CN115656957A - FDA-MIMO target parameter estimation method for accelerating iterative convergence - Google Patents
FDA-MIMO target parameter estimation method for accelerating iterative convergence Download PDFInfo
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Abstract
The invention discloses an FDA-MIMO target parameter estimation method for accelerating iterative convergence, which relates to the technical field of target positioning and lays a foundation for improving target DOA and distance estimation performance by means of unfolding mutual-prime linear arrays and different-sign mutual-prime frequency offset expansion array apertures and signal bandwidths; the method comprises the steps of adopting an ESPRIT algorithm to quickly obtain DOA and distance initial estimated values, dividing output signals into slices from different dimensions, performing least square fitting on the slice signals, substituting the initial estimated values and performing alternate iteration until a support matrix is converged, and finally obtaining the DOA and distance accurate estimated values, so that accelerated convergence of an iteration process is realized, the calculation burden caused by disordered iteration is avoided, the calculation complexity is greatly reduced, the system efficiency is improved, and the method is easier to implement in engineering.
Description
Technical Field
The invention relates to the technical field of target positioning, in particular to an FDA-MIMO target parameter estimation method for accelerating iterative convergence.
Background
The FDA-MIMO radar uses an FDA (Frequency control Array) as a transmitting end and a phased Array as a receiving end, and realizes a high-precision target detection function by using angle and distance correlation characteristics of the FDA and spatial diversity of the MIMO (Multiple Input Multiple Output) radar, and is widely applied to the fields of radar target parameter estimation, clutter interference suppression, beam forming, radar imaging and the like at present.
The FDA-MIMO radar is taken as an active system radar, and the target detection performance of the FDA-MIMO radar mainly depends on a radar architecture and a radar detection method. When the FDA-MIMO radar is used for a target parameter estimation task, the array aperture size of the radar and the bandwidth of a transmitted signal determine the performance of parameter estimation. Most of the existing FDA-MIMO radar system architectures adopt a uniform architecture or a sparse architecture, such as a co-prime architecture, a nested architecture and the like, and the aperture and the signal bandwidth of an architecture array are not fully expanded, so that the improvement of target angle and distance estimation is limited.
On the other hand, the target parameter estimation algorithm is also an important factor affecting the target parameter estimation performance. The existing target parameter estimation algorithm mainly comprises a search algorithm, such as a Multiple Signal Classification (MUSIC) algorithm, a sparse reconstruction algorithm and the like, wherein the calculation complexity of the algorithm is in direct proportion to the search precision, and the requirements of the system on effectiveness and reliability cannot be met; target parameter Estimation algorithms based on rotation invariant characteristics, such as Signal parameter Estimation (ESPRIT) algorithms and propagation operator algorithms with the help of rotation invariant technology, have the advantage of computational complexity, but the parameter Estimation accuracy cannot meet the requirements.
Therefore, a completely new target angle and distance estimation method needs to be proposed to solve the above problems.
Disclosure of Invention
Aiming at the defects in the prior art, the FDA-MIMO target parameter estimation method for accelerating iterative convergence provided by the invention solves the problem that the existing FDA-MIMO radar target DOA (Direction Of Arrival angle) and distance estimation technology cannot give consideration to both speed and precision.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
an FDA-MIMO target parameter estimation method for accelerating iterative convergence comprises the following steps:
s1, constructing a transmitting end and a receiving end of the FDA-MIMO radar as non-folding co-prime linear arrays, and transmitting electromagnetic waves meeting different-sign co-prime frequency offset through the transmitting end;
s2, acquiring the electromagnetic waves reflected by each target through a receiving end, and performing matched filtering on the electromagnetic waves to obtain output signals;
s3, processing the eigenvalue of the covariance matrix of the output signal by a step ratio method to obtain a target number, and dividing the eigenvector of the covariance matrix of the output signal according to the target number to obtain a signal subspace;
s4, carrying out initialization estimation on each target parameter through an ESPRIT algorithm according to the signal subspace;
s5, slicing a snapshot accumulation matrix of the output signal from multiple dimensions, substituting the sliced snapshot accumulation matrix into an initialized estimation result of each target parameter through a least square method, and performing iterative operation to obtain a convergence result of a sending direction matrix and a receiving direction matrix;
and S6, obtaining the estimation result of each target parameter according to the convergence result of the sending direction matrix and the receiving direction matrix.
Further, in the step S1, the transmitting end and the receiving end have the same array structure, and both include a sub-array 1 and a sub-array 2; the subarray 1 comprises M array elements, and the distance between every two array elements is Nxd; one boundary array element of the subarray 1 belongs to the subarray 2; the subarray 2 comprises N array elements, and the distance between every two array elements is M x d; m and N are relatively prime integers, and d is the spacing between basic array elements;
the frequency of electromagnetic waves transmitted by each array element at the transmitting end is as follows:
wherein f is i Frequency f of electromagnetic wave for transmitting ith array element of transmitting end 0 For reference frequency, Δ f is the base frequency offset, Δ f < > 0 。
Further, the step S3 includes the following sub-steps:
s31, calculating to obtain a covariance matrix of the output signal;
s32, performing eigenvalue decomposition on the covariance matrix of the output signals to obtain each eigenvalue and corresponding eigenvector of the covariance matrix, and sequencing the eigenvalues in a descending order;
s33, obtaining the target number according to each characteristic value of the covariance matrix of the output signals by adopting a step ratio method;
and S34, selecting the eigenvectors corresponding to the eigenvalues of which the serial numbers of the covariance matrix of the output signals are less than or equal to the target number to form a signal subspace.
Further, the step S31 obtains a covariance matrix of the output signal by the following calculation:
R＝XX H /L
wherein R is the covariance matrix of the output signals, X is the snapshot accumulation matrix of the output signals, X H Is the conjugate transpose of X, and L is the number of fast beats.
Further, the eigenvalues of the covariance matrix of the output signal obtained by decomposing the eigenvalues in step S32 are λ sequentially 1 To
Q being total 2 A characteristic value; and is
Q is the total number of array elements at the transmitting end, and Q = M + N-1.
Further, in step S33, the target number is obtained by using a step ratio method according to the following formula:
wherein K is the number of targets, mu p Is the p-th step ratio, λ p For the p-th eigenvalue, λ, of the covariance matrix of the output signal p+1 For the p +1 th eigenvalue of the covariance matrix of the output signal, p ∈ [1,Q [ ] 2 -1]，
To find mu p Maximum time index p value.
Further, the step S5 includes the following sub-steps:
s51, slicing the output signal snapshot accumulation matrix into Q slices so that:
X q ＝A t D q (A r )S+N q
wherein, X q For output signals snapshotting the q-th block of the accumulation matrix, Y l For the first block of the first transformation matrix Y of the output signals, Z q For the qth block of the second transformation matrix Z of the output signals, q ∈ [1,Q]，l∈[1,L]，D q (A r ) Is a receiving direction matrix A r Of the q-th row elements of (2), D l (S T ) Is S T Of the first row elements of (a), S T In order to support the transpose of the matrix S,
is a transmission direction matrix A t Transpose of (D) q (A t ) Is A t A diagonal matrix of the q-th row elements,
is A r Transpose of (N) q Is the q block of the noise matrix N, N l Is the Lth block of the noise matrix N;
s52, establishing initial values of a receiving direction matrix and a sending direction matrix by using the initialized estimation result of each target parameter;
and S53, performing least square fitting on the snapshot accumulation matrix of the sliced output signal according to the initial values of the receiving direction matrix and the sending direction matrix, and alternately iterating until convergence to obtain the convergence results of the sending direction matrix and the receiving direction matrix.
Further, the least square fitting in step S53 includes:
wherein the content of the first and second substances,
to support the iterative values of the matrix S,
is composed of
The transpose of (a) is performed,
is a transmission direction matrix A t The value of the iteration of (a) is,
is a receiving direction matrix A r The value of the iteration of (a) is,
is composed of
The transpose of (a) is performed,
is composed of
Is transposed, (.) + For generalized inverse matrix operation, the case is Khatri-Rao product operation.
Further, the step S6 includes the following sub-steps:
s61, obtaining DOA estimated values of all targets according to the convergence result of the receiving direction matrix by the following formula:
wherein the content of the first and second substances,
for the estimated DOA value of the kth target, k ∈ [1,K ∈ ]]，
Is a DOA error parameter, [ ·] T For matrix transposition operations [ ·] + For generalized inverse matrix operation, 1 Q A column vector of dimension Q and elements 1,
as a result of convergence of the receive direction matrix
Is a function of the phase angle, q 1 Is a first parameter vector, q 1 ＝[-2π(M-1)Nd/λ 0 ,...,-2πNd/λ 0 ,0,2πMd/λ 0 ,...,2π(N-1)Md/λ 0 ] T ，λ 0 Is a reference wavelength;
s62, obtaining the distance estimation result of each target according to the convergence result of the sending direction matrix and the receiving direction matrix by the following formula:
wherein the content of the first and second substances,
is the distance estimate for the kth target,
as a parameter of the distance error,
as a result of convergence of the transmit direction matrix
The k-th column of (c), q 2 Is a second parameter vector, q 2 ＝[-4π(M-1)NΔf/c,...,-4πNΔf/c,0,4πMΔf/c,...,4π(N-1)MΔf/c] T And c is the speed of light,
is composed of
The vector of the conjugate of (a) and (b),
is the Hadamard product.
The beneficial effects of the invention are as follows:
(1) The aperture and the signal bandwidth of the array are expanded by means of the non-folding co-prime linear array and the different-sign co-prime frequency offset, and a foundation is laid for improving the DOA and the distance estimation performance of a target.
(2) The initial DOA and distance estimation values are quickly obtained by adopting an ESPRIT algorithm. In order to further improve the estimation performance, output signals are divided into slices from different dimensions, least square fitting is carried out on the slice signals, the slice signals are substituted into initial estimation values, alternate iteration is carried out until a support matrix is converged, and finally DOA and accurate distance estimation values are obtained.
(3) In the design of least square fitting, the estimation precision of target parameters is guaranteed by using the trilinear alternating least squares, and meanwhile, the accelerated convergence of an iteration process is realized by using an initial estimation value, so that the calculation burden caused by disordered iteration is avoided, and the calculation complexity is greatly reduced.
Drawings
Fig. 1 is a flowchart of an FDA-MIMO target parameter estimation method for accelerating iterative convergence according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a non-folded co-linear array architecture according to an embodiment of the present invention;
FIG. 3 is a scatter plot of the parameter estimation results according to the embodiment of the present invention;
FIG. 4 is a graph illustrating the comparison of computational complexity between an embodiment of the present invention and other methods;
FIG. 5 is a graph comparing the root mean square error of DOA as a function of signal to noise ratio for an embodiment of the present invention and other methods;
FIG. 6 is a graph comparing RMS error as a function of signal to noise ratio for embodiments of the present invention and other methods;
FIG. 7 is a graph comparing the DOA root mean square error with snapshot count for embodiments of the present invention and other methods;
FIG. 8 is a comparison of RMS error versus snapshot count for embodiments of the present invention and other methods.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
As shown in fig. 1, in an embodiment of the present invention, an FDA-MIMO target parameter estimation method for accelerating iterative convergence includes the following steps:
s1, constructing a transmitting end and a receiving end of the FDA-MIMO radar as non-folding co-prime linear arrays, and transmitting electromagnetic waves meeting the co-prime frequency offset of different numbers through the transmitting end.
As shown in fig. 2, the transmitting end and the receiving end have the same array structure, and both include a sub-array 1 and a sub-array 2; the subarray 1 comprises M array elements, and the distance between every two array elements is Nxd; one boundary array element of the subarray 1 belongs to the subarray 2; the subarray 2 comprises N array elements, and the distance between every two array elements is M x d; m and N are relatively prime integers, and d is the spacing between basic array elements;
the frequency of electromagnetic waves transmitted by each array element at the transmitting end is as follows:
wherein, f i Frequency f of electromagnetic wave for transmitting ith array element of transmitting end 0 For reference frequency, Δ f is the base frequency offset, Δ f < f 0 。
S2, the electromagnetic waves reflected by the targets are obtained through the receiving end, and matched filtering is carried out on the electromagnetic waves to obtain output signals.
Suppose there are K far-field independent targets (theta) in a noisy environment k ,r k ) K =1,2,.., K, then the output signal x (t) is:
wherein A is r ＝[a r (θ 1 ),a r (θ 2 ),…,a r (θ K )]To receive the direction matrix, A t ＝[a t (θ 1 ,r 1 ),a t (θ 2 ,r 2 )...,a t (θ K ,r K )]For a transmit direction matrix, an operation is a Khatri-Rao product,
is a Kronecher product operation, theta 1 To theta K Is DOA, r of each object 1 To r K For each target distance, K is the number of targets, n (t) is the mean 0, and the variance is δ 2 And is independent of the signal vector s (t).
And S3, processing the eigenvalue of the covariance matrix of the output signal by a step ratio method to obtain a target number, and dividing the eigenvector of the covariance matrix of the output signal according to the target number to obtain a signal subspace.
Step S3 comprises the following substeps:
s31, calculating a covariance matrix of the output signal according to the following formula:
R＝XX H /L
wherein R is the covariance matrix of the output signals, X is the snapshot accumulation matrix of the output signals, X H Is the conjugate transpose of X, and L is the number of fast beats.
And S32, performing eigenvalue decomposition on the covariance matrix of the output signals to obtain each eigenvalue and corresponding eigenvector of the covariance matrix, and sequencing the eigenvalues in a descending order.
The eigenvalue of the covariance matrix of the output signal obtained by decomposing the eigenvalue is lambda in turn 1 To
Q being total 2 A characteristic value; and is provided with
Q is the total number of array elements at the transmitting end, and Q = M + N-1.
S33, obtaining the target number according to each characteristic value of the covariance matrix of the output signals by adopting a step ratio method according to the following formula:
wherein K is the number of targets, mu p Is the p-th step ratio, λ p For the p-th eigenvalue, λ, of the covariance matrix of the output signal p+1 For the p +1 th eigenvalue of the covariance matrix of the output signal, p ∈ [1,Q ] 2 -1]，
To find mu p Maximum time index p value.
And S34, selecting the eigenvectors corresponding to the eigenvalues of which the serial numbers of the covariance matrix of the output signals are less than or equal to the target number to form a signal subspace.
And S4, carrying out initialization estimation on each target parameter through an ESPRIT algorithm according to the signal subspace.
In this embodiment, since the signal subspace and the noise subspace are orthogonal, and the direction matrix is orthogonal to the noise subspace, there is one full-valued matrix
So that the signal subspace E s = AT is true, and both ends are blocked
Wherein the content of the first and second substances,
from E s From line 1 to line (M-1) (M + N-1),
from E s From line M + N to line M (M + N-1), A 1 And A 2 Is like and A 2 ＝A 1 Φ θ,N ，
e is the natural logarithm base, and lambda is the wavelength, and can be obtained by further derivation
To pair
Decomposing the characteristic value to obtain
And
pair E s = AT both ends are re-blocked
Wherein the content of the first and second substances,
from E s To the (M-1) (M + N-1) +1 line
The components of the light-emitting diode array are combined,
from E s To (1) a
Line to last line composition, A 3 And A 4 Similarly, and A 4 ＝J 3 Φ θ,M ，
Further derivation can be found
The reconstructed output signal is X' = JX, where J is the reconstruction matrix
Then A '= JA, further derivation may yield E' S = A' T, both ends are blocked to obtain
Wherein
From E' s From line 1 to line (M-1) (M + N-1),
from E' s Line (M + N) to line (M + N-1) of (A' 1 And A' 2 Similarly and A' 2 ＝A′ 1 Φ θr,N ，
Further derivation can be found
To get E' s = A' T both ends are partitioned again to obtain
Wherein the content of the first and second substances,
from E' s From line (M-1) (M + N-1) +1 to line (M + N-2) (M + N-1),
from E' s From line M (M + N-1) +1 to the last line, A' 3 And A' 4 Similarly and A' 4 ＝A′ 3 Φθ r,M Further derived, can be obtained
Extraction of
Phase expansion is carried out, a constant term part in the expanded phase is eliminated, arcsin inverse function operation is carried out, and the kth target DOA estimated value set S of the subarray 1 is obtained θ,N,k Wherein, in the step (A),
is composed of
The kth element of (1). To pair
The same operation is carried out to obtain the kth target DOA estimated value set S of the subarray 2 θ,M,k If the true initial DOA estimation value is the same as the DOA estimation value
Wherein the content of the first and second substances,
and
is respectively from S θ,N,k And S θ,M,k The closest estimate is selected. By using
And
elimination
And
the medium DOA information is available
Extraction of
Phase expansion is carried out on the phase, the constant term part in the expanded phase is eliminated to obtain the k-th target distance estimated value of the subarray 1, and S is combined r,N,k Wherein, in the step (A),
is composed of
The kth element of (1). To pair
The same operation is carried out to obtain the kth target distance estimation value set S of the subarray 2 r,M,k Then the real initial distance estimation value is
Wherein the content of the first and second substances,
and
are respectively from S r,N,k And S r,M,k The closest estimate is selected.
And S5, slicing the snapshot accumulation matrix of the output signal from multiple dimensions, substituting the initial estimation result of each target parameter by a least square method, and performing iterative operation to obtain the convergence results of the sending direction matrix and the receiving direction matrix.
Step S5 includes the following substeps:
s51, slicing the output signal snapshot accumulation matrix into Q slices so that:
X q ＝A t D q (A r )S+N q
wherein, X q For output signals snapshotting the q-th block of the accumulation matrix, Y l For the first block of the first transformation matrix Y of the output signal, Z q For the qth block of the second transformation matrix Z of the output signals, q ∈ [1,Q]，l∈[1,L]，D q (A r ) Is a receiving direction matrix A r Of the q-th row elements of (2), D l (S T ) Is S T Of the first row elements of (a), S T In order to support the transpose of the matrix S,
is a transmission direction matrix A t Transpose of (D) q (A t ) Is A t A diagonal matrix of the q-th row elements,
is A r Transpose of (N) q Is the q-th block of the noise matrix N, N l The ith block of the noise matrix N.
And S52, constructing initial values of a receiving direction matrix and a transmitting direction matrix by using the initialized estimation result of each target parameter.
And S53, performing least square fitting on the snapshot accumulation matrix of the sliced output signal according to the initial values of the receiving direction matrix and the sending direction matrix, and alternately iterating until convergence to obtain the convergence results of the sending direction matrix and the receiving direction matrix.
The least square fitting comprises:
wherein the content of the first and second substances,
to support the iterative values of the matrix S,
is composed of
The method (2) is implemented by the following steps,
is a transmission direction matrix A t The value of the iteration of (a) is,
is a receiving direction matrix A r The value of the iteration of (a) is,
is composed of
The transpose of (a) is performed,
is composed of
Is transposed, (.) + For generalized inverse matrix operation, the case is Khatri-Rao product operation.
And S6, obtaining the estimation result of each target parameter according to the convergence result of the sending direction matrix and the receiving direction matrix.
Step S6 includes the following substeps:
s61, obtaining DOA estimated values of all targets according to the convergence result of the receiving direction matrix by the following formula:
wherein the content of the first and second substances,
for the estimated DOA value of the kth target, k ∈ [1,K ∈ ]]，
Is a DOA error parameter [ ·] T For matrix transposition operations [ ·] + For generalized inverse matrix operation, 1 Q A column vector of dimension Q and elements 1,
as a result of convergence of the receive direction matrix
Is a function solving the phase angle, q 1 Is a first parameter vector, q 1 ＝[-2π(M-1)Nd/λ 0 ,...,-2πNd/λ 0 ,0,2πMd/λ 0 ,...,2π(N-1)Md/λ 0 ] T ，λ 0 Is a reference wavelength;
s62, obtaining the distance estimation result of each target according to the convergence result of the sending direction matrix and the receiving direction matrix by the following formula:
wherein the content of the first and second substances,
is the distance estimate for the kth target,
as a parameter of the distance error, is,
as a result of convergence of the transmit direction matrix
The k-th column of (c), q 2 Is a second parameter vector, q 2 ＝[-4π(M-1)NΔf/c,...,-4πNΔf/c,0,4πMΔf/c,...,4π(N-1)MΔf/c] T And c is the speed of light,
is composed of
The vector of the conjugate of (a) and (b),
is the Hadamard product.
The invention is further illustrated below with reference to the results of the MALTAB simulation experiment:
for evaluating the invention, consider an FDA-MIMO radar system, where the transmitting end and the receiving end are non-folded linear array of reciprocity, where N =3, M =4, reference frequency f 0 =10GHz, fundamental frequency offset Δ f =300KHz. To evaluate the performance of different algorithms, root Mean Square Error (RM) was introducedSE) that
Wherein the content of the first and second substances,
represents the angle of arrival (DOA) or distance estimate, β, of the kth object at the p-th Monte Carlo simulation k Representing the true DOA or distance value of the kth target and P representing the number of monte carlo simulations.
Fig. 3 is a scatter diagram of the estimation result of the target parameters of the present invention, where the SNR is =10dB, the fast beat number is L =200, the number of monte carlo simulations is P =500, the target number is K =2, and each target parameter is (θ) ( 1 ,r 1 )＝(20°,200m)，(θ 2 ,r 2 ) = (22 °,220 m). It can be known from observing fig. 3 that the method can estimate the DOA and the distance value of two mutually close targets with higher accuracy, which is mainly benefited by the array aperture without folding and co-prime linear array expansion and the signal bandwidth of different sign and co-prime frequency offset expansion. The results of fig. 3 effectively verify the reliability of the present invention in improving target DOA and distance estimation performance.
Fig. 4 is a comparison graph of computational complexity of the present invention and other methods, including conventional tal and ESPRIT algorithms, where the number of fast beats is L =200 and the number of targets is K =2. It can be known from observing fig. 4 that, because the method adopts ESPRIT initialization instead of random initialization, the number of alternate iterations is greatly reduced, and the iteration efficiency is greatly improved, the calculation complexity of the method is far lower than that of the traditional TALS algorithm, the real-time estimation requirement of the target parameter can be met, and the method is more beneficial to engineering realization. In addition, although the calculation complexity of the method is higher than that of the ESPRIT algorithm, the estimation precision of the method is higher than that of the ESPRIT algorithm, and the requirement of an actual task on the target parameter estimation precision can be met. The results of fig. 4 effectively verify the effectiveness of the inventive method in target DOA and range estimation.
FIGS. 5-6 are graphs showing the RMS error confidence of DOA and range for the present invention and other methodsA comparison graph of noise ratio variation, wherein the number of fast beats is L =200, the number of monte carlo simulations is P =500, the number of targets is K =2, and each target parameter is (θ) ( 1 ,r 1 )＝(20°,200m)，(θ 3 ,r 3 ) = 40 °,300m, the other parameters are in accordance with the simulation parameter settings of fig. 3. Fig. 7-8 are graphs comparing the root mean square error of DOA and distance as a function of snapshot number for the present invention and other methods, where SNR =0dB, and other parameters are consistent with the simulation parameter settings of fig. 5-6. The comparison algorithms in fig. 5-8 include the conventional tal algorithm, ESPRIT algorithm, and crammel Circle (CRB). As can be seen from the observation of FIGS. 5-8, the method of the present invention gradually decreases the estimation error of DOA and distance parameters with the increase of the signal-to-noise ratio or the number of snapshots, and gradually improves the estimation performance, which is always superior to the ESPRIT algorithm. Meanwhile, the RMSE curves of the method and the traditional TALS algorithm are overlapped, which shows that the performance of the method and the performance of the traditional TALS algorithm are consistent, but the calculation complexity of the method is far lower than that of the traditional TALS algorithm, so the method is more suitable for real-time estimation of target parameters. The results of fig. 5-8 effectively demonstrate the superiority of the method of the present invention in improving target DOA and range estimation performance.
In conclusion, the invention lays a foundation for improving the DOA and the distance estimation performance of the target by means of the folding-free co-prime linear array and the different-sign co-prime frequency offset expansion array aperture and the signal bandwidth; the method comprises the steps of adopting an ESPRIT algorithm to quickly obtain DOA and distance initial estimated values, dividing output signals into slices from different dimensions, performing least square fitting on the slice signals, substituting the initial estimated values and performing alternate iteration until a support matrix is converged, and finally obtaining the DOA and distance accurate estimated values, so that accelerated convergence of an iteration process is realized, the calculation burden caused by disordered iteration is avoided, the calculation complexity is greatly reduced, the system efficiency is improved, and the method is easier to implement in engineering.
Claims (9)
1. An FDA-MIMO target parameter estimation method for accelerating iterative convergence is characterized by comprising the following steps:
s1, constructing a transmitting end and a receiving end of the FDA-MIMO radar as non-folding co-prime linear arrays, and transmitting electromagnetic waves meeting the different-sign co-prime frequency offset through the transmitting end;
s2, acquiring the electromagnetic waves reflected by each target through a receiving end, and performing matched filtering on the electromagnetic waves to obtain output signals;
s3, processing the eigenvalue of the covariance matrix of the output signal by a step ratio method to obtain a target number, and dividing the eigenvector of the covariance matrix of the output signal according to the target number to obtain a signal subspace;
s4, carrying out initialization estimation on each target parameter through an ESPRIT algorithm according to the signal subspace;
s5, slicing the snapshot accumulation matrix of the output signal from multiple dimensions, substituting the initialized estimation result of each target parameter by a least square method, and performing iterative operation to obtain the convergence results of the sending direction matrix and the receiving direction matrix;
and S6, obtaining the estimation result of each target parameter according to the convergence result of the sending direction matrix and the receiving direction matrix.
2. The FDA-MIMO target parameter estimation method for accelerated iterative convergence according to claim 1, wherein in step S1, the transmitting end and the receiving end have the same array structure and both comprise a subarray 1 and a subarray 2; the subarray 1 comprises M array elements, and the distance between every two array elements is Nxd; one boundary array element of the subarray 1 belongs to the subarray 2; the subarray 2 comprises N array elements, and the distance between every two array elements is M x d; m and N are relatively prime integers, and d is the spacing between basic array elements;
the frequency of electromagnetic waves transmitted by each array element at the transmitting end is as follows:
wherein f is i Sending the frequency f of electromagnetic wave to the ith array element of the sending end 0 For reference frequency, Δ f is the base frequency offset, Δ f < f 0 。
3. The method of claim 2, wherein the step S3 comprises the following sub-steps:
s31, calculating to obtain a covariance matrix of the output signal;
s32, performing eigenvalue decomposition on the covariance matrix of the output signals to obtain each eigenvalue and corresponding eigenvector of the covariance matrix, and sequencing the eigenvalues in a descending order;
s33, obtaining the target number according to each characteristic value of the covariance matrix of the output signals by adopting a step ratio method;
and S34, selecting the eigenvectors corresponding to the eigenvalues of which the serial numbers of the covariance matrix of the output signals are less than or equal to the target number to form a signal subspace.
4. The method of claim 3, wherein the step S31 is to calculate a covariance matrix of the output signal by the following formula:
R＝XX H /L
wherein R is the covariance matrix of the output signals, X is the snapshot accumulation matrix of the output signals, X H Is the conjugate transpose of X, and L is the number of fast beats.
5. The FDA-MIMO target parameter estimation method for accelerated iterative convergence according to claim 4, wherein the eigenvalues of the covariance matrix of the output signals obtained by decomposing the eigenvalues in the step S32 are λ sequentially 1 To
Q being total 2 A characteristic value; and is
Q is the total number of array elements at the transmitting end, and Q = M + N-1.
6. The method of claim 5, wherein the step S33 is implemented by using a step ratio method to obtain the target number according to the following formula:
wherein K is the number of targets, mu p Is the p-th step ratio, λ p For the p-th eigenvalue, λ, of the covariance matrix of the output signal p+1 For the p +1 th eigenvalue of the covariance matrix of the output signal, p ∈ [1,Q [ ] 2 -1]，
To find mu p Maximum time index p value.
7. The FDA-MIMO target parameter estimation method for accelerated iterative convergence according to claim 6, wherein the step S5 comprises the following substeps:
s51, slicing the output signal snapshot accumulation matrix into Q slices so that:
X q ＝A t D q (A r )S+X q
wherein, X q For output signals snapshotting the q-th block of the accumulation matrix, Y l For the first block of the first transformation matrix Y of the output signals, Z q For the qth block of the second transformation matrix Z of the output signals, q ∈ [1,Q]，l∈[1,L]，D q (A r ) Is a receiving direction matrix A r Of the q-th row elements of (2), D l (S T ) Is S T Of the first row elements of (a), S T In order to support the transpose of the matrix S,
is a transmission direction matrix A t Transpose of (D) q (A t ) Is A t A diagonal matrix of the q-th row elements,
is A r Transpose of (N) q Is the q block of the noise matrix N, N l Is the l-th block of the noise matrix N;
s52, establishing initial values of a receiving direction matrix and a sending direction matrix by using the initialized estimation result of each target parameter;
and S53, performing least square fitting on the snapshot accumulation matrix of the sliced output signal according to the initial values of the receiving direction matrix and the sending direction matrix, and alternately iterating until convergence to obtain the convergence results of the sending direction matrix and the receiving direction matrix.
8. The method of claim 7, wherein the least squares fitting in step S53 comprises:
wherein the content of the first and second substances,
to support the iterative values of the matrix S,
is composed of
The transpose of (a) is performed,
is a transmission direction matrix A t The value of the iteration of (a) is,
is a receiving direction matrix A r The value of the iteration of (a) is,
is composed of
The transpose of (a) is performed,
is composed of
Is transposed, (.) + For generalized inverse matrix operation, the case is Khatri-Rao product operation.
9. The method of claim 8, wherein the step S6 comprises the following sub-steps:
s61, obtaining DOA estimated values of all targets according to the convergence result of the receiving direction matrix by the following formula:
wherein the content of the first and second substances,
for the estimated DOA value of the kth target, k ∈ [1,K ∈ ]]，
Is a DOA error parameter, [ ·] T For matrix transposition operations [ ·] + For generalized inverse matrix operation, 1 Q A column vector of dimension Q and elements 1,
as a result of convergence of the receive direction matrix
Is a function of the phase angle, q 1 Is a first parameter vector, q 1 ＝[-2π(M-1)Nd/λ 0 ,...,-2πNd/λ 0 ,0,2πMd/λ 0 ,...,2π(N-1)Md/λ 0 ] T ，λ 0 Is a reference wavelength;
s62, obtaining the distance estimation result of each target according to the convergence result of the sending direction matrix and the receiving direction matrix by the following formula:
wherein the content of the first and second substances,
is the distance estimate for the kth target,
as a parameter of the distance error,
as a result of convergence of the transmit direction matrix
The k-th column of (c), q 2 Is a second parameter vector, q 2 ＝[-4π(M-1)NΔf/c,...,-4πNΔf/c,0,4πMΔf/c,...,4π(N-1)MΔf/c] T And c is the speed of light,
is composed of
The vector of the conjugate of (a) and (b),
is the Hadamard product.
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