CN104569915A - Positioning method used in multiple photoelectric detection systems and based on target movement model - Google Patents

Abstract

The invention discloses a positioning method used in multiple photoelectric detection systems and based on a target movement model. Under the premise that multiple photoelectric detection stations only report orientation information of an aerial target, pure orientation passive positioning is conducted on the aerial target through a batch processing positioning algorithm on the basis of the target movement model. In an actual environment, compared with a traditional method used for static target positioning after asynchronous orientation information is synchronized to be at the same moment, the positioning method has the advantages that time synchronization does not need to be conducted on the orientation information, introduced errors can be reduced to a large degree, and the pure orientation positioning precision of the moving target is improved.

Description

The localization method of based target motion model in many Photodetection systems

Technical field

The present invention relates to a kind of technical field of target location, particularly the localization method of based target motion model in many Photodetection systems.

Background technology

Through the research and development of many decades, Technology for Target Location all makes significant progress on Theory and applications, has been widely used in the various fields such as military affairs, space flight, environment measuring.The not outside electromagnetic radiation signal of passive Technology for Target Location in Photodetection system, therefore has the advantages such as hidden performance is good, viability is strong compared with active location.In general, in passive Technology for Target Location, location technology is roughly divided into two types by the number according to research station: Single passive location and Multi-Station passive location.And according to location mechanism, then location technology can be divided into positioning using TDOA and Pure orientation passive location.

In air defence system, the asynchronous Pure orientation information using many photodetections station to report is carried out passive location to aerial target and is become more and more important.The cardinal principle of traditional bearing-only location method is that first the detection data at the many photodetections station reporting sequential inconsistent is carried out time synchronized, after asynchronous azimuth information is synchronized to synchronization, then carry out cross bearing according to the method for static target location, adopt Least Square Method target location.But in engineer applied under practical circumstances, in the face of acquisition station is disposed sparse, detection overlapping ranges is less; Or acquisition station dispose relatively intensive can multistation Continuous Tracking is carried out to target simultaneously and to these application scenarioss of maneuvering target tracking time; the larger error that the principle in classic method, target azimuth being extrapolated to synchronization can be introduced usually; and it can not meet to everyways such as the continuity of target locating and precision the air defence system demand day by day risen, this makes to seek a kind of new definition method that can be adapted to carry out passive location demand to aerial target in many Photodetection systems becomes a new research topic.

In many Photodetection systems, when the asynchronous Pure orientation information using multistation to report carries out passive location to aerial target, after existing traditional bearing-only location method needs that asynchronous azimuth information is synchronized to synchronization, carry out cross bearing according to the method for static target location.But in actual conditions, moving target orientation is extrapolated to synchronization and usually can introduces comparatively big error, affect positioning precision; Simultaneously in Practical Project because photodetection station is disposed sparse, detect crossover region between standing less, each station reports sequential inconsistent, is difficult to the good location effect of guarantee to target.

Summary of the invention

Goal of the invention: technical matters to be solved by this invention is for the deficiencies in the prior art, the localization method of based target motion model in a kind of many Photodetection systems is provided, improve the Continuous Tracking ability to low target in many Photodetection systems, improve target location accuracy.

In order to solve the problems of the technologies described above, the invention discloses the localization method of based target motion model in a kind of many Photodetection systems, in many Photodetection systems, if moving air target is measured its azimuth information by when top n photodetection station, to the step that target positions be:

Step 1: receive when top n photodetection station is to the set of measurements of target azimuth;

Suppose have N number of acquisition station to detect target, N be greater than 1 integer, the site position coordinates of this N number of acquisition station is respectively (x ₁, y ₁) ^t, (x ₂, y ₂) ^t... (x _n, y _n) ^t, the wherein transposition of subscript T representing matrix.Within a time cycle, the target azimuth measured value that i-th acquisition station reports is θ _i, corresponding measuring intervals of TIME is t _i, then within this time cycle, N number of photodetection station is [(θ to the set of measurements of this target ₁, t ₁), (θ ₂, t ₂) ... (θ _n, t _n)].

Step 2: according to the movement characteristic of aerial target, is divided into two kinds of situations: target linear uniform motion and target uniformly accelerated motion, builds the measurement system of equations to target azimuth, i.e. calculation matrix;

Use variable r ₁, r ₂, r _nrepresent target and t respectively _idistance between i-th photodetection station that moment is corresponding, i=1,2 ..., N; With variable (x _s, y _s) ^trepresent the initial position of target, wherein subscript S is used to identify the symbol that x and y is initial position; With (v _x, v _y) ^trepresent target velocity variable, wherein v _xrepresent the speed component in x direction, v _yrepresent the speed component in y direction, subscript T represents the transposition of vector; With (a _x, a _y) ^trepresent the acceleration variable of target, wherein a _xrepresent the component of acceleration in x direction, a _yrepresent the component of acceleration in y direction;

(1) transformation matrix is measured with the photodetection station that A1 represents in target linear uniform motion situation, W1 represents the variable vector in target linear uniform motion situation, B1 represents the vector that photodetection station location coordinate forms, and so target linear uniform motion measurement system of equations is:

A1 × W1=B1 formula 1

Wherein:

${\left[\begin{array}{ccccccccc}-\sin {\mathrm{\θ}}_1& 0& 0& ...& 0& 1& 0& t_1& 0\\ -\cos {\mathrm{\θ}}_1& 0& 0& ...& 0& 0& 1& 0& t_1\\ 0& -{\sin \mathrm{\θ}}_2& 0& ...& 0& 0& 1& t_2& 0\\ 0& -{\cos \mathrm{\θ}}_2& 0& ...& 0& 0& 1& 0& t_2\\ .& .& & .& & & .& & \\ .& .& & .& & & .& & \\ .& .& & .& & & .& & \\ 0& 0& 0& ...& -\sin {\mathrm{\θ}}_N& 1& 0& t_N& 0\\ 0& 0& 0& ...& -\cos {\mathrm{\θ}}_N& 0& 1& 0& t_N\end{array}\right]}_{2N\×(N+4)}$

W1＝[r ₁,r ₂,···,r _N,x _s,y _s,v _x,v _y] _N+4 ^T

$B1={[x_1,y_1,x_2,y_2...x_N,y_N]}_{2N}^T$

(2) A2 represents that the acquisition station in uniformly accelerated motion situation measures transformation matrix, and W2 represents the variable vector in uniformly accelerated motion situation, and target uniformly accelerated motion model measurement system of equations is:

A2 × W2=B2 formula 2

Wherein:

$A2={\left[\begin{array}{ccccccccccc}-\sin {\mathrm{\θ}}_1& 0& 0& ...& 0& 0& 1& 0& t_N& 0& t_N^2/2\\ -\cos {\mathrm{\θ}}_1& 0& 0& ...& 0& 1& 0& t_N& 0& t_N^2/2& 0\\ 0& -\sin {\mathrm{\θ}}_2& 0& ...& 0& 0& 1& 0& t_n& 0& t_N^2/2\\ 0& -{\cos \mathrm{\θ}}_2& 0& ...& 0& 1& 0& t_N& 0& t_N^2/2& 0\\ .& .& .& & & & & & .& & \\ .& .& .& & & & & & .& & \\ .& .& .& & & & & & .& & \\ 0& 0& 0& ...& -\sin {\mathrm{\θ}}_N& 0& 1& 0& t_N& 0& t_N^2/2\\ 0& 0& 0& ...& -\cos {\mathrm{\θ}}_N& 1& 0& t_N& 0& t_N^2/2& 0\end{array}\right]}_{2N\×(N+6)}$

W2＝[r ₁,r ₂,···,r _N,x _s,y _s,v _x,v _y,a _x,a _y] _N+6 ^T

$B2={[x_1,y_1,x_2,y_2...x_N,y_N]}_{2N}^T$

Step 3: the measurement system of equations obtained based on step 2, resolves target movement model, obtains initial position and the movement velocity of target;

(1) solution in target linear uniform motion situation:

As 2N<N+4 (i.e. N<4), R (A1) <R (A1, B1) system of equations has infinitely organizes solution more;

As 2N=N+4 (i.e. N=4), R (A1)=R (A1, B1)=2N system of equations has unique solution;

As 2N>N+4 (i.e. N>4), R (A1)=R (A1, B1) <2N system of equations has least square solution,

The wherein order of R representing matrix.

When N >=4, least squares estimate is adopted to solve W1, so have:

$\hat{W}1={\left({A1}^{T}A1\right)}^{-1}{A1}^{T}B1$ Formula 3

Wherein for the estimated value of W1 calculated by formula 3.

The initial position of target and movement velocity are:

formula 4

Wherein for the estimated value of target initial position, for target velocity is in X-axis, the estimated value in Y direction.

(2) solution in target uniformly accelrated rectilinear motion situation:

As 2N<N+6 (i.e. N<6), R (A2) <R (A2, B2) system of equations has infinitely organizes solution more;

As 2N=N+6 (i.e. N=6), R (A2)=R (A2, B2)=2N system of equations has unique solution;

As 2N>N+6 (i.e. N>6), R (A2)=R (A2, B2) <2N system of equations has least square solution,

The wherein order of R representing matrix.

When N >=6, least squares estimate is adopted to solve W2, so have:

$\widehat{W2}={\left({A2}^{T}A2\right)}^{-1}{A2}^{T}B2$ Formula 5

Wherein for the estimated value of W2 calculated by formula 5.

The initial position of target and movement velocity are:

(formula 6)

Wherein for the estimated value of target initial position, for target velocity is in X-axis, the estimated value in Y direction, for aimed acceleration is in X-axis, the estimated value in Y direction.

Step 4: for step 4 resolve target initial position and the movement velocity of acquisition, estimate the current location of target.

(1) current location (x of target in linear uniform motion situation _t, y _t):

formula 7

formula 8

(2) current location (x of target in linear uniform motion situation _t, y _t):

formula 9

formula 10.

The present invention is under multiple photodetection station only reports the prerequisite of the azimuth information of aerial target, and based target motion model, carries out Pure orientation passive location by batch processing location algorithm to aerial target.In actual environment, compared with the classic method of locating by static target after asynchronous azimuth information is synchronized to synchronization,

The present invention does not need azimuth information to carry out time synchronized, batch processing location algorithm is set up by establishing target motion model, certainly the problem of aerial target Pure orientation passive location, can reduce the error of introducing largely, improves the precision of moving target bearing-only location.Through engineering test, the present invention disposes sparse at photodetection station, detect between site crossover region less when, precision and the continuity of moving target bearing-only location can be improved, the problem that each photodetection station reports sequential inconsistent can be solved, obvious advantage is had than traditional localization method (first time synchronized uses Least Square Method target location again) in locating effect and tracking continuity, can complement one another with traditional localization method in engineering practice, there is good engineering adaptability.

Accompanying drawing explanation

To do the present invention below in conjunction with the drawings and specific embodiments and further illustrate, above-mentioned and/or otherwise advantage of the present invention will become apparent.

Fig. 1 is the object localization method theory diagram based on motion model of the present invention.

Fig. 2 is that schematic diagram is located to aerial target in photodetection station.

Fig. 3 is positioning result ratio in example scenario 1.

Fig. 4 is example scenario 2 positioning result.

Fig. 5 example scenario 3 positioning result.

Embodiment

As shown in Figure 1, the invention discloses the localization method of based target motion model in many Photodetection systems, the localization method of based target motion model in many Photodetection systems, comprises the following steps:

Step 1: receive when top n photodetection station is to the set of measurements in aerial target orientation;

Step 2: according to the movement characteristic of aerial target, is divided into two kinds of situations: target linear uniform motion and target uniformly accelerated motion, builds the measurement system of equations to target azimuth, i.e. calculation matrix;

Step 3: the measurement system of equations obtained based on step 2, resolves target movement model, obtains initial position and the movement velocity of target;

Step 4: for step 4 resolve target initial position and the movement velocity of acquisition, estimate the current location of target.

Under Descartes's rectangular coordinate system, suppose that the initial position of aerial target projected position is in the plane x ₀=(x _s, y _s) ^t, target velocity vector v=(v _x, v _y) ^t, so target is at the position x of t _tfor:

X _t=x ₀+ vt formula 1

As shown in Figure 2, suppose have N number of acquisition station to detect target, the site position coordinates of this N number of acquisition station is respectively (x ₁, y ₁) ^t, (x ₂, y ₂) ^t... (x _n, y _n) ^t.

Suppose within a time cycle, the target azimuth measured value that i-th acquisition station reports is θ _i, corresponding measuring intervals of TIME is t _i, use variable r _irepresent that target is at t _ithe distance of moment and i-th acquisition station.

The present invention propose the target bearing-only location method based on motion model will stand in the measurement orientation reported in the time cycle according to N number of photodetection, N be greater than 1 integer, the current location of target is estimated.

According to the movement characteristic of aerial target, the foundation of aerial target motion model can be divided into two kinds of situations, target linear uniform motion and target uniformly accelrated rectilinear motion:

Situation 1: target linear uniform motion

Can draw according to i-th geometric relationship between acquisition station and target, target is at t _ithe position in moment:

$x_{t_i}=x_i+r_i\sin {\mathrm{\&theta;}}_i,y_{t_i}=y_i+r_i\cos {\mathrm{\&theta;}}_i$ Formula 2

Wherein i=1,2 ... N, θ _iit is the measured value at i-th photodetection station.

Formula 12 is substituted into formula 11, can obtain:

$\left\{\begin{array}{c}-r_i\sin {\mathrm{\&theta;}}_i+x_s+v_x{t}_i=x_i\\ -r_i\cos {\mathrm{\&theta;}}_i+y_s+v_y{t}_i=y_i\end{array}\right.$

Then N the measurement of N number of acquisition station within a time cycle can obtain the system of equations measured equation form by 2N:

$\left\{\begin{array}{c}-r_1\sin {\mathrm{\&theta;}}_1+x_s+v_x{t}_1=x_1\\ -r_1\cos {\mathrm{\&theta;}}_1+y_s+v_y{t}_1=y_1\\ -r_2\sin {\mathrm{\&theta;}}_2+x_s+v_x{t}_2=x_2\\ -r_2\cos {\mathrm{\&theta;}}_2+y_s+v_y{t}_2=y_2\\ .\\ .\\ .\\ -r_N\sin {\mathrm{\&theta;}}_N+x_s+v_x{t}_N=x_N\\ -r_N\cos {\mathrm{\&theta;}}_N+y_s+v_y{t}_N=x_N\end{array}\right.$

Write above system of equations as matrix form, can be obtained:

A1 × W1=B1 formula 3

Wherein A1 represents linear uniform motion transformation matrix, and W1 represents variable vector, and B1 represents the vector that photodetection station coordinates forms.

${\left[\begin{array}{ccccccccc}-\sin {\mathrm{\&theta;}}_1& 0& 0& ...& 0& 1& 0& t_1& 0\\ -\cos {\mathrm{\&theta;}}_1& 0& 0& ...& 0& 0& 1& 0& t_1\\ 0& -{\sin \mathrm{\&theta;}}_2& 0& ...& 0& 0& 1& t_2& 0\\ 0& -{\cos \mathrm{\&theta;}}_2& 0& ...& 0& 0& 1& 0& t_2\\ .& .& & .& & & .& & \\ .& .& & .& & & .& & \\ .& .& & .& & & .& & \\ 0& 0& 0& ...& -\sin {\mathrm{\&theta;}}_N& 1& 0& t_N& 0\\ 0& 0& 0& ...& -\cos {\mathrm{\&theta;}}_N& 0& 1& 0& t_N\end{array}\right]}_{2N\&times;(N+4)}$

W1＝[r ₁,r ₂,···,r _N,x _s,y _s,v _x,v _y] _N+4 ^T

$B1={[x_1,y_1,x_2,y_2...x_N,y_N]}_{2N}^T$

Position (the x of acquisition station in formula 3 ₁, y ₁) ... (x _n, y _n) and measured value θ _iwith time t _iare all known variables, target is to the distance r of acquisition station _i, initial position (x _s, y _s) and speed (v _x, v _y) be all known variables.That is to say and solve N+4 unit Linear Equations formula 3, its situation of separating is as follows:

As 2N<N+4 (i.e. N<4), R (A1) <R (A1, B1) system of equations has infinitely organizes solution more;

As 2N=N+4 (i.e. N=4), R (A1)=R (A1, B1)=2N system of equations has unique solution;

As 2N>N+4 (i.e. N>4), R (A1)=R (A1, B1) <2N system of equations has least square solution,

The wherein order of R representing matrix.

When N>=4, formula 3 has solution, adopts least squares estimate to W ₁solve, so have:

$\hat{W}1={\left({A1}^{T}A1\right)}^{-1}{A1}^{T}B1$ Formula 4

By the known W of formula 3 ₁the initial position of target and movement velocity can be obtained by following formula:

formula 5

After the initial position obtaining target and movement velocity, just can obtain target position at any one time according to formula 1.

In actual use, can be initial time by the current moment receiving acquisition station azimuth information, the historical data that other acquisition stations report, retrodicting as initial position, the time interval gets negative value, and the initial position obtained by formula 5 is like this exactly the current location of target.

In practical engineering application, the situation having within a short period of time more than 4 photodetection stations to detect same target is less, will be restricted and can not use when using said method to carry out Pure orientation target localization.In this case, can solve by using the repetitive measurement data at single photodetection station, thus obtain the estimated value of target location.Be located in the time cycle n the measurement data that have received from m station, as long as it meets m >=2, the condition of n >=4, such as, have 3 photodetection stations to report respectively with the metrical information of a collection of target each 2 times, amount to 6 measurement data, formula 5 still can solve.

Situation 2: target uniformly accelerated motion

When moving target do normal acceleration motor-driven time, if the acceleration of target is a=(a _x, a _y) ^t, the equation of motion of target is:

X _t=x ₀+ vt+at ²/ 2 formula 6

The process of establishing of model is similar to the target linear uniform motion of situation 1, and wherein A2 represents linear uniform motion transformation matrix, and W2 represents variable vector, and B2 represents the vector that photodetection station coordinates forms.

$A2={\left[\begin{array}{ccccccccccc}-\sin {\mathrm{\&theta;}}_1& 0& 0& ...& 0& 0& 1& 0& t_N& 0& t_N^2/2\\ -\cos {\mathrm{\&theta;}}_1& 0& 0& ...& 0& 1& 0& t_N& 0& t_N^2/2& 0\\ 0& -\sin {\mathrm{\&theta;}}_2& 0& ...& 0& 0& 1& 0& t_n& 0& t_N^2/2\\ 0& -{\cos \mathrm{\&theta;}}_2& 0& ...& 0& 1& 0& t_N& 0& t_N^2/2& 0\\ .& .& .& & & & & & .& & \\ .& .& .& & & & & & .& & \\ .& .& .& & & & & & .& & \\ 0& 0& 0& ...& -\sin {\mathrm{\&theta;}}_N& 0& 1& 0& t_N& 0& t_N^2/2\\ 0& 0& 0& ...& -\cos {\mathrm{\&theta;}}_N& 1& 0& t_N& 0& t_N^2/2& 0\end{array}\right]}_{2N\&times;(N+6)}$

W2＝[r ₁,r ₂,···,r _N,x _s,y _s,v _x,v _y,a _x,a _y] _N+6 ^T

$B2={[x_1,y_1,x_2,y_2...x_N,y_N]}_{2N}^T$

As 2N<N+6 (i.e. N<6), R (A2) <R (A2, B2) system of equations has infinitely organizes solution more;

As 2N=N+6 (i.e. N=6), R (A2)=R (A2, B2)=2N system of equations has unique solution;

As 2N>N+6 (i.e. N>6), R (A2)=R (A2, B2) <2N system of equations has least square solution,

The wherein order of R representing matrix.

When N >=6, least squares estimate is adopted to solve W2, so have:

$\widehat{W2}={\left({A2}^{T}A2\right)}^{-1}{A2}^{T}B2$ Formula 7

Wherein for the estimated value of W2 calculated by formula 8.

By the initial position of the known target of formula 6 and movement velocity be:

Wherein for the estimated value of target initial position, for target velocity is in X-axis, the estimated value in Y direction, for aimed acceleration is in X-axis, the estimated value in Y direction.

After obtaining the initial position of target, movement velocity, acceleration, just can obtain target position at any one time according to formula 6.

Feature of the present invention comprises:

1) target localization is carried out according to the passive Pure orientation metrical information of multistation;

2) do not need azimuth information to carry out time synchronized;

3) target localization is carried out by setting up the calculation of target movement model measurement solution of equations;

4) target movement model is divided into linear uniform motion and uniformly accelrated rectilinear motion two kinds;

5) resolve according to carrying out Linear Equations to target movement model system of equations the initial position and movement velocity that obtain target;

6), after obtaining target initial position and movement velocity, according to the relation of aerial target projected position and initial projections position and velocity vector on two dimensional surface under Descartes's rectangular coordinate system, the current time position obtaining target is resolved.

First the classic method that time synchronized adopts Least Square Method target location is again carried out relative to according to the multistation detection data reporting sequential inconsistent, there is better target localization performance and precision, and better engineering adaptability: dispose sparse at acquisition station, detect crossover region between standing less; Acquisition station is disposed relatively intensive, and investigative range is overlapping and under the actual scene such as locating and tracking changing course maneuvering target mutually, and the inventive method has better target localization effect than classic method.

Embodiment

In order to the method proposed the present invention is verified, the checking of confidentiality has been carried out in Egyptian export-oriented photodetection group network system, by building five example scenario, will method of the present invention be used and use the positioning result of conventional mapping methods and target actual position to be analyzed.In following proof procedure, the azimuthal error at each photodetection station is all set to the Gaussian distribution meeting zero-mean, standard deviation sigma=1 ⁰.It should be noted that, in order to directly consider the locating effect of the inventive method and classic method, the target trajectory provided in following scene checking is the direct result of location Calculation, not to the smoothing process of result.

Example scenario 1:

X-06, X-07, X-08 station, 3 photodetection stations is disposed relatively sparse, and namely the detection at three stations is occured simultaneously and not exclusively overlapped, and simulates a collection of target, lot number is S015, and speed is 500 kilometers/hour, 85 degree, course, move eastwards from west, the detection data at 3 stations reports frequency to be 12 times per minute.Positioning result is as shown in Fig. 3 (design sketch must use expressing gradation), the position line being wherein numbered X-06/001 represents the target azimuth of X-06 detection, the position line being numbered X-07/001 represents the target azimuth of X-07 detection, the position line being numbered X-08/001 represents the target azimuth of X-08 detection, exist in the investigative range of X-07 some only X-07 can detect and the undetectable region of X-06 and X-08, as shown in Figure 3, the target designation that method of the present invention is oriented is T016, the positioning result target designation obtained from traditional least square method is T015.As can be seen from Figure 3 when target S015 fly out X-08 investigative range after, T015 no longer upgrades, and T016 still can rely on the directional bearing line of X-07 to upgrade continuously, that is, localization method of the present invention has positioning performance more better than traditional location algorithm when photodetection station is disposed sparse.

Example scenario 2:

5 acquisition stations J-08, J-09, J-11, J-13, J-14 dispose relatively intensive, namely there is not investigative range without the situation of occuring simultaneously, simulating a collection of target lot number is S015, speed is 500 kilometers/hour, 175 degree, course, from J-14 station to the direction motion of J-08 station, the detection datas at 5 stations report frequency to be 6 times per minute, use the inventive method and traditional least square method to position calculating simultaneously.As shown in Figure 4, the target that wherein method of the present invention is oriented is T016 to positioning result, and traditional least square method positioning result is T015.Can find out, the track of T016 than the track of T015 more close to the real motion track of simulated target S015, the track of T016 is also more smooth than the track of T015 simultaneously, therefore can reach a conclusion, when this photodetection station is disposed relatively intensive, the positioning precision of method of the present invention is better than classic method.

Example scenario 3:

The deployment of acquisition station is identical with example scenario 2, simulates a collection of target S015, and speed is 500 kilometers/hour, does the motion of automobile in 175 degree to 0 degree, course, and the detection data at 5 stations reports frequency to be 12 times per minute.Use the inventive method and traditional least square method to position calculating, notify the location Calculation module in the inventive method when simulated target is motor-driven, location Calculation module switches to motor-driven computation model by original at the uniform velocity computation model.As shown in Figure 5, the target that wherein the inventive method is oriented is T016, and traditional least square method positioning result is T015 in the positioning result contrast of two kinds of methods.By finding out in Fig. 5 that when the target S015 motion of automobile, the tracking effect of T016 is obviously better than T015, therefore at this type of under scene of maneuvering target location, the inventive method has better target locating performance than classic method.

Can be found out by above 3 scenes, when being applied in Egyptian export-oriented photodetection group network system, the bearing-only location method of the based target motion model that the present invention proposes, compared to conventional mapping methods, the present invention disposes sparse at photodetection station, detect between standing crossover region less when, there is reasonable locating effect; Simultaneously because localization method of the present invention is based target motion model, can also solve the problem that each photodetection station reports sequential inconsistent, compared to conventional mapping methods, the passive location of the present invention to process aerial target has better engineering adaptability.

The invention provides the localization method of based target motion model in a kind of many Photodetection systems; the method and access of this technical scheme of specific implementation is a lot; the above is only the preferred embodiment of the present invention; should be understood that; for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.The all available prior art of each ingredient not clear and definite in the present embodiment is realized.

Claims (5)

1. in Photodetection system more than, the localization method of based target motion model, is characterized in that, comprises the following steps:

Step 1: receive when top n photodetection station is to the set of measurements in aerial target orientation;

Step 2: according to the movement characteristic of aerial target, is divided into two kinds of situations: target linear uniform motion and target uniformly accelerated motion, builds the measurement system of equations to target azimuth, i.e. calculation matrix;

Step 3: the measurement system of equations obtained based on step 2, resolves target movement model, obtains initial position and the movement velocity of target;

Step 4: for step 4 resolve target initial position and the movement velocity of acquisition, estimate the current location of target.

2. method according to claim 1, is characterized in that, step 1 comprises:

Suppose have N number of photodetection station to detect target, N be greater than 1 integer, the site position coordinates at N number of photodetection station is respectively (x ₁, y ₁) ^t, (x ₂, y ₂) ^t... (x _n, y _n) ^t, the wherein transposition of subscript T representing matrix; Within a time cycle, the target azimuth measured value that i-th photodetection station reports is θ _i, corresponding measurement moment t _i, then within this time cycle, N number of photodetection station is [(θ to the set of measurements of this target ₁, t ₁), (θ ₂, t ₂) ... (θ _n, t _n)], i span 1 ~ N.

3. method according to claim 1, is characterized in that, step 2 comprises:

Use variable r ₁, r ₂..., r _nrepresent target and t respectively _idistance between i-th photodetection station that moment is corresponding, i=1,2 ..., N; With variable (x _s, y _s) ^trepresent the initial position of target, wherein subscript S is used to identify the symbol that x and y is initial position; With (v _x, v _y) ^trepresent target velocity variable, wherein v _xrepresent the speed component in x direction, v _yrepresent the speed component in y direction, subscript T represents the transposition of vector; With (a _x, a _y) ^trepresent the acceleration variable of target, wherein a _xrepresent the component of acceleration in x direction, a _yrepresent the component of acceleration in y direction;

Transformation matrix is measured with the photodetection station that A1 represents in target linear uniform motion situation, W1 represents the variable vector in target linear uniform motion situation, B1 represents the vector that photodetection station location coordinate forms, and so target linear uniform motion measurement system of equations is:

A1 × W1=B1 formula 1,

Wherein:

$A1={\left[\begin{array}{ccccccccc}-{\sin \mathrm{\&theta;}}_1& 0& 0& ...& 0& 1& 0& t_1& 0\\ -\cos {\mathrm{\&theta;}}_1& 0& 0& ...& 0& 0& 1& 0& t_1\\ 0& -{\sin \mathrm{\&theta;}}_2& 0& ...& 0& 1& 0& t_2& 0\\ 0& -{\cos \mathrm{\&theta;}}_2& 0& ...& 0& 0& 1& 0& t_2\\ .& .& & .& & & .& & \\ .& .& & .& & & .& & \\ .& .& & .& & & .& & \\ 0& 0& 0& ...& -\sin {\mathrm{\&theta;}}_N& 1& 0& t_N& 0\\ 0& 0& 0& ...& -{\cos \mathrm{\&theta;}}_N& 0& 1& 0& t_N\end{array}\right]}_{2N\&times;(N+4)},$

W1＝[r ₁,r ₂,…,r _N,x _s,y _s,v _x,v _y] _N+4 ^T，

$B1={[x_1,y_1,x_2,y_2\&CenterDot;\&CenterDot;\&CenterDot;x_N,y_N]}_{2N}^T,$

Measure transformation matrix with the acquisition station that A2 represents in uniformly accelerated motion situation, W2 represents the variable vector in uniformly accelerated motion situation, and target uniformly accelerated motion model measurement system of equations is:

A2 × W2=B1 formula 2,

Wherein:

$A2={\left[\begin{array}{ccccccccccc}-{\sin \mathrm{\&theta;}}_1& 0& 0& ...& 0& 0& 1& 0& t_N& 0& t_N^2/2\\ -{\cos \mathrm{\&theta;}}_1& 0& 0& ...& 0& 1& 0& t_N& 0& t_N^2/2& 0\\ 0& -\sin {\mathrm{\&theta;}}_2& 0& ...& 0& 0& 1& 0& t_n& 0& t_N^2/2\\ 0& -\cos {\mathrm{\&theta;}}_2& 0& ...& 0& 1& 0& t_N& 0& t_N^2/2& 0\\ .& .& & .& & & & & .& & \\ .& .& & .& & & & & .& & \\ .& .& & .& & & & & .& & \\ 0& 0& 0& ...& -\sin {\mathrm{\&theta;}}_N& 0& 1& 0& t_N& 0& t_N^2/2\\ 0& 0& 0& ...& -{\cos \mathrm{\&theta;}}_N& 1& 0& t_N& 0& t_N^2/2& 0\end{array}\right]}_{2N\&times;(N+6)},$

W2＝[r ₁,r ₂,…,r _N,x _s,y _s,v _x,v _y,a _x,a _y] _N+6 ^T。

4. method according to claim 1, is characterized in that, step 3 comprises:

Solution in target linear uniform motion situation:

Work as 2N<N+4, namely during N<4, R (A1) <R (A1, B1) system of equations has infinitely organizes solution more;

Work as 2N=N+4, namely during N=4, R (A1)=R (A1, B1)=2N system of equations has unique solution;

Work as 2N>N+4, namely during N>4, R (A1)=R (A1, B1) <2N system of equations has least square solution;

The wherein order of R representing matrix;

When N >=4, least squares estimate is adopted to solve W1, so have:

$\hat{W}1={\left({A1}^{T}A1\right)}^{-1}{A1}^{T}B1$ Formula 3,

Wherein for the estimated value of variable vector W1 calculated by formula 3;

The initial position of target and movement velocity are:

formula 4,

Wherein for the estimated value of target initial position, for target velocity is in X-axis, the estimated value in Y direction;

Solution in target uniformly accelrated rectilinear motion situation:

Work as 2N<N+6, namely during N<6, R (A2) <R (A2, B2) system of equations has infinitely organizes solution more;

Work as 2N=N+6, namely during N=6, R (A2)=R (A2, B2)=2N system of equations has unique solution;

Work as 2N>N+6, namely during N>6, R (A2)=R (A2, B2) <2N system of equations has least square solution,

The wherein order of R representing matrix;

When N >=6, least squares estimate is adopted to solve W2, so have:

$\hat{W}2={\left({A2}^{T}A2\right)}^{-1}{A2}^{T}B2$ Formula 5,

Wherein for the estimated value of variable vector W2 calculated by formula 5;

The initial position of target and movement velocity are:

formula 6,

Wherein for the estimated value of target initial position, for target velocity is in X-axis, the estimated value in Y direction, for aimed acceleration is in X-axis, the estimated value in Y direction.

5. method according to claim 1, is characterized in that, step 4 comprises:

Current location (the x of target in linear uniform motion situation _t, y _t):

formula 7,

formula 8,

Current location (the x of target in linear uniform motion situation _t, y _t):

formula 9,

formula 10.