CN104076342B - A kind of method of target of prediction RCS under radar tracking state - Google Patents

Abstract

The method that the invention discloses target of prediction RCS under a kind of radar tracking state, comprising: step 1, and the exponent number of the predictive filter of target setting radar cross section RCS is M, step 2, radar receiving target is the echo s to the n moment from the n-M+1 moment_i, and record is the distance to n moment target from the n-M+1 moment, follow the tracks of the speed of moment target for n, and from the n-M+1 moment angle to n moment target velocity and target range, step 3, try to achieve the estimated value at the target complex magnitude to the n moment from the n-M+1 moment, step 4, obtain target in the target velocity in n+1 moment and the angle predicted value of target range, step 5, try to achieve the autocorrelation matrix of target RCS value and the cross-correlation column vector of target RCS value, step 6, try to achieve the predictive filter coefficient of target RCS, step 7, obtain the predicted value in the target RCS in n+1 moment.

Description

A kind of method of target of prediction RCS under radar tracking state

Technical field

The invention belongs to Radar Technology field, relate to the method for target of prediction RCS under a kind of radar tracking state, for predictionThe RCS value in next moment of target in radar tracking process.

Background technology

Target RCS long-pending (RadarCrossSection, RCS) is a parameter for weighing target scattering characteristics,Generally carry out objective definition RCS by the intensity of back scattering energy. The structure of the main and target of target RCS and surface dielectric, thunderReach the factors such as frequency, polarization mode and object attitude angle relevant. From radar equation, target RCS directly affects target and returnsThe size of wave power, thus target RCS directly affects the signal to noise ratio of target echo signal. And the size of target signal to noise ratio is to manyPower division in scheduling of resource and the phased-array radar of standing in radar all has material impact. In the time of radar lock on,If the distance of known target RCS and target, can estimate to obtain the signal to noise ratio of target echo signal. At target signal to noise ratioUnder known condition, multistation radar can call the radar of high s/n ratio target is observed, and makes scheduling of resource more reasonable;And phased-array radar can distribute required transmitting power according to the signal to noise ratio of target, make radar power obtain more effective profitWith. Therefore,, under radar tracking state, the prediction of goal in research RCS is significant.

At present, do not find the documents and materials of target RCS prediction under research radar tracking state. Existing signal-to-noise ratio (SNR) estimation sideMethod is not considered the variation of target RCS yet, and just the RCS value of hypothetical target remains unchanged. And in fact, the RCS of targetValue is constantly to change, if can target RCS be predicted, can obtain better signal-to-noise ratio (SNR) estimation.

Summary of the invention

For the problems referred to above, the present invention proposes the method for target of prediction RCS under a kind of radar tracking state, realize under predictionOne follows the tracks of the RCS value of moment target.

For achieving the above object, the present invention is achieved by the following technical solutions.

Under radar tracking state, a method of target of prediction RCS, is characterized in that, comprises the following steps:

Step 1, the span of the exponent number M of the predictive filter of the radar cross section RCS of target setting be 1 totan(2arcsin(c/(4fd)))r/(v_maxT_r) between integer, wherein, tan () represents tan, arcsin () representArcsin function, c represents the light velocity, and f represents the carrier frequency of radar, and d represents the mean value of target length, and r represents target rangeMean value, v_maxRepresent the maximal rate of target, T_rRepresent pulse recurrence interval;

Step 2, radar receiving target is the echo s to the n moment from the n-M+1 moment_i; And record from the n-M+1 moment extremelyThe distance r of n moment target_i, follow the tracks of the speed v of moment target for n_n, and from the n-M+1 moment to n moment target speedThe angle α of degree and target range_i, i=n-M+1, n-M+2,, n, the exponent number that M is predictive filter, n is natureNumber;

Step 3, according to target from the n-M+1 moment target echo s to the n moment_iWith target range r_i, try to achieve at oneselfThe estimated value η of the target complex magnitude in n-M+1 moment to n moment_i＝s_i×(r_i/r₁)²，r_iRepresent the distance of i moment target,r₁Be the distance of the 1st moment target, i=n-M+1, n-M+2,, n, the exponent number that M is predictive filter; × representProduct;

Step 4, the target range r according to target in the n moment_n, the n moment the speed v of target_n, the n moment orderThe angle α of mark speed and target range_n, obtain according to the following formula target velocity and the target range angle of target in the n+1 momentPredicted value

${\widehat{\mathrm{\α}}}_{n+1}=\mathrm{\π}-\arccos \left(\frac{T_r{v}_n-r_n\cos \left({\mathrm{\α}}_n\right)}{\sqrt{r_n^2+{\left(T_r{v}_n\right)}^2-2T_r{r}_n\cos \left({\mathrm{\α}}_n\right)}}\right)$

Wherein, arccos () represents inverse cosine function, and cos () represents cosine function, T_rRepresent pulse recurrence interval;

Step 5, according to the angle α of the target velocity to the n moment and target range from the n-M+1 moment_i，I=n-M+1, n-M+2,, n, tries to achieve the autocorrelation matrix R of target RCS value, and autocorrelation matrix R is that a M is capableM column matrix, autocorrelation matrix R form is:

Wherein, ρ () represents correlation coefficient function, and the expression formula of correlation coefficient function is:

$\mathrm{\ρ}\left(u_1\right)=\mathrm{jinc}\left(\frac{4\mathrm{fd}\sin (u_1/2)}{c}\right)$

In formula, u₁The input variable that represents correlation coefficient function, f represents the carrier frequency of radar, d represents the mean value of target length, cRepresent the light velocity, jinc () represents jinc function, and jinc function definition is:

$\mathrm{jinc}\left(u_2\right)=\frac{2\×J_1\left(\mathrm{\π}{u}_2\right)}{\mathrm{\π}{u}_2}$

Wherein, J₁() represents first kind first-order bessel function, u₂For the input variable of jinc function;

According to the angle α to n moment target velocity and target range from the n-M+1 moment_iWith n+1 moment target velocity withThe predicted value of target range angleI=n-M+1, n-M+2,, n, the cross-correlation of trying to achieve target RCS value be listed as toAmount P, cross correlation vector P is the column vector of a M dimension, cross correlation vector P concrete form is:

P＝[-ρ(α_n+1-α_n)-ρ(α_n+1-α_n-1)...-ρ(α_n+1-α_n-M+1)]^T

Wherein, []^TRepresent transposition, ρ () represents correlation coefficient function;

Step 6, according to autocorrelation matrix R and cross-correlation column vector P, tries to achieve the predictive filter coefficient of target RCSW＝R^-1P, the expression formula of predictive filter coefficient W is:

W＝[w₁,...,w_k,...,w_M]^T

Wherein, w_kFor k the element of predictive filter coefficient W, k=1,2 ..., M; M represents the exponent number of predictive filter;(·)^-1Representing matrix inversion operation;

Step 7, according to predictive filter coefficient W and from the n-M+1 moment estimated value η to n moment target complex magnitude_i，I=n-M+1, n-M+2,, n, obtains the predicted value at the target complex magnitude in n+1 momentAsk for the predicted value of n+1 moment target RCSWherein, Σ represents to askAnd computing, k=1,2 ..., M, w_kFor k the element of predictive filter coefficient W, ()^*Represent to get conjugation.

The embodiment of the present invention is with respect to the situation of the RCS value of unpredictable target in prior art, and the present invention utilizes next momentTarget velocity and the angle of target range, and predictive filter predicts the RCS value of next moment target, obtainsNext follow the tracks of the RCS predicted value of moment target.

Brief description of the drawings

Below in conjunction with the drawings and specific embodiments, the present invention will be further described.

Fig. 1 is the general flow chart of realizing of the present invention;

Fig. 2 is the motion model figure of target in the present invention;

Fig. 3 is the curve map of target RCS actual value in the present invention; Abscissa represents to follow the tracks of the moment, and ordinate represents targetThe actual value of RCS;

Fig. 4 is the curve map of target RCS estimated value in the present invention; Abscissa represents to follow the tracks of the moment, and ordinate represents targetThe observation of RCS;

Fig. 5 is the curve map of predicting the target RCS predicted value obtaining with the present invention; Abscissa represents to follow the tracks of the moment, vertical seatMark represents the predicted value of target RCS;

Fig. 6 is the curve map by target RCS predicated error of the present invention; Abscissa represents to follow the tracks of the moment, and ordinate represents orderMark RCS prediction error value.

Detailed description of the invention

With reference to Fig. 1, the method for target of prediction RCS under a kind of radar tracking state of the present invention is described, its concrete steps are as follows.

Step 1, the span of the exponent number M of the predictive filter of the radar cross section RCS of target setting be 1 totan(2arcsin(c/(4fd)))r/(v_maxT_r) between integer, wherein, tan () represents tan, arcsin () representArcsin function, c represents the light velocity, and f represents the carrier frequency of radar, and d represents the mean value of target length, and r represents target rangeMean value, v_maxRepresent the maximal rate of target, T_rRepresent pulse recurrence interval.

According to the max calculation amount allowing, be no more than under the condition of max calculation amount, the exponent number M of predictive filter is in valueScope [1, tan (2arcsin (c/ (4fd))) r/ (v_maxT_r)] in get maximum integer.

Step 2, radar receiving target is the echo s to the n moment from the n-M+1 moment_i; And record from the n-M+1 moment extremelyThe distance r of n moment target_i, follow the tracks of the speed v of moment target for n_n, and from the n-M+1 moment to n moment target speedThe angle α of degree and target range_i, i=n-M+1, n-M+2,, n, the exponent number that M is predictive filter, n is natureNumber.

Step 3, according to target from the n-M+1 moment target echo s to the n moment_iWith target range r_i, try to achieve at oneselfThe estimated value η of the target complex magnitude in n-M+1 moment to n moment_i＝s_i×(r_i/r₁)²，r_iRepresent the distance of i moment target,r₁Be the distance of the 1st moment target, i=n-M+1, n-M+2,, n, the exponent number that M is predictive filter; × representProduct.

The estimated value η of the target complex magnitude of trying to achieve here_iThe actual value that is target complex magnitude adds the result after noise, targetThe estimated value of RCSi＝n-M+1,n-M+2,···,n，(·)^*Represent to get conjugation.

Step 4, the target range r according to target in the n moment_n, the n moment the speed v of target_n, the n moment orderThe angle α of mark speed and target range_n, obtain according to the following formula target velocity and the target range angle of target in the n+1 momentPredicted value

${\widehat{\mathrm{\α}}}_{n+1}=\mathrm{\π}-\arccos \left(\frac{T_r{v}_n-r_n\cos \left({\mathrm{\α}}_n\right)}{\sqrt{r_n^2+{\left(T_r{v}_n\right)}^2-2T_r{r}_n\cos \left({\mathrm{\α}}_n\right)}}\right)$

Wherein, arccos () represents inverse cosine function, and cos () represents cosine function, T_rRepresent pulse recurrence interval.

Step 5, according to the angle α of the target velocity to the n moment and target range from the n-M+1 moment_i，I=n-M+1, n-M+2,, n, tries to achieve the autocorrelation matrix R of target RCS value, and autocorrelation matrix R is that a M is capableM column matrix, autocorrelation matrix R form is:

Wherein, ρ () represents correlation coefficient function, and the expression formula of correlation coefficient function is:

$\mathrm{\ρ}\left(u_1\right)=\mathrm{jinc}\left(\frac{4\mathrm{fd}\sin (u_1/2)}{c}\right)$

In formula, u₁The input variable that represents correlation coefficient function, f represents the carrier frequency of radar, d represents the mean value of target length, cRepresent the light velocity, jinc () represents jinc function, and jinc function definition is:

$\mathrm{jinc}\left(u_2\right)=\frac{2\×J_1\left(\mathrm{\π}{u}_2\right)}{\mathrm{\π}{u}_2}$

Wherein, J₁() represents first kind first-order bessel function, u₂For the input variable of jinc function.

According to the angle α to n moment target velocity and target range from the n-M+1 moment_iWith n+1 moment target velocity withThe predicted value of target range angleI=n-M+1, n-M+2,, n, the cross-correlation of trying to achieve target RCS value be listed as toAmount P, cross correlation vector P is the column vector of a M dimension, cross correlation vector P concrete form is:

P＝[-ρ(α_n+1-α_n)-ρ(α_n+1-α_n-1)...-ρ(α_n+1-α_n-M+1)]^T

Wherein, []^TRepresent transposition, ρ () represents correlation coefficient function.

The RCS value of target is only relevant with observation angle, in the time that two observation angle intervals are very little, and these two observation angle correspondencesTarget RCS value there is stronger correlation. According to the correlation of target target RCS value, this method is used dimension to receive a stepFallout predictor completes the prediction to target RCS, for solving of corresponding Yule-Walker equation, can use direct squareThe battle array method of inverting, or the method such as Burg recursive algorithm solves, and this example uses direct matrix in verse method.

Step 6, according to autocorrelation matrix R and cross-correlation column vector P, tries to achieve the predictive filter coefficient of target RCSW＝R^-1P, the expression formula of predictive filter coefficient W is:

W＝[w₁,...,w_k,....w_M]^T。

Wherein, w_kFor k the element of predictive filter coefficient W, k=1,2 ..., M; M represents the exponent number of predictive filter;(·)^-1Representing matrix inversion operation.

If the correlation of target RCS is very strong, may cause autocorrelation matrix R nonsingular, while causing matrix inversion, occurMistake, in this case, can replace matrix inversion operation with descriptor matrix inversion operation.

Step 7, according to predictive filter coefficient W and from the n-M+1 moment estimated value η to n moment target complex magnitude_i，I=n-M+1, n-M+2,, n, obtains the predicted value at the target complex magnitude in n+1 momentAsk for the predicted value of n+1 moment target RCSWherein, Σ represents to askAnd computing, k=1,2 ..., M, w_kFor k the element of predictive filter coefficient W, ()^*Represent to get conjugation.

Below in conjunction with emulation experiment, effect of the present invention is described further.

1. simulation parameter is set: the carrier frequency f=900MHz of radar, pulse recurrence interval T_r=10ms, target is that length isThe Aircraft Targets of 10m, the exponent number M=20 of predictive filter, that follows the tracks of the moment adds up to 2400, uses Feko software imitativeThe true actual value that produces the target complex magnitude of Aircraft Targets in [0 °, 360 °] scope, Feko software is that a target RCS is imitativeTrue software, just can emulation obtains the actual value of target complex magnitude at Feko software input target type, target length and carrier frequency.

2. set up target movement model: as shown in Figure 2, target is done linear uniform motion with the speed of 340m/s; At radarIn the 1st moment of following the tracks of, target is 50km to the distance of radar, and the angle of target velocity and target range is 54 °, noiseThan being 15dB.

3. emulation content

(1) actual value of simulation objectives RCS

According to simulation parameter setting and target movement model, calculate 2400 and follow the tracks of corresponding target velocity and order of momentThe scope of the angle of subject distance is [54 °, 62.3087 °], takes out the actual value of the target complex magnitude in [54 °, 62.3087 °] scopeFor emulation, by the actual value delivery value of the target complex magnitude in the 21st 2400 moment of moment to the and squared after obtain the 21stThe actual value of the target RCS in 2400 moment of moment to the, true by the target RCS in the 21st 2400 moment of moment to theValue is drawn as two-dimensional curve, as shown in Figure 3.

As shown in Figure 3, the actual value of target RCS is the curve of a smoother, and variation tendency obviously and have a ruleProperty, this regularity has also shown that target RCS is worth predictability.

(2) estimated value of simulation objectives RCS

According to signal to noise ratio and the distance of each tracking moment target and the actual value of target complex magnitude in the 1st tracking moment,The actual value of target complex magnitude is added to multiple white Gaussian noise, obtain the estimated value of target complex magnitude, by target complex magnitudeEstimated value delivery value and squared after obtain the estimated value of target RCS. By the target RCS in the 21st 2400 moment of moment to theEstimated value be drawn as two-dimensional curve, as shown in Figure 4.

As shown in Figure 4, due to noise, the estimated value of target RCS randomized jitter in certain amplitude, deposits in curveAt very many burrs, still, the target RCS actual value phase in the overall variation trend of target RCS estimated value and Fig. 3With.

(3) predicted value of simulation objectives RCS

By target movement model, obtain target range, target velocity and target velocity and the target range at place of each tracking momentAngle. According to the estimated value of above parameter and target complex magnitude, according to the step of the inventive method, at predictive filterIn the situation of exponent number M=20, follow the tracks of the moment at the 20th to the 2400th target RCS is predicted, obtain at the 21st o'clockCarve the predicted value to the 2401st moment target RCS, get the predicted value delivery of the 21st 2400 moment of moment to the target RCSAfter value, be drawn as two-dimensional curve, as shown in Figure 5.

As shown in Figure 5, the overall variation trend of target RCS predicted value is identical with target RCS actual value, and target RCS is pre-Near the size of measured value randomized jitter actual value, this is mainly that noise causes. Comparison diagram 5 and Fig. 3 are known, the present inventionMethod can complete the prediction to target RCS, can dope preferably the variation tendency of target RCS.

(4) predicated error of simulation objectives RCS

Corresponding the subtracting each other of actual value by the predicted value of target RCS with target RCS, obtains the predicated error of target RCS, willAfter the predicated error delivery value of target RCS, be drawn as two-dimensional curve, as shown in Figure 6.

The mean value of asking for the 21st 2400 moment of moment to the scope internal object RCS predicated error is approximately 1.54, prediction essenceDegree meets actual requirement, illustrates that the inventive method can predict the RCS value of target preferably.

Claims (1)

1. a method of target of prediction RCS under radar tracking state, is characterized in that, comprises the following steps:

Step 1, the span of the exponent number M of the predictive filter of the radar cross section RCS of target setting be 1 totan(2arcsin(c/(4fd)))r/(v_maxT_r) between integer, wherein, tan () represents tan, arcsin () representArcsin function, c represents the light velocity, and f represents the carrier frequency of radar, and d represents the mean value of target length, and r represents target rangeMean value, v_maxRepresent the maximal rate of target, T_rRepresent pulse recurrence interval;

Step 2, radar receiving target is the echo s to the n moment from the n-M+1 moment_i; And record from the n-M+1 moment extremelyThe distance r of n moment target_i, follow the tracks of the speed v of moment target for n_n, and from the n-M+1 moment to n moment target speedThe angle α of degree and target range_i, i=n-M+1, n-M+2 ..., n, the exponent number that M is predictive filter, n is natureNumber;

Step 3, according to target from the n-M+1 moment target echo s to the n moment_iWith target range r_i, try to achieve at oneselfThe estimated value η of the target complex magnitude in n-M+1 moment to n moment_i＝s_i×(r_i/r₁)²，r_iRepresent the distance of i moment target,r₁Be the distance of the 1st moment target, i=n-M+1, n-M+2 ..., n, the exponent number that M is predictive filter; × representProduct;

Step 4, the target range r according to target in the n moment_n, the n moment the speed v of target_n, the n moment orderThe angle α of mark speed and target range_n, the angle of described target velocity and target range is that target velocity direction and target arrive thunderThe angle that the direction vector reaching becomes, obtains target according to the following formula at the target velocity in n+1 moment and target range anglePredicted value

${\widehat{\mathrm{\α}}}_{n+1}=\mathrm{\π}-arccos\left(\frac{T_r{v}_n-r_{n}cos\left({\mathrm{\α}}_n\right)}{\sqrt{r_n^2+{\left(T_r{v}_n\right)}^2-2T_r{v}_n{r}_{n}cos\left({\mathrm{\α}}_n\right)}}\right)$

Wherein, arccos () represents inverse cosine function, and cos () represents cosine function, T_rRepresent pulse recurrence interval;

Step 5, according to the angle α of the target velocity to the n moment and target range from the n-M+1 moment_i，I=n-M+1, n-M+2 ..., n, tries to achieve the autocorrelation matrix R of target RCS value, and autocorrelation matrix R is that a M is capableM column matrix, autocorrelation matrix R form is:

Wherein, ρ () represents correlation coefficient function, and the expression formula of correlation coefficient function is:

$\mathrm{\ρ}\left(u_1\right)=jinc\left(\frac{4fdsin(u_1/2)}{c}\right)$

In formula, u₁The input variable that represents correlation coefficient function, f represents the carrier frequency of radar, d represents the mean value of target length, cRepresent the light velocity, jinc () represents jinc function, and jinc function definition is:

$jinc\left(u_2\right)=\frac{2\×J_1\left({\mathrm{\πu}}_2\right)}{{\mathrm{\πu}}_2}$

Wherein, J₁() represents first kind first-order bessel function, u₂For the input variable of jinc function;

According to the angle α to n moment target velocity and target range from the n-M+1 moment_iWith n+1 moment target velocity withThe predicted value of target range angleI=n-M+1, n-M+2 ..., n, the cross-correlation of trying to achieve target RCS value be listed as toAmount P, cross correlation vector P is the column vector of a M dimension, cross correlation vector P concrete form is:

P＝[-ρ(α_n+1-α_n)-ρ(α_n+1-α_n-1)…-ρ(α_n+1-α_n-M+1)]^T

Wherein, []^TRepresent transposition, ρ () represents correlation coefficient function;

Step 6, according to autocorrelation matrix R and cross-correlation column vector P, tries to achieve the predictive filter coefficient of target RCSW＝R^-1P, the expression formula of predictive filter coefficient W is:

W＝[w₁,…,w_k,…,w_M]^T

Wherein, w_kFor k the element of predictive filter coefficient W, k=1,2 ..., M; M represents the exponent number of predictive filter;(·)^-1Representing matrix inversion operation;

Step 7, according to predictive filter coefficient W and from the n-M+1 moment estimated value η to n moment target complex magnitude_i，I=n-M+1, n-M+2 ..., n, obtains the predicted value at the target complex magnitude in n+1 momentAsk for the predicted value of n+1 moment target RCSWherein, Σ represents to askAnd computing, k=1,2 ..., M, w_kFor k the element of predictive filter coefficient W, ()^*Represent to get conjugation.