CN103746699A - Signal reconstruction method based on rotation matrix error estimation for alternative sampling system - Google Patents

Signal reconstruction method based on rotation matrix error estimation for alternative sampling system Download PDF

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CN103746699A
CN103746699A CN201410042694.5A CN201410042694A CN103746699A CN 103746699 A CN103746699 A CN 103746699A CN 201410042694 A CN201410042694 A CN 201410042694A CN 103746699 A CN103746699 A CN 103746699A
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CN103746699B (en
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马仑
郑暄
杨鹏
马锐捷
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Changan University
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Abstract

The invention discloses a signal reconstruction method based on rotation matrix error estimation for an alternative sampling system. The method comprises the following steps: I, initial parameter setting; II, training sample construction: transforming sample sequences of M A/D (Analog to Digital) conversion chips in the same time interval t to a frequency domain by means of fast Fourier transform to obtain M training samples, wherein the M training samples construct a training sample set; III, time base error estimation: selection of dual frequency points for error estimation, covariance matrix estimation, feature decomposition, extraction of a large feature value and a corresponding feature vector thereof and time base error estimation; IV, gain error estimation; V, gain error compensation; VI, weight vector reconstruction; VII, signal reconstruction in a frequency domain; VIII, inverse fast Fourier transform. The method disclosed by the invention is simple in steps, reasonable in design, convenient to implement and good in application effect, and the problems of complex error estimating process, large calculation amount, large signal error after reconstruction and the like existing in the conventional signal reconstruction method for a parallel alternative sampling system can be solved effectively.

Description

Alternating sampling system signal reconstructing method based on spin matrix estimation error
Technical field
The present invention relates to a kind of alternating sampling system signal reconstructing method, especially relate to a kind of alternating sampling system signal reconstructing method based on spin matrix estimation error.
Background technology
Along with the continuous expansion of Digital Signal Processing range of application, the frequency bandwidth of required processing signals (abbreviation bandwidth) scope is also increasing.From the viewpoint of signal bandwidth, signal can be divided into narrow band signal, broadband signal and ultra-broadband signal three classes.Narrow band signal is in most of the cases sampled and just can be reached high-precision object with single ADC conversion chip; Under the prerequisite that meets sampling thheorem, broadband signal generally also can be sampled with single two-forty ADC conversion chip, but general precision is lower, can not carry out sampling with high precision, cannot meet the instructions for use of great dynamic range, and the hardware cost of circuit is higher; And for ultra-broadband signal, under the prerequisite that meets sampling thheorem, existence conditions is generally difficult to sample with single ADC conversion chip.
Thereby, for broadband signal and ultra-broadband signal (signal bandwidth even goes up gigabit tens to hundreds of million), meeting sampling thheorem and do not meeting under the prerequisite of sampling thheorem with single ADC conversion chip, sampling with high precision and the reconstruct that realize signal are all difficult to achieve the goal.If utilize theory and the method for Digital Signal Processing, by multiple low rates, a multi-channel sampling system of high-precision ADC conversion chip formation,, can realize the sampling with high precision of signal and the Real-time Reconstruction of signal under certain condition.The basic theories of basis signal processing, for the sampling system of M passage, the minimum undistorted sample frequency of the each ADC conversion chip of system requirements is the 1/M that adopts single ADC conversion chip to sample, along with the significantly reduction that ADC conversion chip sampling rate is required, make the contradiction between signal bandwidth and sampling rate obtain very large improvement.In actual use procedure, above-mentioned multi-channel sampling system is on the one hand when keeping ADC conversion chip sampling rate constant, and the M in the time of system can being allowed the maximum signal bandwidth of input rise to single ADC conversion chip sampling doubly; On the other hand, in keeping system, allow the maximum signal bandwidth of input when constant, can adopt low rate, high-precision ADC conversion chip to sample to input signal, reach the object that reconstructs the high-speed, high precision sample sequence of signal with M low rate, sampling with high precision sequence, solve the contradiction between sampling rate and sampling precision.The signal processing system such as modern radar, communication, requires directly antenna receiving signal to be carried out processing after digitlization again conventionally.For broadband signal, this requires ADC conversion chip to have very high switching rate, but its sampling rate often doubles, and quantified precision will be similar to and decline one, thereby causes the dynamic range about 6dB that declines; And the stability of sampling clock also will decline along with the raising of sampling rate, thereby this reduces signal to noise ratio aggravation Aperture Jitter, and cost also can sharply increase.
Time-interleaved Sampling techniques, front end utilizes the parallel successively sampling of multi-disc ADC conversion chip, and rear end serial is multiplexed, can effectively solve the contradiction between sampling rate and signal bandwidth and sampling rate and sampling precision.But, because it depends on each interchannel accurate cooperation, with respect to single channel sampling, there is more systematic error.First, the gain between each passage ADC conversion chip and biasing are difficult to accomplish strict consistent; Secondly, the sampling clock phase between parallel channel also cannot be realized accurate control (time base deviation) under prior art condition.Therefore, multi-channel system error will cause sample waveform nonlinear distortion, reduce systematic function.
For above problem, lot of documents has proposed different systematic error methods of estimation, as signal spectra analytic approach, correlation method, parameter model, the blind estimation technique etc., but signal spectra analytic approach, correlation method and parameter model all require known pumping signal that frequency spectrum is pure as calibration source mostly, estimation procedure complexity, and need again to proofread and correct after error parameter variation; Though and the blind estimation technique is without special incentive signal, needs repeatedly iteration and be difficult for convergence, amount of calculation is larger.
< < electronic letters, vol > > 37 (10) in 2009: in 2298-2301 by field library, Pan Huiqing, the non-homogeneous integrated correction method of self adaptation > > in < < parallel sampling that Wang Zhi has just delivered mono-literary composition and < < in 2010 electronic measurements and instrument journal > > 24 (1): in 34-38 by Pan Huiqing, field library, proposed to utilize adaptive control technology in the non-homogeneous signal adaptive reconstructing method of base > > mono-literary composition in the time of in < < time-interleaved sampling that leaf Peng etc. is delivered, utilize minimum mean square error criterion that mismatch error is estimated to be converted into multidimensional nonlinear optimization problem, respectively to time base error, gain error and biased error are carried out the method for iteration.But because the method is not considered the impact of noise, under Low SNR, estimated accuracy will decline, and is easily absorbed in addition local minimum point in iterative process.In 09 phase < < system engineering in 2012 and electronic technology > > by Ma Lun, Liao Guisheng, in time-interleaved sampling system estimation error > > mono-literary composition of the < < that Lu Dan delivers based on subspace projection, a kind of time-interleaved sampling system error estimation based on subspace projection technique has been proposed, the method is carried out respectively after Fourier transform processing (owing to adopting low rate ADC conversion chip to Sampling for Wide-Band Signal the sampled data of each passage, single channel sample data will produce spectral aliasing), the output of multichannel frequency domain sample is regarded as to array output, the orthogonal property estimating channel mismatch error of the noise subspace that utilizes frequency domain linear phase vector corresponding to multichannel time delay and obtained by sampled data.But, owing to needing to carry out iteration in estimation error process, face equally amount of calculation and be absorbed in greatly and easily the difficulties such as local minimum point.
To sum up, currently used time-interleaved Sampling techniques are ripe and perfect not enough, and existing time-interleaved sampling system error estimation all exists to some extent estimation procedure complexity, needs repeatedly iteration and is difficult for convergence, amount of calculation more greatly, is easily absorbed in the defects such as local minimum point and deficiency.The problems such as correspondingly, the signal reconfiguring method based on above-mentioned existing time-interleaved sampling system error estimation also exists that method step is simple, amount of calculation is large, result of use is poor, the signal errors after reconstruct is large.
Summary of the invention
Technical problem to be solved by this invention is for above-mentioned deficiency of the prior art, a kind of alternating sampling system signal reconstructing method based on spin matrix estimation error is provided, its method step simple, reasonable in design and realize convenient, result of use is good, the problem such as can effectively solve that estimation error process complexity, amount of calculation that existing time-interleaved sampling system signal reconfiguring method exists are large, the signal errors after reconstruct is large.
For solving the problems of the technologies described above, the technical solution used in the present invention is: a kind of alternating sampling system signal reconstructing method based on spin matrix estimation error, is characterized in that the method comprises the following steps:
Step 1, the defeated setting of initial parameter: by parameter input unit, input need be carried out the sample frequency f of quantity M, M described A/D conversion chip of the A/D conversion chip that adopts in the time-interleaved sampling system of estimation error sbandwidth bps with sampled broadband signal s (t); Described parameter input unit and data processor join;
Step 2, training sample build: first get the sample sequence of M described A/D conversion chip in same time period t, include n sampled signal, wherein n=t × f in the sample sequence of each described A/D conversion chip s; Again the sample sequence of M described A/D conversion chip is done to fast Fourier transform to frequency domain, M training sample of corresponding acquisition;
M training sample is respectively the training sample of M sampling channel of described time-interleaved sampling system, and a training sample set of M training sample composition;
Step 3, time base error are estimated: adopt data processor and utilize training sample set constructed in step 2, the time base error of described time-interleaved sampling system is estimated, process is as follows:
Step 301, estimation error are chosen with bifrequency point: from [f s/ 2, f s/ 2] in, choose at random two numerical value f 1and f 2the a pair of Frequency point of using as estimation error, wherein f 1> f 2and Δ f=f 1-f 2;
Step 302, covariance matrix: from described training sample, concentrate that to find out frequency values be f 1sample data composition training sample A, and from described training sample, concentrate that to find out frequency values be f 2sample data composition training sample B; Afterwards, calculate respectively the covariance matrix R of training sample A and training sample B aand R b;
Step 303, feature decomposition: to covariance matrix R aand R bcarry out respectively feature decomposition, obtain R a=U a∑ a(U a) hand R b=U b∑ b(U b) h; Wherein, and it is by M characteristic vector
Figure BDA0000463638050000042
the matrix forming;
Figure BDA0000463638050000043
and it represents with M characteristic value
Figure BDA0000463638050000044
for the diagonal matrix of diagonal entry, and M characteristic value
Figure BDA0000463638050000045
descending arrangement;
Figure BDA0000463638050000046
and it is by M characteristic vector
Figure BDA0000463638050000047
the matrix forming;
Figure BDA0000463638050000048
and it represents with M characteristic value
Figure BDA0000463638050000049
for the diagonal matrix of diagonal entry, and M characteristic value
Figure BDA00004636380500000410
descending arrangement; The computing of H representing matrix conjugate transpose;
Step 304, large characteristic value and characteristic of correspondence vector thereof extract: M characteristic value from step 303
Figure BDA00004636380500000411
in, extract front 2I+1 large characteristic value
Figure BDA00004636380500000412
and 2I+1 corresponding characteristic vector
Figure BDA00004636380500000413
recycling formula
Figure BDA00004636380500000414
to 2I+1 characteristic vector
Figure BDA00004636380500000415
be out of shape respectively, obtain 2I+1 vector
Figure BDA0000463638050000051
wherein j is positive integer and j=1 ..., 2I+1; Meanwhile, M characteristic value from step 303
Figure BDA0000463638050000052
in, extract front 2I+1 large characteristic value
Figure BDA0000463638050000053
and 2I+1 corresponding characteristic vector
Figure BDA0000463638050000054
wherein,
Step 305, time base error are estimated: according to formula
Figure BDA0000463638050000056
draw the time delay error vector of described time-interleaved sampling system
Figure BDA0000463638050000057
in formula, ∠ represents to get phase angle, τ=[0,1/Mf s... (M-1)/Mf s] t;
Figure BDA0000463638050000058
wherein
Figure BDA0000463638050000059
for 2I+1 the characteristic vector extracting in step 304
Figure BDA00004636380500000510
summation;
Figure BDA00004636380500000511
for 2I+1 in step 304 vector summation; &Delta; ^ &tau; = [ 0 , &Delta; ^ &tau; 1 , &CenterDot; &CenterDot; &CenterDot; , &Delta; ^ &tau; M - 1 ] T ,
Figure BDA00004636380500000514
for the time base error of M sampling channel;
Step 4, gain error are estimated: adopt data processor and according to the time delay error vector drawing in step 3
Figure BDA00004636380500000515
gain error to described time-interleaved sampling system estimates, process is as follows:
Step 401, time base error compensation: the time delay error vector that utilizes the described time-interleaved sampling system drawing in step 3 to ideal frequency domain steering vector, P ' (f) compensates, and draws the frequency domain steering vector p after time base error compensation i(f), wherein p i &prime; ( f ) = [ 1 , e - j 2 &pi; ( f + if s ) &tau; , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi; ( f + if s ) ( M - 1 ) &tau; ] T , p i ( f ) = [ 1 , e - j 2 &pi; ( f + if s ) ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi; ( f + if s ) ( M - 1 ) ( &tau; + &Delta; ^ &tau; M - 1 ) ] T , I is positive integer and i=-I ... 0 ... I;
Step 402, utilize formula D i=diag{p i(f) }, to the frequency domain steering vector p after time base error compensation in step 401 i(f) be out of shape, obtain vectorial D i;
Step 403, according to formula
Figure BDA00004636380500000519
obtain matrix W;
In formula,
Figure BDA00004636380500000520
or wherein
Figure BDA00004636380500000522
for 2I+1 the characteristic vector extracting in step 304
Figure BDA00004636380500000523
composition matrix and
Figure BDA00004636380500000524
for 2I+1 the characteristic vector extracting in step 304
Figure BDA00004636380500000526
composition matrix and U S b = [ u 1 b , &CenterDot; &CenterDot; &CenterDot; , u 2 I + 1 b ] ;
Step 404, feature decomposition: matrix W is carried out to feature decomposition, and take out eigenvalue of maximum characteristic of correspondence vector G=[1, g 2..., g m] t;
Step 405, gain error are estimated: according to formula
Figure BDA00004636380500000528
draw the gain error vector of described time-interleaved sampling system
Figure BDA00004636380500000529
wherein
Figure BDA00004636380500000530
1, g 1..., g m-1be respectively the gain error of M sampling channel;
Step 5, gain error compensation: adopt data processor and utilize the gain error vector of the described time-interleaved sampling system drawing in step 405
Figure BDA0000463638050000061
to the frequency domain steering vector p after time base error compensation in step 402 i(f) compensate, draw the frequency domain steering vector p after gain error compensation i' ' (f), wherein p i &prime; &prime; ( f ) = [ 1 , g 2 &CenterDot; e - j 2 &pi; ( f + if s ) ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , g M &CenterDot; e - j 2 &pi; ( f + if s ) ( M - 1 ) ( &tau; + &Delta; ^ &tau; M - 1 ) ] T , I is positive integer and i=-I ... 0 ... I;
Step 6, weight vector reconstruct: adopt data processor and according to
Figure BDA0000463638050000063
calculate weight vector w i(f); In formula, R (f) is the covariance matrix of training sample f, wherein f=[-f s/ 2, f s/ 2]; The training sample f sample data composition training sample of serving as reasons described training sample to concentrate all frequency values be f;
Signal reconstruction in step 7, frequency domain: adopt data processor and according to formula
Figure BDA0000463638050000064
described time-interleaved sampling system is needed to reconstruction signal
Figure BDA0000463638050000065
be reconstructed, obtain the reconstruction signal S in frequency domain i(f);
The described sample sequence that needs reconstruction signal to comprise M described A/D conversion chip in same time period T
Figure BDA0000463638050000066
and it is denoted as
Figure BDA0000463638050000067
wherein S ^ ( n ) = [ S ^ 0 ( n ) , S ^ 1 ( n ) , &CenterDot; &CenterDot; &CenterDot; , S ^ M - 1 ( n ) ] T , Wherein m is numbering and the m=0 of M described A/D conversion chip, 1 ..., M-1; In formula, for by the described reconstruction signal that needs
Figure BDA00004636380500000610
do fast Fourier transform to the signal obtaining after frequency domain, and
Figure BDA00004636380500000611
Step 8, inverse fast Fourier transform: adopt data processor that the reconstruction signal in the frequency domain obtaining in step 7 is made to inverse fast Fourier transform, obtain the signal S (n) after reconstruct; Wherein S (n)=[S 0(n), S 1(n) ..., S m-1(n)] t, and the signal S (n) after reconstruct comprises the sample sequence S of M described A/D conversion chip after reconstruct m(n).
The above-mentioned alternating sampling system signal reconstructing method based on spin matrix estimation error, is characterized in that: while carrying out weight vector reconstruct in step 6, process is as follows:
Step 601, w i(0) calculate: according to formula
Figure BDA00004636380500000612
calculate w i(0); Wherein w i(0) weight vector while being f=0, p i' ' (0) be according to the frequency domain steering vector p after gain error compensation in step 5 ifrequency domain steering vector during f=0 that ' ' (f) draws; R (0) is the covariance matrix of training sample 0, the training sample 0 sample data composition training sample of serving as reasons described training sample to concentrate all frequency values be 0;
Step 602, weight vector w i(f) calculate: according to formula w i(f)=B (f) w i(0), calculate w i(f); In formula, B ( f ) = diag { 1 , e - j 2 &pi;f ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi;f ( ( M - 1 ) &tau; + &Delta; ^ &tau; M - 1 ) } .
The above-mentioned alternating sampling system signal reconstructing method based on spin matrix estimation error, is characterized in that: after time base error has been estimated in step 305, draw a time delay error vector of described time-interleaved sampling system, also need to enter afterwards step 306;
Step 306, return to step 301, again from [f s/ 2, f s/ 2] in, choose at random a pair of Frequency point that two numerical value are used as estimation error, and according to step 302 to the method in step 305, draw the time delay error vector of described time-interleaved sampling system;
Step 307, one or many repeating step 306, draw the time delay error vector of one or more described time-interleaved sampling systems;
Step 308, the multiple time delay error vectors that draw under present case are averaged, as the time delay error vector of described time-interleaved sampling system
Figure BDA0000463638050000072
The above-mentioned alternating sampling system signal reconstructing method based on spin matrix estimation error, is characterized in that: n=100～1000 in step 2.
The above-mentioned alternating sampling system signal reconstructing method based on spin matrix estimation error, is characterized in that: while getting the sample sequence of M described A/D conversion chip in a time period t in step 2, adopt sliding window method to choose.
The above-mentioned alternating sampling system signal reconstructing method based on spin matrix estimation error, it is characterized in that: the sampling system of time-interleaved described in step 1 comprises multiple A/D conversion chips, multiple time delay control modules of respectively sampling time of multiple described A/D conversion chips being controlled, multiple data processing units that respectively multiple described A/D conversion chip institute sampled signal carried out to Fourier transform processing, the data processor that joins with multiple described data processing units and multiple described data processing units signal after treatment is joined with the multiplexer of data array formal output with multiplexer respectively, multiple described time delay control modules are joined with multiple described A/D conversion chips respectively, multiple described A/D conversion chips join with multiple described data processing units respectively, multiple described time delay control modules control by data processor and it all joins with data processor.
The above-mentioned alternating sampling system signal reconstructing method based on spin matrix estimation error, it is characterized in that: described time-interleaved sampling system also comprises multiple gain control module of joining with multiple described A/D conversion chips respectively, and multiple described gain control module are connected on respectively between multiple described A/D conversion chips and multiple described data processing unit; Described gain control module is amplifier or attenuator; Multiple described gain control module are controlled by data processor and it all joins with data processor.
The above-mentioned alternating sampling system signal reconstructing method based on spin matrix estimation error, is characterized in that: the time delay error vector that estimates described time-interleaved sampling system in step 3
Figure BDA0000463638050000081
after, described data processor is according to the time delay error vector of estimating to draw
Figure BDA0000463638050000082
multiple described time delay control modules are controlled respectively.
The above-mentioned alternating sampling system signal reconstructing method based on spin matrix estimation error, is characterized in that: the gain error vector that estimates described time-interleaved sampling system in step 4
Figure BDA0000463638050000083
after, described data processor is according to the gain error vector of estimating to draw multiple described gain control module are controlled respectively.
The present invention compared with prior art has the following advantages:
1, time base error method of estimation is simple, reasonable in design and realize conveniently, and estimates because time base error is independent of gain error, thereby has avoided the impact of this Uncertainty of gain error on time base error estimated accuracy.
2, time base error estimation is simple with gain error method of estimation, without carrying out iteration, can directly to time base error and gain error, carry out high accuracy estimation.And the present invention is separation with gain error and estimate respectively by time base error, not only without iteration, reduce amount of calculation, can also improve estimated accuracy, avoid being absorbed in local minimum point.Because the frequency domain linear phase vector of two frequency channels in time-interleaved sampling system only differs a diagonal matrix, (be spin matrix C, wherein the parameter in spin matrix C is consistent with the parameter in B, difference is only that spin matrix C is diagonal matrix, vector of B, that is to say that B is the another kind of representation of spin matrix C) and this spin matrix mainly by time base error, determined, based on the corresponding relation of above characteristic and frequency domain linear phase vector and signal subspace, the present invention is without iteration, can direct estimation time base error and gain error, and sane to remaining biased error and noise.
3, time base error estimation is high with the estimated accuracy of gain error, and under signal to noise ratio prerequisite, the deviation of estimated time base error approximately than existing adaptive approach estimated accuracy, improve 2 times.For improving the sampling precision of time-interleaved sampling system, estimate the time delay error vector of time-interleaved sampling system after, data processor can be according to the time delay error vector of estimating to draw
Figure BDA0000463638050000093
multiple time delay control modules are controlled respectively; And, estimate the gain error vector of time-interleaved sampling system after, data processor can be according to the gain error vector of estimating to draw
Figure BDA0000463638050000095
multiple described gain control module are controlled respectively.Thereby, can effectively solve existing time-interleaved sampling system error estimation and all exist to some extent estimation procedure complexity, repeatedly iteration and difficult convergence, amount of calculation more greatly, to be easily absorbed in the defects such as local minimum point and deficiency.
4, signal reconfiguring method is simple, amount of calculation is little and it is convenient to realize, signal errors after reconstruct is little, the problem such as can effectively solve that the method step that the signal reconfiguring method of existing time-interleaved sampling system exists is simple, amount of calculation is large, result of use is poor, the signal errors after reconstruct is large.
To sum up, the inventive method step simple, reasonable in design and realize convenient, result of use is good, the problem such as can effectively solve that estimation error process complexity, amount of calculation that existing time-interleaved sampling system signal reconfiguring method exists are large, the signal errors after reconstruct is large.
Below by drawings and Examples, technical scheme of the present invention is described in further detail.
Accompanying drawing explanation
Fig. 1 adopts the schematic block circuit diagram of time-interleaved sampling system for the present invention.
Fig. 2 is method flow block diagram of the present invention.
Fig. 3 is the change curve schematic diagram that gain error estimated accuracy of the present invention changes with signal to noise ratio.
Fig. 4 is the change curve schematic diagram that time base error estimated accuracy of the present invention changes with signal to noise ratio.
Description of reference numerals:
1-A/D conversion chip; 2-time delay control module; 3-data processing unit;
4-multiplexer; 5-parameter input unit; 6-data processor;
7-gain control module.
Embodiment
A kind of alternating sampling system signal reconstructing method based on spin matrix estimation error as shown in Figure 2, comprises the following steps:
Step 1, the defeated setting of initial parameter: by parameter input unit 5, input need be carried out the sample frequency f of quantity M, M described A/D conversion chip 1 of the A/D conversion chip 1 that adopts in the time-interleaved sampling system of estimation error sbandwidth bps with sampled broadband signal s (t).Described parameter input unit 5 is joined with data processor 6.
Wherein, M is positive integer and M >=3.
Step 2, training sample build: first get the sample sequence of M described A/D conversion chip 1 in same time period t, include n sampled signal, wherein n=t × f in the sample sequence of each described A/D conversion chip 1 s; Again the sample sequence of M described A/D conversion chip 1 is done to fast Fourier transform to frequency domain, M training sample of corresponding acquisition.
M training sample is respectively the training sample of M sampling channel of described time-interleaved sampling system, and a training sample set of M training sample composition.
In the present embodiment, in M training sample, in each training sample, include n sample data.
In the present embodiment, n=100～1000 in step 2.
During actual use, can according to specific needs, the value size of n be adjusted accordingly.
Step 3, time base error are estimated: adopt data processor 6 and utilize training sample set constructed in step 2, the time base error of described time-interleaved sampling system is estimated, process is as follows:
Step 301, estimation error are chosen with bifrequency point: from [f s/ 2, f s/ 2] in, choose at random two numerical value f 1and f 2the a pair of Frequency point of using as estimation error, wherein f 1> f 2and Δ f=f 1-f 2.
Step 302, covariance matrix: from described training sample, concentrate that to find out frequency values be f 1sample data composition training sample A, and from described training sample, concentrate that to find out frequency values be f 2sample data composition training sample B; Afterwards, calculate respectively the covariance matrix R of training sample A and training sample B aand R b.
In the present embodiment, while getting the sample sequence of M described A/D conversion chip 1 in a time period t in step 2, adopt sliding window method to choose, and the sample covariance matrix of sliding window notebook data that method samples is to covariance matrix R aand R bestimate.Actual carry out sample build time, specifically interim with reference to < < system engineering and electronic technology > > 2007 the 09th, disclosed author is Ma Lun, Li Zhenfang, Liao Guisheng and name are called the sliding window method of recording in the document of multichannel low rate method of sampling > > of < < wideband radar signal chooses the method for estimation of sample and covariance matrix, calculate the covariance matrix R of training sample A and training sample B aand R b.
Step 303, feature decomposition: to covariance matrix R aand R bcarry out respectively feature decomposition, obtain R a=U a∑ a(U a) hand R b=U b∑ b(U b) h; Wherein,
Figure BDA0000463638050000111
and it is by M characteristic vector
Figure BDA0000463638050000112
the matrix forming;
Figure BDA0000463638050000113
and it represents with M characteristic value for the diagonal matrix of diagonal entry, and M characteristic value
Figure BDA0000463638050000115
descending arrangement;
Figure BDA0000463638050000116
and it is by M characteristic vector
Figure BDA0000463638050000117
the matrix forming;
Figure BDA0000463638050000118
and it represents with M characteristic value for the diagonal matrix of diagonal entry, and M characteristic value
Figure BDA00004636380500001110
descending arrangement; The computing of H representing matrix conjugate transpose.
Step 304, large characteristic value and characteristic of correspondence vector thereof extract: M characteristic value from step 303
Figure BDA00004636380500001111
in, extract front 2I+1 large characteristic value and 2I+1 corresponding characteristic vector
Figure BDA00004636380500001113
recycling formula
Figure BDA00004636380500001114
to 2I+1 characteristic vector
Figure BDA00004636380500001115
be out of shape respectively, obtain 2I+1 vector
Figure BDA00004636380500001116
wherein j is positive integer and j=1 ..., 2I+1; Meanwhile, M characteristic value from step 303
Figure BDA00004636380500001117
in, extract front 2I+1 large characteristic value
Figure BDA00004636380500001118
and 2I+1 corresponding characteristic vector wherein,
Figure BDA00004636380500001120
wherein, 2I is spectral aliasing number of times.
Step 305, time base error are estimated: according to formula
Figure BDA00004636380500001121
draw the time delay error vector of described time-interleaved sampling system
Figure BDA00004636380500001122
in formula, ∠ represents to get phase angle, τ=[0,1/Mf s... (M-1)/Mf s] t;
Figure BDA00004636380500001123
wherein for 2I+1 the characteristic vector extracting in step 304
Figure BDA00004636380500001125
summation;
Figure BDA00004636380500001126
for 2I+1 in step 304 vector
Figure BDA00004636380500001127
summation; &Delta; ^ &tau; = [ 0 , &Delta; ^ &tau; 1 , &CenterDot; &CenterDot; &CenterDot; , &Delta; ^ &tau; M - 1 ] T , for the time base error of M sampling channel.
In the present embodiment, in step 303
Figure BDA00004636380500001130
wherein C be spin matrix and C = diag { 1 , e - j 2 &pi;&Delta;f ( &tau; + &Delta; ^ &tau; 2 ) , &CenterDot; &CenterDot; &CenterDot; e - j 2 &pi;&Delta;f ( ( M - 1 ) &tau; + &Delta; ^ &tau; M ) } , U S a = [ u 1 a , &CenterDot; &CenterDot; &CenterDot; U 2 I + 1 a ] For 2I+1 large characteristic value the subspace that characteristic of correspondence vector is opened is signal subspace,
Figure BDA0000463638050000123
for 2I+1 large characteristic value
Figure BDA0000463638050000124
the subspace that characteristic of correspondence vector is opened is signal subspace, formula
Figure BDA0000463638050000125
represent the rotation relationship of two signal subspaces.
Wherein, B = [ 1 , e - j 2 &pi;&Delta;f ( &tau; + &Delta; ^ &tau; 2 ) , &CenterDot; &CenterDot; &CenterDot; e - j 2 &pi;&Delta;f ( ( M - 1 ) &tau; + &Delta; ^ &tau; M ) ] T . Because C is identical with the parameter of B inside, it is not only that C is a diagonal matrix, and B is a vector, thereby B is the another kind of expression-form of spin matrix C.
Step 4, gain error are estimated: adopt data processor 6 and according to the time delay error vector drawing in step 3
Figure BDA0000463638050000127
gain error to described time-interleaved sampling system estimates, process is as follows:
Step 401, time base error compensation: the time delay error vector that utilizes the described time-interleaved sampling system drawing in step 3 to ideal frequency domain steering vector, P ' (f) compensates, and draws the frequency domain steering vector p after time base error compensation i(f), wherein p i &prime; ( f ) = [ 1 , e - j 2 &pi; ( f + if s ) &tau; , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi; ( f + if s ) ( M - 1 ) &tau; ] T , p i ( f ) = [ 1 , e - j 2 &pi; ( f + if s ) ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi; ( f + if s ) ( M - 1 ) ( &tau; + &Delta; ^ &tau; M - 1 ) ] T , I is positive integer and i=-I ... 0 ... I.
Step 402, utilize formula D i=diag{p i(f) }, to the frequency domain steering vector p after time base error compensation in step 401 i(f) be out of shape, obtain vectorial D i.
Step 403, according to formula
Figure BDA00004636380500001211
obtain matrix W.
In formula,
Figure BDA00004636380500001212
or wherein
Figure BDA00004636380500001214
for 2I+1 the characteristic vector extracting in step 304 composition matrix and
Figure BDA00004636380500001216
Figure BDA00004636380500001217
for 2I+1 the characteristic vector extracting in step 304
Figure BDA00004636380500001218
composition matrix and U S b = [ u 1 b , &CenterDot; &CenterDot; &CenterDot; , u 2 I + 1 b ] .
Step 404, feature decomposition: matrix W is carried out to feature decomposition, and take out eigenvalue of maximum characteristic of correspondence vector G=[1, g 2..., g m] t.
Step 405, gain error are estimated: according to formula
Figure BDA00004636380500001220
draw the gain error vector of described time-interleaved sampling system
Figure BDA00004636380500001221
wherein 1, g 1..., g m-1be respectively the gain error of M sampling channel.
In the present embodiment, after time base error has been estimated in step 305, draw a time delay error vector of described time-interleaved sampling system, also need to enter afterwards step 306;
Step 306, return to step 301, again from [f s/ 2, f s/ 2] in, choose at random a pair of Frequency point that two numerical value are used as estimation error, and according to step 302 to the method in step 305, draw the time delay error vector of described time-interleaved sampling system.
Step 307, one or many repeating step 306, draw the time delay error vector of one or more described time-interleaved sampling systems.
Step 308, the multiple time delay error vectors that draw under present case are averaged, as the time delay error vector of described time-interleaved sampling system
Figure BDA0000463638050000131
Like this, by step 306, to step 308, can further improve the estimated accuracy of time delay error, choose multiple Frequency point repeating steps 306 and estimate respectively to draw time delay error vector after time base error averages
Figure BDA0000463638050000132
and when gain error is estimated, the time delay error vector after average based on this
Figure BDA0000463638050000133
estimate.
In the present embodiment, in step 307, the number of times of repeating step 306 is 2 times～10 times.
And, while carrying out time base error compensation in step 401, utilize the time delay error vector of the described time-interleaved sampling system drawing in step 308
Figure BDA0000463638050000134
carry out time base error compensation.
Step 5, gain error compensation: adopt data processor 6 and utilize the gain error vector of the described time-interleaved sampling system drawing in step 405
Figure BDA0000463638050000135
to the frequency domain steering vector p after time base error compensation in step 402 i(f) compensate, draw the frequency domain steering vector p after gain error compensation i' ' (f), wherein p i &prime; &prime; ( f ) = [ 1 , g 2 &CenterDot; e - j 2 &pi; ( f + if s ) ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , g M &CenterDot; e - j 2 &pi; ( f + if s ) ( M - 1 ) ( &tau; + &Delta; ^ &tau; M - 1 ) ] T , I is positive integer and i=-I ... 0 ... I.
Step 6, weight vector reconstruct: adopt data processor 6 and according to
Figure BDA0000463638050000137
calculate weight vector w i(f); In formula, R (f) is the covariance matrix of training sample f, wherein f=[-f s/ 2, f s/ 2]; The training sample f sample data composition training sample of serving as reasons described training sample to concentrate all frequency values be f.
In the present embodiment, when covariance matrix R (f) is estimated, its method with to covariance matrix R aand R bthe method of estimating is identical.
Signal reconstruction in step 7, frequency domain: adopt data processor 6 and according to formula
Figure BDA0000463638050000138
described time-interleaved sampling system is needed to reconstruction signal
Figure BDA0000463638050000139
be reconstructed, obtain the reconstruction signal S in frequency domain i(f).
The described sample sequence that needs reconstruction signal to comprise M described A/D conversion chip 1 in same time period T
Figure BDA0000463638050000141
and it is denoted as
Figure BDA0000463638050000142
wherein S ^ ( n ) = [ S ^ 0 ( n ) , S ^ 1 ( n ) , &CenterDot; &CenterDot; &CenterDot; , S ^ M - 1 ( n ) ] T , Wherein m is numbering and the m=0 of M described A/ D conversion chip 1,1 ..., M-1; In formula,
Figure BDA0000463638050000144
for by the described reconstruction signal that needs
Figure BDA0000463638050000145
do fast Fourier transform to the signal obtaining after frequency domain, and S ^ ( f ) = [ S ^ 0 ( f ) , S ^ 1 ( f ) , &CenterDot; &CenterDot; &CenterDot; S ^ M - 1 ( f ) ] T .
Step 8, inverse fast Fourier transform: adopt data processor 6 that the reconstruction signal in the frequency domain obtaining in step 7 is made to inverse fast Fourier transform, obtain the signal S (n) after reconstruct; Wherein S (n)=[S 0(n), S 1(n) ..., S m-1(n)] t, and the signal S (n) after reconstruct comprises the sample sequence S of M described A/D conversion chip 1 after reconstruct m(n).
In the present embodiment, as shown in Figure 1, the sampling system of time-interleaved described in step 1 comprises multiple A/D conversion chips 1, multiple time delay control modules 2 of respectively sampling time of multiple described A/D conversion chips 1 being controlled, multiple data processing units 3 that respectively 1 sampled signal of multiple described A/D conversion chips carried out to Fourier transform processing, the data processor 6 that joins and multiple described data processing unit 3 signal after treatment is joined with the multiplexer 4 of data array formal output with multiplexer 4 with multiple described data processing units 3 respectively, multiple described time delay control modules 2 are joined with multiple described A/D conversion chips 1 respectively, multiple described A/D conversion chips 1 join with multiple described data processing units 3 respectively, multiple described time delay control modules 2 are controlled by data processor 6 and multiple described time delay control module 2 is all joined with data processor 6.The sample frequency of multiple described A/D conversion chips 1 is all identical.
In the present embodiment, for improving the sampling precision of described time-interleaved sampling system, in step 3, estimate the time delay error vector of described time-interleaved sampling system
Figure BDA0000463638050000147
after, described data processor 6 is according to the time delay error vector of estimating to draw multiple described time delay control modules 2 are controlled respectively.
Meanwhile, described time-interleaved sampling system also comprises multiple gain control module 7 of joining with multiple described A/D conversion chips 1 respectively, and multiple described gain control module 7 are connected on respectively between multiple described A/D conversion chips 1 and multiple described data processing unit 3.Described gain control module 7 is amplifier or attenuator.
In the present embodiment, in step 4, estimate the gain error vector of described time-interleaved sampling system
Figure BDA0000463638050000151
after, described data processor 6 is according to the gain error vector of estimating to draw
Figure BDA0000463638050000152
multiple described gain control module 7 are controlled respectively.
To sum up, while adopting the present invention to carry out estimation error, without carrying out iteration, can directly to time base error and gain error, carry out high accuracy estimation.And the present invention is separation with gain error and estimate respectively by time base error, not only without iteration, reduce amount of calculation, can also improve estimated accuracy, avoid being absorbed in local minimum point.And because time base error is independent of gain error, estimate, thereby avoided the impact of this Uncertainty of gain error on time base error estimated accuracy.
While carrying out weight vector reconstruct in above-mentioned steps six, need estimate one by one [f s/ 2, f s/ 2] the covariance matrix R (f) of each Frequency point ask inverse of a matrix in, thereby amount of calculation is very large.
In the present embodiment, while carrying out weight vector reconstruct in step 6, process is as follows:
Step 601, w i(0) calculate: according to formula
Figure BDA0000463638050000153
calculate w i(0); Wherein w i(0) weight vector while being f=0, p i' ' (0) be according to the frequency domain steering vector p after gain error compensation in step 5 ifrequency domain steering vector during f=0 that ' ' (f) draws; R (0) is the covariance matrix of training sample 0, the training sample 0 sample data composition training sample of serving as reasons described training sample to concentrate all frequency values be 0.
Step 602, weight vector w i(f) calculate: according to formula w i(f)=B (f) w i(0), calculate w i(f); In formula, B ( f ) = diag { 1 , e - j 2 &pi;f ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi;f ( ( M - 1 ) &tau; + &Delta; ^ &tau; M - 1 ) } .
Owing to having estimated the high-precision time-delay error vector of described time-interleaved sampling system in step 3
Figure BDA0000463638050000155
thereby can directly draw B ( f ) = diag { 1 , e - j 2 &pi;f ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi;f ( ( M - 1 ) &tau; + &Delta; ^ &tau; M - 1 ) } . And, the weight vector w in the time of only need estimating f=0 i(0), directly draw [f s/ 2, f s/ 2] weight vector of other Frequency point in.That is to say, will only need to calculate a covariance matrix and ask inverse of a matrix, can complete the whole frequency spectrum reconfiguration of described time-interleaved sampling system, not only greatly reduce amount of calculation, but also be conducive to keep taking out amplitude and the intrinsic relation of phase place of frequency spectrum.
For the estimated accuracy of contrast error estimation that the present invention adopts, referring to the gain A RMSE(drawing after 100 empirical averages under the different signal to noise ratio (snr) conditions shown in Fig. 3 and Fig. 4 is gain error) and time base ARMSE(time base error) estimated accuracy, by Fig. 3 and Fig. 4, can be found out in signal to noise ratio and be greater than in 20dB situation, error estimation of the present invention and self-adaptation control method estimated accuracy are almost identical; But when signal to noise ratio is less than 15dB, error estimation of the present invention has shown good robustness.
The above; it is only preferred embodiment of the present invention; not the present invention is imposed any restrictions, every any simple modification of above embodiment being done according to the technology of the present invention essence, change and equivalent structure change, and all still belong in the protection range of technical solution of the present invention.

Claims (9)

1. the alternating sampling system signal reconstructing method based on spin matrix estimation error, is characterized in that the method comprises the following steps:
Step 1, the defeated setting of initial parameter: by parameter input unit (5), input need be carried out the sample frequency f of quantity M, M described A/D conversion chip (1) of A/D conversion chip (1) that adopts in the time-interleaved sampling system of estimation error sbandwidth bps with sampled broadband signal s (t); Described parameter input unit (5) is joined with data processor (6);
Step 2, training sample build: first get the sample sequence of M described A/D conversion chip (1) in same time period t, include n sampled signal, wherein n=t × f in the sample sequence of each described A/D conversion chip (1) s; Again the sample sequence of M described A/D conversion chip (1) is done to fast Fourier transform to frequency domain, M training sample of corresponding acquisition;
M training sample is respectively the training sample of M sampling channel of described time-interleaved sampling system, and a training sample set of M training sample composition;
Step 3, time base error are estimated: adopt data processor (6) and utilize training sample set constructed in step 2, the time base error of described time-interleaved sampling system is estimated, process is as follows:
Step 301, estimation error are chosen with bifrequency point: from [f s/ 2, f s/ 2] in, choose at random two numerical value f 1and f 2the a pair of Frequency point of using as estimation error, wherein f 1> f 2and Δ f=f 1-f 2;
Step 302, covariance matrix: from described training sample, concentrate that to find out frequency values be f 1sample data composition training sample A, and from described training sample, concentrate that to find out frequency values be f 2sample data composition training sample B; Afterwards, calculate respectively the covariance matrix R of training sample A and training sample B aand R b;
Step 303, feature decomposition: to covariance matrix R aand R bcarry out respectively feature decomposition, obtain R a=U a∑ a(U a) hand R b=U b∑ b(U b) h; Wherein,
Figure FDA0000463638040000011
and it is by M characteristic vector
Figure FDA0000463638040000012
the matrix forming;
Figure FDA0000463638040000013
and it represents with M characteristic value
Figure FDA0000463638040000014
for the diagonal matrix of diagonal entry, and M characteristic value
Figure FDA0000463638040000015
descending arrangement;
Figure FDA0000463638040000016
and it is by M characteristic vector
Figure FDA0000463638040000017
the matrix forming; and it represents with M characteristic value
Figure FDA0000463638040000022
for the diagonal matrix of diagonal entry, and M characteristic value
Figure FDA0000463638040000023
descending arrangement; The computing of H representing matrix conjugate transpose;
Step 304, large characteristic value and characteristic of correspondence vector thereof extract: M characteristic value from step 303
Figure FDA0000463638040000024
in, extract front 2I+1 large characteristic value
Figure FDA0000463638040000025
and 2I+1 corresponding characteristic vector
Figure FDA0000463638040000026
recycling formula
Figure FDA0000463638040000027
to 2I+1 characteristic vector
Figure FDA0000463638040000028
be out of shape respectively, obtain 2I+1 vector wherein j is positive integer and j=1 ..., 2I+1; Meanwhile, M characteristic value from step 303
Figure FDA00004636380400000210
in, extract front 2I+1 large characteristic value
Figure FDA00004636380400000211
and 2I+1 corresponding characteristic vector
Figure FDA00004636380400000212
wherein,
Figure FDA00004636380400000213
Step 305, time base error are estimated: according to formula
Figure FDA00004636380400000214
draw the time delay error vector of described time-interleaved sampling system
Figure FDA00004636380400000215
in formula, ∠ represents to get phase angle, τ=[0,1/Mf s... (M-1)/Mf s] t;
Figure FDA00004636380400000216
wherein
Figure FDA00004636380400000217
for 2I+1 the characteristic vector extracting in step 304
Figure FDA00004636380400000218
summation;
Figure FDA00004636380400000219
for 2I+1 in step 304 vector
Figure FDA00004636380400000220
summation; &Delta; ^ &tau; = [ 0 , &Delta; ^ &tau; 1 , &CenterDot; &CenterDot; &CenterDot; , &Delta; ^ &tau; M - 1 ] T , for the time base error of M sampling channel;
Step 4, gain error are estimated: adopt data processor (6) and according to the time delay error vector drawing in step 3 gain error to described time-interleaved sampling system estimates, process is as follows:
Step 401, time base error compensation: the time delay error vector that utilizes the described time-interleaved sampling system drawing in step 3
Figure FDA00004636380400000223
to ideal frequency domain steering vector, P ' (f) compensates, and draws the frequency domain steering vector p after time base error compensation i(f), wherein p i &prime; ( f ) = [ 1 , e - j 2 &pi; ( f + if s ) &tau; , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi; ( f + if s ) ( M - 1 ) &tau; ] T , p i ( f ) = [ 1 , e - j 2 &pi; ( f + i f s ) ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi; ( f + if s ) ( M - 1 ) ( &tau; + &Delta; ^ &tau; M - 1 ) ] T , I is positive integer and i=-I ... 0 ... I;
Step 402, utilize formula D i=diag{p i(f) }, to the frequency domain steering vector p after time base error compensation in step 401 i(f) be out of shape, obtain vectorial D i;
Step 403, according to formula obtain matrix W;
In formula,
Figure FDA00004636380400000227
or
Figure FDA00004636380400000228
wherein
Figure FDA00004636380400000229
for 2I+1 the characteristic vector extracting in step 304
Figure FDA0000463638040000031
composition matrix and
Figure FDA0000463638040000032
Figure FDA00004636380400000319
for 2I+1 the characteristic vector extracting in step 304
Figure FDA0000463638040000033
composition matrix and U S b = [ u 1 b , &CenterDot; &CenterDot; &CenterDot; , u 2 I + 1 b ] ;
Step 404, feature decomposition: matrix W is carried out to feature decomposition, and take out eigenvalue of maximum characteristic of correspondence vector G=[1, g 2..., g m] t;
Step 405, gain error are estimated: according to formula
Figure FDA0000463638040000035
draw the gain error vector of described time-interleaved sampling system wherein
Figure FDA0000463638040000037
1, g 1..., g m-1be respectively the gain error of M sampling channel;
Step 5, gain error compensation: adopt data processor (6) and utilize the gain error vector of the described time-interleaved sampling system drawing in step 405
Figure FDA0000463638040000038
to the frequency domain steering vector p after time base error compensation in step 402 i(f) compensate, draw the frequency domain steering vector p after gain error compensation i' ' (f), wherein p i &prime; &prime; ( f ) = [ 1 , g 2 &CenterDot; e - j 2 &pi; ( f + if s ) ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , g M &CenterDot; e - j 2 &pi; ( f + if s ) ( M - 1 ) ( &tau; + &Delta; ^ &tau; M - 1 ) ] T , I is positive integer and i=-I ... 0 ... I;
Step 6, weight vector reconstruct: adopt data processor (6) and according to
Figure FDA00004636380400000310
calculate weight vector w i(f); In formula, R (f) is the covariance matrix of training sample f, wherein f=[-f s/ 2, f s/ 2]; The training sample f sample data composition training sample of serving as reasons described training sample to concentrate all frequency values be f;
Signal reconstruction in step 7, frequency domain: adopt data processor (6) and according to formula
Figure FDA00004636380400000311
described time-interleaved sampling system is needed to reconstruction signal
Figure FDA00004636380400000312
be reconstructed, obtain the reconstruction signal S in frequency domain i(f);
The described sample sequence that needs reconstruction signal to comprise M described A/D conversion chip (1) in same time period T
Figure FDA00004636380400000313
and it is denoted as
Figure FDA00004636380400000314
wherein S ^ ( n ) = [ S ^ 0 ( n ) , S ^ 1 ( n ) , &CenterDot; &CenterDot; &CenterDot; , S ^ M - 1 ( n ) ] T , Wherein m is numbering and the m=0 of M described A/D conversion chip (1), 1 ..., M-1; In formula,
Figure FDA00004636380400000316
for by the described reconstruction signal that needs
Figure FDA00004636380400000317
do fast Fourier transform to the signal obtaining after frequency domain, and S ^ ( f ) = [ S ^ 0 ( f ) , S ^ 1 ( f ) , &CenterDot; &CenterDot; &CenterDot; S ^ M - 1 ( f ) ] T ;
Step 8, inverse fast Fourier transform: adopt data processor (6) that the reconstruction signal in the frequency domain obtaining in step 7 is made to inverse fast Fourier transform, obtain the signal S (n) after reconstruct; Wherein S (n)=[S 0(n), S 1(n) ..., S m-1(n)] t, and the signal S (n) after reconstruct comprises the sample sequence S of M described A/D conversion chip (1) after reconstruct m(n).
2. according to the alternating sampling system signal reconstructing method based on spin matrix estimation error claimed in claim 1, it is characterized in that: while carrying out weight vector reconstruct in step 6, process is as follows:
Step 601, w i(0) calculate: according to formula
Figure FDA0000463638040000041
calculate w i(0); Wherein w i(0) weight vector while being f=0, p i' ' (0) be according to the frequency domain steering vector p after gain error compensation in step 5 ifrequency domain steering vector during f=0 that ' ' (f) draws; R (0) is the covariance matrix of training sample 0, the training sample 0 sample data composition training sample of serving as reasons described training sample to concentrate all frequency values be 0;
Step 602, weight vector w i(f) calculate: according to formula w i(f)=B (f) w i(0), calculate w i(f); In formula, B ( f ) = diag { 1 , e - j 2 &pi;f ( &tau; + &Delta; ^ &tau; 1 ) , &CenterDot; &CenterDot; &CenterDot; , e - j 2 &pi;f ( ( M - 1 ) &tau; + &Delta; ^ &tau; M - 1 ) } .
3. according to the alternating sampling system signal reconstructing method based on spin matrix estimation error described in claim 1 or 2, it is characterized in that: after in step 305, time base error has been estimated, a time delay error vector that draws described time-interleaved sampling system, also needs to enter step 306 afterwards;
Step 306, return to step 301, again from [f s/ 2, f s/ 2] in, choose at random a pair of Frequency point that two numerical value are used as estimation error, and according to step 302 to the method in step 305, draw the time delay error vector of described time-interleaved sampling system;
Step 307, one or many repeating step 306, draw the time delay error vector of one or more described time-interleaved sampling systems;
Step 308, the multiple time delay error vectors that draw under present case are averaged, as the time delay error vector of described time-interleaved sampling system
Figure FDA0000463638040000043
4. according to the alternating sampling system signal reconstructing method based on spin matrix estimation error described in claim 1 or 2, it is characterized in that: n=100～1000 in step 2.
5. according to the alternating sampling system signal reconstructing method based on spin matrix estimation error described in claim 1 or 2, it is characterized in that: while getting the sample sequence of M described A/D conversion chip (1) in a time period t in step 2, adopt sliding window method to choose.
6. according to the alternating sampling system signal reconstructing method based on spin matrix estimation error described in claim 1 or 2, it is characterized in that: the sampling system of time-interleaved described in step 1 comprises multiple A/D conversion chips (1), multiple time delay control modules (2) of respectively sampling time of multiple described A/D conversion chips (1) being controlled, multiple data processing units (3) that respectively multiple described A/D conversion chips (1) institute sampled signal carried out to Fourier transform processing, the data processor (6) that joins with multiple described data processing units (3) respectively and multiple described data processing units (3) signal after treatment is joined with the multiplexer (4) of data array formal output with multiplexer (4), multiple described time delay control modules (2) are joined with multiple described A/D conversion chips (1) respectively, multiple described A/D conversion chips (1) join with multiple described data processing units (3) respectively, multiple described time delay control modules (2) are controlled by data processor (6) and it all joins with data processor (6).
7. according to the alternating sampling system signal reconstructing method based on spin matrix estimation error claimed in claim 6, it is characterized in that: described time-interleaved sampling system also comprises multiple gain control module (7) of joining with multiple described A/D conversion chips (1) respectively, and multiple described gain control module (7) are connected on respectively between multiple described A/D conversion chips (1) and multiple described data processing unit (3); Described gain control module (7) is amplifier or attenuator; Multiple described gain control module (7) are controlled by data processor (6) and it all joins with data processor (6).
8. according to the alternating sampling system signal reconstructing method based on spin matrix estimation error claimed in claim 6, it is characterized in that: the time delay error vector that estimates described time-interleaved sampling system in step 3
Figure FDA0000463638040000051
after, described data processor (6) is according to the time delay error vector of estimating to draw
Figure FDA0000463638040000052
multiple described time delay control modules (2) are controlled respectively.
9. according to the alternating sampling system signal reconstructing method based on spin matrix estimation error claimed in claim 7, it is characterized in that: the gain error vector that estimates described time-interleaved sampling system in step 4 after, described data processor (6) is according to the gain error vector of estimating to draw
Figure FDA0000463638040000054
multiple described gain control module (7) are controlled respectively.
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CN109507698A (en) * 2018-09-28 2019-03-22 西南电子技术研究所（中国电子科技集团公司第十研究所） The anti-interference steering vector automatic correction system of satellite navigation
CN109507698B (en) * 2018-09-28 2022-07-08 西南电子技术研究所（中国电子科技集团公司第十研究所） Automatic correction system for anti-interference guide vector of satellite navigation
CN110232166A (en) * 2019-01-18 2019-09-13 华东理工大学 A kind of weighing belt Analysis of error source method based on feature selecting
CN110232166B (en) * 2019-01-18 2023-01-31 华东理工大学 Belt scale error source analysis method based on feature selection

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