the extended object.

[0063] Figure 3 is an estimation error diagram of the motion state of the extended object. DETAILED DESCRIPTION

[0064] The present application will be described in detail below in combination with the drawings, and the simulation environment parameters are set as follows:

[0065] S represents the shape parameters of the deformed super-ellipse of the extended object p = (a x ,a yr, e, ta, b) = (3, 3, 0, 2.5, 0.6, -0.6), sampling interval At = 1 s, the extended target starts to move from t = 1 s, the total time T = 40 s, the center position lz at the initial moment is at the origin, the velocity vector in the x-axis and y-axis is [10 m / s, 10 m / s], a and b are respectively taken as and S p The state transition matrix F p (t) and the covariance matrix Q p (t), R p (t) are set as follows:

[0066] F p (t) = I6

[0067] Q p (t) = diag(0.02, 0.02, 1, 0.02, 0.02, 0.02) 2

[0068] Q(t) = diag(2[m], 2[m], 2[m / s], 2[m / s]) 2

[0069] R p (t) = diag(0.1[m], 0.1[m]) 2

[0070] The number of particle groups N = 1500, the number of measurements obeys Poisson distribution with mean λ M = 30:

[0071] M ~ Poisson(30)

[0072] The algorithm performs tracking at t = 2 s, and the posterior information obtained from t = 1 s is:

[0073] S p (1) = (4, 4, 0, 1, 0, 0)

[0074] x(1) = (1, 1, 10, 10) T

[0075]

[0076] The extended target tracking algorithm simulation is carried out under the given environmental parameters of the environmental conditions, the tracking effect is shown, and finally the estimation error of the motion state and the shape parameter is evaluated through Monte Carlo experiment. In order to have a more accurate description of the tracking error, the center estimation error and the shape estimation error of the deformed hyperellipse are quantified. The center estimation error is defined as E xt :

[0077]

[0078]

[0079] where, is its statistical average in time, N MC = 100 represents the number of Monte Carlo experiments, is the true motion state of the extended target center at time t, x t|t,n is the state estimate. Because the shape parameter of the target is more, this paper uses the overlap degree of the estimated shape and the true shape to quantify the error of shape estimation. The true shape area and the estimated shape area of the nth experiment are and S t|t,n , and their overlapping area is The error is described by and Description:

[0080]

[0081]

[0082]

[0083]

[0084] where and are and statistical average in time, it can be seen that and the smaller the estimation error is as they are closer to 1.

[0085] Tracking effect:

[0086] Figure 1 The simulation effect diagram of the extended target tracking algorithm under the proposed condition is shown. In order to verify the reliability of the algorithm, the prior information of the deformed hyper-elliptical shape at the initial time is set as a slightly larger circle. At the four time points enlarged in the figure, it can be seen that the measurement points are uniformly distributed in the target contour, and with the passage of time, the estimated shape gradually evolves from a circle to a quadrilateral, and then approximates to the true shape. By comparing the positions of the true and estimated centers in the figure, the distance between them always remains within a reasonable range, which shows the effectiveness of the algorithm in estimating the motion state of the extended target. Figure 2 and Figure 3 show the statistical results of 100 Monte Carlo experiments The variation of the errors can be seen from the figures. The motion state estimation error and the shape estimation error can reach the convergent state quickly and keep a stable value in the initial tracking stage. Table 1 shows the tracking errors under different λ M For the convenience of observation, the statistical average of the errors is adopted It can be seen that when λ M = 30, the convergent state can be approached.

[0087] Table 1

[0088]

Claims

1. A method for extended target tracking based on deformed super-ellipses, characterized in that, The method comprises the following steps: S1, establishing a motion and measurement model; The present application relates to a method for measuring a three-dimensional object (1) in a coordinate system (2) by means of a plurality of sensors (3) arranged in a coordinate system (4) and a computer (5) for processing the measurement data, wherein the object (1) is illuminated by means of a light source (6) and the sensors (3) are arranged in a coordinate system (4) which is offset from the coordinate system (2) of the object (1) to be measured. The measurement set of time is defined as The number of measurements obeys the Poisson distribution, and the measurements are uniformly generated on the contour and inside of the deformed superellipse; the deformed superellipse is described by shape parameters ; wherein, respectively represent the long and short semi-axes, the rotation angle, the squareness, the thinning and the twisting degree, and the center of the superellipse is defined as the translation parameter ; the two-dimensional space coordinates before transformation are represented by ; and the coordinates after transformation are represented by ; and the inverse transformation formula is: ， ， ， ， The remaining parameters are defined as : ， wherein is a state transition matrix for the state parameters, is a state transition matrix for the state parameters, is a process noise with mean 0 and covariance matrix is composed of two-dimensional position coordinates and velocity The state equation of the deformed hyper-elliptical center is as follows: ， wherein, represents a white noise with mean 0 and covariance matrix , represents a state transition matrix, represents a sampling interval: ， S2, initializing particles; In a first instant, The groups of particles form a matrix , the elements of the first column of the matrix representing a group of particles , each group of particles corresponding one-to-one to eight shape parameters; S3, calculating path length; In Instantaneous measurement And particle , , according to the given inverse transform formula and particle parameters On First rotation and translation of the inverse transform to get the coordinates , set two vector direction with Step vector And , , , using the search method to get the center in Direction of the radius : (1) According to the particle parameters The inverse transformation is performed on to obtain and the result of calculating is obtained, wherein the calculation formula of is: ， wherein is a two-dimensional spatial coordinate, is a description of the superellipse, indicating the major and minor axes and the degree of squaring; (2) According to the result, it is judged whether inside the deformed super-ellipse, if not, return to , otherwise, proceed to (3); (3) , repeat (1), determine from the result of whether inside the deformed super-ellipse, if yes, repeat (3), otherwise, proceed to (4); (4) , repeat (1), determine from the result of whether inside the deformed superellipse, if so, record the coordinates and proceed to (5), otherwise repeat (4); (5) , repeat (1), according to the result of determine whether inside the deformed super-ellipse, if yes, repeat (5), otherwise, proceed (6); (6) , repeat (1), according to the result of the determination whether inside the deformed super-ellipse, if yes, record the coordinates and return , otherwise repeat (6); S4, calculating posterior probability; Because the measurements are uniformly distributed in the deformed hyperellipse, a measurement equation is established: ， ， where, denotes the measurement noise of the measurements, the covariance is , the random variable obeys a uniform distribution: This uniform distribution is approximated as a Gaussian distribution with mean 0 and variance 1 / 4: Substituting this into the above equation gives the posterior probability of the measurement set : ， ， ， wherein is a fixed minimum value; S5, particle filtering; At Start time, update For measurement mean: ， ， Traversing a set of measurements and The posterior probability is computed by means of S4 for particle filtering, and the particle weights are normalized to obtain an estimate of the shape parameters of the deformed super-ellipse The updated particles are used for the next iteration; to prevent overestimation of the shape, the particle weights are divided by the area of the deformed super-ellipse ​ ， S6, Kalman filtering; The measurement point of the deformed super-ellipse center obtained after particle filtering is , let be the estimation covariance matrix of the motion state at time , and be the estimation covariance matrix of the particle filter about the center position at time . ， Observation matrix: ， After Kalman filtering, motion state estimation is obtained and center position estimation : ， ， ， ， The estimation of the time shape parameter is completed.​​​

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