Navigation signal blind separation method, system and equipment in alpha pulse interference environment based on Gaussian kernel filtering and medium

Abstract

The invention discloses a navigation signal blind separation method, system and equipment in an alpha pulse interference environment based on Gaussian kernel filtering, and a medium, and aims to improve the signal processing performance in a complex interference environment. According to the method, alpha pulse interference in aliasing signals is suppressed by adopting a Gaussian kernel filtering technology, and effective suppression of the alpha pulse interference is realized by reasonably designing filtering parameters; two correlation matrixes are subjected to joint diagonalization, and a joint diagonal matrix is used as an initial value of a left aliasing matrix and a right aliasing matrix in a blind separation algorithm, so that the convergence speed of aliasing matrix estimation is effectively improved; then, separating the signals after the pulse interference is suppressed by using a blind separation algorithm of joint diagonalization and an initial value of a left and right aliasing matrix; experimental results show that the method has excellent performance in the aspects of suppressing impulse noise influence and signal separation, and the problems that a traditional method is insufficient in alpha impulse interference suppression and poor in signal separation performance are effectively solved; systems, devices, and media are used to implement the methods.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a navigation signal blind separation method, system, equipment and medium in an alpha pulse interference environment based on Gaussian kernel filtering. Background Art

[0002] In the field of modern signal processing, with the rapid development of communication, navigation and radar systems, signal processing technology is facing an increasingly complex interference environment. Especially in the processing of aliased signals with wide bandwidth and multiple signal sources, noise and interference have become the main obstacles affecting the quality of signal recovery. Among them, alpha pulse interference, due to its prominent pulse and strong non-Gaussian characteristics, has brought great challenges to traditional interference suppression and separation algorithms.

[0003] Alpha stable distribution is a distribution with asymmetric and heavy-tail characteristics, which is widely present in practical scenarios, such as random interference in wireless communications, radar signals, and impulse noise environments. Unlike traditional Gaussian noise, alpha pulse interference does not have a closed-form probability density function, so its characteristics are determined by the following characteristic functions:

[0004]

[0005] Among them, the characteristic exponent α controls the impulse nature of the distribution, the symmetry parameter β represents the symmetry of the distribution, the scale parameter γ, also known as the dispersion coefficient, controls the overall amplitude or intensity of the noise, and the location parameter δ determines the center offset of the distribution.

[0006] In signal processing, the impulse nature of alpha pulse interference makes the amplitude of occasional interference signals far exceed the normal signal level, resulting in the signal no longer having finite second-order and higher-order moments. This noise characteristic places extremely high demands on filtering and signal separation. At present, traditional interference suppression methods (such as linear filtering, Wiener filtering, and wavelet denoising) are not effective in processing alpha pulse interference. These methods usually assume that the noise distribution is Gaussian. When the noise exhibits a heavy-tail characteristic, the filtering effect is greatly reduced. In addition, these methods are prone to losing important signal features during the denoising process, resulting in a decrease in signal quality. There are many alpha pulse interference suppression techniques. The fractional lower order statistics (FLO) developed based on the fractional lower order theory is often used to suppress impulse noise. In the context of alpha stable distribution noise, the signal no longer has finite second-order and higher-order moments, so the signal processing method based on finite order moments fails. To address this problem, Zhao Dadi used the fractional low-order statistics (FLOS) function to suppress alpha pulse interference (Zhao Dadi. Research on LFM signal parameter estimation method under alpha stable distribution [D]. Xidian University, 2022. DOI: 10.27389 / d.cnki.gxadu.2022.000652.), but this method is very sensitive to the choice of parameter p, and requires obtaining prior information on alpha pulse interference to estimate the value of the characteristic index of alpha pulse interference, and there is a lack of unified theoretical criteria for how to choose the appropriate order. Ping Jiarong used a mapping function to map the infinite amplitude of the received signal noise to a finite interval (Ping Jiarong, Li Sai, Lin Yunhang. Modulation identification of UAV cluster MIMO signals under alpha stable distribution noise and multipath interference [J]. Systems Engineering and Electronics, 2024, 46(11): 3920-3929.), but this method is not stable enough for signal processing at different amplitudes. Liu Mingqian et al. used the logarithmic transformation method, that is, a nonlinear transformation function, to compress and transform the LFM signal interfered by alpha pulses, thereby suppressing the influence of alpha pulse interference (Xi'an University of Electronic Science and Technology. Method, system, equipment and medium for parameter estimation of multi-component linear frequency modulation signals in symbiotic chirp-ultra-wideband radio system: 202410693572.6[P]. 2024-09-24.). The logarithmic transformation can significantly reduce the influence of high-amplitude interference, and at the same time, combined with nonlinear amplitude adjustment, the signal is smoothed. However, excessive amplification of small-amplitude signals by logarithmic transformation may lead to loss of details. In complex interference environments, the interference suppression performance of the signal is limited.Luo Jinjun et al. proposed to use the limiter method to suppress alpha pulse interference (Luo Jinjun. Research on signal detection methods under non-Gaussian alpha stable distribution noise [D]. National University of Defense Technology, 2018. DOI: 10.27052 / d.cnki.gzjgu.2018.000256.). The limiter method is to set a threshold to eliminate abnormal amplitudes. Although the implementation principle is simple, it is difficult to select the optimal threshold. Therefore, these methods are difficult to achieve good interference suppression effects when dealing with alpha pulse interference.

[0007] In recent years, blind source separation algorithms have attracted much attention in the field of signal processing. They use the statistical characteristics of observed signals to separate source signals and can effectively solve the problem of signal aliasing. Herault and Jutten first proposed an adaptive feedback neural network algorithm, which successfully separated mixed independent source signals (Jutten C, Herault J. Space or time adaptive signal processing by neural network models [J]. AIP Conference Proceedings, 1986, 151 (1): 206-211.). In 1994, Comon proposed the classic independent component analysis (ICA) method for linear instantaneous mixed signals. It assumes independence and non-Gaussianity between source signal components and has a good separation effect on positive definite mixture models (Comon P. Independent component analysis, a new concept [J]. Signal Processing, 1994, 36 (3): 287-314.). Nobutaka Ito proposed a FastFCA blind source separation method, which uses the properties of diagonal matrices to complete the matrix inversion by inverting the diagonal elements (N.Ito, R.Ikeshita, H.Sawada and T.Nakatani, "A JointDiagonalization Based Efficient Approach to Underdetermined Blind AudioSource Separation Using the Multichannel Wiener Filter," in IEEE / ACMTransactions on Audio, Speech, and Language Processing, vol.29, pp.1950-1965, 2021). However, in complex noise environments, the separation accuracy and robustness of blind separation algorithms still need to be improved. The traditional joint diagonalization method assumes that the noise is Gaussian distributed, and the separation performance drops significantly when faced with alpha pulse interference.

[0008] In summary, the existing technology has the following deficiencies when processing complex interference signals:

[0009] (1) Limited suppression effect of alpha pulse interference: Traditional filtering methods are difficult to achieve good interference suppression effect when dealing with alpha pulse interference;

[0010] (2) Limited separation accuracy: Blind separation algorithms are susceptible to interference in high-noise environments, resulting in deviations in separation results;

[0011] (3) Low computational efficiency: Some complex separation algorithms have high computational complexity when faced with large-scale data, making it difficult to meet real-time application requirements. Summary of the invention

[0012] In order to overcome the defects of the above-mentioned prior art, the purpose of the present invention is to propose a method, system, equipment and medium for blind separation of navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering. Aiming at the problems of strong impulse nature of alpha pulse interference, poor effect of traditional interference suppression methods and low separation accuracy of blind separation algorithms in complex noise environments, the present invention combines Gaussian kernel nonlinear transformation and non-orthogonal joint diagonalization algorithm to significantly improve the suppression effect and signal separation performance, effectively reduce pulse interference in the signal, improve signal quality, and achieve high-precision separation of source signals, which is suitable for signal processing applications in complex interference environments.

[0013] In order to achieve the above object, the technical solution adopted by the present invention is:

[0014] A method for blind separation of navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering specifically comprises the following steps:

[0015] The first step is to obtain the aliased signal X containing alpha pulse interference from the sensor or data source. r =[x r (1),x r (2),...,x r (T)]; aliased signal X r It is generated by multi-source signals passing through the channel and alpha pulse interference;

[0016] In the second step, the aliased signal X obtained in the first step is subjected to Gaussian kernel transformation to suppress alpha pulse interference. The aliased signal is processed using a nonlinear transformation function based on the Gaussian kernel to obtain the interference suppressed signal X filtered =[x filtered (1),x filtered (2),...,x filtered (T)];

[0017] Step 3: Signal X after interference suppression filtered The correlation matrix group of different time delays is R x (τ l ),l=1,2,...,L, firstly, the two correlation matrices are jointly diagonalized, and the calculated joint diagonalized matrix is ​​used as the initial left and right aliasing matrix V(0) and Then the interference suppressed signal X filtered Use the joint diagonalization method to perform blind source separation and separate the target signal

[0018] In the first step, the aliased signal X r =[x r (1),x r (2),…,x r (T)] The aliased signal x at time t r (t) is generated by multi-source signals passing through the channel and alpha pulse interference:

[0019] x r (t) = A·s(t) + n(t)

[0020] Among them, x r (t) = [x 1 (t),x 2 (t),...,x M (t)] T is the received aliased signal, A is the channel aliasing matrix, s(t)=[s 1 (t),s 2 (t),...,s N (t)] T is the transmitted multi-source signal, n(t)=[n 1 (t),n 2 (t),...,n M (t)] T is the alpha pulse interference; where the alpha pulse interference is expressed by the characteristic function:

[0021]

[0022] in,

[0023]

[0024] Among them, the characteristic index α controls the impulse nature of the distribution; the symmetry parameter β is the symmetry of the distribution; the scale parameter γ, also known as the dispersion coefficient, controls the overall amplitude or intensity of the noise; and the location parameter δ determines the center offset of the distribution.

[0025] The specific method of the second step is: perform a nonlinear transformation based on a Gaussian kernel on the aliased signal interfered by the alpha pulse as follows:

[0026]

[0027] Then all received signals can be expressed as follows after nonlinear transformation based on Gaussian kernel:

[0028] X filtered =[x filtered (1),x filtered (2),...,x filtered (T)]

[0029] Among them, x r (t) is the aliased signal received at time t, |x r (t)| is the modulus of the aliased signal sequence at time t, x filtered (t) is the aliasing signal after nonlinear transformation, is the source signal after nonlinear transformation, is the interference signal after nonlinear transformation, σ is each sample x in the received signal matrix r (t), a is also the median of the modulus of each sample in the received signal matrix, that is, the samples are arranged in order of their modulus values ​​to form a series, and the values ​​in the middle of the series are σ and a; when the received aliased signal undergoes a nonlinear transformation based on the Gaussian kernel, the signal that is strongly interfered by the alpha pulse, that is, the amplitude of the alpha pulse interference is much larger than the original signal, will be compressed to zero after the nonlinear transformation, thereby reducing the influence of the pulse interference, and for the signal that is less affected by the alpha pulse interference, that is, the amplitude of the interference is not obvious compared with the original signal, after the nonlinear transformation, the original amplitude is approximately maintained, thereby achieving the suppression of the alpha pulse interference.

[0030] The specific method of the third step is:

[0031] 3.1. Source signal after nonlinear transformation τ l Delay correlation matrix It is expressed as:

[0032]

[0033] Among them, σ n (τ l ) indicates that the source signal after the nth filtering is at τ l Correlation coefficient of time delay; x filtered (t) is the aliased signal after nonlinear transformation, that is, x r (t) The signal after alpha pulse interference suppression is approximately the received signal without alpha pulse interference. For convenience of representation, x filtered (t) is uniformly written as x(t), It is written as s(t); then, the signal τ after alpha pulse interference suppression l The correlation matrix of the time delay is:

[0034] R x (τ l )=E{x(t)x H (t+τ l )}=AE{s(t)s H (t+τ l )}A H

[0035] =Adiag{[σ 1 (τ l ),σ 2 (τ l ),…,σ N (τ l )]}A H

[0036] That is, x(t) with respect to τ l The second-order time delay correlation matrix of has a jointly diagonalizable structure. Similarly, given L different time delays, τ 1 ,…,τ L , the observed signal is about τ 1 ,…,τ L The second-order time-delay correlation matrix of also has a jointly diagonalizable structure;

[0037] To simplify writing, the target matrix R x (τ l ) is expressed as R(l). Based on the inherent scale uncertainty and arrangement uncertainty of blind source separation, the target matrix R(l) is expressed as:

[0038]

[0039] in, is the right aliasing matrix and V is the left aliasing matrix, the right aliasing matrix The left aliasing matrix V and the channel aliasing matrix A are essentially equal matrices, l=1,...,L is a diagonal matrix group;

[0040] 3.2 According to the target matrix R(l), construct the cost function and solve the aliasing matrix:

[0041]

[0042] Where Λ(l)=diag{[λ 1 (l),λ 2 (l),…,λ N (l)]}, V = [v 1 ,v 2 ,…,v N ], Cost function J TQFF They are about three sets of unknown matrices V, and Λ(l),1=1,...,L, that is, if any two sets of unknown parameters are fixed, the cost function is only a quadratic function of the third set of unknown parameters; therefore, the cost function is called TQFF is the triquadratic fitting function;

[0043] 3.3 Calculate the initial left aliasing matrix V(0) = [v 1 (0),v 2 (0),…,v N (0)] and the right aliasing matrix The calculation method of the initial left and right aliasing matrices is:

[0044] First, take two autocorrelation matrices under different time delays as R(j) and R(k), and calculate the joint diagonalization of these two matrices; perform eigendecomposition on the autocorrelation matrix R(j) to obtain eigenvalues ​​and eigenvectors; let the eigenvector matrix of the autocorrelation matrix R(j) be P, and the eigenvalue diagonal matrix be Λ(j), that is,

[0045] R(j)=PΛ(j)P -1

[0046] Use the eigenvector matrix P to perform a similarity transformation on the autocorrelation matrix R(k), and get R'(k) = P -1 R(k)P, perform eigendecomposition on the matrix R'(k) after similarity transformation to obtain eigenvalues ​​and eigenvectors; let the eigenvector matrix of the matrix R'(k) after similarity transformation be Q, that is

[0047] R'(k)=QΛ(k)Q -1

[0048] Among them, the matrix Λ(k) is the eigenvalue diagonal matrix of R'(k); the final joint diagonalization matrix is

[0049] V joint =PQ

[0050] The matrix V joint As the initial value of the left and right aliasing matrices, that is, V(0) = V joint ,

[0051] 3.4 Solve the quadratic fitting function, given the left aliasing matrix V and the right aliasing matrix Estimate the diagonal matrix Λ(l); then given the left aliasing matrix V and the diagonal matrix Λ(l), estimate the right aliasing matrix Finally, the right aliasing matrix is ​​given And the diagonal matrix Λ(l), estimate the left aliasing matrix V, and iterate until convergence; get the estimate of the left aliasing matrix V

[0052] 3.5 Optimizing the objective function J through iteration TQFF , separate the source signal The separation formula is:

[0053]

[0054] in, is the estimated separation matrix, which is obtained by minimizing the non-orthogonal joint diagonalization error function.

[0055] A navigation signal blind separation system in an alpha pulse interference environment based on Gaussian kernel filtering, comprising:

[0056] The signal acquisition module is used for the first step, acquiring the aliased signal containing alpha pulse interference through the sensor or data source, so as to realize the reception and preliminary processing of the navigation signal;

[0057] The Gaussian kernel filter module is used in the second step to suppress alpha pulse interference through a nonlinear transformation function based on the Gaussian kernel, thereby weakening the pulse noise in the aliased signal;

[0058] The blind separation processing module is used in the third step to perform signal dealiasing by calculating the correlation matrix, the initial value of the aliasing matrix, joint diagonalization and iterative optimization of the blind separation objective function, thereby improving the convergence speed of the blind separation algorithm and accurately extracting the target signal.

[0059] A navigation signal blind separation device based on Gaussian kernel filtering in an alpha pulse interference environment, comprising:

[0060] Memory for storing computer programs;

[0061] The processor is used to implement the navigation signal blind separation method in an alpha pulse interference environment based on Gaussian kernel filtering described in the first to third steps when executing the computer program.

[0062] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, it can realize blind separation of navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering based on the method described in the first to third steps.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] 1. Better interference suppression capability: The existing technology mainly relies on linear filtering methods, and has limited ability to suppress sudden pulse interference. The present invention adopts a nonlinear transformation method based on a Gaussian kernel. By performing nonlinear transformation on the aliased signal, the amplitude of the alpha pulse interference is compressed while maintaining the signal characteristics, so that the pulse interference can be effectively attenuated.

[0065] 2. Higher separation accuracy: The present invention optimizes the blind separation objective function by jointly diagonalizing multiple correlation matrices and combining the non-orthogonal joint diagonalization method. It can extract the target signal from the received aliased signal with high accuracy and achieve good blind source separation effect even in complex pulse interference environments.

[0066] 3. Robustness: The present invention suppresses alpha pulse interference, gradually calculates the left and right aliasing matrices during the signal separation process, and combines the non-orthogonal joint diagonalization algorithm. It can still effectively separate the target signal under low signal-to-noise ratio conditions, demonstrating its good robustness and applicability.

[0067] 4. Faster convergence speed: The present invention optimizes the initial value calculation method of the aliasing matrix, which can significantly improve the convergence speed of the algorithm and reduce the computational complexity. Compared with the traditional blind separation algorithm, the calculation amount is lower while ensuring accuracy.

[0068] In summary, the present invention has excellent blind separation performance in complex noise environments by adopting a pulse interference suppression scheme based on Gaussian kernel filtering and a blind separation method based on stepwise joint diagonalization, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0070] Figure 1 This is a flow chart of the blind separation method in an alpha pulse interference environment based on Gaussian kernel filtering.

[0071] Figure 2 is the signal distortion rate (SDR) under different signal-to-noise ratio conditions.

[0072] Figure 3 is the signal-to-interference ratio (SIR) under different signal-to-noise ratio conditions.

[0073] Figure 4 is the signal artifact rate (SAR) under different signal-to-noise ratio conditions.

[0074] Figure 5 is the correlation between the two blind separation signals and the source signal (cor1 and cor2), where Figure 5 (a) is the correlation between the first blind separation signal and the source signal. Figure 5 (b) is the correlation between the second blind separation signal and the source signal.

[0075] Figure 6 is the mutual information (MI) between the two blind separation signals and the source signal 1 and MI 2 ),in, Figure 6 (a) is the mutual information between the first blind separation signal and the source signal, Figure 6 (b) is the mutual information between the second blind separation signal and the source signal.

[0076] Figure 7 It is the curve of the global rejection level (GBL) changing with the number of iterations. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention is described in detail below in conjunction with specific embodiments. It should be noted that the specific embodiments described herein are only used to explain the content of the present invention, rather than to limit the present invention.

[0078] See also Figure 1 , a navigation signal blind separation method in an alpha pulse interference environment based on Gaussian kernel filtering, specifically comprising the following steps:

[0079] S101. Simulate the received signal obtained from the sensor. The source signal S is composed of the navigation signal S 1 and navigation interference signal S 2 A 4×2 aliasing matrix A is randomly generated to represent the linear aliasing relationship during signal propagation. The observed aliasing signal x r (t) is generated according to the following formula:

[0080] x r (t) = A·s(t) + n(t)

[0081] Where s(t)=[s 1 (t),s 2 (t)] T is a multi-source signal, consisting of navigation signal and navigation interference signal, n(t) = [n 1 (t),n 2 (t)] T is additive alpha pulse interference.

[0082] The navigation signal S 1The generation method is as follows: the navigation signal consists of a pseudo-random code (PRN) and a navigation message. The pseudo-random code is a pseudo-random binary code sequence used to measure the arrival time of the signal and then calculate the distance to the satellite. Different satellites use different PRN sequences to distinguish satellite signals. A linear feedback shift register (LFSR) is used to generate a pseudo-random sequence. For example, the C / A code (Coarse / Acquisition Code) of GPS is a 1023-bit pseudo-random code with a period of 1 millisecond. The navigation message contains: ephemeris data (satellite orbit parameters) used to calculate the orbital position of the satellite; clock correction parameters to correct the drift of the satellite clock. Satellite health status, to inform users whether the satellite is available; ionosphere correction parameters, used to correct the propagation delay of the signal in the ionosphere; system time stamp, used to synchronize the satellite and receiver time. GPS uses a data rate of 50bps, each frame length is 1500 bits, and the period is 30 seconds. The PRN code and the navigation message are combined and modulated onto a carrier through BPSK, where the carrier is a high-frequency sine wave used to carry the PRN code and the navigation message. Common GPS bands include the L1 band (1575.42MHz) and the L2 band (1227.60MHz). In the present invention, in order to effectively suppress alpha stable distribution noise and achieve high-precision blind separation of signals, we use the baseband representation of the navigation signal for processing. This omits the demodulation step of the high-frequency carrier, thereby reducing the computational complexity and improving the efficiency of the algorithm. Although the navigation signal is usually modulated onto a high-frequency carrier, the baseband signal contains all the necessary information content. By performing Gaussian kernel nonlinear transformation and blind separation algorithm processing on the baseband signal, our method is also applicable to high-frequency carrier signals in practical applications.

[0083] Interference signal S 2 A variety of interference methods are used for implementation, including sweep frequency interference, single tone interference, and multi-tone interference. The key parameters are:

[0084] Sweep frequency interference: sampling frequency f s =20MHz starting frequency f 0 =4MHz, cut-off frequency f e =6MHz, that is, the sweep frequency range is 4-6MHz and the bandwidth is 2MHz.

[0085] Single tone interference: sampling frequency f s =20MHz, carrier frequency f c =5MHz.

[0086] Multi-tone interference: sampling frequency f s=20MHz, the interference frequencies are 4.5MHz, 5MHz, 5.5MHz, and 6MHz respectively, which are multi-frequency sinusoidal signals.

[0087] Additive alpha pulse interference is expressed as n(t)=[n 1 (t),n 2 (t)] T .

[0088] In this embodiment, the alpha pulse noise is described by a characteristic index α=1.2, a symmetry parameter β=0, a scale parameter γ=1, and a position parameter δ=0.

[0089] S102. Apply Gaussian kernel transformation to the aliased signal X obtained in the first step to suppress alpha pulse interference, and use a nonlinear transformation function based on the Gaussian kernel to process the aliased signal to obtain a signal X after interference suppression. filtered =[x filtered (1),x filtered (2),...,x filtered (T)]; specifically:

[0090] For the received signal, that is, the aliased signal x r (t) Perform Gaussian kernel nonlinear transformation, and the nonlinear transformation function is:

[0091]

[0092] Then all received signals can be expressed as follows after nonlinear transformation based on Gaussian kernel:

[0093] X filtered =[x filtered (1),x filtered (2),...,x filtered (T)]

[0094] Among them, x r (t) is the received aliased signal, |x r (t)| is the modulus of the aliased signal sequence at time t, x filtered (t) is the aliased signal after nonlinear transformation, σ and a are the medians of the modulus of each column vector in the received signal matrix. The received aliased signal is transformed through Gaussian kernel nonlinear transformation, which can effectively suppress the impulse noise of the received signal and maintain the waveform of the source signal.

[0095] S103. Signal X after interference suppression filtered The correlation matrix group of different time delays is R x (τ l),l=1,2,...,L, firstly, the two correlation matrices are jointly diagonalized, and the calculated joint diagonalized matrix is ​​used as the initial left and right aliasing matrix V(0) and Then the interference suppressed signal X filtered Use the joint diagonalization method to perform blind source separation and separate the target signal The specific method is as follows:

[0096] 3.1. Source signal after nonlinear transformation τ l Delay correlation matrix It is expressed as:

[0097]

[0098] Among them, σ n (τ l ) indicates that the source signal after the nth filtering is at τ l Correlation coefficient of time delay; x filtered (t) is the aliased signal after nonlinear transformation, that is, x r (t) The signal after alpha pulse interference suppression is approximately the received signal without alpha pulse interference. For convenience of representation, x filtered (t) is uniformly written as x(t), It is written as s(t); then, the signal τ after alpha pulse interference suppression l The correlation matrix of the time delay is:

[0099] R x (τ l )=E{x(t)x H (t+τ l )}=AE{s(t)s H (t+τ l )}A H

[0100] =Adiag{[σ 1 (τ l ),σ 2 (τ l ),…,σ N (τ l )]}A H

[0101] That is, x(t) with respect to τ l The second-order time delay correlation matrix of has a jointly diagonalizable structure. Similarly, given L different time delays, τ 1 ,…,τ L , the observed signal is about τ 1,…,τ L The second-order time-delay correlation matrix of also has a jointly diagonalizable structure;

[0102] To simplify writing, the target matrix R x (τ l ) is expressed as R(l). Based on the inherent scale uncertainty and arrangement uncertainty of blind source separation, the target matrix R(l) is expressed as:

[0103]

[0104] in, is the right aliasing matrix and V is the left aliasing matrix, the right aliasing matrix The left aliasing matrix V and the channel aliasing matrix A are essentially equal matrices, l=1,...,L is a diagonal matrix group;

[0105] 3.2 According to the target matrix R(l), construct the cost function and solve the aliasing matrix:

[0106]

[0107] Where Λ(l)=diag{[λ 1 (l),λ 2 (l),…,λ N (l)]}, V = [v 1 ,v 2 ,…,v N ], Cost function J TQFF They are about three sets of unknown matrices V, and Λ(l),1=1,...,L, that is, if any two sets of unknown parameters are fixed, the cost function is only a quadratic function of the third set of unknown parameters; therefore, the cost function is called TQFF is the triquadratic fitting function;

[0108] 3.3 Calculate the initial left aliasing matrix V(0) = [v 1 (0),v 2 (0),…,v N (0)] and the right aliasing matrix The calculation method of the initial left and right aliasing matrices is:

[0109] First, take two autocorrelation matrices under different time delays as R(j) and R(k), and calculate the joint diagonalization of these two matrices; perform eigendecomposition on the autocorrelation matrix R(j) to obtain eigenvalues ​​and eigenvectors; let the eigenvector matrix of the autocorrelation matrix R(j) be P, and the eigenvalue diagonal matrix be Λ(j), that is,

[0110] R(j)=PΛ(j)P -1

[0111] Use the eigenvector matrix P to perform a similarity transformation on the autocorrelation matrix R(k), and get R'(k) = P -1 R(k)P, perform eigendecomposition on the matrix R'(k) after similarity transformation to obtain eigenvalues ​​and eigenvectors; let the eigenvector matrix of the matrix R'(k) after similarity transformation be Q, that is

[0112] R'(k)=QΛ(k)Q -1

[0113] Among them, the matrix Λ(k) is the eigenvalue diagonal matrix of R'(k); the final joint diagonalization matrix is

[0114] V joint =PQ

[0115] The matrix V joint As the initial value of the left and right aliasing matrices, that is, V(0) = V joint ,

[0116] 3.4 Use the triquadratic iterative algorithm to solve the triquadratic fitting function, given the left aliasing matrix V and the right aliasing matrix Estimate the diagonal matrix Λ(l); then given the left aliasing matrix V and the diagonal matrix Λ(l), estimate the right aliasing matrix Finally, the right aliasing matrix is ​​given and the diagonal matrix Λ(l), estimate the left aliasing matrix V, and iterate until the algorithm converges; get the estimate of the left aliasing matrix V The specific process is:

[0117] (1) Estimation of diagonal matrix groups

[0118] Let the sub-function:

[0119]

[0120] Fixed unknown matrix V and V and The initial value of is calculated in step 3.3, and the cost function J TQFF The minimum equivalent of the diagonal matrix group Λ(l), l = 1, ..., L is:

[0121]

[0122] Therefore, by minimizing the subfunctions l=1,…,L, to realize the cost function J TQFF (Λ(1),Λ(2),…,Λ(L)) optimization; obviously, the function It can be expressed as:

[0123]

[0124] For any n∈{1,…,N}, the cost function is related to the scalar λ n (l), that is, the conjugate derivative of the nth diagonal element of the diagonal matrix Λ(l) is:

[0125]

[0126] Let the derivative be zero.

[0127]

[0128] When n traverses 1, 2, ... N, we can get the matrix group

[0129]

[0130] After sorting, the above formula can be expressed as the following matrix form:

[0131]

[0132] Among them, vector matrix

[0133]

[0134] Obviously, the fixed matrix V and For any l∈{1,…,L}, the diagonal matrix Λ(l) can be expressed as:

[0135]

[0136] (2) Estimation of the right aliasing matrix:

[0137] Fixed left aliasing matrix V, and diagonal matrix group Cost Function About Right Mix

[0138] Stacked Matrix Minimize; after rearrangement, the cost function It can be expressed as:

[0139]

[0140] Among them, the matrix With the matrix Unrelated; Matrix matrix According to the above formula, the function About Matrix The conjugate derivative of is

[0141]

[0142] Let the derivative be zero, and after sorting, the matrix It can be expressed as:

[0143]

[0144] (3) Estimation of the left aliasing matrix

[0145] Finally, fix the right aliasing matrix And the diagonal matrix group Cost function J TQFF (V) Minimize the left aliasing matrix V; after sorting, the cost function J TQFF (V) can be expressed as:

[0146]

[0147] Among them, the matrix Similarly, function J TQFF (V) Take the jugate derivative with respect to V and set the derivative to zero. After sorting, the matrix V can be expressed as:

[0148]

[0149] Iterate according to the above steps and finally get the estimate of the left aliasing matrix V

[0150] 3.5 Optimizing the objective function J through iteration TQFF , separate the source signal The separation formula is:

[0151]

[0152] in, is the estimated separation matrix, which is obtained by minimizing the non-orthogonal joint diagonalization error function.

[0153] Experimental verification

[0154] In order to verify the performance of blind separation method based on Gaussian kernel filtering in alpha pulse interference environment, we designed a series of experiments to compare the performance of Gaussian kernel method, fractional low-order method, mapping method and logarithmic transformation method in blind signal separation task. The experimental signal is two-way source signal with alpha pulse interference, and the signal-to-noise ratio (SNR) range is set to [-15dB, -5dB] with a step size of 2dB. Under each signal-to-noise ratio condition, the Monte Carlo experimental method is used to perform 100 simulation experiments to calculate the average value to ensure the reliability of the experimental results.

[0155] In the experiment, a variety of evaluation indicators are used, including signal distortion rate (SDR), signal interference rate (SIR), signal artifact rate (SAR), correlation (cor) and mutual information (MI), to quantify the performance of the blind separation algorithm under different signal-to-noise ratio conditions. In addition, by comparing the global rejection level (GRL) of different iterations in the blind separation method of randomly generating initial values ​​and calculating initial values, it can be found that after using the stepwise joint diagonalization method to calculate the initial value, the convergence speed is superior. Next, taking single-tone interference as an example, the performance of the blind separation method based on Gaussian kernel filtering in the alpha pulse interference environment will be analyzed.

[0156] Signal distortion rate (SDR) is an important indicator to measure the matching degree between blind separation signal and source signal. The higher the value, the smaller the signal distortion. Experimental results show that Gaussian kernel method shows strong robustness and superiority in the whole signal-to-noise ratio range. Figure 2 As shown in the figure, under the condition of -15dB signal-to-noise ratio, the SDR of the Gaussian kernel method reaches 7dB, compared with 3.5dB for the fractional low-order method, 5.5dB for the mapping method and -2dB for the logarithmic transformation method. This shows that the Gaussian kernel method has a stronger signal fidelity capability under extremely low signal-to-noise ratio conditions. As the signal-to-noise ratio increases, the SDR of the Gaussian kernel method increases steadily, reaching 12dB when the signal-to-noise ratio is -5dB, while the SDRs of the other three methods are all below 9dB. This result verifies that the Gaussian kernel method has a significant advantage in suppressing alpha pulse interference when dealing with complex noise environments.

[0157] The signal-to-interference ratio (SIR) quantifies the ratio of the target signal to other interference signals in the separated signal, and is an important indicator for evaluating the performance of blind signal separation algorithms. Experimental results show that the SIR of the Gaussian kernel method is better than other methods under different signal-to-noise ratio conditions, especially under low signal-to-noise ratio conditions. Figure 3 As shown in the figure, under the condition of -15dB signal-to-noise ratio, the SIR of Gaussian kernel method reaches 21.5dB, while that of fractional low-order method, mapping method and logarithmic transformation method are 18dB, 19dB and 14dB respectively. This shows that Gaussian kernel method can more effectively suppress the interference of other signals. When the signal-to-noise ratio is -5dB, the SIR of Gaussian kernel method is improved to 27dB, which is 6dB higher than that of logarithmic transformation method, 5dB higher than that of mapping method, and 4dB higher than that of fractional low-order method, demonstrating its excellent ability in suppressing interference signals. Gaussian kernel method can effectively reduce the influence of interference signals, thereby improving the purity of separated signals.

[0158] The signal artifact rate (SAR) measures the degree to which artifacts in the separated signal affect the signal quality. The higher the SAR, the less interference the artifacts have on the signal. Figure 4As shown in the figure, the SAR of the Gaussian kernel method reaches 7.5dB when the signal-to-noise ratio is -15dB, which is significantly better than the fractional low-order method (4dB), mapping method (6dB) and logarithmic transformation method (-1dB). As the signal-to-noise ratio increases, the SAR of the Gaussian kernel method maintains a steady growth, reaching 12.5dB when the signal-to-noise ratio is -5dB, which is 6dB higher than the logarithmic transformation method and about 4dB higher than the fractional low-order method and mapping method. This result shows that the Gaussian kernel method can significantly reduce the impact of artifacts on the signal and maintain high signal quality in a complex noise environment.

[0159] The correlation index is used to quantify the similarity between the blind separation signal and the source signal, and is calculated using the Pearson correlation coefficient. Experiments show that the Gaussian kernel method has a significant advantage in the correlation index. Figure 5 a and Figure 5 b shows the Pearson correlation coefficients cor1 and cor2 between the two separated signals output by the blind separation algorithm and the corresponding source signals. This index measures the restoration quality of the separated signals and the degree of matching with the source signal. Figure 5 As shown in the figure, the Gaussian kernel method is superior to the fractional low-order method, mapping method and logarithmic transformation method in both cor1 and cor2 indicators. Especially under low signal-to-noise ratio conditions (-15dB), the correlation of the Gaussian kernel method remains above 0.85 and 0.92, while the logarithmic transformation method is only 0.5 and 0.71, the fractional low-order method is 0.75 and 0.87, and the mapping method is 0.8 and 0.9. With the increase of signal-to-noise ratio, the correlation index of the Gaussian kernel method is also better. The high correlation of the Gaussian kernel method indicates that its separated signal is closer to the source signal, effectively retaining the original characteristics of the signal.

[0160] Mutual information (MI) is a key indicator to measure the information correlation between the separated signal and the source signal. Figure 6 a and Figure 6 b shows the mutual information MI of the two blind separation signals and the source signal 1 and MI 2 Mutual information is used to quantify the information correlation between signals. The higher the value, the more information the separated signal retains from the source signal. Experimental results show that the Gaussian kernel method has a significant advantage in mutual information. Figure 6 As shown, the MI of the Gaussian kernel method 1 and MI 2 Under low signal-to-noise ratio (-15dB) conditions, the MI of the mapping method reaches 1.5 bits and 2.2 bits respectively. 1 and MI 2Under low signal-to-noise ratio (-15dB) conditions, the mutual information values ​​of the Gaussian kernel method are 1.1 bits and 1.5 bits respectively, the fractional low-order method is 0.85 and 1.3 respectively, and the logarithmic transformation method is 0.4 and 0.6 respectively. As the signal-to-noise ratio increases, the mutual information value of the Gaussian kernel method continues to grow, always maintaining its leading advantage over other methods. This shows that the Gaussian kernel method can retain more original signal information while suppressing alpha pulse interference, achieving a higher degree of information restoration.

[0161] The global rejection level (GRL) is a commonly used performance parameter in blind separation algorithms and can be used to measure the effectiveness of the algorithm. After the initial value is estimated using the stepwise joint diagonalization method, the convergence speed can be greatly improved in the subsequent blind separation steps. The curves of GBL with and without this method at different signal-to-noise ratios are shown in Figure 2. Figure 7 As shown, it can be found that the convergence speed of the joint diagonalization method after initial value calculation is much higher than that of the method without initial value calculation.

[0162] The interference signal in the source signal is changed to swept frequency interference, single-tone interference, and multi-tone interference for comparative experiments. The results show that when the signal-to-noise ratio is -15dB, different alpha pulse interference suppression methods are used to suppress the interference signal and perform blind source separation, as shown in Table 1.

[0163]

[0164] Table 1 Signal-to-disturbance ratio (SDR) of blind separation signals under different pulse suppression methods

[0165] It can be found that under low signal-to-noise ratio conditions, the method proposed in this paper still has relatively excellent alpha pulse interference suppression effect and blind separation effect, and performs stably.

[0166] Combined with the experimental results and graphical analysis, the stepwise joint diagonalization method based on Gaussian kernel of the present invention is significantly better than the fractional low-order method, mapping method and logarithmic transformation method in terms of pulse interference suppression and blind signal separation performance. The specific summary is as follows:

[0167] 1. Interference suppression capability: Figure 2 and Figure 3 As shown in the figure, the Gaussian kernel method performs excellently in terms of SDR and SIR indicators, and can still effectively suppress interference signals under low signal-to-noise ratio conditions.

[0168] 2. Separation accuracy: Figure 5 and Figure 6 As shown in the figure, the Gaussian kernel method performs well in terms of correlation and mutual information indicators and can restore the source signal characteristics more accurately.

[0169] 3. Robustness: Figure 4 and Figure 6As shown in the figure, the Gaussian kernel method still has significant advantages under low signal-to-noise ratio conditions, demonstrating its good robustness and applicability.

[0170] 4. Convergence speed: By using the step-by-step joint diagonalization method to calculate the initial value of the aliasing matrix, the convergence speed of the algorithm can be significantly improved, such as Figure 7 shown.

[0171] In summary, the stepwise joint diagonalization method based on Gaussian kernel has superior blind separation performance in complex noise environments and has broad application prospects.

[0172] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A blind separation method of navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering is characterized by: The following steps are involved: The first step is to obtain the aliased signal X containing alpha pulse interference from the sensor or data source. r =[x r (1),x r (2),…,x r (T)]; aliased signal X r It is generated by multi-source signals passing through the channel and alpha pulse interference; In the second step, the aliased signal X obtained in the first step is subjected to Gaussian kernel transformation to suppress alpha pulse interference. The aliased signal is processed using a nonlinear transformation function based on the Gaussian kernel to obtain the interference suppressed signal X filtered =[x filtered (1),x filtered (2),...,x filtered (T)]; Step 3: Signal X after interference suppression filtered The correlation matrix group of different time delays is R x (τ l ),l=1,2,...,L, firstly, the two correlation matrices are jointly diagonalized, and the calculated joint diagonalized matrix is ​​used as the initial left and right aliasing matrix V(0) and Then the interference suppressed signal X filtered Use the joint diagonalization method to perform blind source separation and separate the target signal 2. The method for blind separation of navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering according to claim 1 is characterized in that: In the first step, the aliased signal X r =[x r (1),x r (2),…,x r (T)] The aliased signal x at time t r (t) is generated by multi-source signals passing through the channel and alpha pulse interference: x r (t)=A·s(t)+n(t) Among them, x r (t)=[x1(t),x2(t),...,x M (t)] T is the received aliased signal, A is the channel aliasing matrix, s(t)=[s1(t),s2(t),...,s N (t)] T is the transmitted multi-source signal, n(t)=[n1(t),n2(t),...,n M (t)] T is the alpha pulse interference; where the alpha pulse interference is expressed by the characteristic function: in, Among them, the characteristic index α controls the impulse nature of the distribution; the symmetry parameter β is the symmetry of the distribution; the scale parameter γ, also known as the dispersion coefficient, controls the overall amplitude or intensity of the noise; and the location parameter δ determines the center offset of the distribution.

3. The method for blind separation of navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering according to claim 1 is characterized in that: The specific method of the second step is: perform a nonlinear transformation based on a Gaussian kernel on the aliased signal interfered by the alpha pulse as follows: Then all received signals can be expressed as follows after nonlinear transformation based on Gaussian kernel: X filtered =[x filtered (1),x filtered (2),...,x filtered (T)] Among them, x r (t) is the aliased signal received at time t, |x r (t)| is the modulus of the aliased signal sequence at time t, x filtered (t) is the aliasing signal after nonlinear transformation, is the source signal after nonlinear transformation, is the interference signal after nonlinear transformation, σ is each sample x in the received signal matrix r (t), a is also the median of the modulus of each sample in the received signal matrix, that is, the samples are arranged in order of their modulus values ​​to form a series, and the values ​​in the middle of the series are σ and a; when the received aliased signal undergoes a nonlinear transformation based on the Gaussian kernel, the signal that is strongly interfered by the alpha pulse, that is, the amplitude of the alpha pulse interference is much larger than the original signal, will be compressed to zero after the nonlinear transformation, thereby reducing the influence of the pulse interference, and for the signal that is less affected by the alpha pulse interference, that is, the amplitude of the interference is not obvious compared with the original signal, after the nonlinear transformation, the original amplitude is approximately maintained, thereby achieving the suppression of the alpha pulse interference.

4. The method for blind separation of navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering according to claim 1 is characterized in that: The specific method of the third step is: 3.

1. Source signal after nonlinear transformation τ l Correlation matrix of time delay It is expressed as: Among them, σ n (τ l ) indicates that the source signal after the nth filtering is at τ l Correlation coefficient of time delay; x filtered (t) is the aliased signal after nonlinear transformation, that is, x r (t) The signal after alpha pulse interference suppression is approximately the received signal without alpha pulse interference. For convenience of representation, x filtered (t) is uniformly written as x(t), It is written as s(t); then, the signal τ after alpha pulse interference suppression l The correlation matrix of the time delay is: R x (τ l )=E{x(t)x H (t+τ l )}=AE{s(t)s H (t+τ l )}TO H =Adiag{[σ1(τ l ),σ2(τ l ),…,s N (t l )]}A H That is, x(t) with respect to τ l The second-order time delay correlation matrix of has a jointly diagonalizable structure. Similarly, given L different time delays, τ1,…,τ L , the observed signal is about τ1,…,τ L The second-order time-delay correlation matrix of also has a jointly diagonalizable structure; To simplify writing, the target matrix R x (τ l ) is expressed as R(l). Based on the inherent scale uncertainty and arrangement uncertainty of blind source separation, the target matrix R(l) is expressed as: in, is the right aliasing matrix and V is the left aliasing matrix, the right aliasing matrix The left aliasing matrix V and the channel aliasing matrix A are essentially equal matrices, l=1,...,L is a diagonal matrix group; 3.2 According to the target matrix R(l), construct the cost function and solve the aliasing matrix: Among them, Λ(l)=diag{[λ1(l),λ2(l),…,λ N (l)]}, V = [v1,v2,…,v N ], Cost function J TQFF They are about three sets of unknown matrices V, and Λ(l),1=1,...,L, that is, if any two sets of unknown parameters are fixed, the cost function is only a quadratic function of the third set of unknown parameters; therefore, the cost function is called TQFF is the triquadratic fitting function; 3.3 Calculate the initial left aliasing matrix V(0) = [v1(0), v2(0), …, v N (0)] and the right aliasing matrix The calculation method of the initial left and right aliasing matrices is: First, take two autocorrelation matrices under different time delays as R(j) and R(k), and calculate the joint diagonalization of these two matrices; perform eigendecomposition on the autocorrelation matrix R(j) to obtain eigenvalues ​​and eigenvectors; let the eigenvector matrix of the autocorrelation matrix R(j) be P, and the eigenvalue diagonal matrix be Λ(j), that is, R(j)=PΛ(j)P -1 Use the eigenvector matrix P to perform a similarity transformation on the autocorrelation matrix R(k), and get R'(k) = P -1 R(k)P, perform eigendecomposition on the matrix R'(k) after similarity transformation to obtain eigenvalues ​​and eigenvectors; let the eigenvector matrix of the matrix R'(k) after similarity transformation be Q, that is R'(k)=QΛ(k)Q -1 Among them, the matrix Λ(k) is the eigenvalue diagonal matrix of R'(k); the final joint diagonalization matrix is V joint =PQ The matrix V joint As the initial value of the left and right aliasing matrices, that is, V(0) = V joint , 3.4 Solve the quadratic fitting function, given the left aliasing matrix V and the right aliasing matrix Estimate the diagonal matrix Λ(l); then given the left aliasing matrix V and the diagonal matrix Λ(l), estimate the right aliasing matrix Finally, the right aliasing matrix is ​​given And the diagonal matrix Λ(l), estimate the left aliasing matrix V, and iterate until convergence; get the estimate of the left aliasing matrix V 3.5 Optimizing the objective function J through iteration TQFF , separate the source signal The separation formula is: in, is the estimated separation matrix, which is obtained by minimizing the non-orthogonal joint diagonalization error function.

5. A blind separation system for navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering, characterized in that: include: The signal acquisition module is used for the first step, acquiring the aliased signal containing alpha pulse interference through the sensor or data source, so as to realize the reception and preliminary processing of the navigation signal; The Gaussian kernel filter module is used in the second step to suppress alpha pulse interference through a nonlinear transformation function based on the Gaussian kernel, thereby weakening the pulse noise in the aliased signal; The blind separation processing module is used in the third step to perform signal dealiasing by calculating the correlation matrix, the initial value of the aliasing matrix, joint diagonalization and iterative optimization of the blind separation objective function, thereby improving the convergence speed of the blind separation algorithm and accurately extracting the target signal.

6. A navigation signal blind separation device based on Gaussian kernel filtering in an alpha pulse interference environment, characterized in that: include: Memory for storing computer programs; A processor is used to implement the navigation signal blind separation method in an alpha pulse interference environment based on Gaussian kernel filtering as described in claims 1 to 4 when executing the computer program.

7. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it can realize blind separation of navigation signals in an alpha pulse interference environment based on Gaussian kernel filtering based on the methods described in claims 1 to 4.

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