CN107092005B - Space-time joint array processing method and device - Google Patents

Space-time joint array processing method and device Download PDF

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CN107092005B
CN107092005B CN201710456595.5A CN201710456595A CN107092005B CN 107092005 B CN107092005 B CN 107092005B CN 201710456595 A CN201710456595 A CN 201710456595A CN 107092005 B CN107092005 B CN 107092005B
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CN107092005A (en
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蒋景飞
臧维明
武震
李昀豪
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Southwest China Research Institute Electronic Equipment
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Abstract

The invention relates to a parameter measurement technology in the field of array signal processing. Aiming at the technical problems in the prior art, the invention provides a space-time combined arrayA column processing method and apparatus. The invention uses the time-space domain joint optimization processing to simultaneously carry out approximate maximum likelihood fitting on the time dimension and space dimension parameter characteristics of the array received signals, thereby estimating the amplitude, phase and direction of arrival of the incident signals with high precision. The invention combines FIR filter coefficients according to time-space domainhTo the incident direction
Figure DEST_PATH_IMAGE002
At a frequency of
Figure DEST_PATH_IMAGE004
Obtaining the original complex amplitude of the signal; then obtaining a two-dimensional power spectrum corresponding to the incident signal; searching all incident directions
Figure 884075DEST_PATH_IMAGE002
At a frequency of
Figure 66795DEST_PATH_IMAGE004
And acquiring a two-dimensional power spectrum of the target about the incident direction and frequency, and estimating the complex amplitude phase, the frequency and the direction of arrival of the incident signal.

Description

Space-time joint array processing method and device
Technical Field
The invention relates to a parameter measurement technology in the field of array signal processing, in particular to a space-time combined array processing method and a space-time combined array processing device.
Background
The array received signal actually contains information in two dimensions. From the time perspective, the amplitude and phase of the signals received by each array element channel at different time points reflect the time domain characteristics of the signals. In terms of space, the signal amplitude and phase relation of different array element channels at the same time reflects the spatial domain characteristics of incident signals.
The existing array processing method utilizes the independently received signals of each channel to obtain the amplitude and phase information of the channel, and then utilizes the amplitude and phase relation among the channels to complete the array spatial domain processing. This is a time-first and then space processing method. Fig. 1 shows a typical frequency domain cumulative array processing method in the prior art. The method comprises the steps of firstly carrying out (windowing) short-time Fourier transform on time signals received by each channel to realize frequency domain accumulation and signal detection, then obtaining the amplitude and phase relation among array channels by utilizing frequency spectrums in different channel signals in the same time window, and finally finishing the direction of arrival estimation of incident signals through subsequent spatial domain array processing.
It can be easily seen that the conventional time-before-space array processing method similar to that of fig. 1 has the following problems:
1) the cumulative detection of the signal is achieved by subjecting the received time domain signal to a (windowed) short time fourier transform. Under the conditions of short signal window length (few signal sampling points) and low signal-to-noise ratio, the estimation accuracy of parameters such as amplitude and phase of a received signal is limited by inherent problems of poor spectral resolution, spectral leakage and the like of the fast fourier transform method.
2) Subsequent spatial domain processing measures the direction of arrival parameters of the incident signal using the estimated signal amplitude and phase. Because the estimation of the amplitude and the phase has errors, and the spatial domain direction of arrival estimation algorithm may further amplify the errors, the performance of the direction of arrival estimation is difficult to guarantee.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problem that the estimation performance of the direction of arrival of subsequent space domain processing is reduced due to the fact that signal amplitude and phase with errors are obtained through time domain processing in the existing time-space-after-space array processing method, a space-time combined array processing method and a space-time combined array processing device are provided. The invention belongs to a parameter measurement technology in the field of array signal processing, and discloses a method or a device for simultaneously performing approximate maximum likelihood fitting on time dimension and space dimension parameter characteristics of an array received signal by utilizing time-space domain joint optimization processing so as to estimate the amplitude, phase and direction of arrival of an incident signal with high precision.
The technical scheme adopted by the invention is as follows:
a spatio-temporal joint array processing method comprises the following steps:
for M array element arrays with any structures, received data can be arranged into a matrix, and an array space-time signal model Y (l) is established;
filtering each row of the array space-time signal model Y (l) to complete time domain optimal fitting, and filtering each row of the array space-time signal model Y (l) to complete space domain optimal fitting to obtain a time-space domain combined FIR filter coefficient h;
according to the time-space domain combined FIR filter coefficient h, for the incident direction thetakFrequency of ωkFiltering the incident signal to obtain the original complex amplitude of the signal; then obtaining a two-dimensional power spectrum of the incident signal relative to the incident direction and frequency;
searching all incident directions thetakFrequency omegakObtaining a two-dimensional power spectrum of the target relative to the incident direction and frequency, wherein if the number of the targets is x, the first x spectral peaks with the highest power spectrum are considered as the spectral peaks corresponding to the target, the frequency and the incident angle corresponding to the position of the spectral peaks are the frequency and the arrival direction estimation of the incident signal of the target, and α corresponding to the position of the spectral peakskIs an estimate of the complex amplitude phase of the incident signal.
Further, the specific process of establishing the array spatio-temporal signal model y (l) is as follows:
for M array element array with arbitrary structure, defining the complex signal time sequence received by M array element as
Figure GDA0002243961940000021
Where l is the sampling instant and C represents the complex set. The data sampled by each array element may be arranged into an L-order vector:
ym(l)＝[ym(l),ym(l+1),…,ym(l+L-1)]T(1)
(1) where T represents the transpose of a vector or matrix;
the data received by the M array elements can be arranged into an array space-time signal model:
Y(l)＝[y1(l),y2(l),…,yM(l)]∈CL×M(2)
(2) each column of the medium L multiplied by M matrix is a received signal time sequence of the same array element at different time, and each row of the medium L multiplied by M matrix is a received data sequence of different array elements at the same time. Thus, each column of y (l) can be considered as a temporal sample of the incident signal, and each row of y (l) can be considered as a spatial sample of the incident signal.
Further, the frequency is ωkAngle of thetakK signals are incident on the array, K is 1, …, K, then:
Figure GDA0002243961940000031
in (3), a (ω)k) For the vector of time sampling factors for the kth source signal, n (l) represents the measurement noise at time l, i.e.:
Figure GDA0002243961940000032
wherein, b (θ)k) The array space sampling factor for the kth source.
Furthermore, the array space-time signal model Y (l) is filtered through the time-space domain combined FIR filter, time domain and space domain optimal fitting is completed, and the time-space domain combined FIR filter coefficient h is obtained.
The specific process of obtaining the coefficient h of the time-space domain combined FIR filter is as follows:
for incident direction of thetakFrequency of ωkDefining a complex vector h of order LtRepresenting the time-domain coefficients, M-order complex vectors h, of a time-space-domain joint FIR filtersRepresenting the spatial coefficients of the spatio-temporal joint FIR filter, the approximate maximum likelihood fit of the spatio-temporal response of the array spatio-temporal signal y (l) can be expressed as:
Figure GDA0002243961940000033
wherein:Hrepresenting the conjugate transpose of a vector or matrix, | | | | | non-conducting phosphor2Representing a vector of complex numbers2A norm;
in (6)
Figure GDA0002243961940000041
And
Figure GDA0002243961940000042
representing the time-domain coefficients h of a joint time-space domain FIR filtertPerforming time-domain filtering on Y (l) to obtain a (omega)k) The signals of the time domain characteristics pass through a time-space domain combined FIR filter without attenuation, and then M array elements are output
Figure GDA0002243961940000043
Spatial sampling with an array
Figure GDA0002243961940000044
Most similar; in the same way as above, the first and second,
Figure GDA0002243961940000045
and
Figure GDA0002243961940000046
Figure GDA0002243961940000047
spatial coefficient h representing time-space domain joint FIR filtersFor YT(l) Performing spatial filtering to obtain a signal having b (theta)k) After the signal with space domain characteristics passes through a time-space domain combined FIR filter without attenuation, L-order time sequence is output
Figure GDA0002243961940000048
Time sampling with array
Figure GDA0002243961940000049
Most similar;
the simplified calculation is carried out on the formula (6) to obtain
Figure GDA00022439619400000410
Further, the two-dimensional power spectrum calculation process is as follows:
for incident direction of thetakFrequency of ωkAccording to the following:
Figure GDA00022439619400000411
obtaining a coefficient h of a time domain coefficient of a time-space domain combined FIR filter;
according to h, reuse
Figure GDA00022439619400000412
The incident direction is theta can be obtainedkFrequency of ωkOriginal complex amplitude α of the incident signalk；
Defining signal with respect to incident direction thetakSum frequency ωkThe two-dimensional power spectrum of (a) is:
Figure GDA00022439619400000413
further, the processing device of the spatio-temporal joint array processing method comprises:
the array space-time signal model building module is used for arranging received data into a matrix for an M array element array with any structure and building an array space-time signal model Y (l); and the number of the first and second groups,
the time-space domain combined FIR filter establishing module is used for filtering each row of the array space-time signal model Y (l) to complete time domain optimal fitting, and filtering each row of the array space-time signal model Y (l) to complete space domain optimal fitting to obtain a coefficient h of the time-space domain combined FIR filter; and the number of the first and second groups,
a two-dimensional power spectrum calculation module for calculating the power spectrum according to h and the incident direction thetakFrequency of ωkObtaining the original complex amplitude of the signal; then obtaining a corresponding two-dimensional power spectrum; and the number of the first and second groups,
a direction of arrival estimation module for searching all incident directions thetakFrequency omegakObtaining a two-dimensional power spectrum of the target relative to the incident direction and frequency, wherein if the number of the targets is x, the first x spectral peaks with the highest power spectrum are considered as the spectral peaks corresponding to the target, the frequency and the incident angle corresponding to the position of the spectral peaks are the frequency and the arrival direction estimation of the incident signal of the target, and α corresponding to the position of the spectral peakskIs an estimate of the complex amplitude phase of the incident signal.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
the method comprises the steps of firstly establishing an array space-time signal model, then carrying out optimization fitting on time domain characteristics and space domain characteristics of received signals through space-time joint optimization processing, and obtaining the estimation of amplitude, phase and direction of arrival parameters of the signals. Compared with the traditional time-before-space array processing method (as shown in FIG. 1):
1) according to the method, the amplitude and the phase of the incident signal are fitted in the time domain and the space domain through space-time joint optimization processing, so that the problem that the subsequent space domain array processing performance is reduced due to the fact that the amplitude and the phase with errors are estimated in advance in the traditional method is solved.
Drawings
The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
fig. 1 is a conventional array processing method.
FIG. 2 is a spatio-temporal associative array processing method of the present invention.
Fig. 3 is a frequency-angle two-dimensional power spectrum (signal-to-noise ratio 10dB) of an incident signal.
Fig. 4 is an amplitude estimation RMSE statistic.
Fig. 5 is the phase estimate RMSE statistics.
FIG. 6 is a direction of arrival estimation RMSE statistic.
Detailed Description
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
Specifically, the method comprises the following steps:
1): for M array element array with arbitrary structure, defining the complex signal time sequence received by M array element as
Figure GDA0002243961940000061
Where l is the sampling instant and C represents the complex set. The data sampled by each array element may be arranged into an L-order vector:
ym(l)＝[ym(l),ym(l+1),…,ym(l+L-1)]T(1)
(1) inTRepresenting the transpose of a vector or matrix.
The data received by the M array elements can be arranged into an array space-time signal model:
Y(l)＝[y1(l),y2(l),…,yM(l)]∈CL×M(2)
(2) each column of the medium L multiplied by M matrix is a received signal time sequence of the same array element at different time, and each row of the medium L multiplied by M matrix is a received data sequence of different array elements at the same time. Thus, each column of y (l) can be considered as a temporal sample of the incident signal, and each row of y (l) can be considered as a spatial sample of the incident signal.
When the frequency is omegakAngle of thetakK signals of (K ═ 1, …, K) are incident on the array, then:
Figure GDA0002243961940000062
in (3), a (ω)k) For the vector of time sampling factors for the kth source signal, n (l) represents the measurement noise at time l, i.e.:
Figure GDA0002243961940000063
b(θk) Array space sampling factor (i.e., array flow pattern vector) for the kth source, take a one-dimensional linear array as an example, if the signal wavelength is λkIncident angle of thetakThe m array element has a distance d relative to the first array elementm-1And then:
Figure GDA0002243961940000064
αkc represents the initial complex amplitude of the kth source radiation signal, which can be directly calculated from the initial amplitude and phase of the signal.
And (3) filtering process of the time-space domain combined FIR filter: as described in the formula (2), each column of the array data matrix y (l) is a time sample of the incident signal, and each row of y (l) is a spatial sample of the incident signal; thus, filtering each column of Y (l) is a temporal processing operation and filtering each column of Y (l) is a spatial processing operation. According to the method, the time-space domain combined FIR filter is optimally designed, and the approximate maximum likelihood fitting of sequence time response and array space response is simultaneously carried out on the data model matrix in the step (2), so that the estimation of the amplitude, the phase and the direction of arrival parameters of the incident signal is realized.
Specifically, θ for the incident directionkFrequency of ωkDefining a complex vector h of order LtRepresenting the time-domain coefficients, M-order complex vectors h, of a time-space-domain joint FIR filtersRepresenting the spatial coefficients of a time-space domain joint FIR filter, the approximate maximum likelihood fit of the space-time response of the array can be expressed as:
Figure GDA0002243961940000071
wherein: h represents the conjugate transpose of the vector or matrix, | | | | | non-woven phosphor2Representing a vector of complex numbers2And (4) norm.
In (6)
Figure GDA0002243961940000072
And
Figure GDA0002243961940000073
representing the time-domain coefficients h of a joint time-space domain FIR filtertPerforming time-domain filtering on Y (l) to obtain a (omega)k) The signals of the time domain characteristics pass through a time-space domain combined FIR filter without attenuation, and then M array elements are output
Figure GDA0002243961940000074
Spatial sampling with an arrayMost similar; in the same way as above, the first and second,
Figure GDA0002243961940000076
and
Figure GDA0002243961940000077
Figure GDA0002243961940000078
spatial coefficient h representing time-space domain joint FIR filtersFor YT(l) Performing spatial filtering to obtain a signal having b (theta)k) After the signal with spatial domain characteristics passes through a filter without attenuation, L-order time sequence is output
Figure GDA0002243961940000079
Time sampling with array
Figure GDA00022439619400000710
Most similar. Therefore, the fitting of the array space response and the time response is completed simultaneously by the formula (6), and the problem of parameter estimation precision loss caused by time domain processing and space domain processing in the traditional method is solved.
2) The formula (6) is simplified to obtain
Figure GDA0002243961940000081
The specific process is as follows:
defining each element of the expression matrix or vector to take complex conjugation, and making:
Figure GDA0002243961940000082
Figure GDA0002243961940000083
Figure GDA0002243961940000084
Figure GDA0002243961940000085
further simplification (6) can lead to:
Figure GDA0002243961940000086
redefining:
Figure GDA0002243961940000087
Figure GDA0002243961940000088
Figure GDA0002243961940000089
then (11) can be simplified to:
Figure GDA00022439619400000810
from (15), the original optimization problem (6) can be rewritten as:
Figure GDA0002243961940000091
(16) about αkThe minimum value is obtained by:
Figure GDA0002243961940000092
by substituting (17) into (16), the original optimization problem becomes:
Figure GDA0002243961940000093
wherein:
Figure GDA0002243961940000094
Figure GDA0002243961940000095
(18) the quadratic programming problem with equality constraint in the convex optimization problem has a global optimal solution, and the analytic form can be expressed as:
h＝[dH(CHQ-1C)-1CHQ-1]H. (21)
3) two-dimensional spatial spectrum search process:
for incident direction of thetakFrequency of ωkThe coefficient h of the time-space domain joint FIR filter can be obtained as shown in (21). According to h, the incident direction is theta which can be obtained by reusing (17)kFrequency of ωkThe original complex amplitude of the incident signal. Defining signal with respect to incident direction thetakSum frequency ωkThe two-dimensional power spectrum of (a) is:
Figure GDA0002243961940000096
searching all possible incident directions thetakFrequency omegakThe two-dimensional power spectrum of the target about the incident direction and frequency can be obtained, under the condition that the number of the known signals is x (the number of the target signals is x, the number of the generated spectral peaks is more than or equal to x), the first x spectral peaks with the highest power are considered as the spectral peaks corresponding to the signals, the frequency and the incident angle corresponding to the positions of the spectral peaks are the frequency and the arrival direction estimation of the incident signals, and α corresponding to the positions of the spectral peaks is obtainedkIs an estimate of the complex amplitude phase of the incident signal.
In the present invention, formula (18) is a quadratic programming problem with equality constraints. (21) An analytic solution of the convex optimization problem is deduced and is also a global optimal solution. In terms of calculation amount, the time domain processing and the space domain processing of the array are combined, two-dimensional search needs to be carried out on the interested frequency and the incident angle according to the filter coefficient obtained in the step (21), and compared with the traditional method, the calculation amount is improved.
The first embodiment is as follows: in order to verify the effectiveness of the invention, an example of parameter estimation based on array processing is designed, and the conditions are as follows:
■, adopting one-dimensional uniform linear array with 16 array elements and 0.04m spacing;
■ array receives 2 signals arriving at the same time, wherein the frequency of signal 1 is 3958MHz, the incident angle is-8 degrees, the frequency of signal 2 is 4050MHz, and the incident angle is 0 degree;
■ the invention adopts the processing mode of fig. 2 to estimate the parameters of the amplitude, phase and direction of arrival of the radiation source through the space-time joint optimization processing, for comparison, the traditional method adopts the short-time Fourier transform to the incident time domain signal to extract the amplitude and phase of the signal, and then utilizes the Capon digital beam scanning method to estimate the direction of arrival parameters of the incident signal.
For the present example, the substeps of the present invention result in:
1) FIG. 3 shows that the array space-time model established in step 1 is filtered by a time-space domain combined FIR filter under the condition of 10dB of signal-to-noise ratio, and then a corresponding two-dimensional power spectrum is obtained. From the results, it can be found that a spectral peak with larger target power is observed at the position corresponding to the correct frequency and space angle of the power spectrum, the measurement deviation of the two target frequencies in the simulation is 0MHz and 0MHz respectively, and the measurement deviation of the azimuth angle is-0.4 degrees and 0.2 degrees respectively.
2) In order to test the accuracy of the present invention in estimating the amplitude and phase of an incident signal. Examples at different signal-to-noise ratios of-20 dB, the Root Mean Square Error (RMSE) was estimated for each signal-to-noise ratio by counting the amplitude and phase over 100 iterations of the experiment. The comparison of the performance of the method for estimating the amplitude and phase of a signal according to the formula (17) of the present invention and the conventional method for performing frequency domain accumulation by using fft is shown in fig. 4 and 5. From the results, it can be seen that the amplitude estimation RMSE and the phase estimation RMSE of the present invention are superior to the conventional amplitude and phase estimation accuracy using fft method under the same conditions, no matter whether the signal-to-noise ratio is high or low. When the time-domain signal-to-noise ratio of the signal is above-10 dB, the amplitude estimation RMSE of the method is within 1dB, and the phase estimation RMSE is within 7 °.
FIG. 6 depicts a comparison of the performance of the method of the present invention and a conventional method of estimating direction of arrival using a Capon digital beam scan after fft extraction of the amplitude and phase. The result of RMSE statistics of 100 times of simulation experiments repeated by each signal-to-noise ratio under different signal-to-noise ratios of-30 to 30dB is shown in the figure. The results show that the performance is poor and the direction finding error is large when the signal-to-noise ratio is below 0dB by adopting the traditional array processing method, and the estimation precision of the direction of arrival is not obviously improved when the signal-to-noise ratio is above 0 dB. With the method herein, the RMSE of the direction of arrival estimation tends to decrease as the signal-to-noise ratio increases, and is superior to the conventional method at all signal-to-noise ratios. At the worst signal-to-noise ratio of-30 dB, the direction of arrival estimate RMSE is about 1.25 °, and at a signal-to-noise ratio of 20dB, the direction of arrival estimate RMSE is about 0.1 °.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed.

Claims (5)

1. A spatio-temporal associative array processing method, comprising:
for M array element arrays with any structures, received data can be arranged into a matrix, and an array space-time signal model Y (l) is established;
filtering each row of the array space-time signal model Y (l) to complete time domain optimal fitting, and filtering each row of the array space-time signal model Y (l) to complete space domain optimal fitting to obtain a time-space domain combined FIR filter coefficient h;
according to the time-space domain combined FIR filter coefficient h, for the incident direction thetakFrequency of ωkFiltering the incident signal to obtain the original complex amplitude of the signal; then obtaining a two-dimensional power spectrum of the incident signal relative to the incident direction and frequency;
searching all incident directions thetakFrequency omegakObtaining the target with respect to the incident direction and frequencyThe known number of the targets is x, the first x spectral peaks with the highest power spectrum are considered as the spectral peaks corresponding to the targets, the frequency and the incident angle corresponding to the positions of the spectral peaks are the frequency and the arrival direction estimation of the target incident signals, and the position of the spectral peak corresponds to αkThe complex amplitude phase estimation of the incident signal is carried out;
filtering the array space-time signal model Y (l) through a time-space domain combined FIR filter to complete time domain and space domain optimal fitting to obtain a time-space domain combined FIR filter coefficient h;
the specific process of obtaining the coefficient h of the time-space domain combined FIR filter is as follows:
for incident direction of thetakFrequency of ωkDefining a complex vector h of order LtRepresenting the time-domain coefficients, M-order complex vectors h, of a time-space-domain joint FIR filtersRepresenting the spatial coefficients of the spatio-temporal joint FIR filter, the approximate maximum likelihood fit of the spatio-temporal response of the array spatio-temporal signal y (l) can be expressed as:
Figure FDA0002360399200000021
wherein: h represents the conjugate transpose of the vector or matrix, T represents the transpose of the vector or matrix, | | | | non-conducting phosphor2Representing a vector of complex numbers2A norm;
in (6)
Figure FDA0002360399200000022
And
Figure FDA0002360399200000023
representing the time-domain coefficients h of a joint time-space domain FIR filtertPerforming time-domain filtering on Y (l) to obtain a (omega)k) The signals of the time domain characteristics pass through a time-space domain combined FIR filter without attenuation, and then M array elements are output
Figure FDA0002360399200000024
Spatial sampling with an array
Figure FDA0002360399200000025
Most similar; in the same way as above, the first and second,
Figure FDA0002360399200000026
and
Figure FDA0002360399200000027
spatial coefficient h representing time-space domain joint FIR filtersFor YT(l) Performing spatial filtering to obtain a signal having b (theta)k) After the signal with space domain characteristics passes through a time-space domain combined FIR filter without attenuation, L-order time sequence is output
Figure FDA0002360399200000028
Time sampling with array
Figure FDA0002360399200000029
Most similar;
the simplified calculation is carried out on the formula (6) to obtain
Figure FDA00023603992000000210
Wherein:
Figure FDA00023603992000000211
and is
Figure FDA00023603992000000212
Figure FDA00023603992000000213
And is
Figure FDA0002360399200000031
Wherein:
b(θk) An array space sampling factor for a kth source;
a(ωk) A vector of time sampling factors for a kth source signal;
defining each element of the expression matrix or vector to take complex conjugation, and making:
Figure FDA0002360399200000032
Figure FDA0002360399200000033
2. a spatio-temporal joint array processing method as defined in claim 1, wherein said establishing an array spatio-temporal signal model y (l) is performed by:
for M array element array with arbitrary structure, defining the complex signal time sequence received by M array element as
Figure FDA0002360399200000034
Where 1 is a sampling time, and C represents a complex set, the data sampled by each array element may be arranged into an L-order vector:
ym(l)＝[ym(l)，ym(l+1)，...，ym(l+L-1)]T(1)
(1) where T represents the transpose of a vector or matrix;
the data received by the M array elements can be arranged into an array space-time signal model:
Y(l)＝[y1(l)，y2(l)，...，yM(l)]∈CL×M(2)
(2) each column of the L × M matrix is a time sequence of received signals of the same array element at different time instants, and each row thereof is a time sequence of received data of different array elements at the same time instant, so that each column of y (L) can be regarded as a time sample of an incident signal, and each row of y (L) can be regarded as a spatial sample of an incident signal.
3. A spatio-temporal associative array processing method according to claim 2, characterized in that the temporal frequency is a frequency ofIs omegakAngle of thetakK signals are incident on the array, K being 1.
Figure FDA0002360399200000041
In (3), a (ω)k) For the vector of time sampling factors for the kth source signal, n (l) represents the measurement noise at time 1, i.e.:
Figure FDA0002360399200000042
wherein, b (θ)k) The array space sampling factor for the kth source.
4. A spatio-temporal associative array processing method according to claim 3, wherein said two-dimensional power spectrum calculation procedure is:
for incident direction of thetakFrequency of ωkAccording to the following:
Figure FDA0002360399200000043
obtaining a coefficient h of a time domain coefficient of a time-space domain combined FIR filter; wherein:
Figure FDA0002360399200000044
and is
Figure FDA0002360399200000045
Figure FDA0002360399200000046
According to h, reuse
Figure FDA0002360399200000047
The incident direction is theta can be obtainedkFrequency of ωkOriginal complex amplitude α of the incident signalk；
And is
Figure FDA0002360399200000051
Wherein:
b(θk) An array space sampling factor for a kth source;
a(ωk) A vector of time sampling factors for a kth source signal;
defining each element of the expression matrix or vector to take complex conjugation, and making:
Figure FDA0002360399200000052
Figure FDA0002360399200000053
defining signal with respect to incident direction thetakSum frequency ωkThe two-dimensional power spectrum of (a) is:
Figure FDA0002360399200000054
5. a spatio-temporal union array processing apparatus based on the spatio-temporal union array processing method of one of claims 1 to 4, comprising:
the array space-time signal model building module is used for arranging received data into a matrix for an M array element array with any structure and building an array space-time signal model Y (l); and the number of the first and second groups,
the time-space domain combined FIR filter establishing module is used for filtering each row of the array space-time signal model Y (l) to complete time domain optimal fitting, and filtering each row of the array space-time signal model Y (l) to complete space domain optimal fitting to obtain a coefficient h of the time-space domain combined FIR filter; and the number of the first and second groups,
a two-dimensional power spectrum calculation module for calculating the power spectrum according to h and the incident direction thetakFrequency of ωkIs sent toAcquiring the original complex amplitude of the signal; then obtaining a corresponding two-dimensional power spectrum; and the number of the first and second groups,
a direction of arrival estimation module for searching all incident directions thetakFrequency omegakObtaining a two-dimensional power spectrum of the target relative to the incident direction and frequency, wherein if the number of the targets is x, the first x spectral peaks with the highest power spectrum are considered as the spectral peaks corresponding to the target, the frequency and the incident angle corresponding to the position of the spectral peaks are the frequency and the arrival direction estimation of the incident signal of the target, and α corresponding to the position of the spectral peakskIs an estimate of the complex amplitude phase of the incident signal.
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