CN102707277B - Multi-target tracking method for information square root factorization - Google Patents

Abstract

The invention discloses a multi-target tracking method for information square root factorization. The multi-target tracking method is used for solving the technical problem of failure in target tracking by radars due to instability of numerical structures of existing target tracking methods. The technical scheme includes that the multi-target tracking method is characterized in that an estimation error variance array is subjected to information square root factorization to set up a numerical stable structural model. Subtraction of two positive semidefinite matrixes in the estimation error variance array is avoided, and symmetric matrixes with negative characteristic values cannot be generated in a processing system with limited word length. By means of information square root factorization of the estimation error variance array, the multi-target tracking structural model is set up, subtraction of two positive semidefinite matrixes in the estimation error variance array is avoided, numerical diffusion in the processing system with limited word length is avoided, and accordingly reliability of a target tracking system is guaranteed while failure in target tracking by radars and faults of a whole radar system are avoided.

Description

The multi-object tracking method that information square root decomposes

Technical field

The present invention relates to a kind of Radar Multi Target tracking, the multi-object tracking method that particularly a kind of information square root decomposes, belongs to areas of information technology.

Background technology

Multitarget Tracking is all widely used at military and civil area, can be used for aerial target and detects, follows the tracks of and attack, Air Missile defence, air traffic control, harbour and marine surveillance etc.In recent years, along with the change of battlefield surroundings, the development of antagonism and anti-countermeasure techniques, has produced the series of problems such as the strong clutter of background, low signal-to-noise ratio, low detection probability and high false alarm rate, and the precision of multi-object tracking method and accuracy are had higher requirement.

The object of multiple target tracking is by received information source corresponding to measurement of detector, forms different observation set or track, according to track, estimates the number of tracked target and the kinematic parameter of each target, realizes the tracking to a plurality of targets.For the basic filtering method of multiple goal state estimation have that alpha-beta filtering, alpha-beta-γ filtering, Kalman filtering, EKF, gaussian sum are approximate, optimal nonlinear filtering, particle filter and auto adapted filtering etc.Alpha-beta and alpha-beta-γ wave filter are due to simple in structure, and calculated amount is little, and when computer resource is short in early days, application is very wide.Kalman filtering is a kind of basic skills of multiple target tracking, but need to know the mathematical models of system, and is only applicable to linear system, has limited the application of algorithm.EKF expands to non-linear field by kalman filtering theory, is similar to the conditional probability distribution of state by a Gaussian distribution; And when approximate condition does not meet, Gaussian sum filter device is similar to the conditional probability distribution of state by the weighted sum of a Gaussian distribution.Optimal nonlinear filtering is described the dynamic process of target with Makov transition probability, have good characteristic, but calculated amount is larger, is therefore never used widely.Particle filter adopts stochastic sampling, because calculated amount is too large and particle degenerate problem, is not suitable for practical application.In order to improve particle filter, Unscented kalman filtering adopts deterministic sampling, and the particle point number of sampling is reduced, and avoided the particle point degenerate problem in particle filter, so its application is very wide.Adaptive filter method, by the detection to target maneuver, is adjusted the state of filter parameter or increase wave filter in real time, makes wave filter adapt in real time target travel, is particularly suitable for the tracking to maneuvering target; At present, actual radar tracking system the most frequently used be still JPDA(Joint Probabilistic Data Association, JPDA) method (James A.Roecker, A Class of Near Optimal JPDA Algorithms, IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, 1994, VOL.30(2): 504-51O), other method great majority are to simplification of JPDA method etc.Yet, in the variance battle array that the method errors such as JPDA are estimated, there are two positive semidefinite matrixs to subtract each other, in the disposal system of limited wordlength, can produce the symmetric matrix that contains positive and negative eigenwert, cause radar tracking enabling objective to lose and follow and whole radar system mistake.

Summary of the invention

In order to solve the unstable technological deficiency that causes radar tracking enabling objective to lose and follow of existing method for tracking target value structure, the invention provides the multi-object tracking method that a kind of information square root decomposes, the method is in the time and measurement renewal of multiple target tracking, by variance of estimaion error battle array being carried out to the decomposition of information square root, set up numerical stability structural model, not having has two positive semidefinite matrixs to subtract each other in the variance battle array of estimation of error, in the disposal system of limited wordlength, can guarantee can not produce the symmetric matrix that contains negative eigenwert, can avoid radar tracking enabling objective to lose follows and whole radar system mistake.

The present invention solves the technical scheme that its technical matters adopts, the multi-object tracking method that a kind of information square root decomposes, and its feature comprises the following steps:

1, in N target following of definition, the discretization model of i target is

x _i(k+1)=Φ(k+1，k)x _i(k)+Λω _i(k)，

Wherein:

for state vector, (x, y, z) is the position coordinates of target under ground reference rectangular coordinate system, ω _i(k) represent that variance is Q _i(k) process noise vector, Φ (k+1, k)=Φ=diag[Φ ₁, Φ ₁, Φ ₁] be state-transition matrix, $\mathrm{\Λ}={\∫}_{\mathrm{kT}}^{(k+1)T}\mathrm{\Φ}(k+1,\mathrm{\τ})\mathrm{\Γ}\left(\mathrm{\τ}\right)\mathrm{d\τ}=\left[\begin{array}{ccc}{\mathrm{\Λ}}_1& 0& 0\\ 0& {\mathrm{\Λ}}_1& 0\\ 0& 0& {\mathrm{\Λ}}_1\end{array}\right],$ Γ (t) is matrix of coefficients, $\mathrm{\Γ}=\left[\begin{array}{ccc}{\mathrm{\Γ}}_1& 0& 0\\ 0& {\mathrm{\Γ}}_1& 0\\ 0& 0& {\mathrm{\Γ}}_1\end{array}\right],$ Γ ₁=[0?0?1] ^T， ${\mathrm{\Φ}}_1=\left[\begin{array}{ccc}1& T& \frac{1}{2}{T}^2\\ 0& 1& T\\ 0& 0& 1\end{array}\right],$ ${\mathrm{\Λ}}_1={\left[\begin{array}{ccc}\frac{1}{6}{T}^3& \frac{1}{2}{T}^2& T\end{array}\right]}^T,$ T is the sampling period;

The time of i target is updated to:

x _i(k+1/k)=S _i(k+1/k)b _i(k+1/k)

$T_1\left[\begin{array}{ccc}{Q}_i^{-\frac{1}{2}}\left(k\right)& 0& 0\\ S_i^{-1}(k/k)\mathrm{\Φ\Λ}& S_i^{-1}(k/k){\mathrm{\Φ}}^{-1}& b_i(k/k)\end{array}\right]=\left[\begin{array}{ccc}{A}_i(k+1)& B_i(k+1)& c_i(k+1)\\ 0& S_i^{-1}(k+1/k)& b_i(k+1/k)\end{array}\right]$

Wherein: n=9, x _i(k+1/k) be i target to (k+1) T one-step prediction value constantly,

for the variance battle array of corresponding one-step prediction error, S _i(k+1/k) be upper triangular matrix, T ₁for orthogonal transform matrix, A _i(k+1), B _i(k+1), c _i(k+1) matrix producing for computation process; Starting condition is x _iand S (0/0) _i(0/0);

2, i target observation equation is: z _i(k)=g _i[x _i(k)]+v _i(k)

Wherein: z _i(k) be the r dimension observation vector to i target, g _i[x _i(k)] be corresponding output, v _i(k) represent that variance is R _i(k) measure noise; Calculate

$T_2\left[\begin{array}{cc}{S}_i^{-1}(k+1/k)& b_i(k+1/k)\\ R_i^{-\frac{1}{2}}(k+1)\left(k\right)H_i(k+1)& R_i^{-\frac{1}{2}}(k+1){\mathrm{\η}}_i(k+1)\end{array}\right]=\left[\begin{array}{cc}{\stackrel{\‾}{S}}_i^{-1}(k+1)& b_i(k+1/k+1)\\ 0& e_i(k+1/k+1)\end{array}\right]\}$

$x_i(k+1/k+1)={\stackrel{\‾}{S}}_i(k+1)b_i(k+1/k+1)$

Wherein: ${\mathrm{\η}}_i(k+1)=\{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\λ}}_{\mathrm{ij}}(k+1)z_{\mathrm{ij}}(k+1)-g_i[x_i(k+1/k)\left]\right\},$ E _i(k+1/k+1) matrix producing for computation process,

for upper triangular matrix, T ₂for orthogonal transform matrix, z _ij(k+1) be the j(j=1 of radar to i target, 2 ..., m) individual echo, x _i(k+1/k+1) be i target (k+1) T filter value constantly, λ _ij(k+1) be weight coefficient, and: $\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\λ}}_{i,j}(k+1)=1,$ $H_i(k+1)=\frac{\∂g_i\left[x_i(k+1)\right]}{\∂x_i(k+1)}{|}_{x_i(k+1)=x_i(k+1/k)};$

3, i tracking method of estimation is:

$\left\{\begin{array}{cc}a=\sqrt{{\left(b_l\right)}^T{b}_l}& \\ s_{\mathrm{lj}}=\left\{\begin{array}{cc}0& j=\mathrm{1,2},\·\·\·,l-1\\ a& j=l\\ \left[(1/a){\left(b_l\right)}^T\right]b_j& j=l+1,l+2,\·\·\·n\end{array}\right.& \\ b_j=b_j-s_{\mathrm{lj}}[b_l/a]& j=l+1,\·\·\·,n\end{array}\right\}l=\mathrm{1,2},\·\·\·,n$

Wherein: n=9, y _jfor Y ^t(k+1) j column vector, $Y(k+1)=\left[\begin{array}{cc}{\stackrel{\‾}{S}}_i^{-T}(k+1)& H_i(k+1)R_i(k+1)d^T(I-{\mathrm{\Ωuu}}^T)\end{array}\right],$ S _ljfor

the capable j column element of l, S _i(k+1/k+1) be upper triangular matrix,

it is i target (k+1) T variance of estimaion error battle array constantly;

$u=\left[\begin{array}{c}1\\ 1\\ \·\\ \·\\ \·\\ 1\end{array}\right],$ $d=\left[\begin{array}{c}{\mathrm{\Δ}}_{i,1}^T(k+1)\\ {\mathrm{\Δ}}_{i,2}^T(k+1)\\ \·\\ \·\\ \·\\ {\mathrm{\Δ}}_{i,m}^T(k+1)\end{array}\right];$

Δ _{i, j}(k+1) be j candidate's echo information vector,

Δ _i，j(k+1)=z _i，j(k+1`)-g _i[x _i(k+1/k)]。

Useful result of the present invention is: by variance of estimaion error battle array being carried out to the decomposition of information square root, set up the multiple target tracking structural model of numerical stability, avoided two positive semidefinite matrixs in the variance battle array of estimation of error to subtract each other, in the disposal system of limited wordlength, there will not be numerical value to disperse, thus guaranteed multi-object tracking method reliability, avoided radar tracking enabling objective lose with and whole radar system mistake.

Below in conjunction with example, the present invention is elaborated.

Embodiment

1, in N target following of definition, the discretization model of i target is

x _i(k+1)=Φ(k+1，k)x _i(k)+Λω _i(k)，

Wherein:

for state vector, (x, y, z) is the position coordinates of target under ground reference rectangular coordinate system, ω _i(k) represent that variance is Q _i(k) process noise vector, Φ (k+1, k)=Φ=diag[Φ ₁, Φ ₁, Φ ₁] be state-transition matrix, $\mathrm{\Λ}={\∫}_{\mathrm{kT}}^{(k+1)T}\mathrm{\Φ}(k+1,\mathrm{\τ})\mathrm{\Γ}\left(\mathrm{\τ}\right)\mathrm{d\τ}=\left[\begin{array}{ccc}{\mathrm{\Λ}}_1& 0& 0\\ 0& {\mathrm{\Λ}}_1& 0\\ 0& 0& {\mathrm{\Λ}}_1\end{array}\right],$ Γ (t) is matrix of coefficients, $\mathrm{\Γ}=\left[\begin{array}{ccc}{\mathrm{\Γ}}_1& 0& 0\\ 0& {\mathrm{\Γ}}_1& 0\\ 0& 0& {\mathrm{\Γ}}_1\end{array}\right],$ Γ ₁=[0?0?1] ^T， ${\mathrm{\Φ}}_1=\left[\begin{array}{ccc}1& T& \frac{1}{2}{T}^2\\ 0& 1& T\\ 0& 0& 1\end{array}\right],$ ${\mathrm{\Λ}}_1={\left[\begin{array}{ccc}\frac{1}{6}{T}^3& \frac{1}{2}{T}^2& T\end{array}\right]}^T,$ T is the sampling period;

The time of i target is updated to:

x _i(k+1/k)=S _i(k+1/k)b _i(k+1/k)

$T_1\left[\begin{array}{ccc}{Q}_i^{-\frac{1}{2}}\left(k\right)& 0& 0\\ S_i^{-1}(k/k)\mathrm{\Φ\Λ}& S_i^{-1}(k/k){\mathrm{\Φ}}^{-1}& b_i(k/k)\end{array}\right]=\left[\begin{array}{ccc}{A}_i(k+1)& B_i(k+1)& c_i(k+1)\\ 0& S_i^{-1}(k+1/k)& b_i(k+1/k)\end{array}\right]$

Wherein: n=9, x _i(k+1/k) be i target to (k+1) T one-step prediction value constantly, for the variance battle array of corresponding one-step prediction error, S _i(k+1/k) be upper triangular matrix, T ₁for orthogonal transform matrix, A _i(k+1), B _i(k+1), c _i(k+1) matrix producing for computation process; Starting condition is x _iand S (0/0) _i(0/0);

2, i target observation equation is: z _i(k)=g _i[x _i(k)]+v _i(k)

Wherein: z _i(k) be the r dimension observation vector to i target, g _i[x _i(k)] be corresponding output, v _i(k) represent that variance is R _i(k) measure noise; Calculate

$T_2\left[\begin{array}{cc}{S}_i^{-1}(k+1/k)& b_i(k+1/k)\\ R_i^{-\frac{1}{2}}(k+1)\left(k\right)H_i(k+1)& R_i^{-\frac{1}{2}}(k+1){\mathrm{\η}}_i(k+1)\end{array}\right]=\left[\begin{array}{cc}{\stackrel{\‾}{S}}_i^{-1}(k+1)& b_i(k+1/k+1)\\ 0& e_i(k+1/k+1)\end{array}\right]\}$

$x_i(k+1/k+1)={\stackrel{\‾}{S}}_i(k+1)b_i(k+1/k+1)$

Wherein: ${\mathrm{\η}}_i(k+1)=\{\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\λ}}_{\mathrm{ij}}(k+1)z_{\mathrm{ij}}(k+1)-g_i[x_i(k+1/k)\left]\right\},$ E _i(k+1/k+1) matrix producing for computation process,

for upper triangular matrix, T ₂for orthogonal transform matrix, z _ij(k+1) be the j(j=1 of radar to i target, 2 ..., m) individual echo, x _i(k+1/k+1) be i target (k+1) T filter value constantly, λ _ij(k+1) be weight coefficient, and:

for example get g _i[x _i(k+1)]=[r _i(k+1) α _i(k+1) β _i(k+1)] ^t, r _ifor radar can be measured oblique distance, α _ifor angular altitude, β _iposition angle, and

$\left\{\begin{array}{c}{r}_i=\sqrt{x_i^2+y_i^2+z_i^2}\\ {\mathrm{\α}}_i={\tan }^{-1}\frac{z_i}{\sqrt{x_i^2+y_i^2}}\\ {\mathrm{\β}}_i={\tan }^{-1}\frac{x_i}{y_i}\end{array}\right.$

$H_i(k+1)=\frac{\∂g_i\left[x_i(k+1)\right]}{\∂x_i(k+1)}{|}_{x_i(k+1)=x_i(k+1/k)}$

$={\left[\begin{array}{ccccccccc}\frac{x_i}{\sqrt{x_i^2+y_i^2+z_i^2}}& 0& 0& \frac{y_i}{\sqrt{x_i^2+y_i^2+z_i^2}}& 0& 0& \frac{z_i}{\sqrt{x_i^2+y_i^2+z_i^2}}& 0& 0\\ \frac{-x_i{z}_i}{(x_i^2+y_i^2+z_i^2)\sqrt{x_i^2+y_i^2}}& 0& 0& \frac{-y_i{z}_i}{(x_i^2+y_i^2+z_i^2)\sqrt{x_i^2+y_i^2}}& 0& 0& \frac{\sqrt{x_i^2+y_i^2}}{(x_i^2+y_i^2+z_i^2)}& 0& 0\\ \frac{y_i}{x_i^2+y_i^2}& 0& 0& \frac{-x_i}{x_i^2+y_i^2}& 0& 0& 0& 0& 0\end{array}\right]}_{x_i(k+1)=x_i(k+1/k)};$

3, i tracking method of estimation is:

$\left\{\begin{array}{cc}a=\sqrt{{\left(b_l\right)}^T{b}_l}& \\ s_{\mathrm{lj}}=\left\{\begin{array}{cc}0& j=\mathrm{1,2},\·\·\·,l-1\\ a& j=l\\ \left[(1/a){\left(b_l\right)}^T\right]b_j& j=l+1,l+2,\·\·\·n\end{array}\right.& \\ b_j=b_j-s_{\mathrm{lj}}[b_l/a]& j=l+1,\·\·\·,n\end{array}\right\}l=\mathrm{1,2},\·\·\·,n$

Wherein: n=9, s _ljfor the capable j column element of l, S _i(k+1/k+1) be upper triangular matrix, be i target (k+1) T variance of estimaion error battle array constantly, y _jfor Y ^t(k+1) j column vector, $Y(k+1)=\left[\begin{array}{cc}{\stackrel{\‾}{S}}_i^{-T}(k+1)& H_i(k+1)R_i(k+1)d^T(I-{\mathrm{\Ωuu}}^T)\end{array}\right];$

$u=\left[\begin{array}{c}1\\ 1\\ \·\\ \·\\ \·\\ 1\end{array}\right],$ $d=\left[\begin{array}{c}{\mathrm{\Δ}}_{i,1}^T(k+1)\\ {\mathrm{\Δ}}_{i,2}^T(k+1)\\ \·\\ \·\\ \·\\ {\mathrm{\Δ}}_{i,m}^T(k+1)\end{array}\right];$

Δ _{i, j}(k+1) be j candidate's echo information vector,

Δ _i，j(k+1)=z _i，j(k+1`)-g _i[x _i(k+1/k)]。

3, i tracking method of estimation is:

$\left\{\begin{array}{cc}a=\sqrt{{\left(b_l\right)}^T{b}_l}& \\ s_{\mathrm{lj}}=\left\{\begin{array}{cc}0& j=\mathrm{1,2},\·\·\·,l-1\\ a& j=l\\ \left[(1/a){\left(b_l\right)}^T\right]b_j& j=l+1,l+2,\·\·\·n\end{array}\right.& \\ b_j=b_j-s_{\mathrm{lj}}[b_l/a]& j=l+1,\·\·\·,n\end{array}\right\}l=\mathrm{1,2},\·\·\·,n$

Wherein: n=9, s _ljfor

the capable j column element of l, S _i(k+1/k+1) be upper triangular matrix,

be i target (k+1) T variance of estimaion error battle array constantly, y _jfor Y ^t(k+1) j column vector, $Y(k+1)=\left[\begin{array}{cc}{\stackrel{\‾}{S}}_i^{-T}(k+1)& H_i(k+1)R_i(k+1)d^T(I-{\mathrm{\Ωuu}}^T)\end{array}\right];$

$u=\left[\begin{array}{c}1\\ 1\\ \·\\ \·\\ \·\\ 1\end{array}\right],$ $d=\left[\begin{array}{c}{\mathrm{\Δ}}_{i,1}^T(k+1)\\ {\mathrm{\Δ}}_{i,2}^T(k+1)\\ \·\\ \·\\ \·\\ {\mathrm{\Δ}}_{i,m}^T(k+1)\end{array}\right];$

Δ _{i, j}(k+1) be j candidate's echo information vector,

Δ _i，j(k+1)=z _i，j(k+1`)-g _i[x _i(k+1/k)]。

Claims (1)

1. the multi-object tracking method that information square root decomposes, is characterized in that comprising the following steps:

(1), in N target following of definition, the discretization model of i target is

x _i(k+1)=Φ(k+1,k)x _i(k)+Λω _i(k)，

Wherein: for state vector, (x, y, z) is the position coordinates of target under ground reference rectangular coordinate system, ω _i(k) represent that variance is Q _i(k) process noise vector, Φ (k+1, k)=Φ=diag[Φ ₁, Φ ₁, Φ ₁] be state-transition matrix,

Γ is matrix of coefficients,

t is the sampling period;

The time of i target is updated to:

x _i(k+1/k)=S _i(k+1/k)b _i(k+1/k)

Wherein: n=9, x _i(k+1/k) be i target to (k+1) T one-step prediction value constantly,

for the variance battle array of corresponding one-step prediction error, S _i(k+1/k) be upper triangular matrix, T ₁for orthogonal transform matrix, A _i(k+1), B _i(k+1), c _i(k+1) matrix producing for computation process; Starting condition is x _iand S (0/0) _i(0/0);

(2), i target observation equation is: z _i(k)=g _i[x _i(k)]+v _i(k)

Wherein: z _i(k) be the r dimension observation vector to i target, g _i[x _i(k)] be corresponding output, v _i(k) represent that variance is R _i(k) measurement noise; Calculate

Wherein: e _i(k+1/k+1) matrix producing for computation process,

for upper triangular matrix, T ₂for orthogonal transform matrix, z _i,j(k+1) be the j(j=1 of radar to i target, 2 ..., m) individual echo, x _i(k+1/k+1) be i target (k+1) T filter value constantly, λ _i,j(k+1) be weight coefficient, and:

(3), i target following method of estimation is:

Wherein: n=9, b _jfor Y ^t(k+1) j column vector, s _ljfor the capable j column element of l, S _i(k+1/k+1) be upper triangular matrix, it is i target (k+1) T variance of estimaion error battle array constantly;

△ _i,j(k+1) be j candidate's echo information vector,

△ _i,j(k+1)=z _i,j(k+1)-g _i[x _i(k+1/k)]。