CN117970231A - Millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM - Google Patents
Millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM Download PDFInfo
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Abstract
The invention belongs to the technical field of radars, and particularly relates to a millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM, which comprises the steps of transmitting and receiving signals, constructing an original radar echo data block, constructing a range Doppler coherent accumulation and target detection, constructing a range Doppler domain array single snapshot receiving signal, compensating a moving target coupling Doppler phase, minimizing a range Doppler domain atomic norm, performing Toeplitz matrix vandermonde decomposition, obtaining a Toeplitz matrix T (u) through solving an equivalent semi-positive rule form of a model, and carrying out frequency retrieval on the T (u) to obtain a DOA estimated value of a target. The invention can obtain higher resolution and estimation precision of the angle of measurement based on the conditions of limited array aperture and low signal-to-noise ratio and on the premise of single snapshot processing, and has the steady performance of processing coherent signals without sacrificing the array aperture.
Description
Technical Field
The invention belongs to the technical field of radars, in particular relates to a moving target arrival azimuth estimation method, and particularly relates to a super-resolution DOA estimation method of a millimeter wave radar moving target based on RD-ANM, which can be used for estimating the arrival azimuth of a moving target of a vehicle-mounted millimeter wave radar.
Background
The vehicle radar aims at acquiring comprehensive and accurate road conditions and environment information in real time, and assisting drivers in making decisions and guaranteeing driving safety. Millimeter wave Radar (MILLIMETER WAVE RADAR, MMW Radar) has high resolution, small volume, good environmental adaptability, high performance and low cost due to high working frequency, and is often regarded as one of core components in the field of active safety of automobiles. At present, research hotspots of vehicle-mounted millimeter wave radars mainly focus on 4D (Four Dimensions) imaging, and the requirement for multi-dimensional high-resolution accurate measurement of target distance-Doppler-azimuth-pitch angle is increasing. In order to meet the high performance requirements of target arrival azimuth (Direction Of Arrival, DOA) estimation precision and angular resolution, and considering the practical system design cost and implementation, a vehicle-mounted millimeter wave radar usually adopts a time division multiplexing-multiple input multiple output (Time Division Multiplexing-Multiple Input Multiple Output, TDM-MIMO) system, and a linear frequency modulation continuous wave (Linear Frequency Modulation Continuous Wave, LFMCW) signal is transmitted to perform channel separation at a receiving end and synthesize an equivalent virtual array, so that a larger array aperture can be obtained, and the angular resolution and estimation precision of a DOA estimation algorithm are improved. In addition to improvement of hardware performance, improving the resolution and accuracy of DOA estimation by a signal processing method of super-resolution DOA estimation is also an important research topic of millimeter wave radar. However, situations such as limited array aperture, fewer snapshots, low signal-to-noise ratio and source coherence are often faced in a vehicle-mounted scene, so how to accurately acquire the azimuth angle information of the moving target wave in the irrational external environment to complete the detection of the target through multi-dimensional information fusion, and thus, the method acts on the following positioning, tracking, identifying and classifying of the target is one of the important problems faced by the vehicle-mounted millimeter wave radar.
Aiming at the problem of estimating the azimuth angle of the moving target of the vehicle-mounted millimeter wave radar, the following common methods exist at present:
The first method is a non-parametric model spectrum estimation algorithm based on measurement data, such as CBF, capon and IAA, which is simple and easy to implement, but is limited by array aperture or signal to noise ratio conditions, and has certain limitations on angular resolution and accuracy.
The second method is a traditional super-resolution estimation algorithm based on subspace decomposition or fitting, such as MUSIC, ML and WSF, and can break through the limitation of array Rayleigh limit to realize DOA super-resolution accurate estimation, but the second method essentially belongs to a parameterization method, the algorithm performance is seriously dependent on preset model parameters, is sensitive to model errors, and has higher requirements on the signal external environment such as snapshot number, signal-to-noise ratio condition and signal source correlation.
The third method is a gridding super-resolution DOA estimation algorithm based on sparse signal representation and compressed sensing theory, such as OMP-DOA, L1-SVD, RVM-DOA and the like, the algorithm is modeled sparsely in a discrete angle domain, the dependence on array aperture is low, the accurate estimation of DOA can be realized under irrational external environments such as few snapshots (even single snapshots), low signal to noise ratio, source correlation/coherence and the like, but the problem of estimating dictionary mismatch by inherent DOA caused by idealized grid assumption exists, and although a learner subsequently proposes technologies such as increasing grid division density, grid uneven division, dictionary self-correction and the like to further correct model errors, the problem of grid mismatch is relieved, but the improvement of algorithm performance is further limited by the increase of calculation instability and conflict with accurate sparse reconstruction conditions.
The method is limited in direction-finding resolution and poor in azimuth resolution, and cannot meet the high-performance requirement of the vehicle millimeter wave on target direction finding. The second algorithm depends on model parameters, and has high requirements on actual application scenes and external signal environments. The third method is based on grid division, has the problem of inherent dictionary mismatch, and restricts the further improvement of algorithm precision and resolution.
Disclosure of Invention
Aiming at the defects of the existing vehicle-mounted millimeter wave radar moving target DOA estimation method, the invention provides a millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM, which can obtain higher angular resolution and estimation precision based on the conditions of limited array aperture and low signal-to-noise ratio and on the premise of single snapshot processing, and has the steady performance of processing coherent signals without sacrificing the array aperture.
The invention discloses a millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM, which comprises the following steps:
step 1) transmitting and receiving signals: each transmitting antenna of the TDM-MIMO array transmits LFMCW signals in a mode of time-sharing alternate circulation operation, and the receiving array sequentially receives corresponding radar echo signals;
Step 2) constructing an original radar echo data block: performing deskewing operation, analog-to-digital conversion and channel separation and merging processing on radar echo signals sequentially received by the TDM-MIMO receiving array, and finally forming an original radar echo Data (Raw Data) block X of the vehicle-mounted millimeter wave radar;
Step 3) range-doppler coherent accumulation and target detection: performing distance Doppler two-dimensional coherent accumulation on an original radar echo data block X of the vehicle-mounted millimeter wave radar to obtain a Range-Doppler Map (RDM) matrix block D of the vehicle-mounted millimeter wave radar, performing target detection processing based on the D, and resolving to obtain target distance and movement speed information;
Step 4), distance Doppler domain array single snapshot received signal construction and moving target coupling Doppler phase compensation: based on D, constructing a Range-Doppler (RD) domain equivalent virtual single-input-multiple-output (Single Input Multiple Output, SIMO) array based on moving target radar echo to receive a single snapshot signal, and compensating a moving target coupling Doppler phase contained in the signal;
(5) Distance Doppler domain atomic norm minimization and Toeplitz matrix vandermonde decomposition: and carrying out frequency preprocessing on the single snapshot signal received by the RD domain equivalent SIMO array, constructing a denoising problem model based on RD domain atomic norm minimization according to an atomic norm theory, obtaining a Toeplitz matrix T (u) by solving an equivalent semi-positive planning form of the model, and carrying out frequency retrieval on the T (u) to obtain a DOA estimated value of the target.
Compared with the prior art, the invention has the following specific advantages:
Firstly, obtaining higher angular resolution and estimation accuracy based on array aperture limitation, low signal-to-noise ratio condition and single snapshot processing precondition: the invention synthesizes the virtual SIMO array according to the TDM-MIMO radar, so that the aperture of the original array is greatly expanded; based on the two-dimensional coherent accumulation of the distance Doppler direction, a virtual SIMO array is constructed in the distance-Doppler domain to receive the single snapshot signal for direction finding of the moving target, so that the signal-to-noise ratio of angle dimension processing is greatly improved; target direction finding is carried out by solving the problem of atomic norm minimization of the range Doppler domain, and the method has higher resolution and accuracy of angle measurement.
Second, possess robust performance that does not sacrifice array aperture processing of coherent signals: according to the invention, the process of reconstructing the sparse signal by using the compressed sensing/sparse representation framework is still basically carried out according to the atomic norm theory, so that the target signal can be decohered without any preprocessing as long as the target space division of the incident signal enables the target space division of the incident signal to meet the sparse characteristic, and the coherent signal can be processed on the premise of not sacrificing the aperture of the array.
Drawings
FIG. 1 is a flowchart of an implementation of a millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM in an embodiment of the present invention;
FIG. 2 is a schematic diagram of a result of performing moving object arrival azimuth estimation by using a millimeter wave radar moving object super-resolution DOA estimation method based on RD-ANM in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a result of resolving a coherent source by using a millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM in an embodiment of the present invention;
fig. 4 is a graph comparing the results of estimating the azimuth angle of arrival of a moving object by using the first and second conventional methods and the method of the present invention, respectively.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
Example 1
Because of the need of forming an effective compact target point cloud, the vehicle millimeter wave radar has higher requirements on the processing capacity of the angle dimension, and besides a larger angle measurement range, the vehicle millimeter wave radar is expected to have higher angle measurement precision and resolution. Under the precondition of limited hardware resources, the vehicle millimeter wave radar further expands the aperture of the physical array by adopting a TDM-MIMO system, thereby improving the angular resolution and the estimation precision of the DOA estimation algorithm. However, non-ideal signal environments are often faced under a vehicle-mounted scene, for example, when a target moves at a high speed, the range migration causes the reduction of coherent accumulation time, and a large amount of independent uniformly-distributed snapshot data cannot be obtained; when the radar itself has limited transmitting power, millimeter wave atmospheric propagation attenuation is larger, and the scattering sectional area of the target is smaller, the signal-to-noise of the received signal is lower; when multipath reflected by the ground or other objects exists in the detection scene or signals from the close-proximity targets with the same distance and the same speed are contained, the received signals contain related (coherent) signals, and the targets to be detected of the millimeter wave radar are mostly moving targets such as vehicles, riders, pedestrians and the like. The invention further provides a millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM, which comprises the following steps with reference to FIG. 1:
(1) Transmitting and receiving signals: each transmitting antenna of the TDM-MIMO array transmits LFMCW signals s T (t) in a mode of time-sharing alternate circulation operation, and the receiving array sequentially receives corresponding radar echo signals Wherein: t represents the time within a pulse, m t represents the transmit element index, and m r represents the receive element index;
(2) Original radar echo data block construction: radar echo signals sequentially received by TDM-MIMO receiving array Performing declivity operation to obtain array receiving difference frequency baseband analog signals/> Analog-to-digital conversion is carried out to obtain an array receiving difference frequency baseband digital signal/>Will/>And carrying out channel separation and combination processing to finally form a receiving difference frequency baseband digital signal X (n, l) of an equivalent SIMO array and an original echo data block X of the vehicle millimeter wave radar, wherein: n represents the fast time variable, l represents the Chirp index during one coherent processing cycle (Coherent Processing Interval, CPI);
(3) Range-doppler coherent accumulation and target detection: performing distance Doppler two-dimensional coherent accumulation on an original radar echo data block X of the vehicle-mounted millimeter wave radar, forming distance Doppler domain receiving data D (q, p) of an equivalent SIMO array and a RDM matrix block D of the vehicle-mounted millimeter wave radar, performing incoherent accumulation, two-dimensional unit average Constant false alarm (CELL AVERAGING-Constant FALSE ALARM RATE, CA-CFAR) detection and Peak Grouping (Peak Grouping) processing on the basis of the D, performing target detection and obtaining corresponding distance and movement speed information of the target Wherein: /(I)Expressing the target distance dissociation calculation value,/>The target motion velocity solution value is represented, q represents the distance dimension DFT conversion result index, and p represents the doppler dimension DFT conversion result index.
(4) Range-doppler domain array single snapshot received signal construction and moving-target coupled doppler phase compensation. Extracting equivalent SIMO array RD domain receiving data D (q peak,ppeak) at a peak distance Doppler unit (q peak,ppeak) in D, constructing RD domain equivalent virtual SIMO array receiving single snapshot signal y based on moving target radar echo, and constructing a compensation vector Γ to compensate the moving target coupling Doppler phase coupled on an array target guiding vector in y to obtain y';
(5) Distance Doppler domain atomic norm minimization and Toeplitz matrix vandermonde decomposition: performing frequency preprocessing on y' to obtain a final required RD domain array receiving single snapshot signal y vir, constructing atoms and atom sets according to an atomic norm theory and a signal form of y vir, constructing a denoising problem model based on RD domain atomic norm minimization, converting the model into an equivalent semi-positive rule problem to solve, and finally performing frequency retrieval on a Toeplitz matrix T (u) obtained by solving to obtain a DOA estimated value corresponding to the target
In addition, the method can obtain a corresponding target orientation by constructing a distance Doppler domain atomic norm denoising problem model and solving an equivalent semi-positive rule form, thereby obtaining higher angle measurement resolution and estimation precision under the conditions of limited array aperture, low signal-to-noise ratio and single snapshot processing, and carrying out decoherence processing on coherent signals without sacrificing array aperture.
Example 2
The millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM is the same as that of the embodiment 1, wherein the step (4) comprises the following steps of the construction of a distance Doppler domain array single snapshot receiving signal and the Doppler phase compensation of moving target coupling:
4a) Range-doppler domain array single snapshot received signal construction. Extracting equivalent SIMO array RD domain receiving data D (q peak,ppeak) at a peak distance Doppler unit (q peak,ppeak) for the RDM matrix block D obtained in the step 3, and constructing an RD domain equivalent virtual SIMO array receiving single snapshot signal y based on moving target radar echo, wherein the specific expression of y is as follows:
Wherein, Represents targets distributed in the peak distance-doppler cell (q peak,ppeak), K represents the total number of targets, a ' (θ) = [ a ' (θ 1),a'(θ2),...,a'(θZ) ] represents the array manifold of the virtual SIMO array, a ' (θ z)＝a(θz) # -represents the virtual SIMO array target steering vector including the moving target doppler coupling phase,The target steering vector representing the virtual SIMO array,Representing a moving target doppler phase vector, s= [ s 1,...,sZ]T,The signal vector and the signal of the z target are respectively represented as a target, w represents the additive white gaussian noise after 2D-DFT processing at each array receiving channel, α z、φz represents the signal amplitude and the fixed phase of the z target, f s represents the ADC sampling rate, n=1, N represents the fast time variable, N represents the number of ADC sampling points in one Chirp, and/>Respectively, the distance and doppler frequency of the z-th target, l=1,..l represents the Chirp index within one CPI, L represents the number of chirps contained within one CPI, and T represents the transpose operator.
4B) Moving target coupled Doppler phase compensation. Because of the switching mechanism of the transmitting antennas under the TDM-MIMO system, a time difference exists between LFMCW signals from different transmitting antennas, the Doppler frequency of a moving object and the phase change caused by the time difference can be coupled to the virtual SIMO array object guiding vector, and thus the object moving speed calculated value obtained in the step 3The compensation vector Γ ' is constructed to compensate the moving target coupling Doppler phase contained in y, so that the specific expression of the compensated RD domain equivalent virtual SIMO array receiving single snapshot signal y ', y ' is as follows:
Wherein, c z >0 and phi z epsilon 0,2 pi respectively represent the amplitude and phase of s z, a (theta z) represents the virtual SIMO array steering vector of the z-th target, Γ' represents the moving target coupled doppler phase compensation vector, and the specific expression is:
The invention constructs a virtual SIMO array single snapshot receiving signal in a range Doppler domain, analyzes the generation principle and the influence caused by the Doppler coupling phase of a moving target contained in the signal, and constructs a corresponding compensation vector to compensate the coupling phase before measuring the target in the range Doppler domain so as to weaken the influence on the subsequent DOA estimation result.
Example 3
The method for estimating super-resolution DOA of millimeter wave radar moving target based on RD-ANM is the same as that of the embodiment 2, wherein the step (5) of minimizing atomic norms of a range Doppler domain and performing vandermonde decomposition of a Toeplitz matrix specifically comprises the following steps:
5a) And (5) frequency pretreatment. And (3) mapping the value range of the DOA estimation parameter theta of the y' obtained in the step (4) from a continuous angle domain to a normalized continuous frequency domain, thereby obtaining a final required specific expression of the RD domain array receiving single snapshot signal y vir,yvir, wherein the specific expression is as follows:
Wherein, Representing a mapping vector,/>Θ z denotes the azimuth angle of arrival of the z-th target, s denotes the target signal vector, a (f) = [ a (f 1),...,a(fZ) ],The virtual SIMO array guiding vector of the z-th target after normalized frequency pretreatment is represented, lambda represents the emission wavelength, d R represents the array element spacing of the TDM-MIMO receiving array, and M represents the total number of receiving array elements of the virtual SIMO array;
5b) The range-doppler domain atomic norms are minimized. According to the atomic norm theory and the signal form of y vir, defining an atom a (f, phi) and an atom set A, and constructing a denoising problem model of an RD domain based on atomic norm minimization, wherein the specific expression is as follows:
Wherein a= { a (f, Φ) =a (f) e jφ,f∈[0,1),φ∈[0,2π)},||·||A,1 is l 1 atomic norm, and the specific expression is:
the denoising problem based on RD domain atomic norm minimization is converted into an equivalent semi-positive programming form to be solved, and the specific expression of the equivalent SDP problem of the original problem is as follows:
Wherein, Representing a data fitting term, λ representing a non-negative regularization coefficient for balancing the fidelity of y vir and the sparseness of the coefficient vector of the atoms that make up x, u representing the optimized variable to be solved, u 1 representing the first element in u, t representing the free variable, is a regularization term that avoids the occurrence of trivial solutions.
5C) The Toeplitz matrix is vandermonde decomposed. Solving the SDP optimization problem can obtain a Toeplitz matrix T (u), wherein the T (u) has a unique vandermonde decomposition form, and the specific expression of the vandermonde decomposition is as follows:
Wherein r=rank (T (u)) < M, p k > 0, Are not equal to each other. Because of the one-to-one mapping relation between DOA estimation parameters theta and T (u), corresponding DOA estimation values can be obtained by carrying out frequency search on the T (u). Frequency search methods such as Prony's Method, subspace Method, etc., wherein MUSIC is selected, and the final DOA estimation result/>, can be obtained after corresponding frequency is searched
According to the method, the DOA estimated value of the target is obtained by constructing the distance-Doppler domain atomic norm minimization denoising problem model and solving the equivalent semi-positive planning form, so that the coherent signal can be processed without sacrificing the array aperture while the method has higher angle measurement precision and resolution.
A more detailed example is given below to further illustrate how the present invention constructs a range-doppler domain array single snapshot received signal and super-resolution DOA estimation of moving targets based on range-doppler domain atomic norm minimization.
Example 4
Referring to fig. 1, the method for estimating super-resolution DOA of millimeter wave radar moving targets based on RD-ANM in this example includes the steps of constructing a range-doppler domain array single snapshot receiving signal and estimating super-resolution DOA of moving targets based on range-doppler domain atomic norm minimization, and specifically includes the following steps:
step 1, transmitting and receiving signals: each transmitting antenna of the TDM-MIMO array transmits LFMCW signals s T (t) in a mode of time-sharing alternate circulation operation, and the receiving array sequentially receives corresponding radar echo signals
1A) A signal is transmitted. The specific expression of each transmitting antenna of the vehicle millimeter wave radar TDM-MIMO array transmitting LFMCW signals s T(t),sT (t) in a mode of time-sharing alternate circulation operation is as follows:
Where rect (. Cndot.) represents a rectangular window function, Representing imaginary symbols, f c representing the carrier frequency of the transmitted signal, T e [0, T up ] representing the time within the pulse, T up representing the frequency modulation time,/>Represents the chirp rate and B represents the chirp bandwidth.
1B) A signal is received. Consider that the transmitting array is a uniform linear array with the array element number of M TX and the array element spacing of d T, and the receiving array is a uniform linear array with the array element number of M RX and the array element spacing of d R, and in general, d R＝λ/2,dT＝MRXdR. The vehicle millimeter wave radar TDM-MIMO array receiving array sequentially receives corresponding radar echo signals The specific expression of (2) is:
Where λ=f c/c denotes the transmission wavelength, c denotes the speed of light, m t＝1,...,MTX denotes the transmission element index, m r＝1,...,MRX denotes the reception element index, T m＝(l-1)Tint+(mt-1)Tc denotes the inter-pulse time, tc=tup+tidle denotes the Chirp repetition period, T idle denotes the idle time, l denotes the Chirp index, T int＝MTXTc denotes the transmission time interval of a specific transmission antenna, Representing echo time delay, R 0 represents target initial distance, v represents target motion velocity, θ represents target azimuth angle of arrival, σ 0 represents target backscattering coefficient.
Step 2, constructing an original radar echo data block: radar echo signals sequentially received by TDM-MIMO receiving arrayPerforming declivity operation to obtain array receiving difference frequency baseband analog signals/> Analog-to-digital conversion is carried out to obtain an array receiving difference frequency baseband digital signal/>Will/>And carrying out channel separation and merging processing to finally form an original echo data block X of the vehicle millimeter wave radar.
2A) And (5) declivating. Assuming that the airspace contains K far-field targets, the target arrival azimuth angles are respectively theta 1,θ2...,θK. Considering the target low uniform motion temporarily, i.e. the range migration does not exceed a range unit, the radar echo signals sequentially received by the receiving array are received according to the reference signal s T (t) in a coherent processing period (Coherent Processing Interval, CPI)Performing declivity operation to obtain array receiving difference frequency baseband analog signals/> The specific expression of (2) is:
Where k=1,..where K represents the target index, l=1,..where L represents the Chirp index in one CPI, L represents the Chirp number contained in one CPI, σ k represents the backscattering coefficient of the kth target, The echo time delay of the kth target is represented, alpha k、φk、Rk、vk represents the amplitude, fixed phase, initial distance and (uniform) motion speed of the difference frequency baseband analog signal of the kth target, and theta k represents the azimuth angle of arrival of the kth target.
2B) And D, analog-to-digital conversion. Receiving difference frequency baseband analog signals to an arrayAnalog-to-digital conversion is carried out to obtain an array receiving difference frequency baseband digital signal/>And taking the influence of noise into consideration, obtaining an array receiving difference frequency baseband digital signalThe specific expression of (2) is:
Where f s denotes the ADC sampling rate, n=1,..n denotes the fast time variable, N denotes the number of ADC sampling points in one Chirp, Representing the distance and Doppler frequency, respectively,/>, of the kth targetAn additive white gaussian noise with a mean of 0 and a variance of σ 2 is represented.
2C) And (5) channel separation and merging treatment. When the radar starts to work, a first receiving array element corresponding to a first transmitting array element is used as a reference array element, and the array receives a difference frequency baseband digital signalPerforming channel separation and combination processing, and finally forming a receiving difference frequency baseband digital signal X (N, L) of an equivalent virtual single input multiple output (Single Input Multiple Output, SIMO) array and an original radar echo Data (Raw Data) block x=x (N, L) of the vehicle-mounted millimeter wave radar, wherein the specific expression of n=1, N, l=1, L, X (N, L) is as follows:
Wherein, Target steering vector representing virtual SIMO array,/>Representing a transmit array target steering vector,/>Representing a receive array target steering vector, T represents a transpose operator,/>Represents Kronecker product operator, m=1,..m, m=m TX×MRX represents the total number of receive array elements of the virtual SIMO array; a' (θ k)＝a(θk) +.Γ represents the target steering vector of a virtual SIMO array containing the moving target doppler coupling phase, +.i represents the Hadamard product operator, Γ represents the moving target doppler phase vector coupled to the virtual SIMO array target steering vector, Γ has the following specific expression:
Step 3, performing Range-Doppler coherent accumulation and target detection, performing Range-Doppler two-dimensional coherent accumulation on an original radar echo data block X of the vehicle-mounted millimeter wave radar to obtain a Range-Doppler Map (RDM) matrix block D of the vehicle-mounted millimeter wave radar, performing target detection processing based on the D, and calculating to obtain corresponding Range and movement speed information of a target
3A) Range-doppler accumulates toward coherence. Performing 2D-DFT (Two-Dimensional Discrete Fourier Transform) processing of Range direction and Doppler direction on an original radar echo data block X of the vehicle-mounted millimeter wave radar, namely performing Two-dimensional coherent accumulation of the Range direction and the Doppler direction, and receiving data D (q, p) in a Range-Doppler (RD) domain and RDM matrix blocks d=d (q, p) of the vehicle-mounted millimeter wave radar, wherein the specific expressions of the Range-Doppler (Range-Doppler, RD) domain and the RDM matrix blocks d=d (q, p), q=1, and the terms of N, p=1, and the terms of L, D (q, p) are as follows:
Wherein D (q, p) represents the 2D-DFT conversion result of the (q, p) th point.
3B) And (5) detecting a target. And carrying out module value superposition/incoherent accumulation on the RDM matrix block of the vehicle-mounted millimeter wave radar along the array element antenna dimension, carrying out two-dimensional unit average Constant false alarm (CELL AVERAGING-Constant FALSE ALARM RATE, CA-CFAR) detection and Peak Grouping (Peak Grouping) processing, and obtaining a target detection plane. Based on the plane, the in-plane distance unit corresponding to the kth target at the momentAnd Doppler Unit/>The position will present peak value, extract the peak value distance-Doppler unit coordinate (q peak,ppeak), can calculate the distance and movement velocity of the target contained in the peak value distance-Doppler unit, the concrete expression of the calculating process is:
Wherein, Representing the range and velocity solutions for the objects contained within the peak range-doppler cell.
And 4, constructing a range-Doppler domain array single snapshot receiving signal and compensating the Doppler phase of the coupling of the moving target. Extracting equivalent SIMO array RD domain receiving data D (q peak,ppeak) at a peak distance Doppler unit (q peak,ppeak) in an RDM matrix block D, constructing an RD domain equivalent virtual SIMO array receiving single snapshot signal y based on moving target radar echo, constructing a compensation vector Γ, and compensating the moving target coupling Doppler phase coupled on an array target guiding vector in y to obtain y'.
4A) Range-doppler domain array single snapshot received signal construction. Returning to the RDM matrix block D, extracting equivalent SIMO array RD domain reception data D (q peak,ppeak) at a peak range-Doppler unit (q peak,ppeak), and constructing an RD domain equivalent virtual SIMO array reception single snapshot signal y based on moving target radar echo, wherein the specific expression of y is as follows:
Wherein, Representing targets distributed within a peak range-doppler cell (q peak,ppeak). A ' (θ) = [ a ' (θ 1),a'(θ2),...,a'(θZ) ] represents the array manifold of the virtual SIMO array, a ' (θ z)＝a(θz) ∈Γ represents the virtual SIMO array target steering vector including the moving target doppler coupling phase, s= [ s 1,...,sZ]T,/>The signal vector and the signal of the z target are respectively represented as a target, and w represents the additive Gaussian white noise after 2D-DFT processing at each array receiving channel.
4B) Moving target coupled Doppler phase compensation. Because a time difference exists between LFMCW signals from different transmitting antennas under the TDM-MIMO system and the doppler frequency of a moving target and the phase change caused by the time difference are coupled to the target steering vector of the virtual SIMO array, a corresponding compensation vector Γ ' needs to be designed to compensate the coupling doppler phase of the moving target, so that the specific expression of the compensated RD-domain equivalent virtual SIMO array receiving single snapshot signal y ', y ' is:
Wherein, c z >0 and phi z epsilon 0,2 pi respectively represent the amplitude and phase of s z, a (theta z) represents the virtual SIMO array steering vector of the z-th target, Γ' represents the moving target coupled doppler phase compensation vector, and the specific expression is:
The invention performs target direction finding based on the range-doppler domain. Firstly, complex data extracted from RD domain still contains phase difference information among array elements; secondly, targets with different distances and speeds can be fully separated in the RD domain, and the distance, the speed and the angle information of the targets can be correlated with each other; finally, obtaining coherent and non-coherent accumulation gains in the RD domain can further improve the performance of target detection and improve the signal-to-noise ratio of angle dimension processing.
Step 5, distance Doppler domain atomic norm minimization and Toeplitz matrix vandermonde decomposition: performing frequency preprocessing on y' to obtain a final required RD domain array receiving single snapshot signal y vir, constructing a denoising problem model based on RD domain atomic norm minimization according to a signal form of y vir, converting the model into an equivalent semi-definite programming SDP problem to solve, and then performing frequency retrieval on a Toeplitz matrix T (u) obtained by solving to obtain a DOA estimated value of a target
5A) And (5) frequency pretreatment. Mapping the value range of the DOA estimation parameter theta of y' from a continuous angle domain to a normalized continuous frequency domain to obtain a final required specific expression of the RD domain array receiving single snapshot signal y vir,yvir, wherein the specific expression is as follows:
Wherein, Representing a mapping vector,/>S represents a target signal vector, a (f) = [ a (f 1),...,a(fZ) ],A virtual SIMO array steering vector representing the z-th target after normalized frequency preprocessing.
5B) The range-doppler domain atomic norms are minimized. According to the signal form of y vir, defining an atom a (f, phi) and an atom set A, and constructing a denoising problem model based on RD domain atomic norm minimization according to an atomic norm theory, wherein the specific expression is as follows:
Wherein a= { a (f, Φ) =a (f) e jφ,f∈[0,1),φ∈[0,2π)},||·||A,1 is l 1 atomic norm, and the specific expression is:
converting a denoising problem model based on RD domain atomic norm minimization into an equivalent semi-positive rule form for solving, wherein the specific expression of the equivalent SDP problem is as follows:
Wherein, Representing a data fitting term, λ representing a non-negative regularization coefficient for balancing the fidelity of y vir and the sparseness of the coefficient vector of the atoms that make up x, u representing the optimized variable to be solved, u 1 representing the first element in u, t representing the free variable, is a regularization term that avoids the occurrence of trivial solutions.
5C) The Toeplitz matrix is vandermonde decomposed. Solving the SDP optimization problem can obtain a Toeplitz matrix T (u), wherein the T (u) has a unique vandermonde decomposition form, and the specific expression of the vandermonde decomposition is as follows:
/>
Wherein r=rank (T (u)) < M, p k > 0, Are not equal to each other. Because of the one-to-one mapping relation between DOA estimation parameters theta and T (u), corresponding DOA estimation values can be obtained by carrying out frequency search on the T (u). Frequency search methods such as Prony's Method, subspace Method, etc., where MUSIC is selected. After the corresponding frequency is searched, the final DOA estimation result/>
According to the method, the distance-Doppler domain atomic norm minimization denoising problem is constructed to solve according to the atomic norm theory, and besides the higher resolution and accuracy of the angle measurement, as the solving process is basically a process of reconstructing the sparse signal by using the compressed sensing/sparse representation framework, the target signal can be decohered without any preprocessing as long as the target space division of the incident signal enables the target space division of the incident signal to meet the sparse characteristic.
The effect of the invention can be further verified by simulation.
The RD-ANM-based millimeter wave radar moving target super-resolution DOA estimation method is the same as that of the embodiment 1-4, and the simulation situation is as follows:
(1) Experimental scenario
The vehicle millimeter wave radar transmitting carrier frequency is 77GHz, one CPI comprises 256 Chirp, the Chirp repetition period is 10 mu s, the effective bandwidth is 150MHz, the ADC sampling rate is 25.6MSPS, the ADC sampling point number is 256 points, the TDM-MIMO adopts a 3T4R mode, the conditions that a plurality of moving targets are the same distance and the same speed but different azimuth angles are considered, the initial distance of the targets is 50m, and the moving speed is 10m/s.
(2) Experimental content and results analysis.
Experiment 1
According to parameter setting in an experimental scene, an LFMCW signal is transmitted by a vehicle millimeter wave radar to detect a target, the moving target wave arrival azimuth angle estimation is carried out by using the RD-ANM-based millimeter wave radar moving target super-resolution DOA estimation method, the target number K=3 is set, the wave arrival azimuth angles of three targets are set to be θ 1＝-40°,θ2＝-15°,θ3 =38°, the echo signal-to-noise ratio is set to be 22.5735dB, and the estimation result is shown in fig. 2 (f).
FIG. 2 (a) is an accumulated result of an array single channel after performing range Doppler two-dimensional coherent accumulation on an original radar echo data block of a vehicle-mounted millimeter wave radar; FIG. 2 (b) is a target detection plane obtained after performing array antenna dimension incoherent accumulation, two-dimensional CA-CFAR detection and peak grouping processing based on a vehicle-mounted millimeter wave radar range-Doppler spectrum matrix block; FIG. 2 (c) is a distance-to-CA-CFAR detection threshold in a two-dimensional CA-CFAR detection; fig. 2 (d) is a doppler direction CA-CFAR detection threshold in two-dimensional CA-CFAR detection. The X-axis coordinates of FIGS. 2 (a) - (d) are distance (m), the Y-axis coordinates are velocity (m/s), and the Z-axis coordinates are amplitude. As can be seen from the results presented by the four graphs, the three moving targets with the same distance and same speed are focused at the same distance doppler unit in the target detection plane, a peak value is presented at the unit, after the coordinates of the peak value distance-doppler unit are obtained, the distance and the speed of the target in the peak value distance-doppler unit can be calculated, the obtained distance and speed calculation values of the three moving targets with the same distance and same speed are respectively 50m and 9.8925m/s, and then the distance and the speed of the target can be related to each other to form three-dimensional parameter information of the target.
FIG. 2 (e) is a target DOA estimation result obtained by not performing pre-compensation processing on the Doppler coupling phase of the moving target before DOA estimation is performed in the RD domain; FIG. 2 (f) shows DOA estimation results obtained by pre-compensating the Doppler coupling phase of the moving target before RD and DOA estimation are performed; the units of the horizontal axis in fig. 2 (e) - (f) are all angles (°), and the units of the vertical axis are all amplitudes (dB). As can be seen from the results shown in fig. 3, if the doppler coupling phase of the moving target is not precompensated before the DOA estimation in the RD domain, there is a larger deviation between the final DOA estimation result and the actual azimuth angle of arrival of the target, and the DOA estimation result after the precompensation of the doppler coupling phase of the moving target can correctly reflect the actual arrival of the target, thereby verifying the necessity of compensating the doppler coupling phase of the moving target included in the array reception before the DOA estimation in the RD domain.
FIG. 3 (a) is a target DOA estimation result of the method of the present invention in the presence of 5 coherent sources; fig. 3 (b) is the target DOA result of the method of the present invention in the presence of 11 coherent sources. The units of the horizontal axis in fig. 3 (a) - (b) are all angles (°), and the units of the vertical axis are all amplitudes (dB). From the results shown in fig. 4, it can be seen that the method of the present invention can perform decorrelated processing on coherent signals without any preprocessing and without sacrificing the array aperture, and can estimate up to 11 coherent sources, and has robust performance of resolving coherent sources.
Experiment 2
According to parameter setting in an experimental scene, an LFMCW signal is transmitted by an on-vehicle millimeter wave radar to detect a target, and a first existing method, a second existing method and a millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM are respectively used for estimating the wave azimuth angle of a moving target, wherein the first existing method is a RD domain-FFT (fast Fourier transform) method and a RD domain-IAA (fast Fourier transform) method, the second existing method is a RD domain-FBSS MUSIC method, the set target number K=3, the wave azimuth angles of three targets are set to be θ 1＝-11.9°,θ2＝1.2°,θ3＝8.7°/θ1＝-5°,θ2＝0°,θ3 DEG or the set target number K=2, the wave azimuth angles of the two targets are set to be θ 1/θ2 = -2 DEG/2, -1 DEG/1, and DOA estimation results are shown in fig. 4.
FIGS. 4 (a) - (b) are graphs comparing DOA estimation results of the methods of the present invention with those of the first and second methods. The units of the horizontal axis in fig. 4 (a) - (b) are all angles (°), and the units of the vertical axis are all amplitudes (dB). As can be seen from the results shown in fig. 4 (a) - (b), the RD domain-FFT is limited by the array aperture, the angular resolution and estimation accuracy of the algorithm are not high, the target orientation of the closer interval cannot be resolved, and a certain deviation exists between the DOA estimation result and the real orientation of the target; the RD domain-FBSS MUSIC and the RD domain-IAA can process coherent information sources, can present sharper spectrum peaks, and have more accurate DOA estimation results; the method has similar performance to the two, and also has higher resolution and accuracy of the angle measurement.
Fig. 4 (c) - (d) are graphs comparing signal-to-noise ratios (Signal to Noise Ratio, SNR) -root mean square errors (Root Mean Square Error, RMSE) for the methods of the invention and methods one and two. The horizontal axis of fig. 4 (c) - (d) are in units of signal to noise ratio (dB) and the vertical axis are in units of RMSE (°). From the results presented in fig. 4 (c) - (d), it can be seen that there is always an unavoidable root mean square error in the RD domain-FFT, the RD domain-FBSS MUSIC, the RD domain-IAA and the inventive method perform approximately, but the root mean square error in the inventive method is lower at low signal-to-noise ratios (fig. 4 (c), typically at-10 dB, RMSEs of the RD domain-FFT, the RD domain-IAA and the RD domain-FBSS MUSIC are 9.5653,3.1078,11.4527 degrees, respectively, and the RMSE of the inventive method is 0.2308 degrees), and this advantage is even more pronounced by further decreasing the angular separation (fig. 4 (d), typically at-10 dB, RMSEs of the RD domain-FFT, the RD domain-IAA and the RD domain-FBSS MUSIC are 8.4476,20.4559,27.8961 degrees, respectively, and the RMSE of the inventive method is 0.5877 degrees).
Fig. 4 (e) - (f) are repeated experimental results of the DOA estimation of the method of the present invention after further reducing the radar echo signal-to-noise ratio, and the number of monte carlo experiments was set to 300. In fig. 4 (e) - (f), the horizontal axis is in degrees (°) and the vertical axis is in the number of experiments. From the results shown in fig. 4 (e) - (f), it can be seen that the lower signal-to-noise ratio boundary of the method of the present invention can clearly distinguish between different targets when the targets come, i.e. the smaller the target comes, the higher the signal-to-noise ratio of the radar original echo data required by the method can be clearly distinguished.
Fig. 4 (g) - (h) show the results of repeated DOA estimation experiments of the method of the present invention after further reducing the number of sources to be estimated and the target to be spaced, with the number of monte carlo experiments set to 300. In fig. 4 (g) - (h), the horizontal axis is in degrees (°) and the vertical axis is in the number of experiments. From the results shown in FIGS. 4 (e) - (f), it can be seen that the method of the present invention can break through the limitation of array aperture under the conditions of small target angle interval (< 5 ℃) and higher signal-to-noise ratio, and the target parameter space interval is far lower thanUnder the condition of the resolution limit, the corresponding target angle parameters can be retrieved with higher probability. /(I)
In summary, the millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM provided by the invention mainly solves the problems of limited array aperture, fewer snapshots, low signal to noise ratio, source coherence and low resolution of the direction finding method under the conditions of target movement, such as lack of decoherence performance, angle finding precision and low resolution in the vehicle-mounted scene. The implementation steps are as follows: 1) The TDM-MIMO transmitting array transmits LFMCW signals, and the receiving array receives corresponding radar echoes; 2) Performing declining operation, analog-to-digital conversion and channel separation and combination processing on the received radar echo, and constructing a radar original echo data block of the vehicle-mounted millimeter wave radar; 3) Performing range-Doppler coherent accumulation and target detection on an original radar echo data block; 4) Constructing a range Doppler domain array single snapshot receiving signal and compensating the coupling Doppler phase of a moving target; 5) And constructing a range Doppler domain atomic norm minimization problem model and acquiring target arrival azimuth information by utilizing vandermonde decomposition of the Torplitz matrix. The method can obtain higher angular resolution and estimation precision based on the conditions of limited array aperture and low signal-to-noise ratio and on the premise of single snapshot processing, has the robust performance of processing coherent signals without sacrificing the array aperture, and can be used for DOA estimation of the moving target of the vehicle-mounted millimeter wave radar.
Claims (5)
1. The millimeter wave radar moving target super-resolution DOA estimation method based on RD-ANM is characterized by comprising the following steps:
step 1) transmitting and receiving signals: each transmitting antenna of the TDM-MIMO array transmits LFMCW signals in a mode of time-sharing alternate circulation operation, and the receiving array sequentially receives corresponding radar echo signals;
step 2) constructing an original radar echo data block: performing declining operation, analog-to-digital conversion and channel separation and merging processing on radar echo signals sequentially received by the TDM-MIMO receiving array, and finally forming an original radar echo data block X of the vehicle-mounted millimeter wave radar;
Step 3) range-doppler coherent accumulation and target detection: performing distance Doppler two-dimensional coherent accumulation on an original radar echo data block X of the vehicle-mounted millimeter wave radar to obtain a distance Doppler spectrum matrix block D of the vehicle-mounted millimeter wave radar, performing target detection processing based on the D, and resolving to obtain target distance and movement speed information;
Step 4), distance Doppler domain array single snapshot received signal construction and moving target coupling Doppler phase compensation: based on D, constructing a range-Doppler domain equivalent virtual SIMO array based on moving target radar echo to receive a single snapshot signal, and compensating a moving target coupling Doppler phase contained in the signal;
Step 5) distance Doppler domain atomic norm minimization and Toeplitz matrix vandermonde decomposition: and carrying out frequency preprocessing on the single snapshot signal received by the distance Doppler domain equivalent SIMO array, constructing a denoising problem model based on the distance Doppler domain atomic norm minimization according to an atomic norm theory, obtaining a Toeplitz matrix T (u) by solving an equivalent semi-positive definite programming form of the model, and carrying out frequency retrieval on the T (u) to obtain the DOA estimated value of the target.
2. The method according to claim 1, wherein step 4) comprises the steps of:
4a) Distance Doppler domain array single snapshot received signal construction: extracting equivalent SIMO array range-Doppler domain received data D (q peak,ppeak) at a peak range-Doppler unit (q peak,ppeak) for the RDM matrix block D obtained in the step 3, and constructing a range-Doppler domain equivalent virtual SIMO array received single snapshot signal y=D (q peak,ppeak) based on moving target radar echoes;
4b) Moving target coupled Doppler phase compensation: through the target movement speed calculation value obtained in the step 3 And constructing a compensation vector Γ 'to compensate the moving target coupling Doppler phase contained in y, so as to obtain a single snapshot signal received by the compensated RD domain equivalent virtual SIMO array, wherein y' =y.
3. A method according to claim 3, characterized in that Γ' has the specific expression:
Wherein, M TX represents the array element number of the transmitting array, M RX represents the array element number of the receiving array, T c represents the Chirp repetition period, f c represents the transmitting signal carrier frequency, and c represents the light speed.
4. The method according to claim 2, wherein the step (5) specifically comprises the steps of:
5a) Mapping the range of the value of the DOA estimation parameter theta of the y ' obtained in the step 4 from the continuous angle domain to the normalized continuous frequency domain, thereby obtaining a final required RD domain array receiving single snapshot signal y vir = y '. The value of the DOA estimation parameter theta of the y ' obtained in the step 4, wherein, Represents a mapping vector, λ=f c/c, represents a transmission wavelength, d R represents a TDM-MIMO receiving array element pitch, and M represents a total number of receiving array elements of the virtual SIMO array;
5b) Range-doppler domain atomic norms are minimized: according to the atomic norm theory and the signal form of y vir, defining an atom a (f, phi) and an atom set A, and constructing a denoising problem model of a range Doppler domain based on atomic norm minimization, wherein the specific expression is as follows:
Wherein a= { a (f, Φ) =a (f) e jφ,f∈[0,1),φ∈[0,2π)},||·||A,1 is l 1 atomic norm, and the specific expression is:
The denoising problem based on the distance Doppler domain atomic norm minimization is converted into an equivalent semi-positive rule form to be solved, and the specific expression of the equivalent SDP problem of the original problem is as follows:
Wherein, Representing a data fitting term, lambda representing a non-negative regularization coefficient for balancing the fidelity of y vir and the sparseness of the coefficient vector of the atoms making up x, u representing the optimized variable to be solved, u 1 representing the first element in u, t representing the free variable, a regularization term that avoids the occurrence of trivial solutions;
5c) Vandermonde decomposition of the toprilz matrix: solving the SDP optimization problem can obtain a Toeplitz matrix T (u), wherein the T (u) has a unique vandermonde decomposition form, and the specific expression of the vandermonde decomposition is as follows:
Wherein r=rank (T (u)) < M, p k > 0, Are not equal to each other;
Obtaining corresponding DOA estimated value by frequency searching T (u)
5. The method according to claim 1, characterized in that in step 5) frequency searching is performed using MUSIC method.
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