CN103353595B - Meter wave radar height measurement method based on array interpolation compression perception - Google Patents
Meter wave radar height measurement method based on array interpolation compression perception Download PDFInfo
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Abstract
本发明公开了一种基于阵列内插压缩感知的测高方法，主要解决多径环境下，尤其是低信噪比和快拍数较少环境下的低仰角测高问题，其实现过程：从雷达回波提取目标信号；通过对消和信号重构得到空域稀疏信号；使用波束形成法得到目标粗测角度；根据粗测角度得到空域，并对其进行划分；利用阵列内插得到虚拟阵列；根据矩阵变换关系得到内插变换矩阵，并对其进行预白化处理；利用白化内插变换矩阵和观测矩阵得到观测信号；利用白化内插变换矩阵和观测信号迭代运算得到目标信号估计值；从目标信号估计值提取目标角度，进而得到目标高度。本发明明显减少了目标信号的采样点数和运算量，有效降低了信号功率谱和空间谱的旁瓣，可用于目标跟踪。
The invention discloses a height measurement method based on array interpolation compressed sensing, which mainly solves the problem of low elevation angle measurement in a multipath environment, especially in an environment with a low signal-to-noise ratio and a small number of snapshots. Its realization process: from Extract the target signal from the radar echo; obtain the sparse signal in the airspace through cancellation and signal reconstruction; use the beamforming method to obtain the rough measurement angle of the target; obtain the airspace according to the rough measurement angle and divide it; use the array interpolation to obtain the virtual array; Obtain the interpolation transformation matrix according to the matrix transformation relationship, and pre-whiten it; use the whitening interpolation transformation matrix and the observation matrix to obtain the observation signal; use the whitening interpolation transformation matrix and the observation signal iterative operation to obtain the estimated value of the target signal; The signal estimate extracts the target angle, which in turn yields the target height. The invention obviously reduces the number of sampling points and calculation amount of the target signal, effectively reduces the side lobe of the signal power spectrum and the space spectrum, and can be used for target tracking.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a method for compressed sensing and height measurement of a meter wave radar, which can be used for target tracking.
Background
The radar world at home and abroad generally holds that the meter-wave radar has the anti-stealth capability. Because the wavelength of the meter-wave radar is longer and the wave beam is wide, particularly when a low-angle target is measured, the wave beam hits the ground, the ground reflection is strong, and the multipath phenomenon of the target is serious, the meter-wave radar has low measurement accuracy and even completely fails. In the radar receiving signal, besides the radio wave refraction effect caused by the nonuniformity of the lower atmosphere, the multipath interference effect caused by the mirror reflection and the diffuse scattering generated on the ground and the sea surface is also provided. Multipath interference has great influence on the low elevation angle measurement accuracy of the radar, and direct wave and multipath reflected wave signals have strong correlation; the included angle between the incident angle of the target direct wave and the incident angle of the multipath reflected wave is small and is usually within one beam width; lobe splitting causes the level of the received signal to flicker, with large signal-to-noise ratio fluctuations. The influence of the topographic relief on the measurement result is great at low elevation angle, particularly on the sea surface with large sea condition or the land of a complex zone, the reflection clutter of the ground (sea) surface is strong, a target signal is often submerged in the clutter, and the instability and the peak of the clutter can cause the false alarm probability to be rapidly increased. Therefore, the height measurement is difficult in a multipath environment, so that the height measurement problem of the meter-wave radar is a difficult problem which is not well solved in the radar field.
In order to better solve the problem of measuring height by meter wave, the main technical approaches adopted mainly comprise: 1. the antenna size is increased, particularly the aperture of the antenna in the height dimension is increased, so that the beam width of the antenna in the vertical dimension is reduced, the angular resolution is improved, and for a higher elevation angle, the height measurement is completed by the beams without hitting the ground; 2. the erection height of the antenna is properly increased, and the upwarp of the wave beam is reduced, so that the low-altitude target can be detected. But for low-altitude targets, the "multipath" problem is unavoidable.
At present, height measurement methods for meter wave radar mainly include the following three types:
(1) multi-frequency lobe splitting altimetry. The method utilizes a plurality of working frequencies to work in a time division mode, the theory is feasible, but the working bandwidths of the plurality of working frequencies are wide, the system is complex, and no practical system exists at present.
(2) A meter wave radar height measurement method based on lobe splitting. The method utilizes the phase relation of the split lobes of different antennas to determine the elevation angle interval of the target, carries out amplitude comparison processing on the received signal to extract a normalized error signal, and finally obtains the height of the target according to the normalized error signal and the elevation angle interval table look-up. The mean square error of the fluctuation on the ground is not more than 1m, the signal-to-noise ratio reaches 16dB, and the height measurement precision can reach 1% of the distance. The Niubu Xiao et al published in the electronic journal of 2007 6 months "height measurement method based on Mibo radar with lobe splitting". The method is a low elevation height measurement method of the meter wave radar which only needs 3 antennas in the vertical dimension. The method is only suitable for flat array places, has high requirement on the flatness of the array places, can only reach 1% of the distance in the height measurement precision, and is difficult to meet the practical use requirements of high precision.
(3) An array super-resolution processing height measurement method. The method applies the super-resolution technology in the array signal processing to the resolution of direct wave signals and multipath signals. Including a feature subspace algorithm and a maximum likelihood algorithm. Wherein:
the characteristic subspace algorithm is applied to the problem that direct waves and multipath signals caused by multipath propagation must face the coherence problem when the elevation measurement is carried out at a low elevation angle. However, when the signal source is completely coherent, the rank of the data covariance matrix will be 1, and the existence of the coherent source makes the signal subspace and the noise subspace mutually permeate, so that the steering vectors of some coherent sources are not completely orthogonal to the noise subspace, which may degrade the performance of many classical feature subspace-like algorithms, or even completely fail.
The maximum likelihood algorithm has simple thought and excellent performance, and has good performance under high signal-to-noise ratio and low signal-to-noise ratio, but the likelihood function solution is a nonlinear multidimensional optimization problem, multidimensional grid search is needed, the calculated amount increases exponentially along with the increase of the number of targets, and the realization process is complicated. For example, a paper published by "low elevation angle processing algorithm of meter wave radar based on differential preprocessing" in the electronic and information science and newspaper in 2009 by zhao shin et al, a paper published by "array interpolation ML meter wave radar height measurement method" in the electric wave science and newspaper in 2009 in 8 months by kui army et al, and a paper published by "maximum likelihood super-resolution height measurement technology research of meter wave radar" in the radar science and technology in 2011 in 9 months by yanxueya et al are disclosed by.
Among the above methods, method 1 is difficult to realize; the method 2 is only suitable for flat position, has poor precision and can not meet the actual requirement; the method 3 has large calculation amount, requires a large number of samples, and has performance reduction and even failure in a multipath environment. Therefore, in the process of processing the problem of low elevation angle height measurement, the existing various height measurement methods have poor effectiveness and are not applicable any more.
Disclosure of Invention
The invention aims to provide a meter wave radar height measurement method based on array interpolation compressed sensing to further reduce the operation amount and improve the angle measurement precision of DOA (direction of arrival) under the condition of low signal-to-noise ratio, aiming at the defects of the prior art.
In order to achieve the purpose, the technical idea of the invention is as follows:
the method comprises the steps of obtaining a virtual array with array elements P, P & gt M by performing array interpolation on M array elements, so that the dimension of array measurement signals is increased, then performing compression sampling on the measurement signals of the virtual array, and finally obtaining the target direction of arrival through sparse reconstruction.
The concrete implementation steps comprise:
(1) extracting a target signal from a radar echo to obtain an array flow pattern matrix V of a real array, and performing clutter cancellation and interference cancellation on the target signal to obtain a target signal x after cancellation and an airspace sparse signal S, wherein the relationship between the target signal x after cancellation and the airspace sparse signal S is as follows:
x=ψS+n，
wherein psi represents an ultra-complete redundant dictionary, the length of the dictionary is c, and n represents white Gaussian noise;
(2) roughly measuring the elevation angle of the offset target signal x by using a digital beam forming method DBF to obtain a roughly measured angle alpha, and further obtaining an airspace O where the elevation angle of the target signal is;
(3) dividing the airspace O into P parts, wherein P > M represents the number of array elements to obtain an airspace matrix theta:
Θ=[αl,αl+Δα,…,αr],
wherein,the left border of the theta is represented,the right border of the theta is represented,represents half-power beamwidth, Δ α is the step size, Δ α =0.1 °;
(4) carrying out array interpolation processing on the real array to obtain an array flow pattern matrix W of the virtual arrayI(ii) a Array flow pattern matrix W according to virtual arrayIAnd an array flow pattern matrix W of the real array to obtain an interpolation transformation matrix B;
(5) the interpolation transformation matrix B is subjected to pre-whitening treatment to obtain a whitening interpolation transformation matrix TI；
(6) Will cancelIs projected onto the whitening interpolation transformation matrix TIObtaining a measurement signal z of the virtual array;
(7) carrying out compression sampling on the measurement signal z by using an F multiplied by P dimension observation matrix phi, wherein F is less than P, and obtaining an F multiplied by 1 dimension observation signal y;
(8) interpolating a transformation matrix T from the observed signal y and the whiteningIOrthogonal matching tracking method in greedy tracking algorithm, pass-throughIteration, namely selecting a local optimal solution to gradually approximate the space domain sparse signal S to obtain an estimated value of the space domain sparse signal S
Wherein | | | purple hair1Representing solving vector 1-norm, s.t representing constraint condition, | | | | | purple2Representing the calculation of a vector 2-norm, psi represents an ultra-complete redundant dictionary, c represents the length of the ultra-complete redundant dictionary psi, i =1,2, …, c, beta represents the noise standard deviation;
(9) defining a target angular range of 6= [ theta ])1,θ2,…,θi,…,θc],Based on the estimated valueOne-to-one correspondence of elements of (a) to elements of theta, i.e.And thetaiCorresponding to each other to obtain a target angle measurement result thetad，d∈i：
Wherein d represents an estimated valueElements s other than zerodA subscript of (a);
(10) according to the target angle measurement result thetadAnd a known target distance R, and obtaining the target height through triangular transformation:
H=Rsin(θd)。
compared with the prior art, the invention has the following advantages:
1) the invention reduces the side lobe of signal power spectrum and space spectrum because of adopting array interpolation processing to the target signal, effectively improves the performance of the height measurement method of the meter wave radar, and provides an effective solution for the height measurement problem of low elevation under the multipath environment, especially under the environment with low signal-to-noise ratio and less snapshot number.
2) The invention adopts the observation matrix to carry out compression sampling processing on the measured signal, thereby not only reducing the operation amount and improving the estimation precision, but also obtaining a better target signal estimation result when the number of samples is less than that of other methods.
Simulation results show that the method can be directly used for estimating the direction of arrival of the coherent signals and has higher angle resolution.
Drawings
The advantages and effects of the method of the present invention are further described below with reference to the accompanying drawings.
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a graph comparing the performance curves of the present invention and two prior art altimetry methods with varying signal-to-noise ratios;
FIG. 3 is a comparison of the results of the target angle estimation of the present invention and two prior art altimetry methods;
FIG. 4 is a comparison of measured angle error results from measured data processing according to the present invention and a prior art method.
Detailed Description
The contents and effects of the present invention will be described in detail below with reference to the accompanying drawings.
Referring to fig. 1, the present invention includes the steps of:
step 1: and extracting a target signal from the radar echo to obtain an array flow pattern matrix W of the real array.
The array radar is a vertically arranged uniform linear array which is composed of M array elements with the interval d.
If K far-field narrow-band signals are incident to the uniform linear array, M>K, signal incident angle of alphaiI =1,2, …, K, the target signal received by the array at time t is:
X(t)=Vs(t)+n(t)，
wherein, X is the M multiplied by 1 dimensional array element receiving data, n is the M multiplied by 1 dimensional white noise, and the zero mean and the variance are sigma2The output noise of each array element is statistically independent; s = [ s ]1,s2,…，si,…，sK]TA signal vector of dimension K × 1; w is an M multiplied by K dimensional array flow pattern matrix:
W=[v(α1),v(α2),…，v(αi),…，v(αK)]，
wherein,for the steering vector of the ith target signal, the superscript T denotes transposition and λ denotes radar signal wavelength.
Step 2: performing clutter cancellation and interference cancellation processing on the target signal X (t) to obtain a cancelled target signal x; and reconstructing the target signal x after cancellation by adopting a space grid division method to obtain a space domain sparse signal S.
Since the clutter-cancellation and interference-cancellation processing on the target signal x (t) belongs to the conventional processing of radar signals, and is not necessarily related to the main content of the present invention, it is not described.
In order to express the space domain sparsity of the target signal x after cancellation, the target signal x after cancellation is processed by adopting space grid division, namely, the space is divided into (alpha) from-180 degrees to 180 degrees1,α2,…,αu,…,αU}，αuIs the U-th angle interval, U =1,2, …, U, U > K;
suppose each alphauAre all related to a target signal suCorrespondingly, a spatial domain sparse signal of U × 1 dimension is constructed: s = [ S ]1,s2,…,su,…,sU]TProjecting the compensated target signal xAnd when the space domain sparse signal S is obtained, only the elements of K positions where the target signal actually exists in the space domain sparse signal S are not zero, and the elements of the other U-K positions are all zero:
S=(x-n)ψ-1，
wherein, the superscript T represents transposition, and psi is an ultra-complete redundant dictionary; the target information contained in x and S is identical, except that x is the representation of the target signal in the array element domain, and S is the representation of the target signal in the space domain.
From the above equation, the target signal x after cancellation can also be written as:
x=ΨS+n。
and step 3: and carrying out angle rough measurement on the target signal x after cancellation by using a digital beam forming method DBF to obtain a rough measurement angle alpha, and further obtaining an airspace O where the elevation angle of the target signal is located.
3a) Using a guide vector v (ξ) = [1, e ]-j2πsin(ξ),…,e-j2π(M-1)sin(ξ)]TAnd carrying out weighted summation on the cancelled target signal x to obtain a rough measurement angle alpha:
wherein argmax represents the parameter for finding the maximum cost function, xi represents the target search angle range, -180 DEG and xi is 180 DEG, L represents the fast beat number, M represents the number of array elements, and x (t)l) Representing the target signal after cancellation, tlRepresenting sampling time, L is more than or equal to 1 and less than or equal to L, superscript T represents transposition, and superscript H represents conjugate transposition;
3b) using half power beamwidthObtaining the space degree at which the target angle is located:
wherein, λ represents radar signal wavelength, and d represents array element spacing.
And 4, step 4: dividing the airspace O into P parts to obtain an airspace matrix theta, P > M, wherein M represents the number of array elements:
Θ=[αl,αl+Δα，…，αr]，
wherein,the left border of the theta is represented,the right border of the theta is represented,representing half-power beamwidth, Δ α is the step size, Δ α =0.1 °.
And 5: carrying out array interpolation processing on the real array to obtain an array flow pattern matrix W of the virtual arrayI。
The real array is subjected to array interpolation processing, namely virtual array elements are added among the array elements of the real array to enlarge the dimension of the array flow pattern matrix W of the real array and obtain the M multiplied by P dimension array flow pattern matrix W of the virtual arrayI：
WI=[vI(αl)，vl(αl+Δα)，…，vI(αj)，…，vI(αr)]，
Wherein,representing the steering vector of the jth target signal of the virtual matrix, M representing the number of array elements, superscript T representing the transposition, alphaj∈Θ，Θ=[αl,αl+Δα,…,αr]Δ α is the step size, Δ α =0.1 °.
Step 6: array flow pattern matrix W according to virtual arrayIAnd obtaining an interpolation transformation matrix B by the array flow pattern matrix W of the real array, and calculating according to the following two conditions:
array flow pattern matrix W according to virtual array without considering noiseIAnd the fixed relation between the array flow pattern matrix W and the interpolation transformation matrix B of the real array: b isHW=WIAnd steering vectors of real arraysAnd the steering vector v of the virtual arrayI(αj) Fixed relation to the interpolating transformation matrix B:
to derive an interpolated transformation matrix B:
B=WIWH(WWH)-1，
wherein,a steering vector representing the real array,
a steering vector representing a virtual matrix, a superscript H representing a conjugate transpose,representing the angle of incidence, alpha, of the target signal before cancellationj∈Θ，Θ=[αl,αl+Δα,…,αr]Δ α is the step size, Δ α =0.1 °;
in the case of noise consideration, the array flow pattern matrix W is based on a virtual arrayIAnd the fixed relation between the array flow pattern matrix W and the interpolation transformation matrix B of the real array: b isH(W+N)=WI+NIAnd steering vectors of real arraysAnd the steering vector v of the virtual arrayI(αj) Fixed relation to the interpolating transformation matrix B:
to derive an interpolated transformation matrix B:
where N represents the noise matrix of the real array and NIA noise matrix representing a virtual matrix, N representing a noise vector of N, NIRepresents NIThe noise vector of (a) is calculated,in order to be the power of the signal,i is the identity matrix.
And 7: the interpolation transformation matrix B is subjected to pre-whitening treatment to obtain a whitening interpolation transformation matrix TI。
7a) Autocorrelation matrix R for interpolation transformation matrix BBAnd (3) carrying out characteristic value decomposition:
RB=B(BHB)-1BH=QΣQH,
where Q denotes an orthogonal matrix, Q = B, Σ denotes a diagonal matrix, Σ = (B)HB)-1The superscript H denotes conjugate transpose;
7b) obtaining a whitening interpolation transformation matrix T through a pre-whitening formula according to the orthogonal matrix Q and the diagonal matrix sigmaI：
TI=Σ1/2QH=(BHB)-1/2BH。
And 8: projecting the target signal x after cancellation to a whitening interpolation transformation matrix TIObtaining a P × 1 dimensional measurement signal of the virtual array: z = TIx=TIψS+TIn, where ψ denotes an overcomplete redundant dictionary, n denotes white noise, and S denotes nullA domain sparse signal.
And step 9: carrying out compression sampling on the measurement signal z by using an F multiplied by P dimension observation matrix phi, wherein F is less than P, namely the dimension of the measurement signal z is reduced to obtain an F multiplied by 1 dimension observation signal y:
y=φz=φTIψs+φTIn。
step 10: interpolating a transformation matrix T from the observed signal y and the whiteningIOrthogonal matching tracking method in greedy tracking algorithm, pass-throughIteration, namely selecting a local optimal solution to gradually approximate the space domain sparse signal S to obtain an estimated value of the space domain sparse signal S
Wherein | | | purple hair1Expression vector solving1-norm, s.t representing constraint, | | | | non-volatile wind2The vector 2-norm is calculated, psi is used for an ultra-complete redundant dictionary, c is used for the length of the ultra-complete redundant dictionary psi, and i =1,2, …, c and beta are used for noise standard deviation.
Step 11: defining a target angular range θ = [ ]1,θ2,…,θi,…,θc]，Based on the estimated valueOne-to-one correspondence of elements of (a) to elements of theta, i.e.And thetaiCorresponding to each other to obtain a target angle measurement result thetad，d∈i：
Wherein d represents an estimated valueElements s other than zerodSubscripts of (a).
Step 12: according to the target angle measurement result thetadAnd a known target distance R, and obtaining the target height through triangular transformation:
H=Rsin(θd)。
the advantages and effects of the invention are further illustrated by the following computational simulation and measured data processing results:
1. simulation conditions
In the simulation process, aiming at equidistant array formed by 20 vertically arranged horizontal polarization antenna array elements, the radar is raised by 20m, the ground reflection coefficient is-0.95, the carrier frequency is 300MHz, only the mirror reflection of the ground is considered, 9 virtual array elements are interpolated between every two array elements, the total array element number of the obtained interpolated array is 191, and the observation matrix dimension is 20.
2. Emulated content
Simulation one: selecting a single static target, and respectively carrying out angle measurement precision simulation on the low elevation angle target by using the existing forward and backward space smooth multiple signal classification method, the alternative projection maximum likelihood method and the invention under the conditions that the distance between the target and a reference antenna is 200km, the direct arrival angle of the target is 2 degrees, the multipath reflection angle is-2.01 degrees, the signal-to-noise ratio of array elements is changed from-10 dB to 30dB, and the fast beat number is 10. The simulation results are shown in fig. 2. Wherein:
the horizontal axis represents the change of the signal-to-noise ratio from-10 dB to 20 dB, and the vertical axis represents the angle measurement error;
the SS-MUSIC represents the angle measurement error of the forward and backward space smooth multiple signal classification method when the signal-to-noise ratio changes according to the horizontal axis,
APML represents the angle error of the alternative projection maximum likelihood method when the signal-to-noise ratio varies along the horizontal axis,
IA-CS represents the angle measurement error of the present invention when the signal-to-noise ratio varies along the horizontal axis.
From fig. 2, it can be derived that, for the angle measurement of the low elevation angle target, the angle measurement error of the existing forward and backward space smooth multiple signal classification method and the alternative projection maximum likelihood method is large, while the angle measurement error of the present invention is minimum.
Simulation II: selecting a single target, and respectively simulating the influence of different elevation angles on algorithm estimation precision by using the existing forward and backward space smooth multiple signal classification method, the alternative projection maximum likelihood method and the method under the conditions that the height of the target is 12000m, the radial direction flies from 50km to 650km, the half wavelength of the array element spacing, the signal-to-noise ratio is 10dB, the snapshot number is 10 and the Monte Carlo experiment times are 100. The simulation results are shown in fig. 3. Wherein:
FIG. 3 (a) is an elevation angle of a conventional forward-backward spatial smoothing multiple signal class method when the distance between a target and a position changes along the horizontal axis;
FIG. 3 (b) is an elevation angle of a conventional alternative projection maximum likelihood method when the distance between the target and the position varies along the horizontal axis;
fig. 3 (c) shows the elevation angle of the present invention when the distance between the target and the location varies along the horizontal axis.
The horizontal axis in fig. 3 represents the distance of the target from the place varying from 0km to 650km, and the vertical axis represents the elevation angle.
It can be derived from fig. 3 that, for the angle measurement of the low elevation angle target, the angle measurement error of the existing forward and backward space smooth multiple signal classification method and the alternative projection maximum likelihood method is large, while the angle measurement error of the present invention is minimum.
3. Angle measurement result of measured data of certain warning radar
The measured data of the warning radar is subjected to angle measurement by using the method and the existing forward and backward space smooth multiple signal classification method, and the angle measurement error is shown in figure 4. Wherein:
the horizontal axis represents the distance between the target and the position, and the vertical axis represents the angle measurement error when the distance changes along with the horizontal axis;
SS-MUSIC represents the angle measurement error of the forward and backward space smooth multiple signal classification method;
IA-CS represent the angle measurement error of the present invention.
As can be seen from fig. 4, the angle measurement error of the conventional forward and backward spatial smoothing multiple signal classification method is large, while the angle measurement error of the present invention is small.
Claims (4)
1. A height finding method based on array interpolation compressed sensing comprises the following steps:
(1) extracting a target signal from a radar echo to obtain an array flow pattern matrix W of a real array, and performing clutter cancellation and interference cancellation on the target signal to obtain a target signal x after cancellation and an airspace sparse signal S, wherein the relationship between the target signal x after cancellation and the airspace sparse signal S is as follows:
x＝ψS+n，
wherein psi represents an ultra-complete redundant dictionary, the length of the dictionary is c, and n represents white Gaussian noise;
(2) roughly measuring the elevation angle of the offset target signal x by using a digital beam forming method DBF to obtain a roughly measured angle alpha, and further obtaining an airspace O where the elevation angle of the target signal is;
(3) dividing the airspace O into P parts, wherein P > M represents the number of array elements to obtain an airspace matrix theta:
Θ＝[αl,αl+Δα,…,αr],
wherein,the left border of the theta is represented,the right border of the theta is represented,represents the half-power beamwidth, Δ α is the step size, Δ α is 0.1 °;
(4) carrying out array interpolation processing on the real array to obtain an array flow pattern matrix W of the virtual arrayI(ii) a Array flow pattern matrix W according to virtual arrayIAnd an array flow pattern matrix W of the real array to obtain an interpolation transformation matrix B;
(5) the interpolation transformation matrix B is subjected to pre-whitening treatment to obtain a whitening interpolation transformation matrix TI；
(6) Projecting the target signal x after cancellation to a whitening interpolation transformation matrix TIObtaining a measurement signal z of the virtual array;
(7) carrying out compression sampling on the measurement signal z by using an F multiplied by P dimension observation matrix phi, wherein F is less than P, and obtaining an F multiplied by 1 dimension observation signal y;
(8) interpolating a transformation matrix T from the observed signal y and the whiteningIOrthogonal matching tracking method in greedy tracking algorithm, pass-through≤β2Iteration, namely selecting a local optimal solution to gradually approximate a sparse signal S in a space domain to obtain spaceEstimation of domain sparse signal S
Wherein | | | purple hair1Representing solving vector 1-norm, s.t representing constraint condition, | | | | | purple2The vector 2-norm is obtained, i is 1,2, …, c and beta represents the standard deviation of noise;
(9) defining a target angle range theta ═ theta1,θ2,…,θi,…,θc]，Based on the estimated valueOne-to-one correspondence of elements of (a) to elements of theta, i.e.And thetaiCorresponding to each other to obtain a target angle measurement result thetad，d∈i：
Wherein d represents an estimated valueElements of middle or non-zeroA subscript of (a);
(10) according to the target angle measurement result thetadAnd a known target distance R, and obtaining the target height through triangular transformation:
H＝Rsin(θd)。
2. the array interpolation compressed sensing altimetry method according to claim 1, wherein in the step (2), an elevation angle rough measurement is performed on the cancelled target signal x by using a digital beam forming method DBF to obtain a rough measurement angle α, and further obtain an airspace o where the elevation angle of the target signal is located, and the method comprises the following steps:
2a) using guide vectorsAnd weighting and summing the x to obtain a rough measurement angle alpha:
wherein argmax represents the parameter for finding the largest cost function, xi represents the target search angle range, -180 DEG.xi.180 DEG, L represents the fast beat number, x (tl) Representing the target signal after cancellation, tlRepresenting sampling time, L is more than or equal to 1 and less than or equal to L, superscript T represents transposition, and superscript H represents conjugate transposition;
2b) using half power beamwidthObtaining the space degree at which the target angle is located:
wherein, λ represents radar signal wavelength, and d represents array element spacing.
3. The array interpolation compressed sensing altimetry method according to claim 1, wherein the array interpolation processing for the real array in step (4) is to add virtual array elements between the array elements of the real array to expand the dimension of the array flow pattern matrix W of the real array, so as to obtain the M × P dimension array flow pattern matrix W of the virtual arrayI：
WI＝[vI(αl),vI(αl+Δα),…,vI(αj),…,vI(αr)]，
Wherein,steering vector, alpha, representing the jth target signal of the virtual matrixj∈Θ。
4. The array interpolation compressed sensing altimetry method according to claim 1, wherein the array flow pattern matrix W according to the virtual array in step (4)IAnd obtaining an interpolation transformation matrix B by the array flow pattern matrix W of the real array, and calculating according to the following two conditions:
array flow pattern matrix W according to virtual array without considering noiseIAnd the fixed relation between the array flow pattern matrix W and the interpolation transformation matrix B of the real array: b isHW＝WIAnd steering vectors of real arraysAnd the steering vector v of the jth target signal of the virtual arrayI(αj) Fixed relation to the interpolating transformation matrix B:to derive an interpolated transformation matrix B:
B＝WIWH(WWH)-1
wherein,a steering vector representing the real array,
a steering vector representing the jth target signal of the virtual matrix,representing the angle of incidence, alpha, of the target signal before cancellationj∈Θ；
In the case of noise consideration, the array flow pattern matrix W is based on a virtual arrayIAnd the fixed relation between the array flow pattern matrix W and the interpolation transformation matrix B of the real array: b isH(W+N)＝WI+NITo do so byAnd the steering vector of the real arrayAnd the steering vector v of the jth target signal of the virtual arrayI(αj) Fixed relation to the interpolating transformation matrix B:to derive an interpolated transformation matrix B:
where N represents the noise matrix of the real array and NIA noise matrix representing a virtual matrix, N representing a noise vector of N, NIRepresents NIThe noise vector of (a) is calculated,in order to be the power of the signal,i is the identity matrix.
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