CN104252579A - Expanded generalized S-dimensional assignment and formation target maneuvering mode judgment method - Google Patents

Abstract

In view of the fact that a traditional multi-sensor maneuvering target tracking method and an existing maneuvering formation target tracking method cannot track targets in a maneuvering formation accurately and easily, the invention provides an expanded generalized S-dimensional assignment and formation target maneuvering mode judgment method based on formation target tracking models under four typical maneuvering modes of integral, split, merged and scattered maneuvering. The method includes: firstly, structuring multiple feasibility partitions based on formation tracks and formation measurement, then structuring an S-dimensional assignment problem based on a cost function of each feasible partition, and finally judging a maneuvering mode of each formation target based on the optimum feasibility partition so as to complete status updating of each track in the formation by utilizing the formation target tracking model under the corresponding maneuvering mode. The problem about accurate tracking of the targets in the maneuvering formation under the condition of multi-sensor detection is well solved.

Description

Expansion Generalized S-Wei distribute formation target maneuver model determination methods

Technical field

The invention belongs to multiple-sensor and multiple-object information integration technology field, provide a kind of expansion Generalized S-Wei to distribute formation target maneuver model determination methods.

Background technology

In the flight path maintenance stage, formation target can occur various motor-driven, now the relative position structure generation convergent-divergent of formation internal object echo, shearing, the conversion of rotation equiaffine, and non-maneuver formation target tracking method is no longer applicable.Traditional maneuvering target tracking method is not enough because considering mobile formation target echo complicacy, be difficult to obtain desirable tracking effect, and existing mobile formation method for tracking target is only simple is studied based on formation entirety, the state updating completing each target in mobile formation that cannot be accurate, real-time.

In formation target motion process, based on specific tactics or object, formation target can be turned at any time, climb, underriding etc. is overall motor-driven, also there will be the distinctive maneuver models of formation target such as division, merging, dispersion, in this case, formation internal object structure will change, and cause the resolution state of multisensor to interior individual goal of forming into columns more complicated, under clutter environment, the accurate tracking problem of multisensor mobile formation target becomes very difficult.Traditional multisensor maneuvering target tracking technology is difficult to follow the tracks of motor-driven formation target, and main cause is: (1), when formation target divides, merges or disperses, traditional maneuvering target tracking model no longer mates; (2) formation internal object is generally at a distance of comparatively near, and thus echo cross influence seriously, adds the impact of clutter, when generation of forming into columns is motor-driven, easily occurs with losing, following the phenomenons such as wrong; (3) when utilizing networking sensor to detect formation target, because sensor is different from the angle of formation internal object, each sensor may be inconsistent to the acquisition mode of same mobile formation target, realizes the complementation of multi-sensor information and reject more difficult.Existing mobile formation method for tracking target mostly based on formation overall to division, merge and study, the flight path replacement problem of formation internal object when generator under multi-sensor detection moves can not be solved, can not meet the Practical Project demand of target tracking domain.

Summary of the invention

The technical matters solved

In view of traditional multisensor maneuvering target tracking method and existing mobile formation method for tracking target are difficult to the fact of accurate tracking mobile formation internal object, the present invention is based on overall motor-driven, division, merge and formation target tracking model under dispersion four kinds of typical motor patterns, propose a kind of expansion Generalized S-Wei and distribute formation target maneuver model determination methods, judge the maneuver model of formation target flight path, thus utilize the formation target tracking model under corresponding maneuver model to complete the state updating of each flight path in formation.

Technical scheme

Expansion Generalized S-Wei of the present invention distributes formation target maneuver model determination methods, first divide based on formation flight path and the multiple feasibility of formation measuring construction, then the cost function structure S-divided based on each feasibility ties up assignment problem, and the feasibility finally based on optimum divides the maneuver model judging each formation target.

Beneficial effect

The method is motor-driven based on entirety, division, merge and formation target tracking model under dispersion four kinds of typical motor patterns, by the measurement characteristic of formation internal object, judge the maneuver model of formation target flight path, thus the state updating of each flight path in utilizing the formation target tracking model under corresponding maneuver model to complete to form into columns, the accurate tracking problem of mobile formation internal object under multi-sensor detection can be solved preferably.

Embodiment

1. the definition of event

If be the measurement number of k moment sensor i, under multi-sensor environment, measurement equation is represented as:

$Z_l^i\left(k\right)=H_i\left(k\right)X^t\left(k\right)+W_l^i\left(k\right),t=\mathrm{1,2},...,T;l=\mathrm{1,2},...,m_{k_i}---\left(1\right)$

In formula, measure represent l the measurement of k moment sensor i; H _ik () is the measurement matrix of sensor i; be there is known covariance and with the zero-mean Gaussian noise of other noise vector statistical iteration all vector; T is target number; The INTEGRATED SIGHT vector that k moment fusion center obtains is

$Z\left(k\right)=\left\{Z_i^s\left(k\right)\right\},i=1,...,m_s;s=1,...,N_s---\left(2\right)$

And suppose that the error in measurement between each sensor is statistical iteration.

If the comprehensive measurement collection that Z (k) is k moment fusion center, defines such as formula shown in (1).Utilize cycle threshold model to carry out the segmentation of forming into columns, and the central point set obtaining each formation is

$\stackrel{\‾}{Z}\left(k\right)=\left\{{\stackrel{\‾}{z}}_i\left(k\right)\right\},i=\mathrm{1,2},...,m_k---\left(3\right)$

In formula, m _kfor the number of forming into columns.

Measure the corresponding relation between Formation Center's flight path based on Formation Center under each formation target maneuver model, the event that definition characterizes each formation maneuvering pattern is:

Event 1: only may be with association, then formation t belongs to overall maneuver model;

Event 2: associate with multiple Formation Center's point, then formation t belongs to division maneuver model simultaneously;

Event 3: etc. multiple formation center flight path simultaneously with association, then form into columns t ₁, t ₂belong to merging maneuver model;

Event 4: the formation be not successfully associated measures, then formation t belongs to dispersion maneuver model.

2. the foundation of basic model

I-th of definition sensor s _sindividual measurement is

In formula, m _stfor the measuring value that sensor provides; m _st=H _s(ω _t, ω _s), i.e. m _stcan by actual position vector ω _t, sensing station ω _snonlinear transformation obtain; for measurement noise, assuming that the measurement noise of each sensing is separate, then false measurement density be:

$f_{a_{{\mathrm{si}}_s}}\left(a\right)=\frac{1}{{\mathrm{\ψ}}_s}---\left(5\right)$

In formula, ψ _sfor the observation area of sensor s.

If until the comprehensive measurement collection that K moment fusion center obtains is

$Z^K={\left\{Z\left(k\right)\right\}}_{k=1}^K---\left(6\right)$

$Z\left(k\right)={\left\{z_{{\mathrm{si}}_s}\left(k\right)\right\}}_{i_s=1}^{m_s\left(k\right)},s=1,...N_s---\left(7\right)$

In formula, N _sfor the number of sensor; m _sk measurement number that () provides for k moment sensor s.

Based on Z (k), cycle threshold method is utilized to complete the segmentation of formation.If U _jfor the jth obtained is formed into columns, by forming into columns, interior each sensor source measured is different, is expressed as

In formula, for U _jmiddle measurement comes from the number of sensor; for U _jin come from the measurement number of sensor s.

If U _jin all measurements be false measurement, definition U _jfor falseness is formed into columns.Suppose that each falseness measures separate, and independent of substantial amount measured value, then U _jthe probability of forming into columns for falseness is

In order to make up the formation measurement that caused by test leakage and the interconnected deficiency of formation target, the formation that in this case each sensor obtains measures the false formation U of collection increase by _s0.Therefore, the formation coming sensor s and whole search coverage measures and can be expressed as

$U_s={\left\{U_{{\mathrm{si}}_s}\right\}}_{i_s=0}^{m_s^U},U={\left\{U_s\right\}}_{s=1}^{N_s}---\left(10\right)$

In formula, the formation detected for sensor s measures number.

3. the division of formation measurement

First the situation of three sensors is considered.Suppose that three sensors correspond to U _tthe formation locating same formation target is measured, then probability function is

In formula, for forming into columns measurement number; U (i _s) be target function, work as i _swhen=0, u (i _s)=0, otherwise u (i _s)=1; for forming into columns corresponding to the probability of a true formation target, and

In formula, for in from the measurement number of real goal.

Suppose to divide γ={ U _t, U _f, wherein, U _tthe formation corresponding interconnected for formation flight path measures subset; U _fform into columns for falseness and measure subset, and at this it is significant to note that:

(1) formation measurement may correspond in multiple formation flight path (when formation merges) or false-alarm, therefore

(2) formation flight path may correspond to and measures (during formation division) in multiple formation, and the measurement of therefore being crossed by formation Trace Association still can be used for other formation flight paths.

Based on above-mentioned 2 points, wherein i _sfor empty set or set in the subset that is combined into of arbitrary element, be no longer single numerical value, but a set, its maximum number for for each sensor, i _sto choose be separate, therefore,

Account part ξ (γ)={ it is true for dividing γ }, and set Γ={ γ } as likely dividing.When formation divide, merge, dispersion etc. motor-driven time, measure from the angle of formation, each sensor should be consistent to the acquisition mode of formation target, so can delete the number of γ in Γ based on this principle.If for dividing set after simplifying, its maximum number is

Differentiate which kind of occurs k moment each formation target motor-driven, will determine exactly to form into columns measures the corresponding relation with formation flight path, namely determines optimum division γ={ U _t, U _f, demand solution formula (15).

$\underset{\mathrm{\γ}\∈\mathrm{\Γ}}{\max }\frac{L\left(\mathrm{\γ}\right)}{L\left({\mathrm{\γ}}_0\right)}---\left(15\right)$

In formula, γ ₀={ U _t=Ф, U _f=U}, i.e. all hypothesis measuring and be false formation of forming into columns.

In formula, for dividing the label set that in γ, the formation of sensor s falseness measures; measure as false probability of forming into columns for sensor s i-th forms into columns; i ₁, i ₂, i ₃correspond respectively to subset ω _ufor form into columns occur motor-driven after actual position; Use maximum likelihood estimation herein replace ω _u, therefore

Illustrate at this derivation.If namely, for formation target U, each sensor all has two measurements of forming into columns corresponding with it, and formation U divides; If U Central Plains comprises T _uindividual target, then occur to divide the number of latter two new formation internal object in the k moment and be

The number of getting two new formation internal objects is appointed to be (t _u, T _u-t _u), then this state lower sensor s the i-th ' _s1, i ' _s2in individual formation, the measurement number of corresponding real goal is respectively t _u, T _u-t _u.Therefore

In formula, divide individual sensor s the i-th ' _s1, i ' _s2target number in individual formation; Formula (19) is substituted into formula (17), can derive in like manner,

Therefore, formula (17) and formula (20) are substituted into formula (15), can optimum division γ be determined ^*.

4.3-ties up the structure of assignment problem

The maximization problem that formula (15) describes is equivalent to following formula

$J^{*}=\underset{\mathrm{\γ}\∈\mathrm{\Γ}}{\min }J\left(\mathrm{\γ}\right)=\underset{\mathrm{\γ}\∈\mathrm{\Γ}}{\min }[\ln L\left({\mathrm{\γ}}_0\right)-\ln \hat{L}\left(\mathrm{\γ}\right)]---\left(21\right)$

Remove L (γ ₀) impact, then

$J\left(\mathrm{\γ}\right)=\underset{U_{i_1{i}_2{i}_3}\∈U}{\mathrm{\Σ}}{c}_{i_1{i}_2{i}_3}---\left(22\right)$

In formula: can obtain according to formula (19) and formula (20).If binary variable and

Because dividing γ with feasibility is one to one, and the broad sense 3-that therefore can obtain formation target tracking ties up assignment problem and is written as

In formula, be respectively the number that three sensor feasibilities divide.Constraint condition is

5. the structure of Generalized S-Wei assignment problem

As employing N _sthe while of individual sensor during observed object, N be obtained _sindividual sensor formation flight path and the mapping relations between measuring of forming into columns, need to form into columns vectorial towards formation flight path structure S-dimension, find out various feasibility and divide, and obtain optimal dividing by the cost that each feasibility of minimization divides.

Structure Generalized S-Wei assignment problem is

Constraint condition is

In formula, for the interconnected variable of scale-of-two, divide one_to_one corresponding with all feasibilities, if divide in γ in feasibility with a Trace Association of truly forming into columns, then otherwise for the cost function that feasibility divides, the mode can tieed up in assignment problem according to 3-is derived and is drawn.

6. formation maneuvering mode decision

If divide γ towards T formation flight path feasibility ^*least-cost, then think γ ^*for most probable division; Based on γ ^*can show that the formation of the multiple sensors interconnected with the flight path t that forms into columns measures to gather based on judged the maneuver model of formation flight path t by 4 events of definition, thus utilize corresponding formation maneuvering model to complete the state updating of each flight path in formation.

Claims (1)

1. expand Generalized S-Wei and distribute formation target maneuver model determination methods, it is characterized in that, differentiate which kind of occurs k moment each formation target motor-driven, will determine exactly to form into columns measures the corresponding relation with formation flight path, namely determines optimum division γ={ U _t, U _f, demand solution following formula:

$\underset{\mathrm{\γ}\∈\mathrm{\Γ}}{\max }\frac{L\left(\mathrm{\γ}\right)}{L\left({\mathrm{\γ}}_0\right)}---\left(1\right)$

In formula, γ ₀={ U _t=Φ, U _f=U}, i.e. all hypothesis measuring and be false formation of forming into columns,

In formula, for dividing the label set that in γ, the formation of sensor s falseness measures; measure as false probability of forming into columns for sensor s i-th forms into columns; i ₁, i ₂, i ₃correspond respectively to subset ω _ufor form into columns occur motor-driven after actual position; Use maximum likelihood estimation herein replace ω _u, therefore

Formula (3) and formula (4) are substituted into formula (1), can optimum division γ be determined ^*.