CN106909779B - MIMO radar Cramér-Rao lower bound calculation method based on distributed treatment - Google Patents

Abstract

The invention belongs to Radar Technology field, it is related to the calculating about the parameter Estimation Performance Evaluating Indexes Cramér-Rao lower bound (CRB) in Radar Signal Processing, suitable for splitting distributed treatment problem when antenna MIMO radar parameter Estimation.Target component θ is defined in the present invention:N-th m reception signal is arranged in a column by sampled value sequence first and constitutes reception signal r_nm, then calculate and receive signal r_nmCovariance matrix C_nm, then estimate part parameter ξ to be estimated_nm, and according to estimated valueCalculate the maximum likelihood estimator of target component θFinally calculate the CRB of target component θ_θ, according toIt calculates separately out and corresponds to x, y, v_x,v_yCarat Metro lower bound.Counting counted Cramér-Rao lower bound using the present invention can be used in the performance that assessment splits antenna external sort algorithm MIMO radar network distribution type joint parameter estimation；Play the role of to radar performance assessment great.

Description

MIMO radar Cramér-Rao lower bound calculation method based on distributed treatment

Technical field

The invention belongs to Radar Technology field, it is related to about the parameter Estimation Performance Evaluating Indexes gram in Radar Signal Processing The calculating of Latin America Luo Jie (CRB), suitable for splitting distributed treatment problem when antenna MIMO radar parameter Estimation.

Background technique

External illuminators-based radar (also referred to as passive radar or passive radar) utilizes the broadcast in ambient enviroment, TV, satellite, hand The signals such as machine base station or WiFi such as are detected to target, are estimated, classified or is imaged at the processing.External illuminators-based radar can be from straight Up to transmitting sample of signal is extracted in wave, as the reference signal of processing target echo, and then the detection and parameter to target are realized Measurement.Since external illuminators-based radar does not need expensive transmitter hardware, itself does not also emit electromagnetic wave, so that external sort algorithm thunder Up to having the characteristics that anti-stealthy, good concealment, be easy to dispose.Further, since external illuminators-based radar utilizes in external environment Existing electromagnetic wave is not take up additional frequency range, does not interfere existing wireless communication system as transmitting signal, has and saves frequency spectrum Resource, environmentally protective advantage.As the coverage area of satellite, mobile phone and other high performance signals in recent years is more and more wider, The attraction of external illuminators-based radar is increasing, using also increasingly wider.Currently, external illuminators-based radar has been widely used in wrapping Include the numerous areas of the business and military affairs such as region of war monitoring, air traffic control, coastal monitoring.

In order to promote the parameter Estimation performance of external radiation source radar system, we introduce MIMO (Multiple Input Multi ple Out) technology, it is the important foundation technology of 3G and 4G mobile communication that MIMO technology, which originates from wireless communication system,. Since this technology is in the immense success of wireless communication field, famous Radar Signal Processing expert Fisher in 2004 for the first time MIMO is used for radar, and proposes the concept of MIMO radar.Multiple transmitter and receivers of MIMO radar are distributed in sky Between different location, each transmitter and receiver is distributed in space different location, and each emission source can use different signals, respectively connect Receipts machine, which detects signal and is passed to center processing unit, to be focused on, and here it is so-called centralized processings.It can also be with Each receiving subelement is first handled reception signal, and acquired results are then transmitted to fusion center processing again, this is distribution Formula processing.The present invention uses distributed approach.

In the Parameter Estimation Problem of radar, in order to measure the parameter Estimation performance of radar system, a quantization is needed Comprehensive evaluation index.Cramér-Rao lower bound (Cramer-Rao Bound, abbreviation CRB) is under the variance of any unbiased estimator Limit.The unbiased estimator that a variance is less than lower limit can not be acquired, provides one to compare the performance of unbiased estimator Standard is common estimation Performance Evaluating Indexes.

In numerous methods of parameter Estimation, the signal unknown for priori probability information generallys use maximal possibility estimation Method, this method is a kind of point estimations with theoretical property, using the parameter of likelihood function maximum as estimator.This estimation The advantages of method is without knowing cost function, therefore to be applicable not only to priori without knowing the prior information of parameter to be estimated The unknown stochastic variable estimation of information, is also applied for nonrandom unknown parameter estimation.

In the Parameter Estimation Problem of MIMO radar, international radar academia has carried out extensive research.Wherein daily Line position information is classified, and MIMO radar, which can be divided into, sets antenna MIMO radar altogether and split antenna MIMO radar.For splitting For the CRB of antenna radar is calculated, existing research be essentially all around centralized processing, such as document 1 (Q.He, Jianbin Hu,Rick S Blum and Yonggang Wu,“Generalized Cramer-Rao bound for joint esti mation of target position and velocity for active and passive radar networks”,IEEE Transac tions on Signal Processing,vol.64,no.8,pp.2078- 2089,2016) in centralized processing method, joint parameter estimation is carried out using maximal possibility estimation, obtains and a kind of generally fits For splitting the joint objective speed and location parameter estimation of antenna MIMO radar, and calculates Cramér-Rao lower bound and calculate The CRB of the estimation performance for target position and speed is gone out.However certain situations in real life, it would be desirable to consider Distributed approach, the distributed treatment for splitting antenna MIMO radar to external sort algorithm are studied.

Summary of the invention

It is an object of the invention to splitting antenna MIMO radar for external sort algorithm, provide a kind of based on distributed treatment MI MO radar Cramér-Rao lower bound calculation method, joint objective speed and the position of antenna MIMO radar are split suitable for external sort algorithm Parameter Estimation is set, carries out maximal possibility estimation, and calculate Cramér-Rao lower bound.

To achieve the above object, the technical solution adopted by the present invention are as follows:

MIMO radar Cramér-Rao lower bound calculation method based on distributed treatment, comprising the following steps:

Include M transmitter and N number of receiver in step 1:MIMO radar system, sets target position (x, y) and speed (v_x,v_y), define target component θ:

N-th m reception signal is arranged in a column by sampled value sequence, constitutes and receives signal r_nm:

Wherein,

Wherein, n=1 ..., N；M=1 ..., M；E_mFor the transmitting signal energy of m-th of transmitter；d_t,mFor target and m The distance of a transmitter, d_r,nIt is target at a distance from n-th of receiver, d_d,nmExpression transmitter is at a distance from receiver, P₀Table It is shown as in d_d,nmRatio of the energy to emitted energy, P are received when=1₁Indicate d_t,m=d_r,nEnergy is received when=1 to emitted energy Ratio；K is hits, T_sFor sampling period, I_K×KIndicate K rank unit matrix；u_d,nm、u_t,nm、f_t,nm、ζ_t,nmIt is corresponding to indicate the n-th m Item goes directly the time delay of wave path, the time delay in target echo path, Doppler frequency, reflection coefficient；s_m[k] is k-th of sampled value, g_m[k] is the window function for receiving signal；

Step 2: calculating and receive signal r_nmCovariance matrix C_nm:

Step 3: the part parameter ξ to be estimated of the n-th m paths of setting_nm:Calculate its estimated value:

It enables:Wherein, w '_nmObey zero-mean, covariance matrix is Q '_nmMultiple Gauss distribution, Q '_nm For about ξ_nmCRB；

Calculate the maximum likelihood estimator of target component θ

Step 4: calculating the CRB of target component θ_θ: CRB_θ=J (θ)^-1, then CRB_θThe diagonal element of matrix is respectively target position Set x, y and target velocity v_x,v_yCarat Metro lower bound.

Wherein,

Step 5: according to:It calculates separately out and corresponds to x, y, v_x,v_yRCRB (under root carat Metro Boundary).

The beneficial effects of the present invention are: the present invention splits antenna MIMO radar for external sort algorithm, provides based on distribution The MIMO radar Cramér-Rao lower bound calculation method of formula processing, counting counted Cramér-Rao lower bound using the present invention can be used in assessment point Set the performance of antenna external sort algorithm MIMO radar network distribution type joint parameter estimation；And the external sort algorithm in practical application MIMO radar, really can be using the accessible maximum performance lower bound of maximal possibility estimation as evaluation when carrying out Radar Signal Processing One of the index of radar system performance quality.To sum up, the present invention can play the role of radar performance assessment great.

Detailed description of the invention

Fig. 1 is simulating scenes schematic diagram in embodiment.

Fig. 2 be in embodiment when target is in (- 20, -20) km, in high DSR, calculating about x, y, v_x,v_y RMSE and the schematic diagram that changes with SNR of RCRB.

Fig. 3 be in embodiment when target is in (- 20, -20) km, in low DSR, calculating about x, y, v_x,v_y RMSE and the schematic diagram that changes with SNR of RCRB.

Specific embodiment

The present invention is described in further details with reference to the accompanying drawings and examples.

In the present embodiment, for the convenience of description, such as being given a definition first:

For transposition, ()^HFor conjugate transposition,Indicate Kronecker product, ⊙ is expressed as Hadamard product, I_K×KTable Show K rank unit matrix.

Consider that an external sort algorithm splits antenna MIMO radar, there is M single antenna transmitter and N number of single antenna receiver, In a cartesian coordinate system, a transmitting antenna of m (m=1 ..., M) and a receiving antenna of n-th (n=1 ..., N) distinguish position InWithM-th of transmitter is in kT_sThe sampled value at moment isT_sFor sampling period, k (k= 1 ..., K) indicate kth time sampling, E_mFor the transmitting signal energy of m-th of transmitter, g_m[k] is the window function for receiving signal, institute In kT_sThe signal of m-th of transmitter that n-th of receiver of moment receives transmitting is

Time delay u_t,nmIt is the function of target position, i.e.,

Wherein,For downward rounding operation symbol, u_d,nm、u_t,nm、f_t,nm、ζ_t,nmThe through wave path of the n-th m item of corresponding expression Time delay, the time delay in target echo path, Doppler frequency and reflection coefficient, reflection coefficient are assumed to constant；w_nm[k] is in kT_s The noise at moment.Assuming that target position (x, y) and speed (v_x,v_y) it is determining unknown；d_t,mFor target and m-th transmitter Distance, d_r,nIt is target at a distance from n-th of receiver, d_d,nmIndicate transmitter at a distance from receiver；p₀It is expressed as in d_d,nm Energy is received when=1 to the ratio of emitted energy；p₁Indicate d_t,m=d_r,nEnergy is received when=1 to the ratio of emitted energy.

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

d_d,nmIt is the function of transmitter and receiver location:

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

Wherein, λ indicates carrier wavelength.

A unknown parameter vector is defined to indicate parameter to be estimated:

The present invention calculates the maximal possibility estimation and CRB for splitting antenna MIMO radar using following steps:

N-th m reception signal is arranged in a column by sampled value sequence for MIMO radar by step 1, is constituted and is received signal r_nm

Wherein,

s_d,nmAnd s_t,nmRespectively indicate the direct-path signal and target echo signal on the n-th m paths, u_d,nmAnd u_t,nmThen The time delay of direct wave and target echo after respectively indicating integer, K are hits, w_nmIt is to obey zero-mean, covariance matrix For Q_nmMultiple Gauss distribution；

Step 2: determining the covariance matrix C for receiving signal_nmFor maximal possibility estimation:

Wherein, R_d,nmnmIndicate transmitting signal in the auto-correlation function of the through wave path of the n-th m item, R_dt,nmnmIndicate the n-th m item The cross-correlation function of direct wave and target echo path, R_t,nmnmIndicate the auto-correlation function of n-th m target echo path；

Step 3: it sets:

u_t,nm=u_t,m+u_r,n (18)

Wherein, ξ_nmFor the part parameter to be estimated of nm paths, it to be used for estimation time delay and Doppler frequency；

According to the following formula

Acquire ξ_nmEstimated value；It enables:

It is assumed that w '_nmObey zero-mean, covariance matrix is Q '_nmMultiple Gauss distribution, Q '_nmIt is about ξ_nmCRB；Then By NM all partial estimation amountsIt is transferred to fusion center and carries out estimation target position and speed；It is assumed that not With the estimated value in pathIt is independent from each other, then available joint probability density function is

According to the following formula:

Acquire the maximum likelihood estimator of θ

Step 4: step 1 to 3 is repeated, according to what is estimatedFinding out its root mean square error is

Wherein L is number of repetition；

In above-mentioned steps 3, ξ_nmCRB calculating process are as follows:

Wherein, R_smTo emit signal s_mAuto-correlation function；

Step 5: calculating the CRB of target component θ_θ, the formula (21) of step 3 is taken known to logarithm

Because to obtainJust need to first it acquireWherein Operator ▽_θ() indicates a scalar to column vector θ derivation, then demand successively goes outTo x, y, v_x,v_yLocal derviation；

Wherein, ρ_nmFor u_t,nmAnd f_t,nmRelated coefficient,For u_t,mWith u_r,nThe sum of CRB,For f_t,nmCRB；Then

Wherein:

CRB_θ=J (θ)^-1 (58)

Corresponding to CRB_θDiagonal element be respectively target position x, y and target velocity v_x,v_yCarat Metro lower bound；

Step 6: according to

It calculates separately out and corresponds to x, y, v_x,v_yRCRB (root carat Metro lower bound).

The working principle of the invention

According to formula (8), the covariance matrix of the n-th m paths is determined

For the present invention using distributed treatment, this just needs us first to estimate the time delay and Doppler's frequency in each path Rate, then this class value is transferred to fusion center, carry out the estimation of final target component.

Define a time delay and Doppler frequency vector ξ_nm, i.e.,

According to the following formula, ξ is calculated_nmEstimator

It enables

It is assumed herein that w '_nmObey zero-mean, covariance matrix Q '_nmFor ξ_nmCRB multiple Gauss distribution；Then by NM Partial estimation amount ξ₁₁,ξ₁₂,...,ξ_NMFusion center is transferred to estimate required target position and speed；It is assumed that different paths Estimated valueIt is independent from each other, then available joint probability density function is

According to the following formula, the maximal possibility estimation of target component is acquired

WhereinFor the maximal possibility estimation of target component θ；

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

Using the formula, ξ can be obtained_nmCRB；

The CRB for calculating target component θ takes known to logarithm formula (64)

Finally utilize formula

CRB=J (θ)^-1 (78)

The CRB of target component is acquired, is recycled

It finds out and corresponds to x, y, v_x,v_yRCRB, i.e. root Cramér-Rao lower bound.

In the present embodiment, calculating maximal possibility estimation based on the external sort algorithm MIMO radar signal model for splitting antenna and CRB, the simulation result that 1000 Monte Carlo Experiments of maximal possibility estimation obtain is as shown in Figure 1 and Figure 2, and wherein parameter setting is such as Under:

Consider that a target is mobile with the speed of (50,30) m/s, in order to which the experiment for being easy to describe is arranged, at one In cartesian coordinate system, target is placed in the position of (- 20, -20) km, by 2 transmitters be placed on (40,150) km and (- 60, 120) position of km；3 receivers are placed on (50,120) km, the position of (10,130) km and (- 40,100) km；Such as Fig. 1 institute Show.Assume that the auto-correlation function for emitting signal is in emulationSample frequencyReflection Coefficient ζ_t,nmIt is constantly equal to 0.6+0.8j.

Wherein, the signal-to-noise ratio for defining reflection path isThrough wave path and Target reflection echo ratio is

From Fig. 2 it can be seen that all RMSE and RCRB reduce with the increase of SNR, and all RMSE curves There is a threshold value, after being greater than threshold value, RMSE begins to approach RCRB, it was demonstrated that the correctness of CRB.

Be illustrated in figure 3 simulating scenes it is constant in the case where, reduce DSR, it can be seen that the lower RMSE of different condition with The coincidence of RCRB does not influence, and further demonstrates the correct of CRB.

The above description is merely a specific embodiment, any feature disclosed in this specification, except non-specifically Narration, can be replaced by other alternative features that are equivalent or have similar purpose；Disclosed all features or all sides Method or in the process the step of, other than mutually exclusive feature and/or step, can be combined in any way.

Claims (1)

1. the MIMO radar Cramér-Rao lower bound calculation method based on distributed treatment, comprising the following steps:

Include M transmitter and N number of receiver in step 1:MIMO radar system, sets target position (x, y) and speed (v_x, v_y), define target component θ:Wherein,For transposition；

N-th m reception signal is arranged in a column by sampled value sequence, constitutes and receives signal r_nm:

Wherein, ⊙ is expressed as Hadamard product；

Wherein, n=1 ..., N；M=1 ..., M；E_mFor the transmitting signal energy of m-th of transmitter；d_t,mFor target and m-th of hair Penetrate the distance of machine, d_r,nIt is target at a distance from n-th of receiver, d_d,nmExpression transmitter is at a distance from receiver, P₀It is expressed as In d_d,nmRatio of the energy to emitted energy, P are received when=1₁Indicate d_t,m=d_r,nEnergy is received when=1 to the ratio of emitted energy Value；K is hits, T_sFor sampling period, I_K×KIndicate K rank unit matrix；u_d,nm、u_t,nm、f_t,nm、ζ_t,nmIt is corresponding to indicate that the n-th m item is straight Up to the time delay of wave path, the time delay in target echo path, Doppler frequency, reflection coefficient；s_m[k] is k-th of sampled value, g_m[k] For the window function for receiving signal；w_nmIndicate Gaussian noise, w_nm[k] is in kT_sThe noise at moment；

Step 2: calculating and receive signal r_nmCovariance matrix C_nm:(·)^HFor conjugate transposition；

Step 3: the part parameter ξ to be estimated of the n-th m paths of setting_nm, calculate its estimated value:

It enables:Wherein, w '_nmObey zero-mean, covariance matrix is Q '_nmMultiple Gauss distribution, Q '_nmFor about ξ_nmCRB；

Calculate the maximum likelihood estimator of target component θ

Step 4: calculating the CRB of target component θ_θ: CRB_θ=J (θ)^-1,

Wherein,

▽_θ() indicates a scalar to column vector θ derivation；

Step 5: according to:It calculates separately out and corresponds to x, y, v_x,v_yRoot carat Metro lower bound.