CN104730537A - Infrared/laser radar data fusion target tracking method based on multi-scale model - Google Patents

Abstract

Provided is an infrared/laser radar data fusion target tracking method based on a multi-scale model. The method comprises the steps that the multi-scale model is built; data collection is carried out on a target, and the distance measurement value, the azimuth angle measurement value and the pitch angle measurement value of the target are obtained; estimation is carried out on angle information obtained by an infrared detection system on a scale 1 through the unscented Kalman filter method; the angle estimation information and the distance information are fused on a scale 2; the target state is estimated through the Kalman filter method on the scale 2; the fused and estimated information is converted on the scale 1, filtering estimation is carried out on the scale 1 through the Kalman filter method, and an accurate filtering estimated value is obtained; the above steps are repeated, and a target movement track is obtained. The multi-scale model is quoted into information fusion, the target movement state is described more comprehensively and accurately, estimation filtering is carried out on the target on different scales, the estimation precision of the target state is improved, and the target tracking precision is improved through information interaction between different scales.

Description

Based on multiple dimensioned model infrared/laser radar data merge method for tracking target

Technical field

The invention belongs to technical field of information processing, particularly relate to a kind of infrared/method for tracking target of laser radar Multi-sensor Fusion.

Background technology

Infrared detection system, as passive detection system, has good concealment, not easily, precision advantages of higher good by electronic interferences, low-altitude detection performance, can provide target information, but infrared detection system can only provide Angle Information for close-in defense weapon system.The distance accuracy of Airborne Lidar examining system is higher, finding range meets short range requirement, but shortage angle information, therefore the two is with the use of realizing message complementary sense, thus complete, accurate metrical information is provided, exact state estimation can be carried out to target, improve system reliability and stability.

But the sample frequency of Airborne Lidar examining system is well below the sample frequency of infrared detection system, make the measurement data of the two asynchronous.And, infrared and combined detection that is laser radar generally completes in spherical coordinate system, and the motion state of target is described usually in rectangular coordinate system, in rectangular coordinate system, the advantage of modeling is that filtering and extrapolation process can realize on linear dynamic model, in spherical coordinate system, modeling then can cause comparatively complicated filtering and extrapolation process, therefore need first the angle information of acquisition and range information to be transformed in rectangular coordinate system in infrared/laser radar dual sensor detection system, then carry out state estimation.Now, the conversion of measuring between dbjective state is nonlinear relationship, due to the coupling of measuring error, no longer meets Kalman filtering condition.Traditional method first carries out registration to asynchronous data, and conversion turns to stationary problem; Then under rectangular coordinate system, carry out state modeling, obtain corresponding converted measurement equation, and then state estimation is carried out to converting measured values Kalman filtering (Converted Measurement KalmanFilter, CMKF) algorithm.The method model is simple, but precision is lower.

Multiscale Theory is a kind of effective method for the problem of Fusion Target state estimator, and a lot of scholar has carried out large quantity research to Multiscale Estimation Theory in recent years, and achieves many achievements in research.Pan Quan etc. propose the multiple dimensioned model of a kind of new linear dynamic, and give method of estimation; For Multiscale System, literary composition to grow into forest etc. and sets up its estimation theory framework and provide corresponding prediction, Filtering and smoothing algorithm.Because infrared/laser radar detection tracker describes dbjective state under different sample frequency, have Analysis On Multi-scale Features, present inventor proposes the method for tracking target that a kind of Multiscale Theory merges mutually with CMKF algorithm.

Summary of the invention

, coordinate conversion measured value different to the sampling rate that exists in object tracking process for infrared/laser radar Multi-sensor Fusion has the problem of deviation and observation noise coupling, the object of the present invention is to provide a kind of based on multiple dimensioned model infrared/laser radar Multi-sensor Fusion method for tracking target.

To achieve these goals, the present invention takes following technical solution:

Based on multiple dimensioned model infrared/laser radar data merge method for tracking target, comprise the following steps:

Step 1, set up multiple dimensioned model according to the sample frequency of infrared detection system and Airborne Lidar examining system, described multiple dimensioned model is:

x(i,k _i+1)＝F(i,k _i)x(i,k _i)+w(i,k _i)

z(i,k _i)＝H(i,k _i)x(i,k _i)+v(i,k _i)

Wherein, F (i, k _i) be k _itime be engraved in systematic state transfer matrix on yardstick i, x (i, k _i) be k _itime be engraved in state vector on yardstick i, w (i, k _i) be system noise, z (i, k _i) be k _itime be engraved in observation vector on yardstick i, H (i, k _i) be k _itime be engraved in observing matrix on yardstick i, v (i, k _i) be observation noise, k _ifor the sampling instant on yardstick i, i=1,2;

Step 2, infrared detection system and Airborne Lidar examining system carry out data acquisition to target respectively, obtain the measurement of azimuth value α of target _m, target pitch angle measurement value β _mwith the distance measure r of target _m;

Step 3, the angle information obtained infrared detection system on yardstick 1 adopt Unscented kalman filtering method to estimate, utilize 2 recurrence methods to carry out initialization, obtain the position angle filtering estimated value α ' of target in filtering _mwith angle of pitch filtering estimated value β ' _m;

Step 4, step 3 obtains the range information that angle estimation information and Airborne Lidar examining system obtain by yardstick 2 merge, calculate the position coordinates (x of target under rectangular coordinate system _m, y _m, z _m):

$\left\{\begin{array}{c}{x}_m=r_m\×\cos {\mathrm{\β}}_m^{\′}\×\cos {\mathrm{\α}}_m^{\′}\\ y_m=r_m\×\cos {\mathrm{\β}}_m^{\′}\×\sin {\mathrm{\α}}_m^{\′}\\ z_m=r_m\×{\sin \mathrm{\β}}_m^{\′}\end{array}\right.;$

Wherein, r _mfor the distance measure of target, α ' _mfor the position angle filtering estimated value of target, β ' _mfor the angle of pitch filtering estimated value of target;

Step 5, on yardstick 2, Kalman filtering method is adopted to estimate dbjective state;

Step 5-1, calculate target without inclined observed reading obtain the converting measured values under rectangular coordinate system $z^u={\[x_m^u,y_m^u,z_m^u\]}^T;$

$\left\{\begin{array}{c}{x}_m^u={\mathrm{\λ}}_{\mathrm{\α}}^{-1}{\mathrm{\λ}}_{\mathrm{\β}}^{-1}{x}_m\\ y_m^u={\mathrm{\λ}}_{\mathrm{\α}}^{-1}{\mathrm{\λ}}_{\mathrm{\β}}^{-1}{y}_m\\ z_m^u={\mathrm{\λ}}_{\mathrm{\β}}^{-1}{z}_m\end{array}\right.;$

Wherein, x _m, y _m, z _mfor the position coordinates of target under rectangular coordinate system, λ _αand λ _βfor without parital coefficient, ${\mathrm{\λ}}_{\mathrm{\α}}=E\[\cos \widetilde{\mathrm{\α}}\]=e^{-\frac{{\mathrm{\σ}}_{\mathrm{\α}}^2}{2}},{\mathrm{\λ}}_{\mathrm{\β}}=E\[\cos \widetilde{\mathrm{\β}}\]=e^{-\frac{{\mathrm{\σ}}_{\mathrm{\β}}^2}{2}},$ for azimuth measurement error, for elevation measurement error, be respectively with variance, E [] represent ask expectation value, [] ^trepresent matrix transpose operation;

Step 5-2, error of calculation variance matrix R _p:

$R_p=\mathrm{cov}\left\{{[x_m^u,y_m^u,z_m^u]}^T\right|r_m,{\mathrm{\α}}_m^{\′},{\mathrm{\β}}_m^{\′}\}=\left[\begin{array}{ccc}{R}_p^{11}& R_p^{12}& R_p^{13}\\ R_p^{21}& R_p^{22}& R_p^{23}\\ R_p^{31}& R_p^{32}& R_p^{33}\end{array}\right];$

$R_p^{11}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2)[1+{{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\cos \left(2{\mathrm{\α}}_m^{\′}\right)][1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}{\cos }^2{\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{22}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2)[1-{{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\cos \left(2{\mathrm{\α}}_m^{\′}\right)][1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}{\sin }^2{\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{33}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2)[1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\sin }^2{\mathrm{\β}}_m^{\′}{{(\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-2)$

$R_p^{12}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2){{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\sin \left(2{\mathrm{\α}}_m^{\′}\right)[1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}\sin {\mathrm{\α}}_m^{\′}\cos {\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{13}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2){\mathrm{\λ}}_{\mathrm{\α}}{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos {\mathrm{\α}}_m^{\′}\sin \left(2{\mathrm{\β}}_m^{\′}\right)+r_m^2\cos {\mathrm{\β}}_m^{\′}\sin {\mathrm{\β}}_m^{\′}\cos {\mathrm{\α}}_m^{\′}({{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}{{\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-{{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}-{\mathrm{\λ}}_{\mathrm{\α}})$

$R_p^{23}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2){\mathrm{\λ}}_{\mathrm{\α}}{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\sin {\mathrm{\α}}_m^{\′}\sin \left(2{\mathrm{\β}}_m^{\′}\right)+r_m^2\cos {\mathrm{\β}}_m^{\′}\sin {\mathrm{\β}}_m^{\′}\sin {\mathrm{\α}}_m^{\′}({{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}{{\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-{{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}-{\mathrm{\λ}}_{\mathrm{\α}})$

In formula ${{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}=E\[\cos 2\widetilde{\mathrm{\α}}\]=e^{-2{\mathrm{\σ}}_{\mathrm{\α}}^2},{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}=E\[\cos 2\widetilde{\mathrm{\β}}\]=e^{-2{\mathrm{\σ}}_{\mathrm{\β}}^2},$ α ' _mfor position angle filtering estimated value, β ' _mfor angle of pitch filtering estimated value, r _mfor distance measure, for the variance of range observation error;

Step 5-3, set up target state equation and measure equation;

After merging, the state equation of target is: x ^u(2, k ₂+ 1)=Ax ^u(2, k ₂)+w ^u(2, k ₂);

Wherein, A is systematic state transfer matrix to the rear, x ^u(2, k ₂) for going state vector to the rear, x ^u(2, k ₂)=[x ', v _x, y ', v _y, z ', v _z] ^t, x ', y ' and z ' are the filter values of the position coordinates of target under rectangular coordinate system, v _x, v _yand v _zbe respectively the speed in x ', y ' and z ' direction, w ^u(2, k ₂) be process noise to the rear;

After merging, the measurement equation of target is: z ^u(2, k ₂)=Bx ^u(2, k ₂)+v ^u(2, k ₂);

Wherein, B is observing matrix to the rear, v ^u(2, k ₂) for going observation noise to the rear;

Step 5-4, filtering upgrade, and adopt Kalman filtering method to carry out filtering:

K ₂filter value and the filtering covariance in-1 moment are respectively x ^u(2, k ₂-1|k ₂-1) and P (k ₂-1|k ₂-1), then k ₂the predicted value x in moment ^u(2 _,k ₂| k ₂-1)=Ax ^u(2, k ₂-1|k ₂-1), k ₂prediction covariance P (2, the k in moment ₂︱ k ₂-1)=AP (k ₂-1 ︱ k ₂-1) A ^t+ Q (2, k ₂), Q (2, k ₂) for removing the variance matrix of process noise to the rear;

Kalman gain matrix K (2, k ₂)=P (2, k ₂| k ₂-1) B ^t/ (R _p+ BP (2, k ₂| k ₂-1) B ^t),

Filtered state value x ^u(2, k ₂| k ₂)=x ^u(2, k ₂| k ₂-1)+K (2, k ₂) (Z ^u-Bx ^u(2, k ₂| k ₂-1)),

Filtered covariance matrix P (2, k ₂| k ₂)=P (2, k ₂| k ₂-1)-K (2, k ₂) AP (2, k ₂| k ₂-1),

Estimating through merging, obtaining filter value x ', y ' and the z ' of the position coordinates of target under rectangular coordinate system;

Step 6, being transformed on yardstick 1 by merging the information estimated, calculating the position angle fine estimation of target with angle of pitch fine estimation with the sampling instant n (k on yardstick 2 ₁-1)+1 as current time, yardstick 1 adopts Kalman filtering method carry out filtering estimation, obtains accurate filtering estimated value:

${\mathrm{\α}}_m^u=\arctan \frac{y^{\′}}{x^{\′}},$

${\mathrm{\β}}_m^u=\arctan \frac{z^{\′}}{\sqrt{x^{\′2}+y^{\′2}}};$

Step 7, repetition step 2, to step 6, until target leaves the investigative range of detection system, obtain target trajectory.

The inventive method more specifically scheme is: yardstick 1 is the sample frequency of infrared detection system, and yardstick 2 is the sample frequency of radar-probing system;

K ₁time be engraved in systematic state transfer matrix on yardstick 1 $F(1,k_1)=[1,T,\frac{T^2}{2},\mathrm{0,0,0};\mathrm{0,1},T,\mathrm{0,0,0};\mathrm{0,0,1,0,0,0};\mathrm{0,0,0,1},T,\frac{T^2}{2};\mathrm{0,0,0,0,1},T;\mathrm{0,0,0,0,0,1}],$ State vector x (1, k ₁)=[α ' _m, v _α, α _α, β ' _m, v _β, α _β], observation vector z (1, k ₁)=[α _m, β _m], observing matrix H (1, k ₁)=[1,0,0,0,0,0; 0,0,0,1,0,0], wherein, T is the sampling period of infrared detection system, α _mfor the measurement of azimuth value of target, β _mfor the pitch angle measurement value of target, α ' _mfor the position angle filtering estimated value of target on yardstick 1, v _αfor α ' _mspeed, a _αfor α ' _macceleration, β ' _mfor the angle of pitch filtering estimated value of target on yardstick 1, v _βfor β ' _mspeed, a _βfor β ' _macceleration;

K ₂time be engraved in systematic state transfer matrix F (2, k on yardstick 2 ₂)=[1,0,0; 0,1,0; 0,0,1], state vector x (2, k ₂)=[r _m, α ' _m, β ' _m], observation vector z (2, k ₂)=[r _m, α ' _m, β ' _m], observing matrix H (2, k ₂)=[1,0,0; 0,1,0; 0,0,1], wherein, r _mfor the distance measure of target;

Infrared detection system is at the sampling rate q of yardstick 1 ₁with the sampling rate q of Airborne Lidar examining system at yardstick 2 ₂meet: q ₁/ q ₂=n, n are positive integer, the sampling instant k of infrared detection system on thin yardstick 1 ₁with the sampling instant k of Airborne Lidar examining system on yardstick 2 ₂between close be: k ₂=n (k ₁-1)+1.

From above technical scheme, the present invention utilizes the multiple dimensioned characteristic of infrared/laser radar detection system keeps track target to set up multiple dimensioned model, after obtaining target measurement value, at thin yardstick, angle information is estimated, then merge at the range information of thick yardstick by the angle information estimated and laser radar, recycling CMKF algorithm is estimated dbjective state, and is transformed into thin yardstick merging the angle information estimated, optimizes angle estimation result further.Proposed by the invention based on multiple dimensioned model infrared/laser radar Multi-sensor Fusion tracking, by multi-scale Data Fusion, improve the estimated accuracy of dbjective state, compared with prior art, there is following beneficial effect:

1, multiple dimensioned model is referred in information fusion, more comprehensive and accurate description target state;

2, at different scale, estimation filtering is carried out to target, and adopt CMKF algorithm to remove deviation, improve the estimated accuracy of dbjective state;

3, mutual by information between different scale, further increases target tracking accuracy.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, below by need in embodiment or description of the prior art use accompanying drawing do simple introduction, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is the process flow diagram of the inventive method;

Fig. 2 is the sampling schematic diagram of infrared detection system and radar-probing system;

Fig. 3 is that the inventive method and prior art are to the arithmetic mean normalization square-error figure of target following;

Fig. 4 is that the inventive method and prior art are to the root-mean-square error figure of target following.

Embodiment

Infrared detection system and Airborne Lidar examining system are usually used in detecting the state of target, because infrared eye sample frequency is more faster than laser radar, therefore by two kinds of detection systems in conjunction with tracking target time, be describe dbjective state under different sample frequency, there is Analysis On Multi-scale Features.The Analysis On Multi-scale Features that the present invention utilizes two kinds of detection systems to merge, propose based on multiple dimensioned CMKF (Multi-scale ConvertedMeasurement Kalman Filter, MCMKF) infrared/laser radar Multi-sensor Fusion method for tracking target.For convenience of description, the sample frequency of infrared detection system is defined as thin yardstick, the sample frequency of radar-probing system is defined as thick yardstick.

Method for tracking target of the present invention is combined at infrared detection system and Airborne Lidar examining system, different sample frequency according to infrared detection system and Airborne Lidar examining system set up multiple dimensioned model, then the data message of target is obtained respectively, thin yardstick is estimated the angle information that infrared detection system obtains, the range information that the angle information that thin yardstick is estimated to obtain and laser radar obtain merges by thick yardstick, recycling CMKF algorithm is estimated dbjective state on thick yardstick, finally be transformed into thin yardstick merging the angle information estimated, the movement locus of final acquisition target.

Fig. 1 is the process flow diagram of the inventive method, is described in detail to the inventive method below in conjunction with Fig. 1, and method for tracking target of the present invention comprises the following steps:

Step 1, set up multiple dimensioned model according to the sample frequency of infrared detection system and radar-probing system, described multiple dimensioned model is:

x(i,k _i+1)＝F(i,k _i)x(i,k _i)+w(i,k _i)

z(i,k _i)＝H(i,k _i)x(i,k _i)+v(i,k _i)

Wherein, F (i, k _i) be k _itime be engraved in systematic state transfer matrix on yardstick i, x (i, k _i) be k _itime be engraved in state vector on yardstick i, x (i, k _i+ 1) be k _ithe state vector on yardstick i is engraved in, w (i, k when+1 _i) be system noise, z (i, k _i) be k _itime be engraved in observation vector on yardstick i, H (i, k _i) be k _itime be engraved in observing matrix on yardstick i, v (i, k _i) be observation noise, k _ifor the sampling instant on yardstick i, i=1, yardstick during 2, i=1 is thin yardstick, and yardstick during i=2 is thick yardstick;

K ₁time be engraved in systematic state transfer matrix on yardstick 1 (thin yardstick) $F(1,k_1)=[1,T,\frac{T^2}{2},\mathrm{0,0,0};\mathrm{0,1},T,\mathrm{0,0,0};\mathrm{0,0,1,0,0,0};\mathrm{0,0,0,1},T,\frac{T^2}{2};\mathrm{0,0,0,0,1},T;\mathrm{0,0,0,0,0,1}],$ T is the sampling period of infrared detection system, k ₁time be engraved in state vector x (1, k on yardstick 1 ₁)=[α ' _m, v _α, a _α, β ' _m, v _β, a _β], α ' _mfor the position angle filtering estimated value of target on yardstick 1, v _αfor α ' _mspeed, a _αfor α ' _macceleration, β ' _mfor the angle of pitch filtering estimated value of target on yardstick 1, v _βfor β ' _mspeed, a _βfor β ' _macceleration, k ₁time be engraved in observation vector z (1, k on yardstick 1 ₁)=[α _m, β _m], α _mfor the measurement of azimuth value of target, β _mfor the pitch angle measurement value of target, k ₁time be engraved in observing matrix H (1, k on yardstick 1 ₁)=[1,0,0,0,0,0; 0,0,0,1,0,0];

K ₂time be engraved in systematic state transfer matrix F (2, k on yardstick 2 (thick yardstick) ₂)=[1,0,0; 0,1,0; 0,0,1], k ₂time be engraved in state vector x (2, k on yardstick 2 ₂)=[r _m, α ' _m, β ' _m], r _mfor the distance measure of target, k ₂time be engraved in observation vector z (2, k on yardstick 2 ₂)=[r _m, α ' _m, β ' _m], the observation vector on yardstick 2 is identical with state vector, k ₂time be engraved in observing matrix H (2, k on yardstick 2 ₂)=[1,0,0; 0,1,0; 0,0,1];

Infrared detection system is at the sampling rate q of yardstick 1 ₁with the sampling rate q of Airborne Lidar examining system at yardstick 2 ₂meet: q ₁/ q ₂=n, n are positive integer, the sampling instant k of infrared detection system on thin yardstick 1 ₁with the sampling instant k of Airborne Lidar examining system on yardstick 2 ₂between close be: k ₂=n (k ₁-1)+1;

Step 2, infrared detection system and radar-probing system carry out data acquisition to target respectively;

With the platform at infrared detection system and radar-probing system place for true origin, the sensor of two detection systems is observed a certain target moved with uniform velocity respectively, and the data collected comprise the distance measure r by the target of laser radar detection system acquisition _mand the measurement of azimuth value α of the target to be gathered by infrared detection system _mwith the pitch angle measurement value β of target _m;

Step 3, on yardstick 1, Unscented kalman filtering (Unscented Kalman Filter is adopted to the angle information that infrared detection system obtains, UKF) method is estimated, utilize 2 recurrence methods to carry out initialization in filtering, after the filtering of UKF method is estimated, obtain the position angle filtering estimated value α ' of more accurate target _mwith angle of pitch filtering estimated value β ' _m;

UKF method is based on Unscented transform, and utilize a series of sampled point chosen, be similar to the probability density function of state vector, UKF method step is as follows:

The time of state upgrades: calculate k ₁time scale 1 on (2n _x+ 1) individual sampled point ξ _jand the weights W of correspondence _j,

$\left\{\begin{array}{c}{\mathrm{\ξ}}_0=x(1,k_1|k_1),j=0\\ {\mathrm{\ξ}}_j=x(1,k_1|k_1)+{\left(\sqrt{(n_x+\mathrm{\ρ})P(1,k_1|k_1)}\right)}_j,j=\mathrm{1,2},...,n_x\\ {\mathrm{\ξ}}_{j+n_x}=x(1,k_1|k_1){-{\left(\sqrt{(n_x+\mathrm{\ρ})P(1,k_1|k_1)}\right)}_j,j=\mathrm{1,2},...,n_x}_{}\end{array}\right.$

$\left\{\begin{array}{c}{W}_0^{\left(c\right)}=\frac{\mathrm{\ρ}}{\left(\mathrm{\ρ}{+n}_x\right)}+(1-{\mathrm{\α}}^2+\mathrm{\β})\\ W_0^{\left(m\right)}=\frac{\mathrm{\ρ}}{\left(\mathrm{\ρ}{+n}_x\right)}\\ W_i^{\left(m\right)}=W_i^{\left(c\right)}=\frac{\mathrm{\ρ}}{\left(\mathrm{\ρ}{+n}_x\right)},j=\mathrm{1,2},...,2n_x\end{array}\right.$

Wherein, x (1, k ₁| k ₁) be k ₁time be engraved in state vector on yardstick 1, n _xfor the dimension of state vector, ρ is scale parameter, is generally 0, P (1, k ₁| k ₁) be k ₁time be engraved in state covariance on yardstick 1, α is the distance that sampled point arrives average, is generally very little positive number, and β is distributions parameter, represent (n _x+ ρ) P (1, k ₁| k ₁) the jth row of root mean square matrix or jth row, with be respectively average and the variance weighting used of sampled point;

Each sampled point is substituted into thin yardstick x (1, k ₁+ 1)=F (1, k ₁) x (1, k ₁) convert, system noise can be ignored, x _j(1, k ₁+ 1|k ₁)=F (1, k ₁) ξ _j, j=0,1 ..., 2n _x, obtain new sampled point set;

One step status predication: $x(1,k_1+1|k_1)=\underset{j=0}{\overset{2n_x}{\mathrm{\Σ}}}{W}_j^{\left(m\right)}{x}_j(1,k_1+1|k_1);$

One step status predication covariance:

$P(1,k_1+1|k_1)=\underset{j=0}{\overset{2n_x}{\mathrm{\Σ}}}{W}_j^{\left(c\right)}(x_j(1,k_1+1|k_1)-x(1,k_1+1\left|k_1\right)){\left(x_j\right(1,k_1+1\left|k_1\right)-x(1,k_1+1|k_1\left)\right)}^T+Q(1,k_1);$

Q (1, k in formula ₁) be the process noise covariance on yardstick 1;

Measurement updaue: utilize a step status predication, a step status predication covariance recalculates sampled point ξ _s:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_0=x(1,k_1+1|k_1),s=0\\ {\mathrm{\ξ}}_s=x(1,k_1+1|k_1)+{\left(\sqrt{(n_x+\mathrm{\ρ})P(1,k_1+1|k_1)}\right)}_s,s=\mathrm{1,2},...,n_x\\ {\mathrm{\ξ}}_{s+n_x}=x(1,k_1+1|k_1){-{\left(\sqrt{(n_x+\mathrm{\ρ})P(1,k_1+1|k_1)}\right)}_s,s=\mathrm{1,2},...,n_x}_{}\end{array}\right.$

Each sampled point is substituted into thin yardstick z (1, k ₁)=H (1, k ₁) x (1, k ₁) conversion, observation noise can be ignored: z _j(1, k ₁+ 1|k ₁)=H (1, k ₁) ξ _s, obtain new sampled point set;

Calculating observation amount covariance:

$P_z(1,k_1+1|k_1)=\underset{j=0}{\overset{2n_x}{\mathrm{\Σ}}}{W}_j^{\left(c\right)}(z_j(1,k_1+1|k_1)-z(1,k_1+1\left|k_1\right)){\left(z_j\right(1,k_1+1\left|k_1\right)-z(1,k_1+1|k_1\left)\right)}^T+R(1,k_1);$

Wherein, $z(1,k_1+1|k_1)=\underset{j=0}{\overset{2n_x}{\mathrm{\Σ}}}{W}_j^{\left(m\right)}{z}_j(1,k_1+1|k_1),$ R (1, k ₁) be the noise covariance on yardstick 1;

Calculating observation amount and quantity of state covariance:

$P_{\mathrm{xz}}(1,k_1+1|k_1)=\underset{j=0}{\overset{2n_x}{\mathrm{\Σ}}}{W}_j^{\left(c\right)}(x_j(1,k_1+1|k_1)-x(1,k_1+1\left|k_1\right)){\left(z_j\right(1,k_1+1\left|k_1\right)-z(1,k_1+1|k_1\left)\right)}^T;$

Filtering upgrades:

UKF gain matrix: K (1, k ₁+ 1)=P _xz(1, k ₁+ 1|k ₁) P _z(1, k ₁+ 1|k ₁) ^-1;

State updating: x (1, k ₁| k ₁)=x (1, k ₁+ 1|k ₁)+K (1, k ₁+ 1) (z (1, k ₁+ 1|k ₁)-z (1, k ₁+ 1|k ₁));

State covariance upgrades: P (1, k ₁+ 1|k ₁+ 1)=P (1, k ₁+ 1|k ₁)-K (1, k ₁+ 1) P _z(1, k ₁+ 1|k ₁) K (1, k ₁+ 1) ^t;

Estimate after filtering, obtain position angle estimated value and angle of pitch estimated value;

Step 4, step 3 obtains the range information that angle estimation information and Airborne Lidar examining system obtain by yardstick 2 merge, observed reading is transformed into rectangular coordinate system, calculates the position coordinates of target under rectangular coordinate system;

The sample frequency of infrared detection system is more faster than the sample frequency of radar-probing system, and its sample frequency is the integral multiple of radar-probing system sample frequency, when radar-probing system obtains the distance measure of target, namely, on yardstick 2, angle estimation information step 3 obtained and the distance measure of laser radar merge;

In object tracking process, in rectangular coordinate system, the advantage of modeling is that filtering and extrapolation process can realize on linear dynamic model, and in spherical coordinate system, modeling can make filtering and extrapolation process complicate; Due to the data that measured value that is infrared and radar-probing system acquisition is in spherical coordinate system, in order to describe dbjective state in rectangular coordinate system, need first the angle information of acquisition and range information to be merged, namely angle information and range information is utilized to determine target location, observation information under spherical coordinate system is transformed in rectangular coordinate system, calculates the position coordinates (x of the target under rectangular coordinate system _m, y _m, z _m):

$\left\{\begin{array}{c}{x}_m=r_m\×\cos {\mathrm{\β}}_m^{\′}\×\cos {\mathrm{\α}}_m^{\′}\\ y_m=r_m\×\cos {\mathrm{\β}}_m^{\′}\×\sin {\mathrm{\α}}_m^{\′}\\ z_m=r_m\×{\sin \mathrm{\β}}_m^{\′}\end{array}\right.;$

Wherein, r _mfor the distance measure of target, α ' _mfor the position angle filtering estimated value of target, β ' _mfor the angle of pitch filtering estimated value of target;

Step 5, employing CMKF algorithm are estimated dbjective state on yardstick 2;

As can be seen from step 4, coordinate conversion is a non-linear process, measured value under spherical coordinate system causes converting measured values to have partially after coordinate conversion, independently Gaussian noise through coordinate conversion be also no longer Gaussian, and intercouple between converted measurement error, no longer meet linear Kalman filter condition, therefore CMKF algorithm is adopted to calculate error mean and the variance of converting measured values, go partially to the converting measured values under rectangular coordinate system, obtain new converted measurement equation, then this measures equation is linear under rectangular coordinate system, available Kalman filtering algorithm carries out filtering,

Step 5-1, calculate target without inclined observed reading change through non-linear scale and remove the converting measured values obtained under rectangular coordinate system to the rear

$\left\{\begin{array}{c}{x}_m^u={\mathrm{\λ}}_{\mathrm{\α}}^{-1}{\mathrm{\λ}}_{\mathrm{\β}}^{-1}{x}_m\\ y_m^u={\mathrm{\λ}}_{\mathrm{\α}}^{-1}{\mathrm{\λ}}_{\mathrm{\β}}^{-1}{y}_m\\ z_m^u={\mathrm{\λ}}_{\mathrm{\β}}^{-1}{z}_m\end{array}\right.;$

Wherein, x _m, y _m, z _mfor the position coordinates of target under rectangular coordinate system, λ _αand λ _βfor without parital coefficient, ${\mathrm{\λ}}_{\mathrm{\α}}=E\[\cos \widetilde{\mathrm{\α}}\]=e^{-\frac{{\mathrm{\σ}}_{\mathrm{\α}}^2}{2}},{\mathrm{\λ}}_{\mathrm{\β}}=E\[\cos \widetilde{\mathrm{\β}}\]=e^{-\frac{{\mathrm{\σ}}_{\mathrm{\β}}^2}{2}},$ for azimuth measurement error, for elevation measurement error, the two is separate white Gaussian noise, be respectively with variance, E [] represent ask expectation value, [] ^trepresent matrix transpose operation;

Step 5-2, error of calculation variance matrix R _p:

$R_p=\mathrm{cov}\left\{{[x_m^u,y_m^u,z_m^u]}^T\right|r_m,{\mathrm{\α}}_m^{\′},{\mathrm{\β}}_m^{\′}\}=\left[\begin{array}{ccc}{R}_p^{11}& R_p^{12}& R_p^{13}\\ R_p^{21}& R_p^{22}& R_p^{23}\\ R_p^{31}& R_p^{32}& R_p^{33}\end{array}\right];$

$R_p^{11}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2)[1+{{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\cos \left(2{\mathrm{\α}}_m^{\′}\right)][1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}{\cos }^2{\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{22}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2)[1-{{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\cos \left(2{\mathrm{\α}}_m^{\′}\right)][1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}{\sin }^2{\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{33}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2)[1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\sin }^2{\mathrm{\β}}_m^{\′}{{(\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-2)$

$R_p^{12}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2){{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\sin \left(2{\mathrm{\α}}_m^{\′}\right)[1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}\sin {\mathrm{\α}}_m^{\′}\cos {\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{13}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2){\mathrm{\λ}}_{\mathrm{\α}}{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos {\mathrm{\α}}_m^{\′}\sin \left(2{\mathrm{\β}}_m^{\′}\right)+r_m^2\cos {\mathrm{\β}}_m^{\′}\sin {\mathrm{\β}}_m^{\′}\cos {\mathrm{\α}}_m^{\′}({{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}{{\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-{{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}-{\mathrm{\λ}}_{\mathrm{\α}})$

$R_p^{23}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2){\mathrm{\λ}}_{\mathrm{\α}}{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\sin {\mathrm{\α}}_m^{\′}\sin \left(2{\mathrm{\β}}_m^{\′}\right)+r_m^2\cos {\mathrm{\β}}_m^{\′}\sin {\mathrm{\β}}_m^{\′}\sin {\mathrm{\α}}_m^{\′}({{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}{{\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-{{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}-{\mathrm{\λ}}_{\mathrm{\α}})$

In formula ${{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}=E\[\cos 2\widetilde{\mathrm{\α}}\]=e^{-2{\mathrm{\σ}}_{\mathrm{\α}}^2},{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}=E\[\cos 2\widetilde{\mathrm{\β}}\]=e^{-2{\mathrm{\σ}}_{\mathrm{\β}}^2},$ α ' _mfor position angle filtering estimated value, β ' _mfor angle of pitch filtering estimated value, r _mfor distance measure, for the variance of range observation error;

Step 5-3, set up target state equation and measure equation;

After merging, the state equation of target is: x ^u(2, k ₂+ 1)=Ax ^u(2, k ₂)+w ^u(2, k ₂);

Wherein, A is systematic state transfer matrix to the rear, x ^u(2, k ₂) for going state vector to the rear, x ^u(2, k ₂)=[x ', v _x, y ', v _y, z ', v _z] ^t, x ', y ' and z ' are the filter value of target at the position coordinates of rectangular coordinate system, v _x, v _yand v _zbe respectively the speed of x ', y ' and z ', w ^u(2, k ₂) be process noise to the rear;

The present embodiment adopts at the uniform velocity model, then remove systematic state transfer matrix to the rear $A=\left\{\begin{array}{cccccc}1& T^{\′}& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& T^{\′}& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& T^{\′}\\ 0& 0& 0& 0& 0& 1\end{array}\right\},$ The sampling period that T ' is radar-probing system;

After merging, the measurement equation of target is: z ^u(2, k ₂)=Bx ^u(2, k ₂)+v ^u(2, k ₂);

Wherein, B is observing matrix to the rear, B=[1,0,0,0,0,0; 0,1,0,0,0,0; 0,0,0,0,1,0; 0,0,0,0,0,1], v ^u(2, k ₂) for going observation noise to the rear, its average is zero, variance is R _p;

Step 5-4, filtering upgrade, and the target state equation after conversion and measurement equation are all linear under rectangular coordinate system, and Kalman filtering method can be adopted to carry out filtering:

K ₂filter value and the filtering covariance in-1 moment are respectively x ^u(2, k ₂-1|k ₂-1) and P (k ₂-1|k ₂-1), then k ₂the predicted value x in moment ^u(2, k ₂| k ₂-1)=Ax ^u(2, k ₂-1|k ₂-1), k ₂prediction covariance P (2, the k in moment ₂︱ k ₂-1)=AP (k ₂-1 ︱ k ₂-1) A ^t+ Q (2, k ₂), Q (2, k ₂) for removing the variance matrix of process noise to the rear;

Kalman gain matrix K (2, k ₂)=P (2, k ₂| k ₂-1) B ^t/ (R _p+ BP (2, k ₂| k ₂-1) B ^t),

Filtered state value x ^u(2, k ₂| k ₂)=x ^u(2, k ₂| k ₂-1)+K (2, k ₂) (Z ^u-Bx ^u(2, k ₂| k ₂-1)),

Filtered covariance matrix P (2, k ₂| k ₂)=P (2, k ₂| k ₂-1)-K (2, k ₂) AP (2, k ₂| k ₂-1),

Estimating through merging, obtaining target at filter value x ', the y ' of the position coordinates of rectangular coordinate system and z ';

Step 6, being transformed on yardstick 1 by merging the information estimated, further optimizing angle estimation result;

Utilize the positional information that step 5 obtains, calculate the position angle fine estimation of target with angle of pitch fine estimation

${\mathrm{\α}}_m^u=\arctan \frac{y^{\′}}{x^{\′}},$

${\mathrm{\β}}_m^u=\arctan \frac{z^{\′}}{\sqrt{x^{\′2}+y^{\′2}}};$

Again position angle fine estimation and angle of pitch fine estimation are turned back on yardstick 1, with the sampling instant n (k on yardstick 2 ₁-1)+1 as current time, yardstick 1 adopts Unscented kalman filtering method carry out filtering estimation, and because current angle estimation value has merged the range information that radar-probing system obtains, estimated accuracy is higher;

Step 7, repetition step 2, to step 6, until target leaves the investigative range of detection system, obtain target trajectory.

Effect of the present invention can be further illustrated by following simulation result:

During emulation, contrast by the method for tracking target based on CMKF algorithm of prior art and the inventive method.

Simulated conditions is as follows: infrared eye and laser ranging collection are in true origin, and target moves with uniform velocity at three dimensions, v _x=200m/s, v _y=0, v _z=150m/s, the initial information of target is [10000, pi/2,0], σ _r=10m, σ _α=0.002rad, σ _β=0.002rad.The sampling period of infrared eye is 0.02s, and the sampling period of range finder using laser is 0.1s, and the simulation time of system is 20s.

Table 1

Table 1 lists root-mean-square error (the Average Euclidean Error of two kinds of methods, be called for short AEE) and root-mean-square error (root mean-square error, RMSE), the error of the inventive method is all less than the method for tracking target based on CMKF algorithm of prior art as shown in Table 1, describe the validity of the inventive method method, and estimated accuracy significantly improves.

If evaluated error and estimate covariance and true error coupling, arithmetic mean normalization square-error (Averaged Normalized Estimation Error Squared is called for short ANEES) is 1; If ANEES is less than (being greater than) 1, the result that the wave filter that illustrates that actual value is less than (being greater than) is estimated.Fig. 3 is the present invention with the method for tracking target based on CMKF algorithm to the arithmetic mean normalized mean squared error figure of target following, ANEES as can be seen from Figure 3 based on the method for tracking target of CMKF algorithm is less than 1 always, illustrate that the square error that wave filter is estimated is too pessimistic, and the inventive method after the starting stage always close to 1, illustrate that evaluated error and estimate covariance are close to actual value.

Fig. 4 is the present invention with the method for tracking target based on CMKF algorithm to the root-mean-square error figure of target following, dot-and-dash line in Fig. 4 represents the pursuit path of the method for tracking target based on CMKF algorithm, dotted line represents the fusion tracking track of the inventive method, as can be seen from Figure 4, dot-and-dash line is almost always higher than dotted line, namely the RMSE of the inventive method is less than the error of the method for tracking target based on CMKF algorithm always, illustrates that the evaluated error of the inventive method is less than the evaluated error based on the method for tracking target of CMKF algorithm.

The above, it is only preferred embodiment of the present invention, not any pro forma restriction is done to the present invention, although the present invention discloses as above with preferred embodiment, but and be not used to limit the present invention, any those skilled in the art, do not departing within the scope of technical solution of the present invention, make a little change when the technology contents of above-mentioned announcement can be utilized or be modified to the Equivalent embodiments of equivalent variations, in every case be the content not departing from technical solution of the present invention, according to any simple modification that technical spirit of the present invention is done above embodiment, equivalent variations and modification, all still belong in the scope of technical solution of the present invention.

Claims (2)

1. based on multiple dimensioned model infrared/laser radar data merge method for tracking target, it is characterized in that, comprise the following steps:

Step 1, set up multiple dimensioned model according to the sample frequency of infrared detection system and Airborne Lidar examining system, described multiple dimensioned model is:

x(i,k _i+1)＝F(i,k _i)x(i,k _i)+w(i,k _i)

z(i,k _i)＝H(i,k _i)x(i,k _i)+v(i,k _i)

Wherein, F (i, k _i) be k _itime be engraved in systematic state transfer matrix on yardstick i, x (i, k _i) be k _itime be engraved in state vector on yardstick i, w (i, k _i) be system noise, z (i, k _i) be k _itime be engraved in observation vector on yardstick i, H (i, k _i) be k _itime be engraved in observing matrix on yardstick i, v (i, k _i) be observation noise, k _ifor the sampling instant on yardstick i, i=1,2;

Step 2, infrared detection system and Airborne Lidar examining system carry out data acquisition to target respectively, obtain the measurement of azimuth value α of target _m, target pitch angle measurement value β _mwith the distance measure r of target _m;

Step 3, the angle information obtained infrared detection system on yardstick 1 adopt Unscented kalman filtering method to estimate, utilize 2 recurrence methods to carry out initialization, obtain the position angle filtering estimated value α ' of target in filtering _mwith angle of pitch filtering estimated value β ' _m;

Step 4, step 3 obtains the range information that angle estimation information and Airborne Lidar examining system obtain by yardstick 2 merge, calculate the position coordinates (x of target under rectangular coordinate system _m, y _m, z _m):

$\left\{\begin{array}{c}{x}_m=r_m\×\cos {\mathrm{\β}}_m^{\′}\×\cos {\mathrm{\α}}_m^{\′}\\ y_m=r_m\×\cos {\mathrm{\β}}_m^{\′}\×\sin {\mathrm{\α}}_m^{\′}\\ z_m=r_m\×\sin {\mathrm{\β}}_m^{\′}\end{array}\right.;$

Wherein, r _mfor the distance measure of target, α ' _mfor the position angle filtering estimated value of target, β ' _mfor the angle of pitch filtering estimated value of target;

Step 5, on yardstick 2, Kalman filtering method is adopted to estimate dbjective state;

Step 5-1, calculate target without inclined observed reading obtain the converting measured values under rectangular coordinate system $z^u={[x_m^u,y_m^u,z_m^u]}^T;$

$\left\{\begin{array}{c}{x}_m^u={\mathrm{\λ}}_{\mathrm{\α}}^{-1}{\mathrm{\λ}}_{\mathrm{\β}}^{-1}{x}_m\\ y_m^u={\mathrm{\λ}}_{\mathrm{\α}}^{-1}{\mathrm{\λ}}_{\mathrm{\β}}^{-1}{y}_m\\ z_m^u={\mathrm{\λ}}_{\mathrm{\β}}^{-1}{z}_m\end{array}\right.;$

Wherein, x _m, y _m, z _mfor the position coordinates of target under rectangular coordinate system, λ _αand λ _βfor without parital coefficient, ${\mathrm{\λ}}_{\mathrm{\α}}=E\left[\cos \widetilde{\mathrm{\α}}\right]=e^{-\frac{{\mathrm{\σ}}_{\mathrm{\α}}^2}{2}},{\mathrm{\λ}}_{\mathrm{\β}}=E\left[\cos \widetilde{\mathrm{\β}}\right]=e^{-\frac{{\mathrm{\σ}}_{\mathrm{\β}}^2}{2}},$ for azimuth measurement error, for elevation measurement error, be respectively with variance, E [] represent ask expectation value, [] ^trepresent matrix transpose operation;

Step 5-2, error of calculation variance matrix R _p:

$R_p=\mathrm{cov}\left\{{[x_m^u,y_m^u,z_m^u]}^T\right|r_m,{\mathrm{\α}}_m^{\′},{\mathrm{\β}}_m^{\′}\}=\left[\begin{array}{ccc}{R}_p^{11}& R_p^{12}& R_p^{13}\\ R_p^{21}& R_p^{22}& R_p^{23}\\ R_p^{31}& R_p^{32}& R_p^{33}\end{array}\right];$

$R_p^{11}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2)[1+{{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\cos \left(2{\mathrm{\α}}_m^{\′}\right)][1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}{\cos }^2{\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{22}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2)[1-{{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\cos \left(2{\mathrm{\α}}_m^{\′}\right)][1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}{\cos }^2{\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{33}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2)[1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\sin }^2{\mathrm{\β}}_m^{\′}({{\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-2)$

$R_p^{12}=\frac{1}{4}(r_m^2+{\mathrm{\σ}}_r^2){{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}\sin \left(2{\mathrm{\α}}_m^{\′}\right)[1+{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos \left(2{\mathrm{\β}}_m^{\′}\right)]+r_m^2{\cos }^2{\mathrm{\β}}_m^{\′}\sin {\mathrm{\α}}_m^{\′}\cos {\mathrm{\α}}_m^{\′}[{\left({\mathrm{\λ}}_{\mathrm{\α}}{\mathrm{\λ}}_{\mathrm{\β}}\right)}^{-2}-2]$

$R_p^{13}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2){\mathrm{\λ}}_{\mathrm{\α}}{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}\cos {\mathrm{\α}}_m^{\′}\sin \left(2{\mathrm{\β}}_m^{\′}\right)+r_m^2\cos {\mathrm{\β}}_m^{\′}\sin {\mathrm{\β}}_m^{\′}\cos {\mathrm{\α}}_m^{\′}({{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}{{\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-{{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}-{\mathrm{\λ}}_{\mathrm{\α}})$

$R_p^{23}=\frac{1}{2}(r_m^2+{\mathrm{\σ}}_r^2){\mathrm{\λ}}_{\mathrm{\α}}{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}{\sin \mathrm{\α}}_m^{\′}\sin \left(2{\mathrm{\β}}_m^{\′}\right)+r_m^2\cos {\mathrm{\β}}_m^{\′}\sin {\mathrm{\β}}_m^{\′}\sin {\mathrm{\α}}_m^{\′}({{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}{{\mathrm{\λ}}_{\mathrm{\β}}}^{-2}-{{\mathrm{\λ}}_{\mathrm{\α}}}^{-1}-{\mathrm{\λ}}_{\mathrm{\α}})$

In formula ${{\mathrm{\λ}}_{\mathrm{\α}}}^{\′}=E\left[\cos 2\widetilde{\mathrm{\α}}\right]=e^{-2{\mathrm{\σ}}_{\mathrm{\α}}^2},{{\mathrm{\λ}}_{\mathrm{\β}}}^{\′}=E\left[\cos 2\widetilde{\mathrm{\β}}\right]=e^{-2{\mathrm{\σ}}_{\mathrm{\β}}^2},$ α ' _mfor position angle filtering estimated value, β ' _mfor angle of pitch filtering estimated value, r _mfor distance measure, for the variance of range observation error;

Step 5-3, set up target state equation and measure equation;

After merging, the state equation of target is: x ^u(2, k ₂+ 1)=Ax ^u(2, k ₂)+w ^u(2, k ₂);

Wherein, A is systematic state transfer matrix to the rear, x ^u(2, k ₂) for going state vector to the rear, x ^u(2, k ₂)=[x ', v _x, y ', v _y, z ', v _z] ^t, x ', y ' and z ' are the filter values of the position coordinates of target under rectangular coordinate system, v _x, v _yand v _zbe respectively the speed in x ', y ' and z ' direction, w ^u(2, k ₂) be process noise to the rear;

After merging, the measurement equation of target is: z ^u(2, k ₂)=Bx ^u(2, k ₂)+v ^u(2, k ₂);

Wherein, B is observing matrix to the rear, v ^u(2, k ₂) for going observation noise to the rear;

Step 5-4, filtering upgrade, and adopt Kalman filtering method to carry out filtering:

K ₂filter value and the filtering covariance in-1 moment are respectively x ^u(2, k ₂-1|k ₂-1) and P (k ₂-1|k ₂-1), then k ₂the predicted value x in moment ^u(2, k ₂| k ₂-1)=Ax ^u(2, k ₂-1|k ₂-1), k ₂prediction covariance P (2, the k in moment ₂︱ k ₂-1)=AP (k ₂-1 ︱ k ₂-1) A ^t+ Q (2, k ₂), Q (2, k ₂) for removing the variance matrix of process noise to the rear;

Kalman gain matrix K (2, k ₂)=P (2, k ₂| k ₂-1) B ^t/ (R _p+ BP (2, k ₂| k ₂-1) B ^t),

Filtered state value x ^u(2, k ₂| k ₂)=x ^u(2, k ₂| k ₂-1)+K (2, k ₂) (Z ^u-Bx ^u(2, k ₂| k ₂-1)),

Filtered covariance matrix P (2, k ₂| k ₂)=P (2, k ₂| k ₂-1)-K (2, k ₂) AP (2, k ₂| k ₂-1),

Estimating through merging, obtaining filter value x ', y ' and the z ' of the position coordinates of target under rectangular coordinate system;

Step 6, being transformed on yardstick 1 by merging the information estimated, calculating the position angle fine estimation of target with angle of pitch fine estimation then with the sampling instant n (k on yardstick 2 ₁-1)+1 as current time, yardstick 1 adopts Kalman filtering method carry out filtering estimation, obtains accurate filtering estimated value:

${\mathrm{\α}}_m^u=\arctan \frac{y^{\′}}{x^{\′}},$

${\mathrm{\β}}_m^u=\arctan \frac{z^{\′}}{\sqrt{x^{\′2}+y^{\′2}}};$

Step 7, repetition step 2, to step 6, until target leaves the investigative range of detection system, obtain target trajectory.

2. as claimed in claim 1 based on multiple dimensioned model infrared/laser radar data merges method for tracking target, it is characterized in that:

Yardstick 1 is the sample frequency of infrared detection system, and yardstick 2 is the sample frequency of radar-probing system;

K ₁time be engraved in systematic state transfer matrix on yardstick 1 $F(1,k_1)=[1,T,\frac{T^2}{2},\mathrm{0,0,0};\mathrm{0,1},T,\mathrm{0,0,0};\mathrm{0,0,1,0,0,0};\mathrm{0,0,0,1},T,\frac{T^2}{2};\mathrm{0,0,0,0,1},T;\mathrm{0,0,0,0,0,1}],$ State vector x (1, k ₁)=[α ' _m, v _α, α _α, β ' _m, v _β, α _β], observation vector z (1, k ₁)=[α _m, β _m], observing matrix H (1, k ₁)=[1,0,0,0,0,0; 0,0,0,1,0,0], wherein, T is the sampling period of infrared detection system, α _mfor the measurement of azimuth value of target, β _mfor the pitch angle measurement value of target, α ' _mfor the position angle filtering estimated value of target on yardstick 1, v _αfor α ' _mspeed, a _αfor α ' _macceleration, β ' _mfor the angle of pitch filtering estimated value of target on yardstick 1, v _βfor β ' _mspeed, a _βfor β ' _macceleration;

K ₂time be engraved in systematic state transfer matrix F (2, k on yardstick 2 ₂)=[1,0,0; 0,1,0; 0,0,1], state vector x (2, k ₂)=[r _m, α ' _m, β ' _m], observation vector z (2, k ₂)=[r _m, α ' _m, β ' _m], observing matrix H (2, k ₂)=[1,0,0; 0,1,0; 0,0,1], wherein, r _mfor the distance measure of target;

Infrared detection system is at the sampling rate q of yardstick 1 ₁with the sampling rate q of Airborne Lidar examining system at yardstick 2 ₂meet: q ₁/ q ₂=n, n are positive integer, the sampling instant k of infrared detection system on thin yardstick 1 ₁with the sampling instant k of radar-probing system on yardstick 2 ₂between close be: k ₂=n (k ₁-1)+1.