CN109975807A - A kind of reduced order subspace angle-measuring method suitable for millimeter wave trailer-mounted radar - Google Patents
A kind of reduced order subspace angle-measuring method suitable for millimeter wave trailer-mounted radar Download PDFInfo
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Abstract
The invention discloses a kind of reduced order subspace angle-measuring methods suitable for millimeter wave trailer-mounted radar object detection field, it is the following steps are included: propose to reduce computation complexity and EMS memory occupation using array mismatch error algorithm first, and optimize beam forming matrix design using prior information；Secondly, proposing a kind of new MUSIC estimation, reflect the finer dimensional information about signal subspace；Furthermore, the relevant situation of two adjacent signals is taken fastly for single, have modified the mathematic(al) representation for receiving signal sample estimates covariance matrix, to enhance the orthogonality of noise subspace and signal subspace, keep its Toeplitz structure, using the method for beamlet space average, under conditions of each beamlet space full rank, the estimated accuracy of sample covariance matrix is improved.
Description
Technical field
The invention belongs to radar signal processing field more particularly to a kind of dimensionality reduction suitable for millimeter wave trailer-mounted radar are empty
Between angle-measuring method.
Background technique
In recent years, automatic Pilot field is flourished, automatic cruising, blind area detection, forward direction Anti-knocking etc. is all its allusion quotation
The application scenarios of type.Millimetre-wave radar system is the indispensable ring of automatic Pilot technical field, it is in more severe gas
It is for example foggy to wait environment, with good performance when dim light, this is laser radar, and the other sensors such as camera institute is not
Have.Wherein CW with frequency modulation (FMCW) radar is a kind of by obtaining distance and speed to continuous wave progress frequency modulation(PFM)
The millimetre-wave radar system of information, in the range of fmcw radar application was limited in very little within a very long time in past.Into
Enter the nineties, the development of solid state microwave millimetric wave device and Digital Signal Processing is that the development of millimeter wave fmcw radar is established
Basis.Millimetre-wave radar has extremely far-reaching application value at military, civilian aspect, and advantage can be summarized as follows:
1, there is massive band width can be used, improve resolution of ranging, effectively eliminate and interfere with each other, without blind area of testing the speed.
2, wavelength is shorter, and beam angle is narrow, and antenna gain is high, spatial resolution can be improved, while component size is small, weight
Amount is light.
3, Atmospheric Absorption effect is stronger than microwave, and decaying is big, is not easy to interfere with each other, and reduces electromagnetic pollution.
Based on FMCW above advantages, also it is widely used in a variety of applications in Vehicular radar system.
The tradition of detection in addition to to(for) target range and speed, vehicle-mounted millimeter wave radar also propose target angle-of- arrival estimation
Higher demand.In in the past few decades, MUSIC algorithm has always been considered as being a kind of effective due to its superior performance
Subspace angle estimation algorithm.But a big problem of MUSIC algorithm is that it generally comprises big quantity sensor is received
Array signal data Eigenvalues Decomposition and spectrum peak search operation, calculation amount is very huge, especially in vehicle-mounted millimeter wave
In fmcw radar system, DSP processing core number is limited, proposes very high want for computation complexity and EMS memory occupation
It asks.Furthermore arrival bearing's estimation under trailer-mounted radar application scenarios is carried out in specific range, the doppler cells where target
, it is actually directed to the reception signal data of a single snap, when there are multiple adjacent targets, receiving signal can not recognize
To be incoherent signal, the Toeplitz structure of signal covariance matrix is received by broken ring, this also proposed angle measurement scheme
New requirement.
Summary of the invention
Goal of the invention: in view of the above problems, the invention proposes a kind of dimensionality reduction suitable for millimeter wave trailer-mounted radar is empty
Between angle-measuring method, on the one hand meet the requirement of low computation complexity and EMS memory occupation amount, on the other hand either single goal is still
All there is superior angle measurement performance in the case where multiple target.
Technical solution: to achieve the purpose of the present invention, the technical scheme adopted by the invention is that as follows: in order to facilitate our department
The description divided, table 1 list the explanation of all Common Parameters in the present invention.
1 Common Parameters explanation of table
A kind of reduced order subspace angle-measuring method suitable for millimeter wave trailer-mounted radar object detection field disclosed by the invention,
Include the following steps.
Step 1: establishing the Estimation of Spatial Spectrum mathematical model of millimeter wave Vehicular radar system, obtain transmitting signal and receive letter
Number mathematic(al) representation；
Step 2: using the number and layout of transmitting antenna needed for millimeter wave Vehicular radar system and receiving antenna, in step
It is expanded on the basis of rapid 1 in the case of establishing more transmitting-receivings to the three-dimensional data structure of the intermediate-freuqncy signal after reception signal mixing；
Step 3: three-dimensional reception signal data resulting to step 2 carries out FFT in fast time dimension and slow time dimension respectively, obtains
The reception of aerial array on to the distance and velocity information of the target vehicle detected and its corresponding range-doppler cells
Signal data vector Y；
Step 4: utilizing the orientation angular range information where detection vehicle needed for trailer-mounted radar, the wave beam of calculation optimization
Form matrix Bopt, the reception signal data vector Y of the aerial array on specific range doppler cells is transformed into from Element space
Beam Domain obtains Beam Domain received signal vector YB；
Step 5: utilizing the resulting Beam Domain receipt signal matrix Y of step 4BCalculate sample covariance matrixAnd it is right
It is modified, obtains amendment sample covariance matrix
Step 6: to the modified sample covariance matrix of step 5Eigenvalues Decomposition is carried out, noise subspace is obtained
It utilizesWithIt establishes new MUSIC and estimates sub- feMUSIC, spectrum peak search is carried out, arrival bearing's estimation is obtained
Further, in the step 1, the transmitting signal waveform of millimeter wave Vehicular radar system is that one group of carrier frequency is f0?
With the linear frequency modulation continuous wave signal (LFMCW) of certain swept bandwidth in transmit cycle, multiple transmitting antennas successively send out by timesharing
It penetrates, in t moment, the transmitting signal s in i-th of periodtThe expression formula of (t, i) are as follows:
Wherein, A, f0,It is transmitting signal amplitude size, carrier frequency and initial phase, μ=B respectively0/ T is frequency modulation
Slope, wherein B0It is swept bandwidth, T is the period of a linear frequency modulation continuous wave.Consider as t=0, radar front with
The radial distance of target vehicle is r, and radial velocity is the target of v, and radially speed is positive close to radar direction in the present invention,
Therefore receive signal srThe expression formula of (t, i) can be written as:
Wherein, A0It is the amplitude for receiving signal, τ=2 (r-vt)/c is the distance between target and radar bring time delay,
C is the light velocity.It receives signal and original transmitted signal carries out mixing operation, and is also referred to as poor by low-pass filter acquisition intermediate-freuqncy signal
Clap signal.In t moment, the expression formula s of i-th of period Beat SignalIF(t, i) can be written as:
Further, in step 2, consider that millimeter wave Vehicular radar system has NtRoot transmitting antenna, NrRoot receiving antenna,
NtRoot transmitting antenna emits identical CW with frequency modulation, total transmit cycle length T in turn1=NtT, and form virtual array.
Emit N altogether in signal processing flow timesaA linear frequency modulation continuous wave.In i-th of transmit cycle, kth piece-root grafting receives day
The echo complex signal of the received m root transmitting antenna transmitting signal of line are as follows:
Wherein, i=1 ..., Nsa, m=1 ..., Nt, k=1 ..., Nr, A, A0,f0,It is transmitting signal amplitude respectively,
Receive the signal amplitude of signal, carrier frequency and initial phase, μ=B0/ T is chirp rate, wherein B0It is swept bandwidth, T
It is transmit cycle length, d is antenna spacing, and θ is the azimuth size where target.
Signal y is emitted to eachk,i(t) it is sampled, sampling number Ns=fsT, wherein fsIt is DSP digit chip
Sample frequency.Then in i-th of transmit cycle, the received m root transmitting antenna transmitting signal of kth root receiving antenna is returned
Wave complex signal sampled signal Indicate the kth piece-root grafting in i-th of transmit cycle
Receive j-th of sampling of the echo complex signal of the received m root transmitting antenna transmitting signal of antenna.In a signal processing flow
Cycle T2It is interior, wherein T2=Nsa·NtT, the sampled signal of the received m root transmitting antenna transmitting signal of kth root receiving antennaAre as follows:
By a transmit cycle T1The echo-signal of the received different transmitting antennas transmitting signals of interior identical receiving antenna into
Row merges, and the reception signal in i-th of transmit cycle isEntire signal processing flow T2Virtual array is formed in time
Wherein, i=1 ..., Nsa, T1=NtT, therefore intermediate-freuqncy signal data matrix is NtNr×Nsa×Ns, it is a three-dimensional
Data vector, time dimension, namely fast time dimension, speed dimension, namely slow time dimension and since multiple-input multiple-output virtual array is brought
Phase dimension, data structure is shown in attached drawing.
Further, in the step 3, to the obtained echo-signal expression formula of step 1, according to the definition in step 2
FFT is carried out to the fast time dimension and slow time dimension that receive data.
Signal will be received and carry out windowing FFT processing, in i-th of transmit cycle, kth root receiving antenna along fast time dimension
Reception signalFor:
In formula, i=1 ..., Nsa, k=1 ..., Nr, wqIt is N for window functionS× 1 column vector, symbol ⊙ represent two
The Hadamard product of vector, i.e. corresponding element are multiplied, and fft (), which refers to, does FFT operation to signal,Indicate i-th of transmit cycle
Interior, kth root receiving antenna finishes the later reception signal of windowing FFT along fast time dimension.
Assuming that there is distance is r, speed is the target of v, then after carrying out FFT to fast time dimension, target spectrum peak value position
It is set to:
Because sawtooth wave frequency sweep cycle T is very small, fr,v≈2B0r/cT.Therefore, fast time dimension can be equivalent to away from
From dimension, spectrum unit can be equivalent to distance unit.
Windowing FFT is carried out to the reception signal of each transmit cycle, every antenna, is obtained
NqFFTFor fast time dimension FFT points.
To YVFSlow time dimension FFT is carried out, with kth root receiving antenna, first of spectrum unit data
For:
In formula, k=1 ..., Nr, l=1 ..., Ns, wsIt is N for window functionsa× 1 column vector,Indicate kth root
Receiving antenna, first of spectrum unit finish windowing FFT along slow time dimension and handle later reception signal.
After then carrying out FFT to slow time dimension, target spectrum peak position are as follows:
After slow time dimension FFT, target spectrum peak value position is only related with speed, therefore slow time dimension can regard speed as
Degree dimension.
To every receiving antenna, the reception signal of different distance unit carries out slow time dimension FFT, obtainsNsFFTFor slow time dimension FFT points.
Consider by fr,vAnd fvIdentified i-th of distance dimension unit, first of speed dimension element memory is in a target carriage
, the complex vector of spectrum unit where taking targetIt is denoted as Y:
The i=1 ..., NqFFT, l=1 ..., NsFFT。
Further, in the step 4, consider a uniform uniform line array, array number M, array element spacing is d, and K is a
Far field narrow band signal source, wherein K≤M, fast time dimension sampling number, also referred to as number of snapshots are N.Far field narrow band signal source model are as follows:
Y=AS+N
In formula, Y is the reception signal of array M × N, and A is the array manifold matrix of M × K, and the transmitting signal that S is K × N is sweared
Amount, the every a line of S is s in step 1 hereinIFMatrix form after (t, i) sampling.Considering that Ν is the additive Gaussian white noise of M × N
Acoustic vector matrix, when number of snapshots N=1, Y is the complex vector Y of spectrum unit where the target in step 3.
The dimension for thinking beam forming matrix B is M × B, and B≤M, while B is a normal orthogonal battle array:
BHB=I
In the application scenarios of vehicle-mounted millimeter wave radar system, visual field (FOV) is a limited angular range, we are not
Need to design the Beam-former of 360 degree of a covering.Under the premise of such, it is believed that the azimuth of required detection vehicle
Information is in known angular range, and using azimuthal range information, we obtain the beam forming matrix of an optimization.
There are two vehicles to be detected, in order to more accurately estimate the azimuth where two cars,
We need to design the beam forming matrix of an optimization.The beam forming matrix B of optimizationoptIt is necessary to meet following condition: by leading
To vector a (θ1),a(θ2), and a (θm) determined by subspace be contained in BoptEach column determined by θ in subspace1, θ2
It is azimuth where two targets, and θmIt can be with is defined as:
θm=(θ1+θ2)/2
Under millimeter wave trailer-mounted radar application scenarios, it can go to obtain the beam forming matrix optimized using following method
Bopt:
Βopt=[υ1 … υB]
Wherein, a (θ) is the steering vector of array, θaAnd θbIt is the boundary of azimuth coverage, υiIt is Q∞B big characteristic values
(λ1≥λ2≥…≥λB> λB+1≥λB+2≥…≥λM=σ2) diagonal matrix as the elements in a main diagonal, ΒoptIt is with υiFor column
Matrix composed by vector, i=1,2 ... B.
Signal complex vector Y is received on specific range doppler cells described in step 3 will pass through a Beam-former,
Beam forming matrix is B described in this stepopt, by the Beam-former, signal Y will be received from Element space and be transformed into wave beam
Domain obtains Beam Domain received signal vector YB。
YB=Bopt HY
Further, in the step 5, Beam Domain received signal vector YBSample covariance matrixIt can indicate
Are as follows:
Wherein, I is unit matrix, T=Bopt HA is the equivalent array manifold matrix of Beam Domain, the steering vector square that A is
Battle array, Rs=E [SSH] it is the auto-covariance matrix for emitting signal, RBIt is the association side for not considering to receive signal beam domain under noise situations
Poor matrix, σ2The variance of white Gaussian noise.
It is limited due to receiving signal length, sample covariance matrixIt is an estimated value to covariance,
Its calculation expression in practical applications is usually written as:
Wherein, YBIt (i) is Beam Domain received signal vector YBI-th of element.In the case where trailer-mounted radar list snap,
Only B data can be used, this has seriously affected the accuracy of covariance matrix, to affect having for angle estimation
Effect property.In the case where single snap (N=1), Beam Domain receipt signal model narrow band signal source in far field according to step 4
Model can be corrected are as follows:
YB=BHAS+BHN
Wherein, YB=[Y1,Y2,…,YB]T, it is the column vector of B × 1, YiFor YBI-th of element, i=1 ..B, B
For Beam-former dimension.
If YBIt is a wide stationary processes, it is according to the knowledge of engineering matrix and Digital Signal Processing it is recognised that wide flat
The covariance matrix of steady processIt must be the symmetrical Toeplitz matrix of conjugation, so sample covariance matrix can be write
Are as follows:
Upper i-th cornerwise element riIt can be written as the auto-correlation function in airspace:
ri=E [Ym+iY* m]
Wherein, Ym+iIndicate YBIn the m+i element, the case where i=0 ..B-1 are a single snap herein, thus from
Matrix dimensionality reduction is at a vector, because a random process can be regarded as, if YBOr ergodic process, then we
The mathematic expectaion instead of sample can be gone with temporal average value, so riIt can further be written as:
In practice, we go to calculate sample covariance matrix using formula below:
If YB=[Y1,Y2,…,YB]T, it is contemplated that the causality of signal, thenIt may finally be written as:
But it is used for expression formula actually Biased estimator for sample estimates covariance above,And riBetween difference
Away from are as follows:
Especially work asWhen invalid, this deviation can not ignore.
In order to improve the performance of array mismatch error angle measuring algorithm in the case of single snap, we are correctedTo ensure that it is one
A unbiased estimation, it is seen that after being modified using following formulaIt is constantly equal to 0, and then is obtained newly's
Expression formula.
From above equation it can be seen that, it is ensured thatIt can physics realization, it is necessary to guarantee that the subscript of Y meets 1≤m+i
≤B.It is also says to the i of some fixation, there are B-i data can be used, B-i times can be and be averaged.Such as r0,
We can go to calculate with B data, this, which is equivalent to, has done B times and be averaged, and for rB-1, can only be estimated with 1 data
Meter, be equivalently employed without do it is any be averaged, this is to covariance matrixEstimation is unfavorable.
So actually riIn maximum i will not usually get B-1, but the 2/3~4/5 of B would generally be taken.But so
The pore size for reducing aerial array is done, the reduction of freedom degree also implies that the number of sources that can be estimated is reduced.So
In the present invention also using the method for dividing beamlet, the dimension of each beamlet is L × L, i-ththA beamlet RiiAs
Original sample covariance matrixIn from the i-th row to the i-th+L row, data block that the i-th column are arranged to the i-th+L.Guaranteeing each wavelet
In the case where beam full rank, the accuracy of sample covariance matrix is improved.
It is eventually used for the sample covariance matrix expression formula of MUSIC algorithm angle measurement are as follows:
Wherein, P is beamlet number, meets B=L+P-1, and the schematic diagram that beamlet divides is shown in attached drawing 2.
Further, in the step 6, sample covariance matrix that the amendment that step 5 obtains is shoutedCarry out characteristic value
It decomposes, obtains noise subspace
Since signal is mutually indepedent with noise, sample covariance matrix can be analyzed to two parts relevant to signal, noise.
It is rightCarrying out feature decomposition has:
In formula, ΣsBe withThe obtained preceding K maximum eigenvalue λ of feature decomposition1≥λ2≥…≥λKAs main diagonal
The diagonal matrix of line element, ΣoIt isRemaining L-K eigenvalue λK+1≥λK+2≥…≥λL=σ2As its leading diagonal member
Element diagonal matrix, wherein L beDimension, K be detection target vehicle number, σ2It is the variance of noise.It is by preceding K
Maximum eigenvalue λ1≥λ2≥…≥λKThe subspace of corresponding characteristic vector namely signal subspace, andIt is by feature
Value λK+1≥λK+2≥…≥λL=σ2The subspace of corresponding characteristic vector namely noise subspace.
In step 6, the new space the MUSIC spectral function of proposition can be written as:
In formula, b (θ)=< BHa(θ)>LIt is the preceding L element of the steering vector of Beam Domain,<>LExpression takes column vector
Preceding L element operation,It isPseudoinverse.Under ideal conditions, it is assumed that there are an orientation angles are θiTarget vehicle, it is right
θ ∈ [0 ° 360 °] is traversed, as θ=θiWhen,siBe orientation angle be θiDetection target
Corresponding to vehicle iThe resulting characteristic value of Eigenvalues Decomposition.And signal subspace with noise subspace is in the ideal case
Mutually orthogonal, that is to say, that the steering vector in signal subspace is also orthogonal with noise subspace, it may be assumed that
Since noise exists, so the steering vector in signal subspace also cannot complete orthogonal, institute with noise subspace
Orientation angular estimation with actually Estimation of Spatial Spectrum is to traverse to θ ∈ [0 ° 360 °], and maximum value Optimizing Search is realized
, that is, the orientation angular estimation of the target vehicle detectedAre as follows:
Wherein,Operation indicates to seek working asObtain corresponding θ value when maximum value.
The utility model has the advantages that compared with prior art, technical solution of the present invention has following advantageous effects:
Limited for millimeter wave Vehicular radar system digital signal processing capability, the high feature of requirement of real-time, use is excellent
The array mismatch error algorithm of change reduces computation complexity and EMS memory occupation amount.For conventional MUSIC method low signal-to-noise ratio,
Target resolution performance declines under the conditions of fewer snapshots, it is difficult to which the shortcomings that adapting to the engineer application under non-ideal condition proposes one
The new MUSIC of kind estimates son, and the letter for including in signal subspace, noise subspace and dominant eigenvalue is utilized to greatest extent
Breath, combines Signal subspace processing robustness height and noise is empty in the high advantage of processing estimated accuracy, is conducive to more mesh
Mark the raising of orientation estimation performance.
Detailed description of the invention
Fig. 1 is inventive algorithm design flow diagram；
Fig. 2 is that beamlet proposed by the invention divides schematic diagram；
Fig. 3 is the curve that the detection probability of success of four kinds of MUSIC algorithms in case study on implementation 1 of the present invention changes with SNR；
Fig. 4 is the curve that the detection angles error mean of four kinds of MUSIC algorithms in case study on implementation 1 of the present invention changes with SNR；
Fig. 5 is the song that the detection angles error to standard deviation of four kinds of MUSIC algorithms in case study on implementation 1 of the present invention changes with SNR
Line；
Fig. 6 is that the angle-resolved probability of success of two kinds of MUSIC algorithms (MA3, MA4) in case study on implementation 2 of the present invention becomes with SNR
The curve of change；
Fig. 7 is that the detection angles error mean of two kinds of MUSIC algorithms (MA3, MA4) in case study on implementation 2 of the present invention becomes with SNR
The curve of change；
Fig. 8 is the detection angles error to standard deviation of two kinds of MUSIC algorithms (MA3, MA4) in case study on implementation 2 of the present invention with SNR
The curve of variation；
Fig. 9 be in case study on implementation 2 of the present invention two kinds of MUSIC algorithms (MA3, MA4) at different angle interval delta θ
The curve that angle-resolved success rate changes with SNR；
Figure 10 is the dimensional Graphics of radar data block in a coherent processing inteval of the present invention；
Figure 11 is the possible azimuthal distribution range of vehicle to be detected in the present invention.
Specific embodiment
Below with reference to specific implementation case, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate this hair
Bright rather than limit the scope of the invention, after the present invention has been read, those skilled in the art are to of the invention various etc.
The modification of valence form falls within the application range as defined in the appended claims.
In this part, we illustrate some specific values as a result, to further illustrate enhancing proposed by the invention
Beam space MUSIC algorithm validity.By following two specific embodiment, analyze adjacent in single goal and two
Under the different condition of Place object, the beam space MUSIC algorithm of the enhancing proposed is superior better than tradition MUSIC algorithm
Property.
We compare the performance of following four difference MUSIC algorithm.For ease of description, they are referred to as MA0
(MUSIC algorithm 0), MA1 (MUSIC algorithm 1), MA2 (MUSIC algorithm 2), MA3 (MUSIC algorithm 3), MA4 (MUSIC algorithm 4).
MA0 is the classical MUSIC algorithm in array element space.MA1 is the beam space MUSIC algorithm using DFT Beam-former.MA2
It is using Beam-former BoptBeam space MUSIC algorithm.MA3 is using Beam-former and sample covariance matrix
Beam space MUSIC algorithm, to maintain its Toeplitz structure in the case where single snap.MA4 is proposed by the present invention
The beam space MUSIC algorithm of enhancing.The specific difference between five kinds of algorithms of different is shown in table 2.
Comparison in difference between 2 five kinds of algorithms of table
Case 1: mono signal source classics MUSIC algorithm is compared with the performance of beam space MUSIC algorithm.In this case column,
We compare different beam space MUSIC algorithm and performance of the classics Element space MUSIC in terms of angle measurement.Signal source
Quantity be K be 1.The boundary θ of angular rangeaAnd θbRespectively in 3 ° and -3 °.Target is located at θ1=2.5 °.Number of snapshots N is 1, battle array
First number M is 8.We select four kinds of different MUSIC algorithms (MA0, MA1, MA2 and MA4) to carry out performance comparison.
From simulation result attached drawing 3 to 5 as can be seen that in four kinds of schemes, the beam space MUSIC of enhancing proposed in this paper
The performance of algorithm (MA4) is all optimal in terms of the probability of success, deviation mean value and standard deviation.And other two kinds of Wave beam formings
MUSIC algorithm is not so good as classics Element space MUSIC algorithm (MA0), because computational complexity is dropped using antenna aperature loss as cost
It is low.In addition, using the beam space MUSIC algorithm (MA1) of DFT Beam-former with worst angularity in four kinds of algorithms
Can, this also demonstrates the optimization beam forming matrix B proposed by the present invention using prior informationoptValidity.
Case 2: compare for the performance of single snap beam space MUSIC algorithm (MA3, MA4) of two adjacent targets.It is first
First, we are illustrated using following two table in the case where two targets, and number of snapshots are reduced to the unfavorable of signal source correlation
It influences.Element number of array M is 8, and wave beam number B is 6.From table 3 it can be seen that in the case where big number of snapshots, noise subspace and
The feature vector orthogonality of steering vector is very significant, but in the case where small snap, noise feature vector obtained and letter
Orthogonality severe exacerbation between work song space, and then lead to the Power estimation of inaccuracy.It can also be seen that using MA3 from table 4
The feature vector of the expression formula of modification sample covariance matrix, maintenance Toeplitz structure, noise subspace and steering vector
Orthogonality is to increase an order of magnitude, this is extremely important for subsequent DOA estimation.
The correlation analysis of 3 MA0 of table
The correlation analysis (N=1) of table 4 MA0, MA3
MA4 is further improved on the basis of MA3.Therefore, MA4 can also guarantee the feature vector of noise subspace and lead
To the orthogonality between vector, meanwhile, the performance of the performance ratio MA3 of angle measurement further increases.Fig. 6-8 shows that the present invention mentions
The beam space MUSIC algorithm of enhancing out is located at θ in two targets1=5 °, θ2Have in the case where=- 5 ° higher
Resolution ratio, the standard deviation of smaller average deviation sum.Fig. 9 shows point of two kinds of MUSIC algorithms under different angle interval
The comparison of resolution probability.When angle interval delta θ is identical, MA4 has higher resolution ratio probability always at identical SNR.Value
It is noted that MA3 is no longer invalid, and MA4 is still effective when two targets are close to Δ θ=4 °.It is assumed that array element
Number M is 8, and wave beam number B is 6, and number of snapshots N is 1.
Claims (7)
1. a kind of reduced order subspace angle-measuring method suitable for millimeter wave trailer-mounted radar object detection field, which is characterized in that should
Method the following steps are included:
Step 1: establishing the Estimation of Spatial Spectrum mathematical model of millimeter wave Vehicular radar system, obtain transmitting signal and receive signal
Expression formula；
Step 2: using the number and layout of transmitting antenna needed for millimeter wave Vehicular radar system and receiving antenna, in step 1
On the basis of expand establish more transmitting-receivings in the case of to the three-dimensional data structure for receiving the intermediate-freuqncy signal after signal mixing；
Step 3: three-dimensional reception signal data resulting to step 2 carries out FFT in fast time dimension and slow time dimension respectively, is visited
The distance and velocity information of the target vehicle measured and its reception signal of the aerial array on corresponding range-doppler cells
Data vector Y；
Step 4: utilizing the orientation angular range information where detection vehicle needed for trailer-mounted radar, the Wave beam forming of calculation optimization
Matrix Bopt, the reception signal data vector Y of the aerial array on specific range doppler cells is transformed into wave beam from Element space
Domain obtains Beam Domain received signal vector YB；
Step 5: utilizing the resulting Beam Domain receipt signal matrix Y of step 4BCalculate sample covariance matrixAnd it is rightIt is repaired
Just, amendment sample covariance matrix is obtained
Step 6: to the modified sample covariance matrix of step 5Eigenvalues Decomposition is carried out, noise subspace is obtainedIt utilizesWithEstablish the space MUSIC spectral function feMUSIC, spectrum peak search is carried out, arrival bearing's estimation is obtained
2. a kind of reduced order subspace angle measurement suitable for millimeter wave trailer-mounted radar object detection field according to claim 1
Method, which is characterized in that in step 1, establish the Estimation of Spatial Spectrum mathematical model of millimeter wave Vehicular radar system, obtain transmitting letter
Number and receive signal expression formula, the method is as follows:
The transmitting signal waveform of millimeter wave Vehicular radar system is that one group of carrier frequency is f0There is certain swept bandwidth in transmit cycle
Linear frequency modulation continuous wave signal, multiple transmitting antennas successively time division emission, in t moment, the transmitting signal s in i-th of periodt
The expression formula of (t, i) are as follows:
Wherein, A, f0,It is transmitting signal amplitude size, carrier frequency and initial phase, μ=B respectively0/ T is chirp rate,
Wherein B0It is swept bandwidth, T is the period of a linear frequency modulation continuous wave, the front and target vehicle as t=0, in radar
Radial distance be r, radial velocity be v target, radially speed is positive close to radar direction, thus receive signal sr(t,i)
Expression formula can be written as:
Wherein, A0It is the amplitude for receiving signal, τ=2 (r-vt)/c is the distance between target and radar bring time delay, and c is light
Speed, receives signal and original transmitted signal carries out mixing operation, and obtains intermediate-freuqncy signal by low-pass filter and be also referred to as beat letter
Number, in t moment, the expression formula s of i-th of period Beat SignalIF(t, i) can be written as:
3. a kind of reduced order subspace angle measurement suitable for millimeter wave trailer-mounted radar object detection field according to claim 2
Method, which is characterized in that in step (2), when expanding foundation mostly transmitting-receiving on the basis of step (1) to reception signal mixing
The three-dimensional data structure of intermediate-freuqncy signal afterwards, the method is as follows:
(2.1) millimeter wave Vehicular radar system has NtRoot transmitting antenna, NrRoot receiving antenna, NtRoot transmitting antenna emits phase in turn
Same CW with frequency modulation, total transmit cycle length T1=NtT, and virtual array is formed, in a signal processing flow time
Emit N altogethersaA linear frequency modulation continuous wave, in i-th of transmit cycle, the received m root transmitting antenna of kth root receiving antenna
Emit the echo complex signal of signal are as follows:
Wherein, i=1 ..., Nsa, m=1 ..., Nt, k=1 ..., Nr, A, A0,f0,It is transmitting signal amplitude respectively, receives
The signal amplitude of signal, carrier frequency and initial phase, μ=B0/ T is chirp rate, wherein B0It is swept bandwidth, T is hair
Cycle length is penetrated, d is antenna spacing, and θ is the azimuth size where target；
(2.2) signal y is emitted to eachk,i(t) it is sampled, sampling number Ns=fsT, wherein fsIt is DSP digit chip
Sample frequency, then in i-th of transmit cycle, the received m root transmitting antenna of kth root receiving antenna transmitting signal is returned
Wave complex signal sampled signal Indicate the kth piece-root grafting in i-th of transmit cycle
J-th of sampling for receiving the echo complex signal of the received m root transmitting antenna transmitting signal of antenna, in a signal processing flow
Cycle T2It is interior, wherein T2=Nsa·NtT, the sampled signal of the received m root transmitting antenna transmitting signal of kth root receiving antennaAre as follows:
By a transmit cycle T1The echo-signal of the received different transmitting antenna transmitting signals of interior identical receiving antenna is closed
And the reception signal in i-th of transmit cycle isEntire signal processing flow T2Virtual array is formed in time
Wherein, i=1 ..., Nsa, T1=NtT, therefore intermediate-freuqncy signal data matrix is NtNr×Nsa×Ns, it is three dimensions
According to vector.
4. a kind of reduced order subspace angle measurement suitable for millimeter wave trailer-mounted radar object detection field according to claim 3
Method, which is characterized in that in step (3), the three-dimensional signal data that receives resulting to step (2) is in fast time dimension and slow time dimension
FFT is carried out respectively, in the distance and velocity information of the target vehicle detected and its corresponding range-doppler cells
The reception signal data vector Y of aerial array, the method is as follows:
(3.1) signal will be received and carries out windowing FFT processing along fast time dimension, if in i-th of transmit cycle, kth piece-root grafting receives day
The reception signal of lineCarry out windowing FFT processing:
In formula, i=1 ..., Nsa, k=1 ..., Nr, wqIt is N for window functionS× 1 column vector, symbol ⊙ represent two vectors
Hadamard product, i.e., corresponding element be multiplied, fft (), which refers to, does FFT operation to signal,It indicates in i-th of transmit cycle,
Kth root receiving antenna finishes the later reception signal of windowing FFT along fast time dimension；
(3.2) radial distance of assuming that there are one radar between is r, radial velocity for v target vehicle, then to fast time dimension
After carrying out FFT, target spectrum peak position are as follows:
If fr,v=2B0R/cT, fast time dimension can be equivalent to distance dimension, and spectrum unit can be equivalent to distance unit；
(3.3) windowing FFT is carried out to the reception signal of each transmit cycle, every antenna, obtained
NqFFTFor fast time dimension FFT points；
(3.4) to YVFSlow time dimension FFT is carried out, if kth root receiving antenna, first of spectrum unit data
It is as follows to carry out FFT processing:
In formula, k=1 ..., Nr, l=1 ..., Ns, wsIt is N for window functionsa× 1 column vector,Indicate that kth piece-root grafting is received
Antenna, first of spectrum unit finish windowing FFT along slow time dimension and handle later reception signal；
After then carrying out FFT to slow time dimension, target spectrum peak position are as follows:
After slow time dimension FFT, target spectrum peak value position is only related with speed, regards slow time dimension as speed dimension；
(3.5) to every receiving antenna, the reception signal of different distance unit carries out slow time dimension FFT, obtainsNsFFTFor slow time dimension FFT points；
(3.6) by fr,vAnd fvIdentified i-th of distance dimension unit, first of speed dimension element memory take in a target vehicle
The complex vector of spectrum unit where targetIt is denoted as Y:
The i=1 ..., NqFFT, l=1 ..., NsFFT。
5. a kind of reduced order subspace angle measurement suitable for millimeter wave trailer-mounted radar object detection field according to claim 4
Method, which is characterized in that in step (4), using needed for trailer-mounted radar detection vehicle where orientation angular range information,
The beam forming matrix B of calculation optimizationopt, by the reception signal data vector Y of the aerial array on specific range doppler cells
It is transformed into Beam Domain from Element space, obtains Beam Domain received signal vector YB, the method is as follows:
(4.1) a uniform uniform line array, array number M are set, array element spacing is d, far field narrow band signal source model are as follows:
Y=AS+N
In formula, Y is the reception signal of array M × N, and A is the array manifold matrix of M × K, and S is the transmitting signal phasor of K × N, this
Locating the every a line of S is s in step (1)IFMatrix form after (t, i) sampling, N are the additive white Gaussian noise vector moment of M × N
Battle array, K are the number in far field narrow band signal source, and K≤M, fast time dimension sampling number, also referred to as number of snapshots are N, when number of snapshots N=1, Y
The complex vector Y of spectrum unit where target as in step (3)；
(4.2) dimension of beam forming matrix B is M × B, and B≤M, while B is a normal orthogonal battle array:
BHB=I
(4.3) there are two vehicles to be detected, in order to estimate two cars with respect to radar level orientation
A beam forming matrix B is designed at angle, remembers that the beam forming matrix B of design is Bopt, the matrix BoptNeed to meet following item
Part: by guiding vector a (θ1), a (θ2) and a (θm) determined by subspace be contained in BoptIt is each column determined by subspace
In, guiding vector is calculated using following formula:
Wherein, d is antenna spacing, and λ is carrier wavelength, θ1, θ2It is azimuth where two targets, and θmIt can be with is defined as:
θm=(θ1+θ2)/2
(4.4) it goes to obtain beam forming matrix B using following methodopt:
Βopt=[υ1…υB]
Wherein, a (θ) is the steering vector of array, θaAnd θbIt is the boundary of azimuth coverage, λ1≥λ2≥…≥λBIt is Q∞Characteristic value
Decompose obtained preceding B big characteristic values, υiIt is feature vector corresponding to this B big characteristic value, ΒoptIt is with υiFor column vector
Composed matrix, i=1,2 ... B；
(4.5) a Wave beam forming square will be passed through by signal complex vector Y being received on specific range doppler cells described in step (3)
Battle array, beam forming matrix are B described in this stepopt, by the beam forming matrix, signal Y will be received and converted from Element space
To Beam Domain, Beam Domain received signal vector Y is obtainedB:
YB=Bopt HY。
6. a kind of reduced order subspace angle measurement suitable for millimeter wave trailer-mounted radar object detection field according to claim 5
Method, which is characterized in that in step (5), utilize the resulting Beam Domain receipt signal matrix Y of step 4BCalculate sample covariance
MatrixAnd it is rightIt is modified, obtains amendment sample covariance matrixMethod is as follows:
(5.1) in number of snapshots N=1, guarantee to sample covariance matrixEstimation be it is unbiased, can be write as:
In formula,It isUpper i-th cornerwise element, can be written as:
Wherein, B is the dimension of beam forming matrix, YmIt is to receive signal phasor YBM-th of element, m=0,1 ..., B-1；
(5.2) method average using beamlet,It indicatesI-th of beamlet, i-th of wavelet beam data
For original sample covariance matrixIn from the i-th row to the i-th+L row, the data block that the i-th column are arranged to the i-th+L, then to i=1,
2 ..., the P sub- beam data blocks of PAveraging obtains final revised sample and repairs variance matrix
Wherein, P is beamlet number, meets B=L+P-1.
7. a kind of reduced order subspace angle measurement suitable for millimeter wave trailer-mounted radar object detection field according to claim 6
Method, which is characterized in that in step (6), to the modified sample covariance matrix of step 5Eigenvalues Decomposition is carried out, is obtained
Noise subspaceIt utilizesWithEstablish space spectral function feMUSIC, spectrum peak search is carried out, arrival bearing's estimation is obtainedMethod is as follows:
(6.1) mutually indepedent with noise due to signal, sample covariance matrix can be analyzed to two relevant to signal, noise
Point, it is rightCarrying out feature decomposition has:
In formula, ΣsBe withThe obtained preceding K maximum eigenvalue λ of feature decomposition1≥λ2≥…≥λKAs leading diagonal member
The diagonal matrix of element, Σ o areRemaining L-K eigenvalue λK+1≥λK+2≥…≥λL=σ2As its elements in a main diagonal
Diagonal matrix, wherein L beDimension, K be detection target vehicle number, σ2It is the variance of noise,It is maximum special by first K
Value indicative λ1≥λ2≥…≥λKThe subspace of corresponding characteristic vector namely signal subspace, andIt is by eigenvalue λK+1
≥λK+2≥…≥λL=σ2The subspace of corresponding characteristic vector namely noise subspace；
(6.2) space the MUSIC spectral function established are as follows:
In formula, b (θ)=< BHa(θ)>LIt is the preceding L element of the steering vector of Beam Domain,<>LIndicate to take the preceding L of column vector a
Element operation,It isPseudoinverse, under ideal conditions, it is assumed that there are an orientation angles are θiTarget vehicle, to θ ∈
[0 ° 360 °] are traversed, as θ=θiWhen,siBe orientation angle be θiDetection target carriage
Corresponding to iThe resulting characteristic value of Eigenvalues Decomposition；
(6.3) θ=θ in the ideal situationiWhen signal subspace and noise subspace be mutually orthogonal namely signal subspace
In steering vector it is also orthogonal with noise subspace, it may be assumed that
Since noise exists, so the steering vector in signal subspace also cannot be completely orthogonal with noise subspace, so real
The orientation angular estimation of Estimation of Spatial Spectrum is to traverse to θ ∈ [0 ° 360 °] on border, and maximum value Optimizing Search is realized to target
Place azimuth angle thetaiEstimationThe orientation angular estimation of the target vehicle detectedAre as follows:
Wherein,Operation indicates to seek working asObtain corresponding θ value when maximum value.
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