CN102798867B - Correlation method for flight tracks of airborne radar and infrared sensor - Google Patents

Abstract

The invention discloses a correlation method for flight tracks of an airborne radar and an infrared sensor. According to the method, angle information observed by the airborne radar and the infrared sensor is fully utilized, wherein the angle information comprises an azimuth angle and a pitch angle. The correlation method comprises the steps of: on the basis of ambiguous comprehensive functions, establishing comprehensive discrimination functions by utilizing the observed information of the airborne radar and the infrared sensor; formulating a decision criterion; and finally determining judgment thresholds through counting characteristics and a correlation rate of the comprehensive judgment functions and then carrying out related judgment. The correlation method for the flight tracks of the airborne radar and the infrared sensor has the positive effect that on the basis of researching the sensor measurement origin uncertainty problem, by taking the airborne radar and the infrared sensor as examples, a driving/driven sensor flight track correlation method is disclosed on the basis of an ambiguous comprehensive theory; and the driving/driven sensor flight track correlation method not only can be used for solving the measurement origin uncertainty problem of multi-sensor observed information, but also can be applied to the flight track correlation problems related to multi-sensor multi-target tracking in the military or civil field.

Description

A kind of airborne radar and infrared sensor Data Association

Technical field

The present invention relates to a kind of airborne radar and infrared sensor Data Association.

Background technology

Maneuvering target tracking is a typical uncertain problem, and its uncertain main manifestations is the uncertainty of target state and the uncertainty of sensor measurement origin.

In the dual sensor detection system that radar/infrared sensor is formed, radar tracking precision is high, gathers comprehensively, comprise the information such as range information and angle, but its interference performance is poor; Infrared sensor can only take measurement of an angle information, and angleonly tracking precision is higher, has stronger antijamming capability.Two kinds of sensors advantage is separately utilized to carry out combined tracking, the signal that can simultaneously utilize each sensor to receive on the one hand merges, the different information realization educated decisions utilizing each sensor to provide on the other hand, make use of information resources more fully, and then improve precision and the reliability of tracker.

The key of hybrid multisensor data fusion is the track association carrying out Dissimilar sensors, namely determines whether the flight path that main passive sensor is set up comes from same target.But, range observation is not had because passive sensor only has measurement of angle, and the data transfer rate of main passive sensor is often inconsistent, thus in main passive sensor data correlation, there is very large uncertainty, bring many difficulties to the realization of main passive sensor track association.The data correlation of Dissimilar sensors has become a current important research direction with fusion.At present, traditional plot-track Association Algorithm has weighted method, revised law, nearest-neighbor method etc., but under intensive targeted environment, traditional plot-track Association Algorithm association accuracy is not high, and when system comprises larger navigation, pick up calibration and conversion and delay error, these methods seem unable to do what one wishes, and above-mentioned traditional plot-track Association Algorithm is applied to main passive sensor data correlation and can faces many difficulties.

Summary of the invention

In order to overcome the above-mentioned shortcoming of prior art, the invention provides a kind of airborne radar and infrared sensor Data Association, take full advantage of the angle information (comprising position angle and the angle of pitch) that airborne radar and infrared sensor observe, first based on Fuzzy Integration Function, the observation information of airborne radar and infrared sensor is utilized to set up comprehensive distinguishing function, then decision rule is formulated, determine its decision threshold finally by the statistical property of comprehensive distinguishing function and association rate, carry out relevant judgement.

The technical solution adopted for the present invention to solve the technical problems is: a kind of airborne radar and infrared sensor Data Association, comprise the steps:

Step one, choose track association discriminant function:

(1) ask between infrared flight path and each radar track about azimuthal comprehensive similarity;

(2) comprehensive similarity about the angle of pitch between infrared flight path and each radar track is asked for;

(3) comprehensive similarity of radar track and infrared sensor is asked for;

(4) select to have that the radar of maximum comprehensive similarity is relevant to infrared sensor is correlated with to S to as most probable radar and infrared flight path _l;

Step 2, determine the decision rule of radar and infrared track association:

High and low thresholding T is set respectively _h, T _l, the correlation circumstance according to following decision rule judgement radar and infrared:

(1) if S _l>=T _h, then radar is relevant to infrared flight path;

(2) if T _l<S _l<T _h, then the correlativity of radar and infrared flight path is uncertain;

(3) if S _l≤ T _h, then radar is uncorrelated with infrared flight path.

Compared with prior art, good effect of the present invention is: measuring on the basis of origin uncertain problem research to sensor, with airborne radar and infrared sensor for example, theoretical based on fuzzy synthesis, propose a kind of main passive sensor Data Association, not only can solve the uncertain problem of the measurement origin that multisensor observation information has, can also be applied in military or civilian field for the track association problem that multi-sensor multi-target tracking relates to.

Embodiment

Suppose there is m bar radar track, because each radar target can be loaded with multiple radiation source, thus, a radar track can be relevant with multiple infrared flight path, and an infrared flight path at the most can be relevant with a radar track.Like this, the relevant issues of an infrared flight path and multiple radar track can turn to following multihypothesis test problem:

H ₀: infrared flight path is uncorrelated with all radar tracks;

H ₁: infrared flight path is relevant with jth bar radar track, 1≤j≤m.And many infrared flight paths and the relevant of many radar tracks can turn to multiple above-mentioned multihypothesis test problem.Thus, the present invention only considers the relevant of an infrared flight path and many radar tracks.

A kind of airborne radar and infrared sensor Data Association, comprise the steps:

Due to measuring error, the sampling period difference of each sensor, before carrying out track association, need the data from each sensor to carry out pre-service, generally include the space-time aligning, gross error rejecting etc. between data.

Step one, choose track association discriminant function

The choosing of track association discriminant function need to make full use of infrared acquisition to position angle and angle of pitch information combine and carry out track association.

(1) ask between infrared flight path and each radar track about azimuthal comprehensive similarity

If Δ θ _j(t _i)=θ _ir(t _i)-θ _j(t _i), θ _ir(t _i) be t _imoment infrared flight path measurement of bearing value; θ _j(t _i) be t _imoment jth bar radar track orientation values, radar and infrared measurement of bearing error is separate, and all obey the Gaussian distribution of zero-mean constant variance, its variance is respectively σ _r, σ _ir, order

${\mathrm{\&xi;}}_j\left(t_i\right)=\frac{{\mathrm{\&Delta;\&theta;}}_j\left(t_i\right)}{\mathrm{\&sigma;}}=\frac{{\mathrm{\&theta;}}_{\mathrm{Ir}}\left(t_i\right)-{\mathrm{\&theta;}}_j\left(t_i\right)}{\mathrm{\&sigma;}}---\left(1\right)$

Wherein, $\mathrm{\&sigma;}=\sqrt{{\mathrm{\&sigma;}}_{\mathrm{Ir}}^2+{\mathrm{\&sigma;}}_r^2}.$

Definition θ _ir(t _i) and θ _j(t _i) between similarity measure degree be

$d_j\left(t_i\right)=\exp \{-{{\mathrm{\&xi;}}_j}^2\left(t_i\right)\}---\left(2\right)$

Obviously, 0≤d _j(t _i)≤1, try to achieve all d _j(t _i) after, just obtain measuring between infrared flight path and jth bar radar track about azimuthal similarity vectors

$D_j=(d_j\left(t_1\right),d_j\left(t_2\right),...,d_j\left(t_{n_j}\right))---\left(3\right)$

For different radar tracks, the dimension of its similarity vectors is different, thus can not select the radar track the most similar to infrared flight path according to the norm of similarity vectors.At this, Fuzzy Integration Function can be introduced and ask for about azimuthal comprehensive similarity between infrared flight path and each radar track, even

$d_j=M_{n_j}\left(D_j\right)=M(d_j\left(t_1\right),d_j\left(t_2\right),...,d_j\left(t_{n_j}\right))---\left(4\right)$

Wherein, for Fuzzy Integration Function, there is isotonicity and comprehensive.Here select for

$d_j=M_{n_j}\left(D_j\right)={\left(\underset{i=1}{\overset{n_j}{\mathrm{\&Pi;}}}{d}_j\left(t_{n_j}\right)\right)}^{\frac{1}{n_j}}---\left(5\right)$

Can to obtain between infrared flight path and each radar track about azimuthal comprehensive similarity by formula (2) and formula (5):

d _j＝exp(-ε _j) （6）

Wherein, ${\mathrm{\&epsiv;}}_j=\frac{1}{n_j}\underset{i=1}{\overset{n_j}{\mathrm{\&Sigma;}}}{{\mathrm{\&xi;}}_j}^2\left(t_i\right).$

(2) comprehensive similarity about the angle of pitch between infrared flight path and each radar track is asked for

In like manner, if be t _imoment infrared flight path pitch angle measurement value; be t _ithe moment jth bar radar track angle of pitch, radar and infrared elevation measurement error is separate, and all obey the Gaussian distribution of zero-mean constant variance, variance is respectively σ _r', σ ' _ir, order

Wherein, ${\mathrm{\&sigma;}}^{\&prime;}=\sqrt{{\mathrm{\&sigma;}}_{\mathrm{Ir}}^{\&prime;2}+{\mathrm{\&sigma;}}_r^{\&prime;2}}.$

In like manner, θ is defined _ir(t _i) and θ _j(t _i) between similarity measure degree be

${d^{\&prime;}}_j\left(t_i\right)=\exp \{-{\mathrm{\&eta;}}_j^2\left(t_i\right)\}---\left(8\right)$

Obviously, 0≤d _j' (t _i)≤1, try to achieve all d _j' (t _i) after, just obtain measuring the similarity vectors about the angle of pitch between infrared flight path and jth bar radar track

${D^{\&prime;}}_j=({d^{\&prime;}}_j\left(t_1\right),{d^{\&prime;}}_j\left(t_2\right),...,{d^{\&prime;}}_j\left(t_{n_j}\right))---\left(9\right)$

Equally, Fuzzy Integration Function can be introduced and ask for comprehensive similarity about the angle of pitch between infrared flight path and each radar track, even

${d^{\&prime;}}_j=M_{n_j}\left({D^{\&prime;}}_j\right)=M({d^{\&prime;}}_j\left(t_1\right),{d^{\&prime;}}_j\left(t_2\right),...,{d^{\&prime;}}_j\left(t_{n_j}\right))---\left(10\right)$

Wherein, for Fuzzy Integration Function, there is isotonicity and comprehensive.Equally, select for

${d^{\&prime;}}_j=M_{n_j}\left({D^{\&prime;}}_j\right)={\left(\underset{i=1}{\overset{n_j}{\mathrm{\&Pi;}}}{d^{\&prime;}}_j\left(t_{n_j}\right)\right)}^{\frac{1}{n_j}}---\left(11\right)$

The comprehensive similarity about the angle of pitch between infrared flight path and each radar track can be obtained by formula (8) and formula (11):

d _j′＝exp(-η _j) （12）

Wherein, ${\mathrm{\&eta;}}_j=\frac{1}{n_j}\underset{i=1}{\overset{n_j}{\mathrm{\&Sigma;}}}{{\mathrm{\&eta;}}_j}^2\left(t_i\right).$

(3) comprehensive similarity of radar track and infrared sensor is asked for

By azimuth information d _j, pitch information d ' _jand orientation and pitching observational error standard deviation sigma, σ ', the comprehensive similarity of radar track j and infrared sensor can be obtained

$S_j=\frac{{\mathrm{\&sigma;}}^{\&prime;}}{\mathrm{\&sigma;}+{\mathrm{\&sigma;}}^{\&prime;}}{d}_j+\frac{\mathrm{\&sigma;}}{\mathrm{\&sigma;}+{\mathrm{\&sigma;}}^{\&prime;}}{d^{\&prime;}}_j---\left(13\right)$

(4) select the radar with maximum comprehensive similarity relevant to infrared sensor right to being correlated with as most probable radar and infrared flight path

Obviously, our radar that should select to have maximum comprehensive similarity is relevant to infrared sensor right to being correlated with as most probable radar and infrared flight path.Namely establish , make

S _l＝max{S _j|j＝1,2,…,m} （14）

Then using radar track 1 and infrared flight path as possible relevant right, and according to S _lsize and the relation of decision threshold make relevant judgement.

Step 2, determine the decision rule of radar and infrared track association

Have found possible infrared and radar track according to above-mentioned discriminant function relevant right, but can not just make the judgement relevant to radar track j of infrared flight path accordingly, because infrared flight path also may be all uncorrelated with all radar tracks.Therefore, still need to make further correlated judgment.

If have found S according to said method _l=max{S _j| j=1,2 ..., m}, namely have found the infrared track association pair of most probable radar, arranges high and low thresholding and is respectively T _h, T _l, the correlation circumstance according to following decision rule judgement radar and infrared:

(1) if S _l>=T _h, be then judged to relevant;

(2) if T _l<S _l<T _h, then uncertain;

(3) if S _l≤ T _h, be then judged to uncorrelated.

When occurring T _l<S _l<T _hif target still in the observation scope of double-sensor system, then should proceed observation, until draw association results, namely meet S _l>=T _hor S _l≤ T _h.

About the selection of decision-making thresholding

Decision-making thresholding will adopt Monte Carlo emulation mode to obtain in the ordinary course of things, specific as follows:

(1) low threshold T _lsetting

Low threshold T _ldetermine leakage dependent probability.Because radar and infrared measuring error is Gaussian distribution that is independent, zero-mean, so ζ _j(t _i) also Gaussian distributed. and can be obtained by formula (3)

E [ξ _j(t _i) | H _j]=0, D [ξ _j(t _i) | H _j]=1, and E [η _j(t _i) | H _j]=0, D [η _j(t _i) | H _j]=1 (15)

Therefore have,

H _j: ξ _j(t _i) ~ N (0,1), and H _j: η _j(t _i) ~ N (0,1) (16)

Select low threshold T _lprinciple, be that infrared flight path and the most contiguous radar track will be made to be judged to Lou relevant probability is β.So, determine low threshold T according to this principle and formula (16) _lstep as follows:

1) given leakage dependent probability β, sampling number n _jwith Monte Carlo experiment number N, counter COUNT is reset, and select an initial threshold data1;

2) two groups of n are produced on computers _jthe random number ξ of individual separate obedience standardized normal distribution _j(t _i), η _j(t _i), i=1,2 ..., n _j, i.e. ξ _j(t _i) ~ N (0,1), η _j(t _i) ~ N (0,1);

3) calculate wherein d _j=exp (-ξ _j), d _j'=exp (-η _j), ${\mathrm{\&eta;}}_j=\frac{1}{n_j}\underset{i=1}{\overset{n_j}{\mathrm{\&Sigma;}}}{{\mathrm{\&eta;}}_j}^2\left(t_i\right);$

4) if S _j<data1, then counter COUNT adds 1;

5) repeat step (2) to (4) N time, assuming that the value of counter COUNT is M, calculate if 0.9 β <P< β, makes T _l=data1, otherwise, according to P value size modification data1, then repeat step (2) to (4), until obtain qualified threshold T _l.

(2) high threshold T _hsetting

High threshold T _hdetermine dependent probability by mistake.Due to by mistake relevant mainly relevant caused to the most contiguous radar track mistake by infrared flight path, therefore high threshold T need be decided according to infrared flight path and the mistake correlation circumstance of the most contiguous radar track _h.Suppose that with the most contiguous radar track of radar track j be flight path l, and establish their intervals in orientation and pitching to be respectively μ ₁σ, μ ₂σ '.Due to

E[ξ _j(t _i)|H _l]＝μ ₁，D[ξ _j(t _i)|H _l]＝1，l≠j

And

Eη _j(t _i)|H _l]＝μ2，D[η _j(t _i)|H _l]＝1，l≠j （17）

Therefore have,

H _l:ξ _j(t _i)~N(μ ₁,1)

And

H _l:η _j(ti)~N(μ ₂,1) （18）

Select high threshold T _hprinciple, be to make infrared flight path and the most contiguous radar track be misjudged as relevant probability is α.So, determine high threshold T according to this principle and formula (18) _hstep as follows:

1) given dependent probability α, sampling number n by mistake _j, interval, target azimuth μ σ and Monte Carlo experiment number N, resets counter COUNT, and selects an initial threshold data2;

2) two groups of n are produced on computers _jthe random number ξ of individual separate obedience standardized normal distribution _j(t _i), η _j(t _i), i=1,2 ..., n _j, i.e. ξ _j(t _i) ~ N (0,1), η _j(t _i) ~ N (0,1);

3) ω is made _j(t _i)=μ ₁+ ξ _j(t _i), υ _j(t _i)=μ ₂+ η _j(t _i);

4) calculate wherein d _j=exp (-ω _j), d _j'=exp (-υ _j), ${\mathrm{\&upsi;}}_j=\frac{1}{n_j}\underset{i=1}{\overset{n_j}{\mathrm{\&Sigma;}}}{{\mathrm{\&upsi;}}_j}^2\left(t_i\right);$

5) if S _j>data2, then counter COUNT adds 1;

6) repeat step (2) to (5) N time, assuming that the value of counter COUNT is M, calculate if 0.9 α <P< α, makes T _h=data2, otherwise, according to P value size modification data2, then repeat step (2) to (5), until obtain qualified threshold T _h.

For given n _j, when target interval is (by μ ₁, μ ₂determine) larger time, likely there is data1>data2, i.e. T _l>T _hsituation, occur that this situation means and can adopt " hard decision ", following three kinds of methods at this moment can be adopted to be revised threshold value:

1) T is selected _h=T _l=data1, the advantage of this system of selection to obtain the mistake dependent probability lower than given wrong dependent probability;

2) T is selected _l=T _h=data2, the advantage of this system of selection to obtain the leakage lower than given leakage dependent probability relevant judgement probability;

3) T is selected _h=T _l=(data1+data2)/2, the feature of this system of selection can be compromised between leakage dependent probability and wrong dependent probability.

Claims (3)

1. airborne radar and an infrared sensor Data Association, is characterized in that: comprise the steps:

Step one, choose track association discriminant function:

(1) ask between infrared flight path and each radar track about azimuthal comprehensive similarity;

(2) comprehensive similarity about the angle of pitch between infrared flight path and each radar track is asked for;

(3) comprehensive similarity of radar track and infrared sensor is asked for;

(4) select to have that the radar of maximum comprehensive similarity is relevant to infrared sensor is correlated with to S to as most probable radar and infrared flight path _l;

Step 2, determine the decision rule of radar and infrared track association:

High and low thresholding T is set respectively _h, T _l, the correlation circumstance according to following decision rule judgement radar and infrared:

(1) if S _l>=T _h, then radar is relevant to infrared flight path;

(2) if T _l< S _l< T _h, then the correlativity of radar and infrared flight path is uncertain;

(3) if S _l≤ T _h, then radar is uncorrelated with infrared flight path;

When occurring T _l< S _l< T _hif target still in the observation scope of double-sensor system, then should proceed observation, until draw association results, namely meet S _l>=T _hor S _l≤ T _h.

2. a kind of airborne radar according to claim 1 and infrared sensor Data Association, is characterized in that: described low threshold T _ldefining method be:

11) given leakage dependent probability β, sampling number n _jwith Monte Carlo experiment number N, counter COUNT is reset, and select an initial threshold data1;

12) two groups of n are produced on computers _jthe random number ξ of individual separate obedience standardized normal distribution _j(t _i), η _j(t _i), i=1,2 ..., n _j;

13) calculate wherein d _j=exp (-ξ _j), d ' _j=exp (-η _j), the variance of described radar bearing measuring error is σ _r, the variance of infrared measurement of bearing error is σ _ir, σ is the variances sigma of radar bearing measuring error _rwith the variances sigma of infrared measurement of bearing error _irthe intermediate variable calculated, its concrete computation process is the variance of described radar elevation measurement error is σ ' _r, the variance of infrared elevation measurement error is σ ' _ir, the variances sigma that σ ' is radar elevation measurement error ' _rwith the variances sigma of infrared elevation measurement error ' _irthe intermediate variable calculated, its concrete computation process is

14) if S _j< data1, then counter COUNT adds 1;

15) step 12 is repeated) to 14) N time, assuming that the value of counter COUNT is M, calculate if 0.9 β < P < β, makes T _l=data1, otherwise, according to P value size modification data1, then repeat step 12) to 14), until obtain qualified threshold T _l;

Described high threshold T _hdefining method be:

21) given dependent probability α, sampling number n by mistake _j, interval, target azimuth μ σ and Monte Carlo experiment number N, counter COUNT is reset, and selects an initial threshold data2;

22) two groups of n are produced on computers _jthe random number ξ of individual separate obedience standardized normal distribution _j(t _i), η _j(t _i), i=1,2 ..., n _j;

23) ω is made _j(t _i)=μ ₁+ ξ _j(t _i), υ _j(t _i)=μ ₂+ η _j(t _i);

24) calculate wherein d _j=exp (-ω _j), d ' _j=exp (-υ _j), ${\mathrm{\&upsi;}}_j=\frac{1}{n_j}\underset{i=1}{\overset{n_j}{\mathrm{\&Sigma;}}}{{\mathrm{\&upsi;}}_j}^2\left(t_i\right);$

25) if S _j> data2, then counter COUNT adds 1;

26) step 22 is repeated) to 25) N time, assuming that the value of counter COUNT is M, calculate if 0.9 α < P < α, makes T _h=data2, otherwise, according to P value size modification data2, then repeat step 2) to 5), until obtain qualified threshold T _h.

3. a kind of airborne radar according to claim 2 and infrared sensor Data Association, is characterized in that: if T _l> T _h, then adopt following three kinds of methods to be revised threshold value:

1) to obtain the mistake dependent probability lower than given wrong dependent probability, then T is selected _h=T _l=data1;

2) to obtain the leakage lower than given leakage dependent probability relevant judgement probability, then T is selected _l=T _h=data2;

3) to compromise between leakage dependent probability and wrong dependent probability, then T is selected _h=T _l=(data1+data2)/2.