CN114488208B - Beidou signal anti-interference method combining empirical wavelet and SPWVD conversion - Google Patents
Beidou signal anti-interference method combining empirical wavelet and SPWVD conversion Download PDFInfo
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Abstract
The invention discloses a Beidou signal anti-interference method combining empirical wavelet and SPWVD transformation, which comprises the following steps: 1. the complex interference signals are represented by analysis; 2. the analysis signals are decomposed into empirical wavelet functions which are arranged according to the frequency sequence, so that the defect that a conventional wavelet base is difficult to construct is overcome, and the mode aliasing phenomenon during the decomposition of complex interference signals is effectively avoided; 3. separating and screening useful information and interference signals for the signals after the empirical wavelet transformation; 4. for the cross terms between existing identical frequency signal components, a smooth pseudo Wigner-Ville distribution (SPWVD) transform is employed for further cancellation. The invention can effectively inhibit the influence of interference and noise of the cross item, keeps good time-frequency positioning characteristics, can be widely applied to GPS, GLONASS, galileo and Beidou navigation satellite signal processing, and has wide application prospect.
Description
Technical Field
The invention belongs to the field of satellite navigation positioning, and particularly relates to a Beidou receiver interference suppression method combining Empirical Wavelet Transform (EWT) and smooth pseudo Wigner-Ville transform.
Background
Beidou satellite navigation technology has become an increasingly important information technology in civil and military applications, and the characteristic of easy interference is exposed in the application field of complex interference environments nowadays. Therefore, it is important to study the anti-interference technology of the Beidou satellite navigation system receiver.
The main three sources causing the interference of the Beidou receiver are: firstly, transmission path interference is caused by interference experienced by Beidou navigation signals propagating from space to ground, and mainly comprises tropospheric interference, ionospheric interference and multipath interference; secondly, non-malicious electromagnetic wave interference is interference generated by a communication system with similar Beidou navigation frequency bands, such as a mobile communication system and a radar system, and the interference is generally weak, but the electromagnetic interference in a specific scene is strong, such as the electromagnetic interference in a wind power plant and a transmission line environment is a main interference source; thirdly, artificial malicious interference, which refers to hold-down interference and deception interference released by enemies in a battlefield environment. The invention is applied to civil scenes, so that the third artificial malicious interference is not considered.
The Direct Sequence Spread Spectrum (DSSS) scheme is a scheme adopted by most satellite navigation systems at present, and can spread the received navigation signal power to a wider bandwidth, but the broadcasting distance of the navigation satellite from the ground signal is too far, so that the signal power reaching the ground end is very weak, and even if the navigation signal adopts the direct spread spectrum technology, the power intensity is weaker than the intensity of the background normal noise.
The methods commonly used in the navigation receiving interference detection mainly include an Automatic Gain Control (AGC) method, a time domain method, a frequency domain method and a wavelet transformation method. The AGC adjusts the navigation input signal level to the range of an analog-to-digital converter (ADC), and performs interference detection by monitoring the AGC level; however, in an environment where the interference is weak, the detection performance of the AGC method may be greatly reduced. For the time domain approach, this approach may be implemented at the digital Intermediate Frequency (IF) level after the ADC at the front end of the navigation receiver. This time domain approach is only effective for narrowband RFI sources, as wideband interference is difficult to distinguish from thermal noise. For frequency domain methods, due to their spectral characteristics, narrowband carrier interference is typically detected. With respect to navigation reception interference detection using time domain methods or frequency domain methods, they cannot fully describe the nature and characteristics of the time-varying interference present in the received navigation signal. The wavelet transform method is a time-frequency domain transform method, which can increase the time scale while analyzing the signal frequency, and push the time-frequency analysis to research climax, however, the wavelet basis of the common wavelet transform is difficult to construct and has the defects of time shift and frequency aliasing. Thus, interference detection has become a critical role in navigation applications.
Disclosure of Invention
The invention aims to solve the defects of the prior art, and provides a Beidou signal anti-interference method combining empirical wavelet and SPWVD conversion, so that the influence of cross term interference and noise can be effectively restrained, and good time-frequency positioning characteristics are reserved, thereby solving the problems of time-frequency compromise, cross term interference, energy disaggregation and the like of navigation receiving signals in scanning interference detection.
The invention solves the technical problems by adopting the following technical scheme:
the invention relates to a Beidou signal anti-interference method combining empirical wavelet and SPWVD conversion, which is characterized by comprising the following steps:
step 1: analyzing and transforming the original continuous time signal received by the Beidou receiver by utilizing the (1) to obtain an analysis signal y a (t)：
In the formula (1), j is a virtual root unit, and y (t) represents an original continuous time signal;representing y (t) a Hilbert transformed signal;
step 2: resolving the signal y a (t) performing empirical wavelet transformation to obtain modal function components with different frequencies and mutually independent;
step 2.1: for the analytic signal y a (t) Fourier transforming to obtain corresponding frequency spectrum y a (ω)；
Step 2.2: in the frequency spectrum y a Finding M local maximum points on (omega), and arranging the M local maximum points in a descending order to obtain ordered local maximum points;
according to the ordered local maximum value points, the local maximum value points are in [0, pi ]]Up-to the spectrum y a (omega) dividing into N consecutive parts to obtain N divided spectral bandsAnd forming n+1 endpoints;
if M is greater than N, reserving the first N-1 local maximum points after sequencing;
if M < N, resetting the parameter N such that n=m;
let omega n Representing boundary points of adjacent n-1 th and n-th spectrum segments, letting the initial boundary point omega 0 =0, end boundary point ω N =pi; n=1, …, N; then the nth spectral band Λ n ＝[ω n-1 ,ω n ]Thereby obtainingWherein omega n-1 Representing boundary points of adjacent n-2 th and n-1 th spectral bins;
step 2.3: an expression of an empirical scale function and a wavelet function expression of an empirical wavelet are respectively constructed using the expression (2) and the expression (3):
in the formula (2) and the formula (3), phi n (omega) represents the nth empirical scale function, ψ n (ω) represents the nth empirical wavelet function, γ represents a constant between 0 and 1, and β (·) is a value of [0,1 ]]A function of (a); omega n+1 Representing boundary points of adjacent nth and n+1th spectral bins;
step 2.4: defining detail correlation coefficients by means of equations (4) and (5), respectivelyApproximate correlation coefficient
In the formula (4), "-" represents a conjugate operation, and when n=1, φ 1 (t) is defined by phi n (ω) inverse fourier transforming to obtain a function value; psi phi type n (t) consists of psi n (omega) function obtained by inverse Fourier transform, y a (t) is defined by y a (ω) inverse fourier transforming the resulting function; f (F) -1 (. Cndot.) represents the inverse Fourier transform;
step 2.5: by using (6) the analysis signal y a (t) reconstructing to obtain an analysis signal y a The empirical mode components of (t) are shown in the formulas (7) and (8):
in equation (6), the convolution operation,is->Fourier transform form of>Represents n=0 +.>Is a value of (2);
in formula (7), y 0 (t) represents an amplitude modulation-frequency modulation single component when n=0,representation->Is an inverse fourier transform form of (a);
in formula (8), y n (t) represents amplitude-modulated-frequency components of different frequencies, n=1, 2,3, N;
step 3: the analysis signal y is compared with the reference signal y by the method (9) a Each modal component y of (t) n (t) performing smooth pseudo-Wigner-Ville transformation to obtain a smooth pseudo-Wigner-Ville time-frequency distribution expression
In the formula (9), the amino acid sequence of the compound,and->Representing y n Transient correlation function of (t),>representation->Conjugation of (2); g (s-t) is a smoothing window function in the frequency axis direction, h (τ) is a smoothing window function in the time domain direction, and g (0) =h (0) =1; s and τ are integral variables;
step 4: using (10) to divide each mode component y n Linear superposition of the smoothed pseudo Wigner-Ville analysis results of (t) to obtain an analysis signal y a (t) smooth pseudo-Wigner-Ville distribution
Step 5: for the analytic signal y a Sliding pseudo-Wigner-Ville distribution of (t)And performing interference detection, and filtering the obtained interference signal by adopting a notch IIR filter, so as to obtain the sliding pseudo Wigner-Ville distribution after filtering.
Compared with the prior art, the invention has the beneficial effects that:
1. the navigation receiving signals subjected to the frequency sweep interference are represented by analysis and then subjected to empirical wavelet transformation, so that the defect that a wavelet basis is difficult to construct in conventional wavelet transformation is overcome, the modal aliasing phenomenon during the decomposition of complex interference signals is effectively avoided, the spectral characteristics of the interference signals and the useful spectral characteristics of the navigation signals can be clearly distinguished, and the method can be widely applied to the processing of GPS, GLONASS, galileo and Beidou navigation satellite signals and has wide application prospect.
2. The invention adopts smooth pseudo Wigner-Ville distribution (SPWVD) time-frequency transformation, can further eliminate the cross terms between the existing signal components with the same frequency while enhancing the self terms, and effectively suppresses the interference and noise influence of the cross terms.
3. The invention adopts the combined empirical wavelet and SPWVD conversion method, improves the energy aggregation performance in the navigation signal interference detection, overcomes the time-frequency compromise problem, and the influence of cross term interference and noise, and obviously improves the interference detection performance.
Drawings
FIG. 1 is a flow chart of a Beidou signal anti-interference method combining empirical wavelet and SPWVD conversion;
FIG. 2a is a WVD scale plot of LFM signals in the presence of AWGN in the prior art;
FIG. 2b is a WVD profile of the LFM signal at AWGN in the prior art;
FIG. 3 is an experimental test protocol of the present invention;
FIG. 4a is a WVD scale plot of a GPS L1-C/A signal with frequency sweep interference in the prior art;
FIG. 4b is a WVD profile of a GPS L1-C/A signal with frequency sweep disturbance in the prior art;
FIG. 5a is a graph of the joint empirical wavelet and SPWVD transform scales of a swept-disturbed GPS L1-C/A signal of the present invention;
FIG. 5b is a graph of the combined empirical wavelet and SPWVD transform profile of a swept-disturbed GPS L1-C/A signal of the present invention.
Detailed Description
In this embodiment, a method for suppressing interference of a beidou receiver combining empirical wavelet transform and smooth pseudo-Wigner-Ville transform, as shown in fig. 1, includes the following steps:
step 1: resolving and transforming the original continuous time signal received by the Beidou receiver by utilizing the (1),obtain the analysis signal y a (t)：
In the formula (1), j is a virtual root unit, and y (t) represents an original continuous time signal;representing y (t) a Hilbert transformed signal;
step 2: will resolve the signal y a (t) performing empirical wavelet transformation to obtain modal function components with different frequencies and mutually independent;
step 2.1: for the analysis signal y a (t) Fourier transforming to obtain corresponding frequency spectrum y a (ω)；
Step 2.2: in the frequency spectrum y a Finding M local maximum points on (omega), and arranging the M local maximum points in a descending order to obtain ordered local maximum points;
according to the ordered local maximum value points, the local maximum value points are in [0, pi ]]Upper pair spectrum y a (omega) dividing into N consecutive parts to obtain N divided spectral bandsAnd forming n+1 endpoints;
if M is greater than N, reserving the first N-1 local maximum points after sequencing;
if M < N, resetting the parameter N such that n=m;
let omega n Representing the boundary points of the n-1 th and n th adjacent spectrum segments, wherein the selection of the boundary points is determined by the median between two adjacent local maximum points, so that the initial boundary point omega 0 =0, end boundary point ω N =pi; n=1, …, N; then the nth spectral band Λ n ＝[ω n-1 ,ω n ]Thereby obtainingWherein omega n-1 Represents adjacent n-2 th and n-1 boundary point of spectrum segment;
step 2.3: an expression of an empirical scale function and a wavelet function expression of an empirical wavelet are respectively constructed using the expression (2) and the expression (3):
in the formula (2) and the formula (3), phi n (omega) represents the nth empirical scale function, ψ n (ω) represents the nth empirical wavelet function, γ represents a constant between 0 and 1, and β (·) is a value of [0,1 ]]Any function above; omega n+1 Representing boundary points of the n-th and n+1-th adjacent spectrum segments, the equations (2) and (3) correspond to the functions of a low-pass filter and a band-pass filter, and each signal component can be obtained after filtering the analysis signal.
Step 2.4: defining detail correlation coefficients by means of equations (4) and (5), respectivelyApproximate correlation coefficient
In the formula (4), "-" represents a conjugate operation, and when n=1, φ 1 (t) is defined by phi n (ω) inverse fourier transforming to obtain a function value; psi phi type n (t) consists of psi n (omega) function obtained by inverse Fourier transform, y a (t) is defined by y a (omega) Fourier inverseTransforming the obtained function; f (F) -1 (. Cndot.) represents the inverse Fourier transform;
step 2.5: by using (6) the analysis signal y a (t) reconstructing to obtain an analysis signal y a The empirical mode components of (t) are shown in the formulas (7) and (8):
signal y a (t) decomposing to obtain amplitude modulation-frequency modulation single component components with frequencies from low to high; in equation (6), the convolution operation,is->Fourier transform form of>Represents n=0 +.>Is a value of (2);
in formula (7), y 0 (t) represents an amplitude modulation-frequency modulation single component when n=0,representation->Is an inverse fourier transform form of (a);
in formula (8), y n (t) represents amplitude-modulated-frequency components of different frequencies, n=1, 2,3, N;
step 3: if a signal contains multiple components in the TF plane, its Wigner-Ville transform (WVD) can be affected by spurious features containing cross terms that occur between each pair of automatic terms. For example, a noisy chirp (Linearly Frequency Modulated, LFM) signal in the presence of AWGN is analyzed, with the SNR set to 3dB. The WVD of the noise LFM signal is provided in fig. 2a, and correspondingly the calculated profile of the WVD is given in fig. 2 b. From the figure, the TF peak representing the noise LFM signal can be observed, but there is a severe cross term in the TF plane, and no energy at all is expected. The presence of cross terms of the analysis signal in the TF plane does not have any physical significance, which makes correct signal interpretation very difficult, which is also a major drawback of the WVD method. The invention thus employs SPWVD methods.
Step 3.1: the analysis signal y is compared with the reference signal y by the method (9) a Each modal component y of (t) n (t) performing smooth pseudo-Wigner-Ville transformation to obtain a smooth pseudo-Wigner-Ville time-frequency distribution expression
In the formula (9), the amino acid sequence of the compound,and->Representing y n Transient correlation function of (t),>representation->Conjugation of (2); g (s-t) is the frequency axisA smoothing window function of direction, h (τ) is a smoothing window function of time domain direction, and g (0) =h (0) =1; s and τ are both integral variables.
Step 4: using (10) to divide each mode component y n Linear superposition of the smoothed pseudo Wigner-Ville analysis results of (t) to obtain an analysis signal y a (t) smooth pseudo-Wigner-Ville distribution
Step 5: analysis signal y obtained by linear superposition a (t)And performing interference detection, and filtering interference signals contained in the interference detection by adopting a notch IIR filter so as to obtain the sliding pseudo Wigner-Ville distribution after filtering.
The experimental test scheme of the invention is shown in fig. 3, a software jammer is adopted to generate a sweep frequency interference signal for GNSS application, and the generated sweep frequency interference is added into GPS samples collected at the front end of a GNSS receiver, so that a GPS signal subjected to sweep frequency interference is generated.
To verify the effectiveness of the method, it was compared with the existing classical method WVD. FIG. 4a depicts the WVD of the GPS L1-C/A signal in the presence of scanning disturbances, with the profile of the WVD correspondingly shown in FIG. 4 b. Although a straight line can be seen on the TF plane representing the frequency modulation law of the scanning disturbance, due to the bilinear nature of WVD, severe cross terms can also be observed, which inevitably leads to errors in the instantaneous frequency estimation. Scanning the interference signal brings difficulty to the detection of the interference, so that the GNSS interference characteristic parameters cannot be extracted correctly by using WVD.
FIG. 5a is C/N 0 =40 dB, jnr=2 dB, the joint empirical wavelet and SPWVD time-frequency transformed scale plot of the swept-interfered GPS L1-C/a signal, fig. 5b is a profile plot. It can be seen that the cross terms are in the TF planeThe method has the advantages that effective inhibition is obtained, TF energy peaks are linearly distributed on a straight line, and the TF energy peaks represent that sweep frequency interference exists in the received GPS L1-C/A signals. The energy aggregation performance in GNSS interference detection is improved, so that the instantaneous frequency estimation of an interference signal is improved.
In summary, the invention provides a Beidou receiver interference suppression method combining empirical wavelet transformation and smooth pseudo Wigner-Ville transformation, which decomposes complex interference signals into empirical wavelet functions arranged according to frequency sequence through analysis representation, so that the defect that a conventional wavelet base is difficult to construct is overcome, and the modal aliasing phenomenon during the decomposition of the complex interference signals is effectively avoided. The signal after the empirical wavelet transformation separates and screens useful information from interfering signals, and for the cross terms between existing signal components of the same frequency, a smooth pseudo Wigner-Ville distribution (SPWVD) transformation is used for further cancellation. The method effectively suppresses the influence of interference and noise of the cross item, maintains good time-frequency positioning characteristics, can be widely applied to GPS, GLONASS, galileo and Beidou navigation satellite signal processing, and has wide application prospect.
Claims (1)
1. A Beidou signal anti-interference method combining empirical wavelet and SPWVD transformation is characterized by comprising the following steps:
step 1: analyzing and transforming the original continuous time signal received by the Beidou receiver by utilizing the (1) to obtain an analysis signal y a (t)：
In the formula (1), j is a virtual root unit, and y (t) represents an original continuous time signal;representing y (t) a Hilbert transformed signal;
step 2: resolving the signal y a (t) performing empirical wavelet transform to obtainEach modal function component with different frequencies and mutually independent;
step 2.1: for the analytic signal y a (t) Fourier transforming to obtain corresponding frequency spectrum y a (ω)；
Step 2.2: in the frequency spectrum y a Finding M local maximum points on (omega), and arranging the M local maximum points in a descending order to obtain ordered local maximum points;
according to the ordered local maximum value points, the local maximum value points are in [0, pi ]]Up-to the spectrum y a (omega) dividing into N consecutive parts to obtain N divided spectral bandsAnd forming n+1 endpoints;
if M is greater than N, reserving the first N-1 local maximum points after sequencing;
if M < N, resetting the parameter N such that n=m;
let omega n Representing boundary points of adjacent n-1 th and n-th spectrum segments, letting the initial boundary point omega 0 =0, end boundary point ω N =pi; n=1, …, N; then the nth spectral band Λ n ＝[ω n-1 ,ω n ]Thereby obtainingWherein omega n-1 Representing boundary points of adjacent n-2 th and n-1 th spectral bins;
step 2.3: an expression of an empirical scale function and a wavelet function expression of an empirical wavelet are respectively constructed using the expression (2) and the expression (3):
in the formula (2) and the formula (3), phi n (omega) represents the nth empirical scale function, ψ n (ω) represents the nth empirical wavelet function, γ represents a constant between 0 and 1, and β (·) is a value of [0,1 ]]A function of (a); omega n+1 Represents adjacent nth and nth +
1 boundary point of spectrum segment; omega is the angular frequency;
step 2.4: defining detail correlation coefficients by means of equations (4) and (5), respectivelyApproximate correlation coefficient W f ε (0,t)：
In the formula (4), "-" represents a conjugate operation, and when n=1, φ 1 (t) is defined by phi n (ω) inverse fourier transforming to obtain a function value; psi phi type n (t) consists of psi n (omega) function obtained by inverse Fourier transform, y a (t) is defined by y a (ω) inverse fourier transforming the resulting function; f (F) -1 (. Cndot.) represents the inverse Fourier transform; τ is an integral variable;
step 2.5: by using (6) the analysis signal y a (t) reconstructing to obtain an analysis signal y a The empirical mode components of (t) are shown in the formulas (7) and (8):
in equation (6), the convolution operation,is->Fourier transform form of>When n=0 is expressedIs a value of (2);
in formula (7), y 0 (t) represents an amplitude modulation-frequency modulation single component when n=0,representation->Is an inverse fourier transform form of (a);
in formula (8), y n (t) represents amplitude-modulated-frequency components of different frequencies, n=1, 2,3, N;
step 3: the analysis signal y is compared with the reference signal y by the method (9) a Each modal component y of (t) n (t) performing smooth pseudo-Wigner-Ville transformation to obtain a smooth pseudo-Wigner-Ville time-frequency distribution expression
In the formula (9), the amino acid sequence of the compound,and->Representing y n Transient correlation function of (t),>representation->Conjugation of (2); g (s-t) is a time domain window function, h (τ) is a frequency domain window function, and g (0) =h (0) =1, s and τ are both integral variables; omega is the angular frequency;
step 4: using (10) to divide each mode component y n Linear superposition of the smoothed pseudo Wigner-Ville analysis results of (t) to obtain an analysis signal y a (t) smooth pseudo-Wigner-Ville distribution
Step 5: for the analytic signal y a Sliding pseudo-Wigner-Ville distribution of (t)And performing interference detection, and filtering the obtained interference signal by adopting a notch IIR filter, so as to obtain the sliding pseudo Wigner-Ville distribution after filtering.
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