CN105182293A - Method for estimating DOA and DOD of MIMO radar based on co-prime array - Google Patents
Method for estimating DOA and DOD of MIMO radar based on co-prime array Download PDFInfo
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The invention discloses a method for estimating the DOA and DOD of an MIMO radar based on a co-prime array, and mainly solves problems in the prior art that an MIMO radar system is low in accuracy of target detection and is small in number of recognizable information sources. The method comprises the following steps: (1) building a co-prime array model; (2) obtaining array receiving data; (3) calculating an array receiving vector; (4) estimating a covariance matrix; (5) drawing an MUSIC power spectrum chart, and estimating DOA and DOD values. The method provided by the invention remarkably improves the accuracy of target detection and increases the number of recognizable information sources. The method can be used for the detection of passive positioning of an airplane, a ship or other moving objects through a radar.
Description
Technical field
The invention belongs to communication technical field, further relate to a kind of multiple-input and multiple-output (Multiple-InputMultiple-Output based on relatively prime array in Radar Technology field, MIMO) radar system direction of arrival (DirectionofArrival, DOA) with objective emission angle (DirectionofDeparture, DOD) combined estimation method.The present invention realizes carrying out target reconnaissance and passive location to aircraft, Ship Motion target by radar.
Background technology
The estimation of DOA and the DOD of signal is an important branch in Array Signal Processing field, it refers to and utilizes aerial array that spatial-acoustic signal, electromagnetic signal are carried out to induction and received, use modern signal processing method to estimate the direction of signal source fast and accurately again, in fields such as radar, sonar, radio communications, there is significant application value.Along with the continuous progress of science and technology, to the degree of accuracy of signal Mutual coupling and and resolution also have more and more higher requirement.
The MIMO radar different waveform signal of multiple antenna transmission, and then receive echoed signal with multiple antenna.DOA and the DOD of MIMO radar estimates that tool has the following advantages: utilize matched filtering technique that its virtual aperture is expanded, thus improve the estimated accuracy of DOA and DOD; Virtual array after matched filtering estimates more target than conventional phased array radar; The waveform diversity transmitted can be utilized to increase the dirigibility of launching beam design more, thus improve the estimated accuracy of DOA and DOD.
The paper " CoprimeSamplingandtheMUSICalgorithm " (" DigitalsignalprocessingworkshopandIEEEsignalprocessinged ucationworkshop " that the people such as PiyaPal deliver at it, pp.289-294,2011.) a kind of DOA estimation method based on relatively prime array is disclosed in.First the method constructs a kind of relatively prime array heterogeneous, and this array is divided into two even submatrixs, and the value at each submatrix array element interval is relatively prime.Then, to this array received to the covariance matrix that formed of signal carry out rearrangement and smoothly wait process.Finally, then carry out the estimation of MUSIC algorithm, final acquisition DOA information.The method has the ability estimated more than the number of signals of array element number, but the weak point that the method still exists is, the method only can estimate generic array radar one dimension DOA value, can not be used for estimating the two dimension angular value in MIMO array radar system.
A kind of method of estimation of bistatic MIMO radar angle is disclosed in the patent " a kind of method of estimation of bistatic MIMO radar angle " (number of patent application CN201410409417.3, publication number CN104215947A) that Harbin Institute of Technology Shenzhen Graduate School applies at it.The method utilizes least square SLS method to carry out target and leaves angle DOD and direction of arrival angle DOA Combined estimator.First, utilize structure least square method to solve rotational invariance equation, then the evaluated error of iteration minimum signal subspace, thus improve the estimated accuracy of signal subspace.But the deficiency that the method still exists is, the method adopts typical linear homogeneous array, causes the signal number of estimation lower than array element number, even None-identified when target number is a lot, causes target acquistion failure.
Summary of the invention
The present invention is directed to the deficiency that above-mentioned prior art exists, propose a kind of MIMO radar DOA based on relatively prime array and DOD method of estimation.The present invention proposes a kind ofly to utilize relatively prime array as the method for signal transmitting and receiving array to estimate DOA and DOD value, improves target reconnaissance accuracy and discernible number of source, to solve the problem that in prior art, MIMO radar system identifiable design number of source is few.
Basic ideas of the present invention are: set up relatively prime Array Model, obtain array received data, and computing array receives vector, estimate covariance matrix, draw MUSIC power spectrum chart and estimate DOA and DOD value.
(1) relatively prime Array Model is set up:
(1a) form relatively prime array with 2P+Q-1 aerial receiver, wherein P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2;
(1b) using each aerial receiver as an array element;
(1c) electromagnetic signal is incided relatively prime array;
(2) array received data are obtained:
Use relatively prime array antenna receiver, snap sampling and matched filtering operation are carried out to extraterrestrial target electromagnetic signal, obtains relatively prime array output signal;
(3) computing array receives vector:
(3a) to the array output signal obtained after each snap sampling and matched filtering operation, a relatively prime matrix is constructed as follows:
Wherein, Y [l] represents the relatively prime matrix carrying out snap and sample and constructed by array output signal after matched filtering operation, x
n,m[l] represents the signal that m the array element that the n-th array element receives is launched, and the span of m is 0,1, ..., M, M represent the number of relatively prime array emitter array element, the span of M is the span of 2P+Q-1, n is 0,1, ..., N, N represent the number of relatively prime array received array element, the span of N is that 2P+Q-1, P, Q represent two relatively prime numbers respectively, and its span is Q > P>=2, the span of l is that 1,2...L, L represent fast umber of beats;
(3b) length of all array element every interval d is split, judge whether cut-point exists array element, if, then positional information corresponding for this array element is expressed as 1, otherwise, then positional information corresponding for this array element is expressed as 0, wherein, the span of d is 0 < d≤λ/2, and λ represents the electromagnetic signal wavelength inciding relatively prime array;
(3c) construct the vector that [(2P-1) Q+1] × 1 is tieed up, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2;
(3d) by positional information corresponding for the array element of relatively prime array, according to the order from first array element to last array element, successively positional information is put into [(2P-1) Q+1] × 1 n dimensional vector n, wherein, P, Q represent two relatively prime numbers respectively, its span is Q > P >=2, obtains array position vector;
(3e) according to the following formula, element position vector is calculated:
ω(n)＝(ν*v
-)(n)
Wherein, ω (n) represents element position vector, and n represents the sequence number of element in element position vector ω (n), and v represents array position vector, and * represents convolution operation, v
-represent the backward array position vector obtained after pair array position vector v carries out reversing operation;
(3f) in element position vector ω (n), choose element numbers be ζ and be worth non-vanishing element, construct irredundant element position vector
wherein, ζ span is-1 ,-2 ... ,-(2P-1) Q, P, Q represent two relatively prime numbers respectively, and its span is Q > P>=2, and r represents irredundant element position vector
the sequence number of middle element, the span of r is 1,2 ... G, G represent irredundant element position vector
length;
(3g) data that in irredundant element position vector, each array element receives according to the following formula, are calculated:
y
r＝Y
i(l)×Y
j H(l)/L
Wherein, y
rrepresent irredundant element position vector
in the reception data of r array element, r represents irredundant element position vector
the sequence number of middle element, the span of r is 1,2 ... G, G represent irredundant element position vector
length, Y
il () represents the i-th row of relatively prime matrix, Y
jl () represents the jth row of relatively prime matrix, ()
hrepresent conjugate transposition operation, i, j represent satisfied
any one group of integer pair of condition, the span of i to be the span of 0≤i≤2P-1, j be 0≤j≤Q-1, P, Q represents two relatively prime numbers respectively, and its span is Q > P>=2, and L represents fast umber of beats;
(3h) array received vector corresponding to irredundant element position vector according to the following formula, is constructed:
y＝[y
1,y
2,…,y
r,…,y
G]
Wherein, y represents irredundant element position vector
corresponding array received vector, y
rrepresent irredundant element position vector
in the reception data of r array element, the span of r is 1,2 ... G, G represent irredundant element position vector
length;
(4) estimate covariance matrix:
According to the following formula, the covariance matrix of array received vector is estimated:
Wherein,
represent the covariance matrix of array received vector, the span of l is that 1,2...L, L represent fast umber of beats, and ∑ represents sum operation, and y represents irredundant element position vector
corresponding array received vector, H represents conjugate transposition operation;
(5) draw multiple signal classification method MUSIC power spectrum chart and estimate direction of arrival angle DOA and objective emission angle DOD value:
(5a) be x-axis coordinate by the direction of arrival angular region of target electromagnetic signal, be y-axis coordinate by the objective emission angular region of target electromagnetic signal, multiple signal classification method MUSIC is adopted to calculate target electromagnetic signal power value, using target electromagnetic signal power value as z-axis coordinate; With x-axis coordinate figure, y-axis coordinate figure, z-axis coordinate figure draws performance number point, is connected by each point of performance number, obtains multiple signal classification method MUSIC power spectrum chart;
(5b) performance number of power spectrum chart is sorted from big to small, K spectrum peak before extracting successively, wherein, K represents the target electromagnetic signal number inciding relatively prime array;
(5c) using the direction of arrival angle DOA value of the x-axis coordinate figure corresponding to the peak point at front K spectrum peak as target, using the objective emission angle DOD value of the y-axis coordinate figure corresponding to the peak point at front K spectrum peak as target.
The present invention has the following advantages compared with prior art:
First, owing to present invention employs the method solved based on direction of arrival angle DOA and objective emission angle DOD simultaneously, overcome relatively prime array in prior art only can be used for estimating generic array radar one dimension DOA value, can not be used for the shortcoming of the two dimension angular value estimated in MIMO array radar system, make the present invention have the higher advantage of target reconnaissance accuracy.
Second, owing to present invention employs the method relatively prime Array Model combined with MIMO radar system, overcome in prior art and adopt typical linear homogeneous array, cause the shortcoming of signal number lower than array element number of estimation, the present invention is made to have under the condition that array element number is identical, the advantage that the discernible number of source of array is many.
Accompanying drawing explanation
Fig. 1 is process flow diagram of the present invention;
Fig. 2 is relatively prime array structure schematic diagram of the present invention;
Relatively prime array elements position vector figure when Fig. 3 is P=2, Q=3 in the present invention;
Fig. 4 is the MUSIC power spectrum chart drawn in emulation experiment of the present invention.
Embodiment
Below in conjunction with accompanying drawing, the present invention is described in further detail.
With reference to accompanying drawing 1, concrete steps of the present invention are as follows.
Step 1, sets up relatively prime Array Model.
Form relatively prime array with 2P+Q-1 aerial receiver, wherein P, Q represent two relatively prime numbers, and its span is Q > P >=2.
Using each aerial receiver as an array element.
Electromagnetic signal is incided relatively prime array.
The concrete steps constructing relatively prime Array Model method are as follows:
The relatively prime Array Model of structure in the embodiment of the present invention is with reference to Fig. 2, the uniform linear array 1 of array element distance is formed with Q aerial receiver, the uniform linear array 2 of array element distance is formed with 2P-1 aerial receiver, the array element distance of linear array 1 is Pd, the array element distance of linear array 2 is Qd, wherein, P, Q represent two relatively prime numbers respectively, its span is Q > P >=2, the span of d is 0 < d≤λ/2, and λ represents the electromagnetic signal wavelength inciding relatively prime array.
First of linear array 1 array element is set to the array element 0 of relatively prime array.
By the array element of the 2P-1 in linear array 2, being positioned over array element 0 spacing distance is successively Qd, 2Qd ..., in the position of (2P-1) Qd, obtain relatively prime array, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2, the span of d is 0 < d≤λ/2, and λ represents the electromagnetic signal wavelength inciding relatively prime array.
From relatively prime array first array element to last array element, successively by each array element called after array element 0, array element 1 ..., array element 2P+Q-2, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2.
Due to Q > P >=2, first array element of linear array 2 is necessarily after the 2nd array element of linear array 1, and linear array 2 is interspersed among linear array 1.In theory when array length is very large time, linear array 1 and linear array 2 in the distance may be overlapping, because the selected of P, Q is relatively prime, the length that linear array 1 and linear array 2 are chosen is limited, so in the present invention, linear array 1 and linear array 2 can not be overlapping, and all array elements of linear array 2 insert in linear array 1 successively, and linear array 1 and linear array 2 are on the same line.
Step 2, obtains array received data.
Use relatively prime array antenna receiver, snap sampling and matched filtering operation are carried out to extraterrestrial target electromagnetic signal, obtains relatively prime array output signal.
Step 3, computing array receives vector.
To the array output signal obtained after each snap sampling and matched filtering operation, construct a relatively prime matrix as follows:
Wherein, Y [l] represents the relatively prime matrix carrying out snap and sample and constructed by array output signal after matched filtering operation, x
n,m[l] represents the arbitrary element in the middle of Y [l], x
n,m[l] represents the signal launching the reception of arrival n-th array element from m array element, and the span of m is 0,1, ..., the span of M, n is 0,1 ..., N, M represents the number of relatively prime array emitter array element, and the value of M is the number that 2P+Q-1, N represent relatively prime array received array element, the value of N is 2P+Q-1, P, Q represents two relatively prime numbers, and its span is Q > P>=2, the span of l is that 1,2...L, L represent fast umber of beats.
The length of all array element every interval d is split, judge whether cut-point exists array element, if, then positional information corresponding for this array element is expressed as 1, otherwise, then positional information corresponding for this array element is expressed as 0, wherein, the span of d is 0 < d≤λ/2, and λ represents the electromagnetic signal wavelength inciding relatively prime array.
Construct the vector that [(2P-1) Q+1] × 1 is tieed up, wherein P, Q represent two relatively prime numbers, and its span is Q > P >=2.
By positional information corresponding for the array element of relatively prime array, according to the order from first array element to last array element, successively positional information is put into [(2P-1) Q+1] × 1 n dimensional vector n, wherein, P, Q represent two relatively prime numbers respectively, its span is Q > P >=2, obtains array position vector.
According to the following formula, element position vector is calculated:
ω(n)＝(ν*v
-)(n)
Wherein, ω (n) represents element position vector, and n represents the sequence number of element in element position vector ω (n), and v represents array position vector, and * represents convolution operation, v
-represent the backward array position vector obtained after pair array position vector v carries out reversing operation, in element position vector the institute of element numbers n likely value is as follows:
-(2P-1)Q,-(2P-1)Q+1,...,(2P-1)Q-1,(2P-1)Q
Wherein, P, Q represent two relatively prime numbers, and its span is Q > P >=2.
Element position vector ω (n) value in the embodiment of the present invention as shown in Figure 3, Fig. 3 represents as relatively prime array P=2, during Q=3, element position vector ω (n) obtained, the horizontal ordinate of Fig. 3 represents element position vector ω (n), and ordinate represents element position multiplicity.
In element position vector ω (n), choose element numbers be ζ and be worth non-vanishing element, be configured to irredundant element position vector
wherein, ζ span is-1 ,-2 ... ,-(2P-1) Q, P, Q represent two relatively prime numbers, and its span is Q > P>=2, and r represents irredundant element position vector
the sequence number of middle element, the span of r is 1,2 ... G, G represent
length, this is in element position vector ω (n) does not choose other elements, because Received signal strength when ζ value is 0 contains noise information, ζ span is 1,2, ..., (2P-1) Received signal strength during Q and ζ span are-1 ,-2 ..., the Received signal strength conjugation each other of-(2P-1) Q, the estimated accuracy of angle can not be increased, if array element receives vector ω (n) for shown in Fig. 3, as relatively prime array P=2, during Q=3, irredundant element position vector
According to the following formula, the data that in irredundant element position vector, each array element receives are calculated:
y
r＝Y
i(l)×Y
j H(l)/L
Wherein, y
rrepresent irredundant element position vector
in the reception data of r array element, r represents irredundant element position vector
the sequence number of middle element, the span of r is 1,2 ... G, G represent
length, Y
il () represents the i-th row of relatively prime matrix, Y
jl () represents the jth row of relatively prime matrix, ()
hrepresent conjugate transposition operation, i, j represent satisfied
any one group of integer pair of condition, the span of i to be the span of 0≤i≤2P-1, j be 0≤j≤Q-1, P, Q represents two relatively prime numbers, and its span is Q > P>=2, and L represents fast umber of beats.
According to the following formula, array received vector corresponding to irredundant element position vector is constructed:
y＝[y
1,y
2,…,y
r,…,y
G]
Wherein, y represents irredundant element position vector
corresponding array received vector, y
rrepresent irredundant element position vector
in the reception data of r array element, the span of r is 1,2 ... G, G represent
length.
Step 4, estimate covariance matrix.
According to the following formula, the covariance matrix of array received vector is estimated:
Wherein,
represent the covariance matrix of array received vector, the span of l is that 1,2...L, L represent fast umber of beats, and ∑ represents sum operation, and y represents irredundant element position vector
corresponding array received vector, H represents conjugate transposition operation.
Step 5, draws MUSIC power spectrum chart and estimates DOA and DOD value.
Being x-axis coordinate by the direction of arrival angular region of target electromagnetic signal, is y-axis coordinate by the objective emission angular region of target electromagnetic signal, adopts multiple signal classification method MUSIC to calculate target electromagnetic signal power value, using target electromagnetic signal power value as z-axis coordinate; With x-axis coordinate figure, y-axis coordinate figure, z-axis coordinate figure draws performance number point, the each point of performance number is connected, obtain multiple signal classification method MUSIC power spectrum chart, wherein, it is-90 ° ~ 90 ° that target electromagnetic signal wave reaches direction angle range, and target electromagnetic signal target emission angle scope is-90 ° ~ 90 °.
The concrete steps obtaining the performance number of multiple signal classification method MUSIC spatial spectrum are as follows:
First, define relatively prime array manifold F, relatively prime array manifold F is the vector that (2PQ+1) × 1 is tieed up, and P, Q represent two relatively prime numbers, and its span is Q > P >=2.
Secondly, according to the following formula, each element in relatively prime array manifold F is calculated:
Wherein, F (δ) represents δ element in relatively prime array manifold F, and the span of δ is 1,2 ... ξ, ξ represent the length of F (δ),
represent
in i-th element,
represent that emission array to objective emission angle is
signal response vector,
represent the objective emission angle of relatively prime array emitter signal,
expression formula be
α
k m-1represent that launching array element for m to objective emission angle is
signal response, the span of m is 0,1 ..., M, M represent in MIMO radar system and launch element number of array, α
kcalculating formula is
d
trepresent spacing between emission array, λ represents the electromagnetic signal wavelength inciding relatively prime array, α
rj(θ
k) represent α
r(θ
k) in a jth element, α
r(θ
k) represent that receiving array is θ to direction of arrival angle
ksignal response vector, θ
krepresent the direction of arrival angle of relatively prime array received signal, α
r(θ
k) expression formula be α
r(θ
k)=[1, β
k..., β
k n-1..., β
k n-1]
t, β
k n-1represent that the n-th reception array element is θ to direction of arrival angle
ksignal response, the span of n is 0,1 ..., N, N represent in MIMO radar system and receive element number of array, β
kcalculating formula is
d
rrepresent spacing between receiving array, λ represents the electromagnetic signal wavelength inciding relatively prime array, and i, j represent and satisfy condition
any one group of integer pair, the span of i to be the span of 0≤i≤2P-1, j be 0≤j≤Q-1, P, Q represents two relatively prime numbers, and its span is Q > P>=2.
Finally, according to the following formula, the performance number of multiple signal classification method MUSIC spatial spectrum is calculated:
Wherein, f
co_musicrepresent the performance number of multiple signal classification method MUSIC spatial spectrum, F represents relatively prime array manifold, H representing matrix conjugate transposition operation, E
nrepresent the covariance matrix of array received data vector
after carrying out svd, the noise subspace be made up of little eigenwert characteristic of correspondence vector.
According to order from high to low from power spectrum chart, find front K the spectrum peak that power is larger, wherein, K represents the target electromagnetic signal number inciding relatively prime array.
Using the direction of arrival angle DOA value of the x-axis coordinate figure corresponding to the peak point at front K spectrum peak as target, using the objective emission angle DOD value of the y-axis coordinate figure corresponding to the peak point at front K spectrum peak as target.
Below in conjunction with analogous diagram, effect of the present invention is further described.
1. simulated conditions:
Emulation of the present invention carries out under the software environment of MATLABR2014a.
2. emulate content:
Emulation experiment of the present invention utilizes 9 aerial receivers to form relatively prime array, wherein the array element distance of relatively prime array midline battle array 1 is 3d, the array element distance of linear array 2 is 4d, d is the half of incoming electromagnetic signal wavelength, fast umber of beats of sampling is 500, target electromagnetic signal wave reaches deflection DOA and observes the angular range in spatial domain be [-90 °, 90 °], its space lattice divides and is spaced apart 1 °, target electromagnetic signal target emission angle DOD observes the angular range in spatial domain be [-90 °, 90 °], its space lattice divides and is spaced apart 1 °, launch first number in Multiinputoutput MIMO radar system and be all 9 with the first number of reception, the target electromagnetic number of signals inciding relatively prime array is 12, the emission angle of target electromagnetic signal and acceptance angle are (-60 °,-50 °), (-50 °,-40 °), (-40 °,-30 °), (-30 °,-20 °), (-20 °, 0 °), (0 °, 10 °), (10 °, 20 °), (20 °, 30 °), (30 °, 40 °), (40 °, 50 °), (50 °, 60 °), (60 °, 70 °), signal to noise ratio (S/N ratio) is 10db.
3. simulated effect analysis:
Fig. 4 is the multiple signal classification method MUSIC power spectrum chart drawn in emulation experiment of the present invention, wherein, x coordinate in Fig. 4 represents the direction of arrival angular region of target electromagnetic signal, y coordinate represents the objective emission angular region of target electromagnetic signal, z coordinate represents the target electromagnetic signal power value adopting multiple signal classification method MUSIC to calculate, and Fig. 4 represents the situation that the target electromagnetic signal power value adopting multiple signal classification method MUSIC to calculate changes with direction of arrival angular region and objective emission angular region.
As can be seen from Figure 4 direction of arrival angle and the objective emission angle target electromagnetic signal power value impact on employing multiple signal classification method MUSIC calculating of target electromagnetic signal is larger, the x-axis coordinate figure corresponding to peak point at the spectrum peak that performance number is larger is as the direction of arrival angle DOA value of target, and the y-axis coordinate figure corresponding to peak point at the spectrum peak that performance number is larger is as the objective emission angle DOD value of target.Adopting relatively prime array linear array 1 array number to be 4, when linear array 2 array number is 5, the present invention can estimate maximum 12 signal sources, more than discernible 8 signal sources of conventional uniform array.Obviously, invention increases target reconnaissance accuracy and discernible number of source higher than the MIMO radar object localization method of prior art, multi-targets recognition shows outstanding performance.
Claims (6)
1., based on relatively prime array MIMO radar DOA and a DOD method of estimation, comprise the steps:
(1) relatively prime Array Model is set up:
(1a) form relatively prime array with 2P+Q-1 aerial receiver, wherein P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2;
(1b) using each aerial receiver as an array element;
(1c) electromagnetic signal is incided relatively prime array;
(2) array received data are obtained:
Use relatively prime array antenna receiver, snap sampling and matched filtering operation are carried out to extraterrestrial target electromagnetic signal, obtains relatively prime array output signal;
(3) computing array receives vector:
(3a) to the array output signal obtained after each snap sampling and matched filtering operation, a relatively prime matrix is constructed as follows:
Wherein, Y [l] represents the relatively prime matrix carrying out snap and sample and constructed by array output signal after matched filtering operation, x
n,m[l] represents the signal that m the array element that the n-th array element receives is launched, and the span of m is 0,1, ..., M, M represent the number of relatively prime array emitter array element, the span of M is the span of 2P+Q-1, n is 0,1, ..., N, N represent the number of relatively prime array received array element, the span of N is that 2P+Q-1, P, Q represent two relatively prime numbers respectively, and its span is Q > P>=2, the span of l is 1,2 ... L, L represent fast umber of beats;
(3b) length of all array element every interval d is split, judge whether cut-point exists array element, if, then positional information corresponding for this array element is expressed as 1, otherwise, then positional information corresponding for this array element is expressed as 0, wherein, the span of d is 0 < d≤λ/2, and λ represents the electromagnetic signal wavelength inciding relatively prime array;
(3c) construct the vector that [(2P-1) Q+1] × 1 is tieed up, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2;
(3d) by positional information corresponding for the array element of relatively prime array, according to the order from first array element to last array element, successively positional information is put into [(2P-1) Q+1] × 1 n dimensional vector n, wherein, P, Q represent two relatively prime numbers respectively, its span is Q > P >=2, obtains array position vector;
(3e) according to the following formula, element position vector is calculated:
ω(n)＝(ν*v
-)(n)
Wherein, ω (n) represents element position vector, and n represents the sequence number of element in element position vector ω (n), and v represents array position vector, and * represents convolution operation, v
-represent the backward array position vector obtained after pair array position vector v carries out reversing operation;
(3f) in element position vector ω (n), choose element numbers be ζ and be worth non-vanishing element, construct irredundant element position vector
wherein, ζ span is-1 ,-2 ... ,-(2P-1) Q, P, Q represent two relatively prime numbers respectively, and its span is Q > P>=2, and r represents irredundant element position vector
the sequence number of middle element, the span of r is 1,2 ... G, G represent irredundant element position vector
length;
(3g) data that in irredundant element position vector, each array element receives according to the following formula, are calculated:
y
r＝Y
i(l)×Y
j H(l)/L
Wherein, y
rrepresent irredundant element position vector
in the reception data of r array element, r represents irredundant element position vector
the sequence number of middle element, the span of r is 1,2 ... G, G represent irredundant element position vector
length, Y
il () represents the i-th row of relatively prime matrix, Y
jl () represents the jth row of relatively prime matrix, ()
hrepresent conjugate transposition operation, i, j represent satisfied
any one group of integer pair of condition, the span of i to be the span of 0≤i≤2P-1, j be 0≤j≤Q-1, P, Q represents two relatively prime numbers respectively, and its span is Q > P>=2, and L represents fast umber of beats;
(3h) array received vector corresponding to irredundant element position vector according to the following formula, is constructed:
y＝[y
1,y
2,…,y
r,…,y
G]
Wherein, y represents irredundant element position vector
corresponding array received vector, y
rrepresent irredundant element position vector
in the reception data of r array element, the span of r is 1,2 ... G, G represent irredundant element position vector
length;
(4) estimate covariance matrix:
According to the following formula, the covariance matrix of array received vector is estimated:
Wherein,
represent the covariance matrix of array received vector, the span of l is 1,2 ... L, L represent fast umber of beats, and Σ represents sum operation, and y represents irredundant element position vector
corresponding array received vector, H represents conjugate transposition operation;
(5) draw multiple signal classification method MUSIC power spectrum chart and estimate direction of arrival angle DOA and objective emission angle DOD value:
(5a) be x-axis coordinate by the direction of arrival angular region of target electromagnetic signal, be y-axis coordinate by the objective emission angular region of target electromagnetic signal, multiple signal classification method MUSIC is adopted to calculate target electromagnetic signal power value, using target electromagnetic signal power value as z-axis coordinate; With x-axis coordinate figure, y-axis coordinate figure, z-axis coordinate figure draws performance number point, is connected by each point of performance number, obtains multiple signal classification method MUSIC power spectrum chart;
(5b) performance number of power spectrum chart is sorted from big to small, K spectrum peak before extracting successively, wherein, K represents the target electromagnetic signal number inciding relatively prime array;
(5c) using the direction of arrival angle DOA value of the x-axis coordinate figure corresponding to the peak point at front K spectrum peak as target, using the objective emission angle DOD value of the y-axis coordinate figure corresponding to the peak point at front K spectrum peak as target.
2. according to claim 1 based on relatively prime array MIMO radar DOA and DOD method of estimation, it is characterized in that: the method for the relatively prime Array Model of structure described in step (1) is as follows:
The first step, the uniform linear array 1 of array element distance is formed with Q aerial receiver, the uniform linear array 2 of array element distance is formed with 2P-1 aerial receiver, the array element distance of linear array 1 is Pd, and the array element distance of linear array 2 is Qd, wherein, P, Q represent two relatively prime numbers respectively, its span is Q > P >=2, and the span of d is 0 < d≤λ/2, and λ represents the electromagnetic signal wavelength inciding relatively prime array;
Second step, is set to the array element 0 of relatively prime array by first of linear array 1 array element;
3rd step, the 2P-1 of linear array 2 array element is positioned over successively with array element 0 at a distance of being Qd, 2Qd ..., in the position of (2P-1) Qd, obtain relatively prime array, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2, the span of d is 0 < d≤λ/2, and λ represents the electromagnetic signal wavelength inciding relatively prime array;
4th step, from relatively prime array first array element to last array element, successively by each array element called after array element 0, array element 1 ..., array element 2P+Q-2, wherein, P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2.
3. according to claim 1 based on relatively prime array MIMO radar DOA and DOD method of estimation, it is characterized in that: in element position vector ω (n) described in step (3e), the span of element numbers n is as follows:
-(2P-1)Q,-(2P-1)Q+1,...,(2P-1)Q-1,(2P-1)Q
Wherein, P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2.
4. according to claim 1 based on relatively prime array MIMO radar DOA and DOD method of estimation, it is characterized in that: the direction of arrival angular region of the target electromagnetic signal described in step (5a) is-90 ° ~ 90 °.
5. according to claim 1 based on relatively prime array MIMO radar DOA and DOD method of estimation, it is characterized in that: the objective emission angular region of the target electromagnetic signal described in step (5a) is-90 ° ~ 90 °.
6. according to claim 1 based on relatively prime array MIMO radar DOA and DOD method of estimation, it is characterized in that: the target electromagnetic signal power value described in step (5a) is obtained by following steps:
The first step, defines relatively prime array manifold F, and relatively prime array manifold F is the vector that (2PQ+1) × 1 is tieed up, and wherein, P, Q represent two relatively prime numbers respectively, and its span is Q > P >=2;
Second step, according to the following formula, calculates each element in relatively prime array manifold F:
Wherein, F (δ) represents δ element in relatively prime array manifold F, and the span of δ is 1,2 ... ξ, ξ represent the length of relatively prime array manifold F,
represent
in i-th element,
represent that emission array to objective emission angle is
signal response vector,
represent the objective emission angle of relatively prime array emitter signal, α
rj(θ
k) represent α
r(θ
k) in a jth element, α
r(θ
k) represent that receiving array is θ to direction of arrival angle
ksignal response vector, θ
krepresent the direction of arrival angle of relatively prime array received signal, i, j represent and satisfy condition
any one group of integer pair, the span of i to be the span of 0≤i≤2P-1, j be 0≤j≤Q-1, P, Q represents two relatively prime numbers respectively, and its span is Q > P>=2;
3rd step, according to the following formula, calculates the target electromagnetic signal power value of multiple signal classification method MUSIC spatial spectrum:
Wherein, f
co_musicrepresent the target electromagnetic signal power value of multiple signal classification method MUSIC spatial spectrum, F represents relatively prime array manifold, E
nrepresent the covariance matrix of array received data vector
after carrying out svd, the noise subspace be made up of little eigenwert character pair vector, H representing matrix conjugate transposition operation.
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