CN106886011A - A kind of MIMO radar Cramér-Rao lower bound computational methods for reflecting through wave action - Google Patents

Abstract

A kind of MIMO radar Cramér-Rao lower bound computational methods for reflecting through wave action of the disclosure of the invention, belong to Radar Technology field, and it is more particularly on the calculating of parameter Estimation performance bound Cramér-Rao lower bound (CRB) in Radar Signal Processing.The Cramér-Rao lower bound calculated using as above step can be used to assess the performance that external sort algorithm MIMO radar joint objective speed and location parameter are estimated, and direct wave in external illuminators-based radar is considered for the influence estimated, and then the more course of work for having reflected external illuminators-based radar parameter Estimation of closer to reality, in this process, it is considered to utilizability of the direct wave for parameter Estimation.

Description

A kind of MIMO radar Cramér-Rao lower bound computational methods for reflecting through wave action

Technical field

The invention belongs to Radar Technology field, it is more particularly on the parameter Estimation performance bound gram in Radar Signal Processing The calculating of Latin America Luo Jie (CRB).

Background technology

External illuminators-based radar refers to detect using the signal of communication existed in environment and estimate target component.Due to Itself cell site need not be provided, external illuminators-based radar has low cost, stabilization is difficult to find, existing frequency spectrum will not be produced The advantage of interference.In the last few years, external illuminators-based radar had had been a great concern.MIMO(Multiple Input Multiple Out) it is a kind of multiple antennas transmit-receive technology, it is a kind of important technology of field of radar.MIMO technology is applied to outer In radiation source radar, the performance of external illuminators-based radar can be greatly enhanced.

It is one of major function of radar system that target component is estimated, in major applications, Parameter Estimation Precision is determined The overall performance of radar system.The parameter Estimation performance of antenna MIMO radar system is split to weigh, it is necessary to a quantization Comprehensive evaluation index.Cramér-Rao lower bound (CRB) is the lower limit of any unbiased esti-mator mean square error (MSE), is classical estimation Performance Evaluating Indexes.

External illuminators-based radar has reference channel for receiving direct-path signal (send-receive) and for connecing in receiving terminal Receive the monitoring passage (transmitting-target-reception) of reflected signal.Direct-path signal is the transmission signal for estimating cell site, so The target component for being monitored passage with the transmission signal estimated afterwards is estimated.How the given one kind of such method of estimation is processed Direct-path signal carries out the monitoring of target component with echo signal, so it is typically suboptimum.Although also, logical in monitoring Road has the measure that some suppress direct-path signal, and monitoring passage is likely to the presence of direct-path signal.Document 1 (X.Zhang,H.Li,J.Liu,and B.Himed,“Joint delay and Doppler estimation for passive sensing with direct-path interference,”IEEE Transactions on Signal Processing, vol.64, no.3, pp.630-640,2016.) consider single-shot list receipts external illuminators-based radar estimation Can, according to as a result, monitoring passage direct-path signal be harmful for the estimation performance of target component, and it be Frequency domain is analyzed to signal.However, the key effect based on direct-path signal for target component, in the through of monitoring passage Ripple signal is likely to estimate it is beneficial for target component.For at present, for the consideration of external sort algorithm MIMO radar The estimation performance evaluation of direct-path signal is extremely necessary.

The content of the invention

The present invention is to obtain a kind of outer spoke for considering through wave action for the not enough technical problem for solving of background technology Penetrate source MIMO radar joint objective speed and location parameter is estimated, carry out maximal possibility estimation, and calculate Cramér-Rao lower bound.

The technical scheme is that a kind of MIMO radar Cramér-Rao lower bound computational methods for reflecting through wave action, the party Method includes：

Step 1：A row are arranged in order for the signal sampling value that MIMO radar receives N number of receiver, are constituted Receive signal r；

Wherein r_dFor direct wave is detected the signal that channel reception is arrived, r_tIt is target echo, w is noise；

r_d=α_ds_d⊙g_d,

r_t=β_ts_t⊙g_t,

Wherein α_dIt is that direct-path signal is monitoring the signal intensity of passage, s_dIt is the direct-path signal of transmitting, g_dIt is direct wave The window function of signal；Equally, β_tIt is the intensity of target echo, s_tIt is target echo signal, g_tIt is the window letter of target echo signal Number；Consider the totally unknown situation of signal in external radiation radar, it is assumed here that transmission signal s_mT () is to obey to have 0 average, Auto-correlation function is R_smThe multiple Gauss random process of (t)；

Step 2：It is determined that the covariance matrix C for receiving signal is used for maximal possibility estimation

C=α_d(G_d⊙R_d⊙G_d ^H)α_d ^H+α_d(G_d⊙R_dt⊙G_t ^H)β_t ^H

+β_t(G_d⊙R_dt⊙G_t ^H)^Hα_d ^H+β_t(G_t⊙R_t⊙G_t ^H)β_t ^H+Q

Wherein,

K is sampling total number, and N is receiving station's number, and M is cell site's number, 1_1×KNMIt is complete 1 row vector of KNM dimensions；

R_d=E (s_ds_d ^H)

R_dt=E (s_ds_t ^H)

R_t=E (s_ts_t ^H)

To seek expectation symbol, Q is the covariance matrix of noise to wherein E；

Step 3：According to following formula

Try to achieve the estimate of θWherein θ is our target components to be estimated, including：Target location x, y and target speed Degree v_x,v_y, it is expressed as：θ=[x, y, v_x,v_y]^T, wherein r is expressed as receipt signal matrix；

Step 4：Repeat step 1 to 3, according to what is estimatedObtaining its root-mean-square error is：

Wherein num is number of repetition；

Step 5：If

Obtain matrix

Wherein, M represents the number of emitter, and N represents the number of receiver, and F is delay, τ to target location x, the derivative of y, τ_nm(n=1 ..., N m=1 ..., M) represents m-th emitter to n-th time delay of receiver, and G is Doppler frequency f pairs The derivative of x, y, f_nm(n=1 ..., Nm=1 ... M) represent Doppler between m-th emitter and n-th receiver frequently Rate, D_tIt is emitter range-to-go d_tTo x, the derivative of y, d_tm(m=1 ..., M) represent that m-th emitter arrives target Distance, D_rIt is receiver range-to-go d_rTo x, the derivative of y, d_rn(n=1 ..., N) represent n-th receiver to target Distance；H is Doppler frequency to target velocity v_x,v_yDerivative；

Step 6：Obtain matrixI-th j element be：

Step 7 is according to formula：

J (θ) is calculated, J (θ) is corresponding to x, y, v_x,v_yFisher's information matrix, can finally obtain：

CRB=J (θ)^-1,

Diagonal element corresponding to CRB is respectively target location x, y and target velocity v_x,v_yCarat Metro lower bound.

The Cramér-Rao lower bound calculated using as above step can be used to assess external sort algorithm MIMO radar joint objective speed The performance estimated with location parameter, and direct wave in external illuminators-based radar is considered for the influence estimated, and then more press close to The course of work for having reflected external illuminators-based radar parameter Estimation of reality, in this process, it is considered to which direct wave is for parameter The utilizability of estimation.

Brief description of the drawings

Fig. 1 be as DSR=95dB, under different SNR calculate for x, y, v_x,v_yRMSE and RCRB schematic diagrames.

Fig. 2 be as DSR=-40dB, under different SNR calculate for x, y, v_x,v_yRMSE and RCRB illustrate Figure.

Specific embodiment

Describe for convenience, be defined as below first：

()^TIt is transposition, ()^HIt is conjugate transposition,To round downwards,Represent Kronecker product.

Consider one and split antenna external sort algorithm MIMO radar, there is M single antenna transmitter and N number of single antenna receiver, In a cartesian coordinate system, m (m=1 ..., M) individual transmitting antenna and the individual reception antennas of n-th (n=1 ..., N) distinguish position InWithM-th emitter is in kT_sThe sampled value at moment isT_sIt is sampling interval, k (k= 1 ..., K) it is sampling numeral, it is assumed that it is orthogonal during the transmission signal of different transmitters.E_mIt is m-th transmission signal of emitter Energy,

So in kT_sThe signal that n-th receiver of moment receives m-th emitter is

Wherein d_d,nmIt is the direct wave distance of m-th emitter and n-th receiver；d_t,mIt is m-th receiver and target The distance between；d_r,nIt is the distance between n-th receiver and target；l_d,nmIt is the time delay of the through wave path of the n-th m bars；l_t,nm And f_t,nmIt is the time delay and Doppler frequency of the n-th m bar reflection paths；ζ_t,nmIt is target reflection factor, it is assumed that it is known；w_nm [k] corresponds to the noise in nm paths；P₀It is in d_d,nmThe ratio of energy and emitted energy is received when=1；P₁It is in d_tm=d_rn The ratio of energy and emitted energy is received when=1.Assuming that transmission signal s_m[k] is that have 0 average and auto-correlation function for R_sm[l] Multiple Gauss random process, be

And g_m[k] is known window function, w_nm[k] is the noise of the n-th m paths.Assuming that position (x, y) and speed (v_x,v_y) it is to determine what unknown needs were estimated.

Apart from d_t,mAnd d_r,nIt is the function of unknown object position (x, y)

Time delay l_d,nm l_t,nmIt is the function of unknown object position (x, y)：

Wherein c represents the light velocity.

f_t,nmIt is unknown object position (x, y) and speed (v_x,v_y) function

Wherein λ represents carrier wavelength.

A unknown parameter vector is defined to represent the parameter to be estimated：

θ=[x, y, v_x,v_y]^T (8)

The signal that n-th receiver receives m-th emitter is

Wherein

s_d,nm=(s_m[1-l_d,nm],...,s_m[K-l_d,nm])^T (11)

g_d,nm=(g_m[1-l_d,nm],...,g_m[K-l_d,nm])^T (12)

s_t,nm=(s_m[1-l_t,nm],...,s_m[K-l_t,nm])^T (14)

g_t,nm=(g_m[1-l_t,nm],...,g_m[K-l_t,nm])^T (15)

w_nm=(w_nm[1],...,w_nm[K])^T (16)

Wherein I_K×KIt is the unit matrix of K × K dimensions, the observation that all receivers are received is

Wherein

α_d=Diag (α₁₁,α₁₂,…,α_NM) (18)

β_t=Diag (β₁₁,β₁₂,…,β_NM) (21)

Noise w assumes to obey 0 average multiple Gauss stochastic variable, and covariance matrix is Q.

The present invention calculates the maximal possibility estimation and CRB of external sort algorithm MIMO radar using following steps：

Signal model (17) of the step 1 more than, it is first determined receive signal r,

R=r_d+r_t+w (25)

The signal sampling value that N number of receiver is received is arranged in a row in order, you can constitutes and receives signal r.

Step 2 determines that signal covariance matrix C is used for maximal possibility estimation

Wherein

R_dIt is the autocorrelation matrix of direct-path signal, i.e. R_d=E (s_ds_d ^H), its submatrix E (s_d,nms_d,n′m′ ^H) it is one The matrix of K × K, as m=m ', wherein the individual elements of kth k ' are R_sm[(k-1)+l_d,n′m-l_d,nm- (k ' -1)], otherwise for 0. is same , R_dtIt is the cross-correlation matrix of direct-path signal and reflected signal, i.e. R_dt=E (s_ds_t ^H), its submatrix E (s_d,nms_t,n′m′ ^H) It is a matrix of K × K, as m=m ', wherein the individual elements of kth k ' are R_sm[(k-1)+l_t,n′m-l_d,nm- (k ' -1)], otherwise for 0.R_tIt is the autocorrelation matrix of reflected signal, i.e. R_t=E (s_ts_t ^H), its submatrix E (s_t,nms_t,n′m′ ^H) it is a square of K × K Battle array, as m=m ', wherein the individual elements of kth k ' are R_sm[(k-1)+l_t,n′m-l_t,nm- (k ' -1)], otherwise it is 0.

Step 3 is according to following formula

Try to achieve the estimate of θ

Step 4 repeat step 1 to 3, according to what is estimatedObtaining its RMSE (root-mean-square error) is

Wherein num is number of repetition.

Step 5 is according to formula

And then draw matrix

Finally try to achieve matrix

Step 6 is assumed

According to formula

Wherein

According to formula

Obtain matrixThe j element of its i-th be

Step 7 is according to formula

J (θ) is calculated, can finally be obtained

CRB=J (θ)^-1 (56)

Diagonal element corresponding to CRB is respectively target location x, y and target velocity v_x,v_yCarat Metro lower bound.

Step 8 basis

Calculate respectively corresponding to x, y, v_x,v_yRCRB (root carat Metro lower bound).

Operation principle of the invention

According to signal model (16), likelihood function can be expressed as

Wherein C represents covariance matrix, is expressed as

So its log likelihood function is

Ignore the second row last constant term, be on unknown parameter vector θ maximal possibility estimations

Calculate Fisher's information matrix formula be

Order

According to chain rule

WhereinIt is the function of θ, and

So

Calculate firstThen

Specific element is as shown in above-mentioned step.

According to document (S.Kay, " Fundamentals of Statistical Signal Processing: Estimation Theory, " Prentice-Hall.Englewood Cli_s, NJ, 1993.), can obtain

It is final available

Calculating maximal possibility estimation and CRB based on external sort algorithm MIMO radar signal model, maximal possibility estimation 1000 The simulation result that secondary Monte Carlo Experiment is obtained such as Fig. 1, shown in 2 figures, wherein parameter setting is as follows：

Consider that a target is moved with the speed of (50,30) m/s, target is located at (- 20,20) km.Assuming that there is M=2 hair Machine is penetrated positioned at (40,150) km and (- 60,120) km, N=3 receiver is located at (50,120) km, (10,130) km with (- 40, 100)km.Sample frequency is set to f_s=13040Hz, the auto-correlation function of transmission signal isReflectance factor ζ_t,nm =0.6+0.8j is for all n and m.Window function g_m(t)=1for0 ＜ t ＜ T.In experiment, we select T/T_s=7 and K= 24。.

Define reflected signal and noise ratioDirect-path signal and noise ratio

DSR=95dB in Fig. 1, it can be seen that all of RMSE reduces with the increase of SCNR, and all of RMSE curves have a threshold value, after threshold value, RMSE begins to RCRB, it was demonstrated that the correctness of CRB.

Fig. 2 DSR=-40dB, identical with Fig. 1, RMSE and RCRB is approached, comparison diagram 1 and Fig. 2, it can be seen that DSR high has more Low threshold value and lower CRB, illustrate that direct wave is helpful for the performance of parameter Estimation in this case.

Claims (1)

1. a kind of MIMO radar Cramér-Rao lower bound computational methods for reflecting through wave action, the method includes：

Step 1：A row are arranged in order for the signal sampling value that MIMO radar receives N number of receiver, are constituted and are received Signal r；

Wherein r_dFor direct wave is detected the signal that channel reception is arrived, r_tIt is target echo, w is noise；

r_d=α_ds_d⊙g_d,

r_t=β_ts_t⊙g_t,

Wherein α_dIt is that direct-path signal is monitoring the signal intensity of passage, s_dIt is the direct-path signal of transmitting, g_dIt is direct-path signal Window function；Equally, β_tIt is the intensity of target echo, s_tIt is target echo signal, g_tIt is the window function of target echo signal； Consider the totally unknown situation of signal in external radiation radar, it is assumed here that transmission signal s_mT () is to obey to have 0 average, from Correlation function is R_smThe multiple Gauss random process of (t)；

Step 2：It is determined that the covariance matrix C for receiving signal is used for maximal possibility estimation

Wherein,

$G_d=1_{1\×KNM}\⊗g_d,$

$G_t=1_{1\×KNM}\⊗g_t,$

K is sampling total number, and N is receiving station's number, and M is cell site's number, 1_1×KNMIt is complete 1 row vector of KNM dimensions；

R_d=E (s_ds_d ^H)

R_dt=E (s_ds_t ^H)

R_t=E (s_ts_t ^H)

To seek expectation symbol, Q is the covariance matrix of noise to wherein E；

Step 3：According to following formula

${\widehat{\mathrm{\θ}}}_{ML}=\arg \underset{\mathrm{\θ}}{max}\{-r^H{C}^{-1}r-ln\[\det \left(C\right)\]\}$

Try to achieve the estimate of θWherein θ is our target components to be estimated, including：Target location x, y and target velocity v_x, v_y, it is expressed as：θ=[x, y, v_x,v_y]^T, wherein r is expressed as receipt signal matrix；

Step 4：Repeat step 1 to 3, according to what is estimatedObtaining its root-mean-square error is：

$RMSE=\sqrt{\[\frac{{{({\widehat{\mathrm{\θ}}}_{ML}-\mathrm{\θ})}_1}^2+{{({\widehat{\mathrm{\θ}}}_{ML}-\mathrm{\θ})}_2}^2+\mathrm{...}+{{({\widehat{\mathrm{\θ}}}_{ML}-\mathrm{\θ})}_{num}}^2}{num}\]}$

Wherein num is number of repetition；

Step 5：If

Obtain matrix

Wherein, M represents the number of emitter, and N represents the number of receiver, and F is delay, τ to target location x, the derivative of y, τ_nm(n =1 ..., N m=1 ..., M) represent m-th emitter to n-th time delay of receiver, G be Doppler frequency f to x, y's Derivative, f_nm(n=1 ..., Nm=1 ... M) represents the Doppler frequency between m-th emitter and n-th receiver, D_tFor Emitter range-to-go d_tTo x, the derivative of y, d_tm(m=1 ..., M) represents m-th emitter range-to-go, D_r It is receiver range-to-go d_rTo x, the derivative of y, d_rn(n=1 ..., N) represent n-th receiver range-to-go；H It is Doppler frequency to target velocity v_x,v_yDerivative；

Step 6：Obtain matrixI-th j element be：

Step 7 is according to formula：

J (θ) is calculated, J (θ) is corresponding to x, y, v_x,v_yFisher's information matrix, can finally obtain：

CRB=J (θ)^-1,

Diagonal element corresponding to CRB is respectively target location x, y and target velocity v_x,v_yCarat Metro lower bound.