Anti-interference method based on data rearrangement and singular value decomposition
阅读说明：本技术 一种基于数据重排和奇异值分解的抗干扰方法 (Anti-interference method based on data rearrangement and singular value decomposition ) 是由 国强 王亚妮 戚连刚 于 2021-10-08 设计创作，主要内容包括：本发明公开了一种基于数据重排和奇异值分解的抗干扰方法,1)将原始信号进行数字化处理,得到离散型的原始信号x；2)计算离散型原始信号的第一次自相关函数及c重自相关函数其中τ为时间延迟量,基于c重自相关函数求得周期调频干扰信号的周期估计值P；3)按照周期估计值P,对离散型的原始信号进行重排,将相同相位位置的离散型原始信号求和组成新的数据矩阵元素,构建得到重排数据矩阵；4)利用奇异值分解方法求得重排数据矩阵中的若干干扰成分λ-(i)；5)消除重排数据矩阵中的至少1个干扰成分,将信号进行逆向重构,获得抑制干扰后信号y。由此,本发明有效降低干扰子空间与信号子空间的交叠,同时有效保护期望信号。(The invention discloses an anti-interference method based on data rearrangement and singular value decomposition, which comprises the following steps of 1) carrying out digital processing on an original signal to obtain a discrete original signal x; 2) calculating the first autocorrelation function of a discrete original signal And c-fold autocorrelation function Wherein tau is a time delay amount and is based on a c-weight autocorrelation function Obtaining a periodic estimated value P of the periodic frequency modulation interference signal; 3) rearranging the discrete original signals according to the period estimated value P, and phase-positioning the discrete original signalsSumming to form new data matrix elements, and constructing to obtain a rearranged data matrix; 4) method for solving a plurality of interference components lambda in rearranged data matrix by using singular value decomposition method i (ii) a 5) And eliminating at least 1 interference component in the rearranged data matrix, and reversely reconstructing the signal to obtain the signal y after interference suppression. Therefore, the invention effectively reduces the overlapping of the interference subspace and the signal subspace and simultaneously effectively protects the expected signal.)
1. An anti-interference method based on data rearrangement and singular value decomposition is characterized in that,
1) carrying out digital processing on the original signal to obtain a discrete original signal x;
2) calculating the first autocorrelation function of a discrete original signalAnd c-fold autocorrelation functionWherein tau is a time delay amount and is based on a c-weight autocorrelation functionObtaining a periodic estimated value P of the periodic frequency modulation interference signal;
3) rearranging the discrete original signals according to the period estimation value P of the periodic frequency modulation interference signals, forming the discrete original signals at the same phase position into new data matrix elements, and constructing to obtain a rearranged data matrix;
4) method for solving a plurality of interference components lambda in rearranged data matrix by using singular value decomposition methodi；
5) And eliminating at least 1 interference component in the rearranged data matrix, and reversely reconstructing the signal to obtain the signal y after interference suppression.
2. The method of claim 1, wherein the method further comprises performing a noise rejection based on data reordering and singular value decompositionThen, the calculation of the estimated period P of the periodic FM interference signal based on the c-fold autocorrelation function means that all the requirements are metGreater than a set similarity thresholdIn (1),peak value ofAnd the corresponding minimum tau which is not 0 is the periodic estimation value of the periodic frequency modulation interference signal and is marked as P.
3. The method of claim 2, wherein the similarity threshold is greater than or equal to 0.9.
4. The method of claim 1, wherein the removing at least 1 interfering component in the rearranged data matrix is a first singular value λ of the singular value matrix obtained by calculation1And setting zero.
5. The anti-interference method based on data rearrangement and singular value decomposition according to claim 1, wherein the step 1) comprises the following steps:
carrying out digital processing on an original signal received by a single-antenna receiver to obtain a discrete original signal and obtain digital received signal vectors x of TT sampling points;
x＝[x(1) x(2),…,x(t),…,x(TT)]T，
wherein
Where t ═ 1,2, … TT denotes the sampling order, snRepresenting the navigation signal of the nth satellite, N being the number of satellites, j representing the periodic FM interference signal, η representing the receiver thermal noise [ ·]TIndicating transposition.
6. The anti-interference method based on data rearrangement and singular value decomposition according to claim 5, wherein the specific steps of the step 2) are as follows:
calculate the first autocorrelation function of x, and record the result asWherein τ is the amount of time delay;
taking TT based on the first autocorrelation function1<TT, carrying out autocorrelation calculation to obtain a double autocorrelation result
TT is taken based on the result of c-1 heavy autocorrelationc<TTc-1Is obtained by autocorrelation calculationWherein C is 1,2, … C is multiple autocorrelation times, and C-fold autocorrelation result is obtained
SearchingTime of flightIs marked as the peak value ofThe corresponding minimum tau which is not 0 is the cycle estimated value of the cycle frequency modulation interference signal and is marked as P.
7. The method according to claim 6, wherein the specific operations of step 3) are as follows:
rearranging the received signals according to the cycle estimation value P of the cycle frequency modulation interference signal to form a rearranged data matrix X,
X＝[x1 x2…xq…xQ]T
wherein the content of the first and second substances,
xq＝[x(q) x(q+P)…x(q+(m-1)P)…]T
wherein Q is 1,2, …, Q is the maximum number of rows, and Q is P/Ts，TsIs the sampling interval; m is 1,2, …, M, satisfies Denotes a downward integer, LsIs the sample data length.
8. The method according to claim 7, wherein the step 4) specifically operates as follows:
singular value decomposition of a rearranged data matrix X
X＝UΣVT
Obtaining a left singular vector matrix U, a right singular vector matrix V, and a singular value matrix sigma, where sigma is diag { λ }1 λ2λ3… }, i.e. singular value matrix sigma-primary diagonal elements are eigenvalues λiThe lower subscript i denotes the order of the main diagonal elements; the other elements are 0;
maximum eigenvalue lambda1Zero, λ1Get a new odds of 0Matrix of singular valuesFurther obtaining a data matrix without interference components
9. The method according to claim 8, wherein the step 5) specifically operates as follows:
reconstructing the data matrix after interference elimination to obtain a signal y required by subsequent processing
Technical Field
The invention relates to the field of radio frequency interference suppression of radio receivers, in particular to a method for realizing suppression of periodic frequency modulation interference of a satellite navigation receiver by utilizing data rearrangement and singular value decomposition.
Background
The periodic frequency modulation interference signals are common types of interference signals in signals received by a satellite navigation receiver, and the interference may be generated in radar and a malicious interference machine and is not easily eliminated by a time domain or frequency domain interference suppression technology. In order to ensure the continuity and reliability of GNSS services, researchers have studied a large number of interference suppression methods starting from the differences between signals and interference in the time-frequency domain, the space domain and the space-time domain. The space domain and space-time domain methods utilize the spatial resolution of a plurality of antennas, have strong capacity of processing a plurality of interferences and have small damage to signals. However, the space cost and economic cost of the antenna array are high, and the antenna array is not suitable for being applied to the field with narrow space and less budget.
The transform domain interference detection and suppression method suitable for the single antenna receiver is still a research hotspot. The conventional single antenna method is to convert the received signal into time-frequency domain, detect the interference parameter, and then eliminate the interference component by using a filter or a blanking technology. Typical time-frequency transformation methods include: Short-Time Fourier Transform (STFT), Wavelet Transform (WT), Wigner-Ville Distribution (WVD), Fractional Fourier Transform (FRFT). The difference in transform domain and its way of computation affects the energy concentration of the interfering signal. The STFT-based method cannot effectively accumulate signal energy and has a resolution problem due to the unchanged window width; the interference parameter estimation precision is seriously influenced by cross terms brought by the nonlinear transformation of the WVD; the FRFT not only solves the problem of cross terms, but also has high estimation precision and stronger robustness, but the discrete non-orthogonality brings larger influence on the receiving performance.
In addition, since the interference still overlaps with the GNSS signal in the time-frequency domain, the interference may cause great damage to the GNSS signal when being eliminated. Therefore, the existing interference suppression method based on time-frequency analysis cannot well process the fast time-varying periodic frequency modulation interference. Therefore, it is still the focus of the researchers in the related field to further improve the performance of the methods for detecting and eliminating the chirp interference signals.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the anti-interference method based on data rearrangement and singular value decomposition is suitable for periodic frequency modulation interference detection and suppression of a single-antenna satellite navigation receiver.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
an anti-interference method based on data rearrangement and singular value decomposition is characterized in that received signals are rearranged according to the periodic characteristics of periodic frequency modulation interference in the received signals, a rearranged data matrix is constructed, interference components in the rearranged data matrix are eliminated through singular value decomposition, then the signals are reconstructed, and signals after interference suppression are obtained.
On the basis of the technical scheme, the invention can be further improved as follows.
Preferably, the steps are as follows:
(1) carrying out digital processing on radio frequency signals received by a single antenna receiver to obtain digital received signal vectors x of TT sampling points;
x＝[x(1) x(2),…,x(t),…,x(TT)]T，
wherein
Where t ═ 1,2, … TT denotes the sampling order, snRepresenting the navigation signal of the nth satellite, N being the number of satellites, j representing the periodic FM interference signal, η representing the receiver thermal noise [ ·]TRepresenting a transpose;
(2) calculate the first autocorrelation function of x, and record the result asWherein τ isA time delay of 0. ltoreq. tau. ltoreq.TT. Ts,TsThe sampling interval is the sampling interval when the original data is processed digitally;
taking TT based on the first autocorrelation function1<TT, carrying out autocorrelation calculation to obtain a double autocorrelation resultThe total amount of the data of the one-time autocorrelation result is about 5% less than that of the data of the first-time autocorrelation function, and the total amount of the data is TT1tA plurality of;
taking TT based on a result of the auto-correlation2<TT1Performing autocorrelation calculation to obtain double autocorrelation resultLet total amount of double autocorrelation result data be TT2tA plurality of;
by analogy, based on the result of c-1-fold autocorrelation, TT is takenc<TTc-1Is obtained by autocorrelation calculationWherein C is 1,2, … C is multiple autocorrelation times, and C-fold autocorrelation result is obtainedThe value of C is not capped theoretically, but the calculated amount is increased, and the requirement can be basically met by selecting the value below 10 in practical application.
SearchingTime of flightIs marked as the peak value ofThe corresponding minimum tau which is not 0 is the periodic frequency modulation interference signal period estimationThe value, denoted as P;
(3) rearranging the received signals according to the cycle estimation value P of the cycle frequency modulation interference signal to form a rearranged data matrix X,
X＝[x1 x2 … xq … xQ]T
wherein the content of the first and second substances,
xq＝[x(q) x(q+P) … x(q+(m-1)P) …]T
wherein Q is 1,2, …, Q is the maximum number of rows, and Q is P/Ts，TsAs explained above, as a sampling interval; m is 1,2, …, M, satisfies Denotes a downward integer, LsIs the sample data length of the original signal. Because the sampling interval is far shorter than the period estimation value P of the periodic frequency modulation interference signal, the interference signal with only single frequency in a single sampling point can be approximately considered, and the data is rearranged according to the period P, and the rearranged matrix element xqThe original signals are sets of discrete original signals located at the same phase position in the period P, and therefore, it can be considered that the frequencies of the interference signals in the same row of data in the rearranged data matrix are the same.
(4) Singular value decomposition of a rearranged data matrix X
X＝UΣVT
Obtaining a left singular vector matrix U, a right singular vector matrix V, and a singular value matrix sigma, where sigma is diag { λ }1λ2 λ3 …λi… }, i.e. singular value matrix sigma-primary diagonal elements are eigenvalues λiThe lower subscript i denotes the order of the main diagonal elements; the remaining elements are 0.
Because the interference component frequencies of each row in the rearranged data matrix are the same, the interference after singular value decomposition is mainly concentrated in the subspace corresponding to the first singular value.
Maximum eigenvalue lambda1Zero, λ1Obtaining a new singular value matrix as 0Further obtaining a data matrix without interference components
(5) Reconstructing the data matrix after interference elimination to obtain a signal y required by subsequent processing
Compared with the prior art, the invention has the following technical effects:
according to the generalized periodic characteristics of the periodic frequency modulation interference signals, a sampling data rearrangement technology is used for constructing a rearranged data matrix, so that periodic frequency modulation interference components in original data are converted into single-frequency interference in each row in the rearranged data matrix, and then the characteristics of the same frequency of the interference components in the rearranged data matrix are utilized, and singular value decomposition is adopted to extract and eliminate the interference components; and then, interference suppression is finished in the frequency domain of the resampled data, and the overlapping of the interference subspace and the signal subspace is effectively reduced, so that the expected signal can be effectively protected while the interference is eliminated.
Drawings
FIG. 1 is a schematic structural diagram of an anti-interference method based on data rearrangement and singular value decomposition according to the present invention;
fig. 2 is a graph comparing interference suppression effects.
Detailed Description
The method of the present invention is further described in detail below with reference to the accompanying drawings and examples. The following examples are intended to illustrate the present application but are not intended to limit the scope of the present application.
The embodiment of the application provides an anti-interference method based on data rearrangement and singular value decomposition according to the generalized periodic characteristics of periodic frequency modulation interference. According to the method, time-frequency transformation of signals is not needed, and the detection and suppression problem of broadband frequency modulation interference is converted into the detection and suppression problem of single-frequency interference signals in a matrix through time domain period estimation, data rearrangement and singular value decomposition processing. The method can concentrate scattered interference energy into a smaller subspace, reduces overlapping of interference and a desired signal, and has less damage to the desired signal when eliminating interference components.
In order to more clearly explain the method, the embodiment of the present application performs a flow description and an effect display through a simulation experiment, but does not limit the scope of the embodiment of the present application. The experimental conditions were: 1 satellite navigation signal is subjected to radio frequency, down conversion and digital processing, and the signal-to-noise ratio (SNR) of the satellite navigation signal is-15 dB; the frequency modulation interference signal has 1 period, and the bandwidth, the frequency sweep period and the center frequency of the interference are respectively 2MHz, 0.4ms and 1.25 MHz; the down-converted center frequency of the receiver is 1.25MHz, and the digital sampling frequency is 5 MHz. The maximum value of the period estimation value is set to 2ms (10)4One sample point), the longest data processing length is 26And (4) sampling points.
FIG. 1 is a schematic block diagram of a method of the present invention, comprising:
s110, digitalizing an original signal:
x＝[x(1) x(2),…,x(t),…,x(TT)]T
where t ═ 1,2, … TT, denotes the sampling time [ ·]TDenotes transposition, x (t) denotes a received signal model:
where s (t) is a satellite navigation signal, jkAnd (t) is a kth periodic frequency modulation signal, such as a sawtooth frequency modulation signal and a sine frequency modulation signal, where K is 1, 2.
S120, calculating the first autocorrelation function of x, and recording the result asWherein τ is the amount of time delay; getPerforming autocorrelation calculation to obtain a double autocorrelation resultRepeatedly takingPerforming autocorrelation calculation to obtainIn this example, c is 1,2,3,4 is the number of multiple autocorrelations, and 4 autocorrelation results are obtained
Search for satisficationIs/are as followsIs recorded as the peak value ofThenThe corresponding minimum non-0 τ is a period estimation value of the periodic frequency modulation interference signal, and is denoted as P, where P is 0.4ms in this example;
s130, according to the cycle estimated value P of the cycle frequency modulation interference signal, the received signal is rearranged to form a data matrix X,
X＝[x1 x2 … xq … xQ]T
wherein the content of the first and second substances,
xq＝[x(q) x(q+P) … x(q+(m-1)P) …]T
wherein Q is 1,2, …, Q is the maximum number of rows, and Q is P/Ts，TsIs the sampling interval; m is 1,2, …, M, satisfies Denotes a downward integer, LsIs the sample data length. Each row in the data matrix appears to contain interference at only a single frequency, and the interference components in each row are at the same frequency.
S140 singular value decomposition of data matrix X
X＝UΣVT
Obtaining a singular vector matrix U having a singular matrix V and a singular value matrix sigma, where sigma is diag { λ }1 λ 2λ 3… }, i.e. singular value matrix sigma-primary diagonal elements are eigenvalues λ·Subscript-indicating the order of the major diagonal; the remaining elements are 0. Because the interference component frequencies of each row in the rearranged data matrix are the same, the interference after singular value decomposition is mainly concentrated in the subspace corresponding to the first singular value.
S141 dividing the maximum eigenvalue lambda1Zero, λ1Obtaining a new singular value matrix as 0Further obtaining a data matrix without interference components
S142, reconstructing the data matrix after interference elimination to obtain a signal y required by subsequent processing
To illustrate the superiority of this method, it was compared with adaptive Wavelet Packet Coefficient Thresholding (WPCT) and multiple short-time Fourier transform (MSTFT), as shown in FIG. 2, let the input interference-to-noise ratio (INR)in) Respectively 25dB, 30dB, 35dB, 40dB, 45dB, 50dB, 55dB and 60dB, respectively processing the signals by adaptive Wavelet Packet Coefficient Thresholding (WPCT) and multiple short-time Fourier transform (MSTFT) to obtain the signals after interference elimination, and respectively comparing the output signal-to-interference-plus-noise ratio (SINR) of the output signals of the three methodsout) A Normalized Mean Square Error (NMSE) of the satellite navigation signal and the original satellite navigation signal, and a correlation acquisition factor (CF) of the satellite signal. As can be seen from the figure, the navigation signal after the interference is eliminated by the method of the present invention has smaller NMSE, which means that the damage to the desired satellite signal during the interference suppression process can be effectively reduced, and the SINRoutAnd CF is higher than the other two comparison algorithms, namely the capability of eliminating interference is better than that of the comparison algorithms, so that the method can ensure the working efficiency of the satellite navigation receiver under the condition of multiple interferences.
In summary, the method of the embodiment can transform the detection and suppression problem of the broadband frequency modulation interference into the detection and suppression problem of the medium-frequency single-frequency interference of the matrix through time domain period estimation, data matrix rearrangement construction and singular value decomposition processing without performing time-frequency transformation on the signal according to the generalized periodic characteristics of the periodic frequency modulation signal. The method can concentrate scattered interference energy into a smaller subspace, reduces overlapping of the interference subspace and the desired signal subspace, and has less damage to the desired signal when eliminating interference components.
It is understood by those skilled in the art that, in the method according to the embodiments of the present application, the sequence numbers of the steps do not mean the execution sequence, and the execution sequence of the steps should be determined by their functions and inherent logic, and should not constitute any limitation to the implementation process of the embodiments of the present application.
Finally, it should be noted that the above examples are only intended to describe the technical solutions of the present invention and not to limit the technical methods, the present invention can be extended in application to other modifications, variations, applications and embodiments, and therefore all such modifications, variations, applications, embodiments are considered to be within the spirit and teaching scope of the present invention.
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