CN106353744A - Multi-parameter combined estimation method based on bi-static FDA-MIMO radars - Google Patents

Abstract

The invention relates to a multi-parameter combined estimation method based on bi-static FDA-MIMO radars. The method comprises the following steps: firstly designing a transmitting signal by utilizing characteristics of FDA and MIMO radars; carrying out matched filtering, vectorization and spatial smooth processing on a receiving signal; then estimating a combined steering vector and estimating a DOA and a speed parameter by utilizing an ESPRIT algorithm, and carrying out decoupling and parameter estimation on the DOD and distance information by combining characteristics of a transmitting waveform; and carrying out ambiguity resolution on a distance result estimated by utilizing an ESPRIT algorithm and combining a distance estimated by virtue of a pulse delay estimation algorithm, and carrying out ambiguity resolution on a speed by virtue of an MUSIC algorithm by combining signal characteristics of a large number of pulses. The method provided by the invention has the advantages that the problem that the distance and speed can not be accurately estimated under the condition of a single PRF can be effectively solved, and the estimation of the three-dimensional position and speed of a target can be realized; and a simulation result shows that the method provided by the invention has good estimation accuracy and stability.

Description

Multiparameter combined estimation method based on bistatic fda-mimo radar

Technical field

The invention belongs to MIMO radar technical field, it is based on bistatic fda-mimo radar particularly to a kind of Multiparameter combined estimation method.

Background technology

So-called mimo radar refers to the waveform using multiple transmitting antennas synchronously transmitting diversity, is connect using multiple simultaneously Receive antenna and receive echo-signal, and focus on a kind of New Type Radar system of receiving and transmitting signal.Mimo radar and traditional phased array The maximum difference of radar is that mimo radar can be realized on degree of freedom by changing array structure or the irrelevant waveform of transmitting Lifting.According to " far and near " of antenna spatial distribution, mimo radar is broadly divided into 2 classes: centralized mimo radar and distributed Mimo radar.The dual-mode antenna positional distance of centralized mimo radar system, compared with " near ", typically all can not reach incoherent mimo Spacing size required by radar.Because each antenna can launch different signals, therefore there is good waveform diversity gain, So as to parameter identification estimated capacity lifting, adaptive technique with and flexible waveform design etc. aspect show good Effect.The antenna of distributed mimo radar transmit-receive array at a distance of relatively " remote " and is distributed in space diverse location.Each antenna is relatively Angle in target has obvious difference, therefore shows good space diversity gain.The advantage of the type radar mainly exists Yu Qineng makes full use of target radar scattering cross-section and amasss (rcs) fluctuation characteristic spatially, thus overcoming target rcs angle scintillations Improve target detection performance and Parameter Estimation Precision.The present invention is mainly with the bistatic radar in centralized mimo radar as object Studied.

The method of existing solution prf and contradiction in velocity estimation mainly has multi-pulse repetition period or irregular The method of repetition.But this method still can produce ambiguous estimation.Because centralized mimo radar can be different by transmitting Waveform realizes waveform diversity gain.Therefore, it is different from conventional radar, mimo radar can be combined with fda technology, utilize Fda makes the carrier frequency of transmission signal form a frequency increment with emission array, thus utilizing single prf by waveform diversity Solve the problems, such as ambiguous estimation.However, this method can produce the coupling of dod and range information on transmitting steering vector, lead to It is unable to estimate out dod and range information in the case of bistatic mimo radar.A kind of solution is to be divided into emission array Two submatrixs, the frequency increment of two submatrixs is different；Another kind of method is to make a transmitting pulse medium frequency increment be 0, next Individual pulse medium frequency increment is not 0, alternate emission, thus using the signal under different pulses, estimate respectively angle information and Range information.The present invention is carried out decoupling using the first solution.Simultaneously because when Doppler frequency shift and carrier frequency and pulse Prolong number relevant, in the case of impulse time delay number is less, it can be ignored for the impact of transmitting steering vector, and is counting Cannot ignore in the case that mesh is larger, therefore can estimate dod and distance in impulse time delay number hour, in impulse time delay number Solve the problems, such as when larger that velocity estimation obscures.Simultaneously for coherent signal, method main at present is Space planar angle and square Battle array Reconstruction Method.The former can make the aperture of radar reduce；Thus reducing estimated accuracy, the latter is for the transmission signal of radar Have certain limitations with parameter estimation, not as the former flexibly, and also can there is the situation of aperture minimizing.

Content of the invention

For overcoming deficiency of the prior art, the present invention provides a kind of connection of the multiparameter based on bistatic fda-mimo radar Close method of estimation, the problem estimated for bistatic centralized mimo radar parameter, in conjunction with fda technology, solve Sing plus weight Frequently under (prf) distance estimations and velocity estimation fuzzy problem, realize target 3-dimensional positioning.

According to design provided by the present invention, a kind of multiparameter Combined estimator based on bistatic fda-mimo radar Method, comprises the steps of:

Step 1, utilize waveform diversity characteristics design transmission signal, according to the frequency increment δ f of transmission signal carrier wave, obtain The transmitted waveform relevant with dod and range information；

Step 2, the transmitted waveform signal receiving is carried out with matched filtering, vectorization and space smoothing are processed, expired The signal covariance matrix of order；

Step 3, be based on signal covariance matrix, using esprit algorithm estimate joint steering vector；

Step 4, estimate doa and speed parameter using joint steering vector, and dod and range information are carried out decoupling with Parameter estimation；

Step 5, information estimated result of adjusting the distance with reference to impulse time delay estimation carry out ambiguity solution process；

Step 6, combine high impulse number l_aUnder signal characteristic speed parameter estimated result is solved by music algorithm Fuzzy Processing.

Above-mentioned, step 1 specifically comprises following content: radar emission array is divided into two with array center for reference point Individual submatrix, the frequency increment of design submatrix 1 is-δ f, and submatrix 2 is that the transmitting steering vector obtaining is:

Wherein, θ_p And r_pIt is respectively target dod and doa, d_tFor the spacing of transmitting antenna, d_rFor the spacing of reception antenna, λ is signal wavelength, and c is light Speed, v is target velocity, r_pFor target to transmitting terminal and receiving terminal apart from sum.

Above-mentioned, it is as follows that step 2 specifically comprises content:

Step 201: matched filtering process is carried out to receipt signal, obtain l (l=1,2 ..., l) the letter under individual pulse Number, it is expressed as:

In formula,For receiving steering vector,For launching steering vector, a^p(v, l) is multiple for target Scattering coefficient and Doppler frequency shift, w (l) is noise vector；

Receipt signal under step 202:l pulse is expressed as: x=[x (1), x (2) ..., x (l)], it is carried out to Quantification treatment obtains signal:

, then signal covariance matrix be expressed as: r_y=e (yy^h), wherein, ⊙ is that khatri-rao amasss, b^l×pV how general () be Strangle vector, h is target scattering coefficient；

Step 203: signal is carried out with space smoothing process, design (l, n) individual smoothing matrix is as follows:

$\begin{array}{c}{z}_{\ln }=\[0_{l_0\×(l-1)}\left|i_{l_0\×l_0}\right|0_{l_0\×(p_v-l)}\]\&circletimes;i_{m\×m}\&circletimes;\[0_{n_0\×(n-1)}\left|i_{n_0\×n_0}\right|0_{n_0\×(p_r-n)}\],\\ l=1,2,\mathrm{...},p_v,n=1,2,\mathrm{...},p_r\end{array}$

, then the signal covariance matrix after smoothing is:

$r_y^f=\frac{1}{p_v{p}_r}\underset{l=1}{\overset{p_v}{\σ}}\underset{n=1}{\overset{p_r}{\σ}}{z}_{ln}{r}_y{z}_{ln}^h=c_0{\mathrm{hh}}^h{c}_0^h=c_0{r}_h^f{c}_0^h$

, wherein,Amass for kronecker, l₀=l-p_v+ 1, n₀=n-p_r+ 1, wherein p_vAnd p_rRepresent respectively and guide to receiving Vector doppler vector carries out the smooth number of times of space smoothing, h=diag (h) λ^t, c₀=z₁₁c₁, work as p_vp_r>=p and l₀n₀During >=p,It is the signal covariance matrix of full rank, wherein p is target total number.

Above-mentioned, it is as follows that step 3 specifically comprises content:

Step 301: feature decomposition is carried out to signal covariance matrix and obtains signal subspaceDue to span{e_s}=span { c₀, then e_sMeet e_s=c₀t^-1；

Step 302: by e_sIt is divided into two sub-spaces e_s1And e_s2, obtainWherein, u_sWith T isCharacteristic vector,For containing the diagonal matrix of dod and velocity information；

Step 303: calculating joint steering vector is

Above-mentioned, it is as follows that described step 4 specifically comprises content:

Step 401: estimate doa and speed using joint steering vector, concrete formula is as follows:

${\hat{v}}_p=\frac{c}{2{\mathrm{\πf}}_{0}t(l_0-1){\mathrm{mn}}_0}\underset{l=1}{\overset{l_0-1}{\σ}}\underset{n=1}{\overset{{\mathrm{mn}}_0}{\σ}}angle\left(\frac{{\hat{c}}_0({\mathrm{lmn}}_0+n,p)}{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+n,p)}\right);$

Step 402: using the feature of transmission signal, dod and distance are carried out decoupling, concrete formula is as follows:

$\begin{array}{c}{\widehat{\mathrm{\β}}}_{p1}=\frac{2}{l_0(m-1)n_0}\underset{l=1}{\overset{l_0}{\σ}}\underset{m=1}{\overset{(m-1)/2}{\σ}}\underset{n=1}{\overset{n_0}{\σ}}angle\left(\frac{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+{\mathrm{mn}}_0+n,p)}{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+(m-1)n_0+n,p)}\right)\\ {\widehat{\mathrm{\β}}}_{p2}=\frac{2}{l_0(m-1)n_0}\underset{l=1}{\overset{l_0}{\σ}}\underset{m=(m+1)/2}{\overset{m-1}{\σ}}\underset{n=1}{\overset{n_0}{\σ}}angle\left(\frac{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+{\mathrm{mn}}_0+n,p)}{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+(m-1)n_0+n,p)}\right)\end{array},$

$\begin{array}{c}{\widehat{\mathrm{\β}}}_{\mathrm{\θ}}={\widehat{\mathrm{\β}}}_{p1}+{\widehat{\mathrm{\β}}}_{p2}\\ {\widehat{\mathrm{\β}}}_r={\widehat{\mathrm{\β}}}_{p1}-{\widehat{\mathrm{\β}}}_{p2}\end{array};$

Step 403: dod and distance are calculated by formula, specific formula for calculation is as follows:

${\widehat{\mathrm{\θ}}}_p=ac\sin \left(\frac{\mathrm{\λ}}{4d_t\mathrm{\π}}{\widehat{\mathrm{\β}}}_{\mathrm{\θ}}\right),{\hat{r}}_p=\frac{c}{4\mathrm{\π}\mathrm{\δ}f}{\widehat{\mathrm{\β}}}_r.$

Above-mentioned, it is as follows that step 5 specifically comprises content: using the actual distance measured by radar pulse is In formula, k_pIt is integer, r_ut=c/f_prfRepresent maximum unambiguous distance,Represent measurement distance；Using fda-mimo thunder Reaching surveyed actual distance isIn formula, q_pIt is integer, r_uδf=c/4 δ f represents maximum no mould Paste distance,Represent estimated distance；Then unambiguous distance can be estimated to draw by following formula:

$s.t.\left\{\begin{array}{c}1\≤k_p\≤n_a\\ |r_{tp}-r_{\mathrm{\δ}fp}|\≤\frac{c}{2b}\end{array}\right..$

Above-mentioned, it is as follows that step 6 specifically comprises content: the relation according to speed and frequency increment under big umber of pulse solves no Fuzzy speed, l_aReceipt signal under pulse is:

In formula, transmitting steering vector:

$a_t^m({\mathrm{\θ}}_p,r_p,v_p,l_a)=\left[\begin{array}{c}{e}^{j2\mathrm{\π}\frac{m-1}{2}{d}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ .\\ .\\ .\\ e^{j2{\mathrm{\πd}}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ 1\\ e^{-j2{\mathrm{\πd}}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ .\\ .\\ .\\ e^{-j2\mathrm{\π}\frac{m-1}{2}{d}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\end{array}\right]$

It is assumed that true velocity isD is integer, v_u=c/2f₀T is velocity ambiguity, utilizes Music Algorithm for Solving d:

$\hat{d}=\arg \underset{d}{max}\left(\frac{1}{c_{v1}{\left(l_a\right)}^h{\hat{u}}_{n1}{\hat{u}}_{n1}^h{c}_{v1}\left(l_a\right)+c_{v2}{\left(l_a\right)}^h{\hat{u}}_{n2}{\hat{u}}_{n2}^h{c}_{v2}\left(l_a\right)}\right)$

In formula, c_v1(l_a) and c_v2(l_a) it is based on two joint steering vectors launching submatrixs.

Beneficial effects of the present invention:

1st, the present invention adopts the method for space smoothing to ensure signal covariance matrix full rank, and doppler vector and reception are led Carry out space smoothing to vector simultaneously, solve and there is velocity estimation and distance under the Sing plus repetition period in prior art and estimate Meter is also easy to produce fuzzy problem, improves parameter estimation performance.

2nd, the present invention makes full use of mimo radar waveform diversity feature, by mimo radar and frequency control battle array fda combine so as to Transmitted waveform does not only have dod information and comprises range information even velocity information, thus realizing dod, doa, distance and speed yet Combined estimator, solve the velocity estimation brought in traditional phased-array radar and distance by the pulse repetition period (prf) Estimate the contradiction of no blur estimation, improve the performance of parameter estimation；Achieve the decoupling, thus allowing of dod and range information Angle and distance Combined estimator is possibly realized, and solves the problems, such as that under single prf, distance estimations obscure；Using Doppler frequency shift and The relation of carrier frequency, achieves the ambiguity solution of velocity estimation when impulse time delay number is larger using music algorithm, thus realizing mesh Mark dod, effective estimation of doa, distance and 4 parameters of speed, so that it is determined that the three-dimensional coordinate of target；Utilization space smooths to be calculated Method, to doppler vector and receive steering vector smoothing processing simultaneously, solve coherent signal and Angle Ambiguity Problem it is ensured that The full rank condition of covariance matrix.

Brief description:

Fig. 1 is bistatic fda-mimo radar system structural representation；

Fig. 2 is the schematic flow sheet of the present invention；

Fig. 3 is the change curve with snr for the phase place launching steering vector under the present invention；

Fig. 4 is the change curve with snr for the root-mean-square error of lower 4 parameters of the present invention；

Fig. 5 is the change curve with sampled point for the root-mean-square error of lower 4 parameters of the present invention；

Fig. 6 be angle ambiguity under the conditions of 4 parameters root-mean-square error with snr change curve.

Specific embodiment:

The present invention is further detailed explanation with technical scheme below in conjunction with the accompanying drawings, and detailed by preferred embodiment Describe bright embodiments of the present invention in detail, but embodiments of the present invention are not limited to this.

Embodiment one, referring to shown in Fig. 1～2, a kind of multiparameter Combined estimator side based on bistatic fda-mimo radar Method, comprises the steps of:

Step 1, utilize waveform diversity characteristics design transmission signal, according to the frequency increment δ f of transmission signal carrier wave, obtain The transmitted waveform relevant with dod and range information is it is ensured that can realize decoupling to dod and range information in parameter estimation procedure Close；

Step 2, the transmitted waveform signal receiving is carried out with matched filtering, vectorization and space smoothing are processed, expired The signal covariance matrix of order；

Step 3, be based on signal covariance matrix, using esprit algorithm estimate joint steering vector；

Step 4, estimate doa and speed parameter using joint steering vector, and dod and range information are carried out decoupling with Parameter estimation；

Step 5, information estimated result of adjusting the distance with reference to impulse time delay estimation carry out ambiguity solution process；

Step 6, combine high impulse number l_aUnder signal characteristic speed parameter estimated result is solved by music algorithm Fuzzy Processing.

The present invention adopts the method for space smoothing to ensure signal covariance matrix full rank, to doppler vector and reception guiding Vector carries out space smoothing simultaneously, solves and there are velocity estimation and distance estimations under the Sing plus repetition period in prior art It is also easy to produce fuzzy problem, improve parameter estimation performance.

Embodiment two, referring to shown in Fig. 1～6, a kind of multiparameter Combined estimator side based on bistatic fda-mimo radar Method, comprises following content:

Step 1, the bistatic mimo radar being constituted based on m transmitting array element, n reception array element, special using waveform diversity Property design transmission signal, according to the frequency increment δ f of transmission signal carrier wave, obtain the transmitted wave relevant with dod and range information Shape, in order to solve the problems, such as dod and range information coupling, radar emission array is divided into two with array center for reference point Submatrix, calculates for convenience, and the frequency increment of design submatrix 1 is-δ f, and submatrix 2 is that the transmitting steering vector obtaining is:

Wherein, θ_pAnd r_pIt is respectively target dod and doa, d_tFor the spacing of transmitting antenna, d_rFor the spacing of reception antenna, λ is signal wave Long, c is the light velocity, and v is target velocity, r_pFor target to transmitting terminal and receiving terminal apart from sum it is ensured that in parameter estimation procedure Dod and range information can be realized decoupling.

Step 2, the transmitted waveform signal receiving is carried out with matched filtering, vectorization and space smoothing are processed, expired The signal covariance matrix of order, specifically comprises following content:

Step 201: matched filtering process is carried out to receipt signal, obtain l (l=1,2 ..., l) the letter under individual pulse Number, it is expressed as:

In formula,For receiving steering vector,For launching steering vector, a^p(v, l) is multiple for target Scattering coefficient and Doppler frequency shift, w (l) is noise vector；

Receipt signal under step 202:l pulse is expressed as: x=[x (1), x (2) ..., x (l)], it is carried out to Quantification treatment obtains signal:

, then signal covariance matrix be expressed as: r_y=e (yy^h), wherein,It is that khatri-rao amasss, b^l×pV how general () be Strangle vector, h is target scattering coefficient；

Step 203: space smoothing process is carried out to signal, situation about annexing in order to avoid angle of arrival, designs (l, n) Individual smoothing matrix is as follows:

$\begin{array}{c}{z}_{\ln }=\[0_{l_0\×(l-1)}\left|i_{l_0\×l_0}\right|0_{l_0\×(p_v-l)}\]\&circletimes;i_{m\×m}\&circletimes;\[0_{n_0\×(n-1)}\left|i_{n_0\×n_0}\right|0_{n_0\×(p_r-n)}\],\\ l=1,2,...,p_v,n=1,2,...,p_r\end{array}$

, then the signal covariance matrix after smoothing is:

$r_y^f=\frac{1}{p_v{p}_r}\underset{l=1}{\overset{p_v}{\σ}}\underset{n=1}{\overset{p_r}{\σ}}{z}_{ln}{r}_y{z}_{ln}^h=c_0{\mathrm{hh}}^h{c}_0^h=c_0{r}_h^f{c}_0^h$

, wherein,Amass for kronecker, l₀=l-p_v+ 1, n₀=n-p_r+ 1, wherein p_vAnd p_rRepresent respectively and guide to receiving Vector doppler vector carries out the smooth number of times of space smoothing, h=diag (h) λ^t, c₀=z₁₁c₁, work as p_vp_r>=p and l₀n₀During >=p,It is the signal covariance matrix of full rank.

Step 3, be based on signal covariance matrix, according to the invariable rotary shape of fda-mimo radar signal, using esprit Algorithm estimates joint steering vector, specifically comprises content as follows:

Step 301: feature decomposition is carried out to signal covariance matrix and obtains signal subspaceMeet e_s =c₀t^-1, wherein, due to span { e_s}=span { c₀, then e_sMeet e_s=c₀t^-1；

Step 302: by e_sIt is divided into two sub-spaces e_s1And e_s2, obtainWherein, u_sWith T isCharacteristic vector,For containing the diagonal matrix of dod and velocity information；

Step 303: calculating joint steering vector is

Step 4, estimate doa and speed parameter using joint steering vector, and dod and range information are carried out decoupling with Parameter estimation, specifically comprises content as follows:

Step 401: estimate doa and speed using joint steering vector, concrete formula is as follows:

${\hat{v}}_p=\frac{c}{2{\mathrm{\πf}}_{0}t(l_0-1){\mathrm{mn}}_0}\underset{l=1}{\overset{l_0-1}{\σ}}\underset{n=1}{\overset{{\mathrm{mn}}_0}{\σ}}angle\left(\frac{{\hat{c}}_0({\mathrm{lmn}}_0+n,p)}{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+n,p)}\right);$

Step 402: using the feature of transmission signal, dod and distance are carried out decoupling, concrete formula is as follows:

$\begin{array}{c}{\widehat{\mathrm{\β}}}_{p1}=\frac{2}{l_0(m-1)n_0}\underset{l=1}{\overset{l_0}{\σ}}\underset{m=1}{\overset{(m-1)/2}{\σ}}\underset{n=1}{\overset{n_0}{\σ}}angle\left(\frac{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+{\mathrm{mn}}_0+n,p)}{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+(m-1)n_0+n,p)}\right)\\ {\widehat{\mathrm{\β}}}_{p2}=\frac{2}{l_0(m-1)n_0}\underset{l=1}{\overset{l_0}{\σ}}\underset{m=(m+1)/2}{\overset{m-1}{\σ}}\underset{n=1}{\overset{n_0}{\σ}}angle\left(\frac{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+{\mathrm{mn}}_0+n,p)}{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+(m-1)n_0+n,p)}\right)\end{array},$

$\begin{array}{c}{\widehat{\mathrm{\β}}}_{\mathrm{\θ}}={\widehat{\mathrm{\β}}}_{p1}+{\widehat{\mathrm{\β}}}_{p2}\\ {\widehat{\mathrm{\β}}}_r={\widehat{\mathrm{\β}}}_{p1}-{\widehat{\mathrm{\β}}}_{p2}\end{array};$

Step 403: dod and distance are calculated by formula, specific formula for calculation is as follows:

${\widehat{\mathrm{\θ}}}_p=ac\sin \left(\frac{\mathrm{\λ}}{4d_t\mathrm{\π}}{\widehat{\mathrm{\β}}}_{\mathrm{\θ}}\right),{\hat{r}}_p=\frac{c}{4\mathrm{\π}\mathrm{\δ}f}{\widehat{\mathrm{\β}}}_r.$

Step 5, information estimated result of adjusting the distance with reference to impulse time delay estimation carry out ambiguity solution process, using radar pulse institute Measurement actual distance beIn formula, k_pIt is integer, r_ut=c/f_prfRepresent maximum unambiguous distance,Represent measurement distance；Using the actual distance that fda-mimo radar is surveyed it isFormula In, q_pIt is integer, r_uδf=c/4 δ f represents maximum unambiguous distance,Represent estimated distance；Then unambiguous distance can be by following formula Estimation draws:

$s.t.\left\{\begin{array}{c}1\≤k_p\≤n_a\\ |r_{tp}-r_{\mathrm{\δ}fp}|\≤\frac{c}{2b}\end{array}\right..$

Step 6, combine high impulse number l_aUnder signal characteristic speed parameter estimated result is solved by music algorithm Fuzzy Processing, the relation according to speed and frequency increment under big umber of pulse solves no fuzzy speed, l_aReceipt signal under pulse For:

In formula, transmitting steering vector:

$a_t^m({\mathrm{\θ}}_p,r_p,v_p,l_a)=\left[\begin{array}{c}{e}^{j2\mathrm{\π}\frac{m-1}{2}{d}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ .\\ .\\ .\\ e^{j2{\mathrm{\πd}}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ 1\\ e^{-j2{\mathrm{\πd}}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ .\\ .\\ .\\ e^{-j2\mathrm{\π}\frac{m-1}{2}{d}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\end{array}\right]$

It is assumed that true velocity isD is integer, v_u=c/2f₀T is velocity ambiguity, utilizes Music Algorithm for Solving d:

$\hat{d}=\arg \underset{d}{max}\left(\frac{1}{c_{v1}{\left(l_a\right)}^h{\hat{u}}_{n1}{\hat{u}}_{n1}^h{c}_{v1}\left(l_a\right)+c_{v2}{\left(l_a\right)}^h{\hat{u}}_{n2}{\hat{u}}_{n2}^h{c}_{v2}\left(l_a\right)}\right)$

In formula, c_v1(l_a) and c_v2(l_a) it is based on two joint steering vectors launching submatrixs.

The Cramér-Rao lower bound (cramer rao bound, crb) that doa estimates is unbiased esti-mator deviation theory lower bound.Foundation The signal model of bistatic fda-mimo radar, the Cramér-Rao lower bound crb of 4 parameters is

$\begin{array}{c}{d}_v=\frac{1}{2ksnr}\frac{12}{lmn(l^2-1){\mathrm{\κ}}_v^2}\\ d_{\mathrm{\θ}}=\frac{1}{2ksnr}\frac{12}{lmn(m^2-1){\mathrm{\κ}}_{\mathrm{\θ}}^2}\\ d_r=\frac{1}{2ksnr}\frac{48m}{ln(m^2-1)(m^2+3){\mathrm{\κ}}_r^2}\end{array}$

Wherein, snr=(e | ξ |²)/(mσ²), l, m, n represent impulse time delay number, transmitting antenna number respectively and receive sky Line number mesh, κ_v=2 π f₀T/c, κ_θ=2 π d_tCos (θ)/λ, κ_r=2 π δ f/c,K represents sampling Count out.

The effect of the present invention can be further illustrated by following emulation experiment.

1) simulated conditions:

Bistatic fda-mimo radar transmit-receive array is even linear array, and parameter setting is as follows:

The parameter setting of the bistatic fda-mimo radar of table 1

2) emulation experiment:

(1) impact to transmitting steering vector for the frequency increment

The impact to transmitting steering vector for the frequency increment is mainly studied in this emulation.The dod of target is 20 °, and distance is 1.5km, speed is 450m/s.Fig. 3 gives the change with pulse for the phase place to launching steering vector for the frequency increment, and dod With distance with impulse time delay number change curve.By simulation result it is found that due to speed and carrier frequency and impulse time delay number Mesh is simultaneously relevant, but because its magnitude is relatively small, therefore when umber of pulse less period, the impact to transmitting steering vector is little, When impulse time delay number is larger, its impact be can not ignore.Using this point, ambiguity solution can be carried out to velocity estimation.

(2) the parameter estimation performance of fda-mimo radar

The parameter estimation performance of fda-mimo radar is mainly studied in this emulation.It is to estimate that performance estimates mean square error first Change curve with snr.Sampling number is that 256, dod is 30 °, and doa is 35 °, and distance is 150km, and speed is 450m/s, wherein Distance and speed all can produce ambiguous estimation.By the simulation result of Fig. 4 it is found that with respect to traditional phased-array radar and mimo Radar, fda-mimo radar can realize the Combined estimator of 4 parameters, and distance and velocity estimation no fuzzy.Simultaneously because The reason mimo radar virtual aperture, its estimated accuracy increases compared with phased-array radar.

Followed by mean square error is with the change curve of sampling number.Snr=0db, coordinates of targets is constant.Emulation by Fig. 5 It is found that increase with sampling number, the estimated accuracy of radar is also improving constantly result.

(3) the solution angle ambiguity performance of fda-mimo radar

In order to verify the performance to angle ambiguity for the method for the present invention, we by the method for the present invention and are provided without space and put down Sliding method is compared.There are 2 targets of angle ambiguity in setting, its dod is 30 ° and 45 °, and doa is 35 ° and 36 °, distance For 150km and 250km, speed is 450m/s and 350m/s.Even if by the simulation result of Fig. 6 it is found that the method for the present invention Remain to effectively the target that there is angle ambiguity be estimated under conditions of low signal-to-noise ratio.

The present invention is not limited to above-mentioned specific embodiment, and those skilled in the art also can make multiple changes accordingly, but Any it is equal to the present invention or similar change all should be covered within the scope of the claims.

Claims (7)

1. a kind of multiparameter combined estimation method based on bistatic fda-mimo radar it is characterised in that: comprise the steps of:

Step 1, utilize waveform diversity characteristics design transmission signal, according to the frequency increment δ f of transmission signal carrier wave, obtain with The dod transmitted waveform relevant with range information；

Step 2, the transmitted waveform signal receiving is carried out with matched filtering, vectorization and space smoothing are processed, and obtain full rank Signal covariance matrix；

Step 3, be based on signal covariance matrix, using esprit algorithm estimate joint steering vector；

Step 4, utilization joint steering vector are estimated doa and speed parameter, and are carried out decoupling and parameter to dod and range information Estimate；

Step 5, information estimated result of adjusting the distance with reference to impulse time delay estimation carry out ambiguity solution process；

Step 6, combine high impulse number l_aUnder signal characteristic by music algorithm, ambiguity solution is carried out to speed parameter estimated result Process.

2. the multiparameter combined estimation method based on bistatic fda-mimo radar according to claim 1, its feature exists In: described step 1 specifically comprises following content: radar emission array is divided into two submatrixs with array center for reference point, The frequency increment of design submatrix 1 is-δ f, and submatrix 2 is that the transmitting steering vector of p-th target obtaining is:

Wherein, θ_pAnd r_p It is respectively target dod and doa, d_tFor the spacing of transmitting antenna, d_rFor the spacing of reception antenna, λ is signal wavelength, and c is the light velocity, v For target velocity, r_pFor target to transmitting terminal and receiving terminal apart from sum.

3. the multiparameter combined estimation method based on bistatic fda-mimo radar according to claim 2, its feature exists In: it is as follows that described step 2 specifically comprises content:

Step 201: matched filtering process is carried out to receipt signal, obtain l (l=1,2 ..., l) the signal under individual pulse, table It is shown as:

In formula,For receiving steering vector,For launching steering vector, a^p(v, l) scatters again for target Coefficient and Doppler frequency shift, w (l) is noise vector；

Receipt signal under step 202:l pulse is expressed as: x=[[x (1), x (2) ..., x (l)]], enters row vector to it Change processes and obtains signal:

,

Then signal covariance matrix is expressed as: r_y=e (yy^h), wherein, ⊙ is that khatri-rao amasss, b^l×pV () is sweared for Doppler Amount, h is target scattering coefficient；

Step 203: signal is carried out with space smoothing process, design (l, n) individual smoothing matrix is as follows:

$\begin{array}{c}{z}_{\ln }=\[0_{l_0\×(l-1)}\left|i_{l_0\×l_0}\right|0_{l_0\×(p_v-l)}\]\&circletimes;i_{m\×m}\&circletimes;\[0_{n_0\×(n-1)}\left|i_{n_0\×n_0}\right|0_{n_0\×(p_r-n)}\]\\ l=1,2,...,p_v,n=1,2,...,p_r\end{array},$ ,

Signal covariance matrix after then smoothing is:

$r_y^f=\frac{1}{p_v{p}_r}\underset{l=1}{\overset{p_v}{\σ}}\underset{n=1}{\overset{p_r}{\σ}}{z}_{\ln }{r}_y{z}_{ln}^h=c_0{\mathrm{hh}}^h{c}_0^h=c_0{r}_h^f{c}_0^h$ ,

Wherein,Amass for kronecker, l₀=l-p_v+ 1, n₀=n-p_r+ 1, wherein p_vAnd p_rRepresent respectively to reception steering vector Carry out the smooth number of times of space smoothing, h=diag (h) λ with doppler vector^t,c₀= z₁₁c₁, work as p_vp_r>=p and l₀n₀During >=p,It is the signal covariance matrix of full rank, wherein p is target total number.

4. the multiparameter combined estimation method based on bistatic fda-mimo radar according to claim 3, its feature exists In: it is as follows that described step 3 specifically comprises content:

Step 301: feature decomposition is carried out to signal covariance matrix and obtains signal subspaceDue to span {e_s}=span { c₀, then e_sMeet e_s=c₀t^-1；

Step 302: by e_sIt is divided into two sub-spaces e_s1And e_s2, obtainWherein, u_sIt is with tCharacteristic vector,For containing the diagonal matrix of dod and velocity information；

Step 303: calculating joint steering vector is

5. the multiparameter combined estimation method based on bistatic fda-mimo radar according to claim 4, its feature exists In: it is as follows that described step 4 specifically comprises content:

Step 401: estimate doa and speed using joint steering vector, concrete formula is as follows:

${\hat{v}}_p=\frac{c}{2{\mathrm{\πf}}_{0}t(l_0-1){\mathrm{mn}}_0}\underset{l=1}{\overset{l_0-1}{\σ}}\underset{n=1}{\overset{{\mathrm{mn}}_0}{\σ}}angle\left(\frac{{\hat{c}}_0\left({\mathrm{lmn}}_0+n,p\right)}{{\hat{c}}_0\left(\left(l-1\right){\mathrm{mn}}_0+n,p\right)}\right);$

Step 402: using the feature of transmission signal, dod and distance are carried out decoupling, concrete formula is as follows:

$\begin{array}{c}{\widehat{\mathrm{\β}}}_{p1}=\frac{2}{l_0(m-1)n_0}\underset{l=1}{\overset{l_0}{\σ}}\underset{m=1}{\overset{(m-1)/2}{\σ}}\underset{n=1}{\overset{n_0}{\σ}}angle\left(\frac{{\hat{c}}_0\left(\left(l-1\right){\mathrm{mn}}_0+{\mathrm{mn}}_0+n,p\right)}{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+(m-1)n_0+n,p)}\right)\\ {\widehat{\mathrm{\β}}}_{p2}=\frac{2}{l_0(m-1)n_0}\underset{l=1}{\overset{l_0}{\σ}}\underset{m=(m+1)/2}{\overset{m-1}{\σ}}\underset{n=1}{\overset{n_0}{\σ}}angle\left(\frac{{\hat{c}}_0\left(\left(l-1\right){\mathrm{mn}}_0+{\mathrm{mn}}_0+n,p\right)}{{\hat{c}}_0\left(\right(l-1){\mathrm{mn}}_0+(m-1)n_0+n,p)}\right)\end{array},$ $\begin{array}{c}{\widehat{\mathrm{\β}}}_{\mathrm{\θ}}={\widehat{\mathrm{\β}}}_{p1}+{\widehat{\mathrm{\β}}}_{p2}\\ {\widehat{\mathrm{\β}}}_r={\widehat{\mathrm{\β}}}_{p1}-{\widehat{\mathrm{\β}}}_{p2}\end{array};$

Step 403: dod and distance are calculated by formula, specific formula for calculation is as follows:

${\widehat{\mathrm{\θ}}}_p=acsin\left(\frac{\mathrm{\λ}}{4d_t\mathrm{\π}}{\widehat{\mathrm{\β}}}_{\mathrm{\θ}}\right),{\hat{r}}_p=\frac{c}{4\mathrm{\π}\mathrm{\δ}f}{\widehat{\mathrm{\β}}}_r.$

6. the multiparameter combined estimation method based on bistatic fda-mimo radar according to claim 5 it is characterised in that: It is as follows that described step 5 specifically comprises content: using the actual distance measured by radar pulse isFormula In, k_pIt is integer, r_ut=c/f_prfRepresent maximum unambiguous distance,Represent measurement distance；Using fda-mimo radar The actual distance surveyed isIn formula, q_pIt is integer, r_uδf=c/4 δ f represents maximum no fuzzy Distance,Represent estimated distance；Then unambiguous distance can be estimated to draw by following formula:

$s.t.\left\{\begin{array}{c}1\≤k_p\≤n_a\\ |r_{tp}-r_{\mathrm{\δ}fp}|\≤\frac{c}{2b}\end{array}\right..$

7. the multiparameter combined estimation method based on bistatic fda-mimo radar according to claim 6, its feature exists In: it is as follows that described step 6 specifically comprises content: the relation according to speed and frequency increment under big umber of pulse solves no fuzzy speed Degree, l_aReceipt signal under pulse is:

In formula, transmitting steering vector:

$a_t^m({\mathrm{\θ}}_p,r_p,v_p,l_a)=\left[\begin{array}{c}{e}^{j2\mathrm{\π}\frac{m-1}{2}{d}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ .\\ .\\ .\\ e^{j2{\mathrm{\πd}}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ 1\\ e^{-j2{\mathrm{\πd}}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\\ .\\ .\\ .\\ e^{-j2\mathrm{\π}\frac{m-1}{2}{d}_t\frac{\sin \left({\mathrm{\θ}}_p\right)}{\mathrm{\λ}}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{r_p}{c}}{e}^{-j2\mathrm{\π}\frac{m-1}{2}\mathrm{\δ}f\frac{v_p}{c}(l_a-1)t}\end{array}\right]$ ,

Assume that true velocity isD is integer, v_u=c/2f₀T is velocity ambiguity, using music algorithm Solution d:

$\hat{d}=\arg \underset{d}{max}\left(\frac{1}{c_{v1}{\left(l_a\right)}^h{\hat{u}}_{n1}{\hat{u}}_{n1}^h{c}_{v1}\left(l_a\right)+c_{v2}{\left(l_a\right)}^h{\hat{u}}_{n2}{\hat{u}}_{n2}^h{c}_{v2}\left(l_a\right)}\right)$

In formula, c_v1(l_a) and c_v2(l_a) it is based on two joint steering vectors launching submatrixs.