A high-dynamic GNSS null widening and deepening anti-jamming method based on triangular distribution

Abstract

The application provides a high-dynamic GNSS null deepening and widening anti-interference method based on a triangular distribution, which comprises setting a variation of an incident angle of an interference signal to follow a triangular probability distribution model, estimating a sampling covariance matrix of a received signal, determining a conversion matrix, namely an expansion matrix, between an average covariance matrix and the sampling covariance matrix based on a disturbance model, using the expansion matrix for null widening, extracting an interference component in an array received signal through orthogonal projection transformation, enhancing the interference component through a weighting coefficient, reconstructing the sampling covariance matrix for null deepening, and performing coning processing on the reconstructed sampling covariance matrix to implement null widening and deepening while suppressing interference by using a PI algorithm. The null width and depth can be adjusted by parameters to adapt to different interference environments, and the anti-interference performance of a navigation receiver is significantly improved.

Description

Technical Field

[0001] This invention relates to interference suppression technology in the field of satellite navigation, and more particularly to a high-dynamic GNSS null widening and deepening anti-interference method based on triangular distribution. Background Technology

[0002] Given the widespread use of GNSS (Global Navigation Satellite System) and the fact that satellite signals are highly susceptible to interference, anti-jamming technology for navigation receivers plays a crucial role in providing stable PNT (Positioning, Navigation, Timing) services.

[0003] In highly dynamic environments, conventional anti-interference algorithms for satellite navigation receivers produce relatively narrow nulls. Rapid changes in the direction of interference can easily cause these nulls to shift out of the nulls, resulting in poor anti-interference performance. An effective method to address the problem of interference shifting out of nulls in highly dynamic environments is null widening. Existing null widening algorithms can be divided into two categories: differential constraints and covariance matrix tapering. The former cannot flexibly control the null widening width, while the latter may lead to shallower nulls. Summary of the Invention

[0004] This invention addresses the null mismatch problem in traditional navigation receivers under high dynamic conditions by proposing a high-dynamic GNSS null widening and deepening anti-interference method based on triangular distribution. This method assumes that the disturbance angle of the interference follows a triangular distribution and derives a conic matrix. To overcome the problem of null shallowing caused by covariance matrix conicating algorithms, the covariance matrix is ​​reconstructed by enhancing the interference components. Finally, the power inversion algorithm is combined to widen and deepen the null, thereby solving the null mismatch problem in high dynamic environments.

[0005] To achieve the above objectives, the specific technical solution of the present invention includes the following steps:

[0006] Step S1: Set the change of the incident angle of the interference signal to follow a triangular probability distribution model, and estimate the sampling covariance matrix of the received signal;

[0007] Step S2: Based on the perturbation model, determine the transformation matrix, i.e. the extended matrix, between the average covariance matrix and the sampled covariance matrix, which is used for null widening;

[0008] Step S3: Extract the interference components in the array received signal through orthogonal projection transformation, enhance the interference components through weighting coefficients, and reconstruct the sampling covariance matrix for null deepening;

[0009] Step S4: Taper the reconstructed sampling covariance matrix;

[0010] Step S5: Use the PI algorithm to suppress interference while widening and deepening the null trap.

[0011] Further, step S1 specifically includes:

[0012] Set up a uniform circular array with M elements. One element is located at the center of the circle, and the remaining M-1 elements are evenly distributed on the circumference of a circle in a certain plane. The radius of the circular array is... λ is the carrier wavelength. Assume that L satellite signals and Q interference signals arrive at the array simultaneously. This represents the elevation and azimuth angles at which the signal from the l-th satellite arrives at the circular array. Let represent the elevation and azimuth angles at which the q-th interfering signal arrives at the circular array. Then, the received signal of the uniform circular array is expressed as:

[0013]

[0014] Among them, s l (t) represents the satellite signal, s q w(t) represents the interference signal, and w(t) represents the noise. Let P be the steering vector of the incident signal. The position matrix of the array element and the direction of arrival of the signal are represented as follows:

[0015]

[0016] The sampling covariance matrix of the received signal is then:

[0017]

[0018] Where N represents the number of sampling points, and X(n) represents the signal after sampling X(t).

[0019] Further, step S2 specifically includes:

[0020] Let the change in the incident angle of the q-th interference signal be the pitch angle Δθ. q and azimuth Δθ q and If the probability distribution follows a triangle within the interval [-β, β], then Δθ q and The probability density functions are as follows:

[0021]

[0022] Where β represents the range of the incident angle of the interference signal, the average covariance matrix of the signal received by the uniform circular array is expressed as:

[0023]

[0024] in, Let I represent the interference power of the q-th interference signal, and I be the identity matrix. express The joint probability density function, Indicates noise power;

[0025] The element in the m-th row and n-th column is represented as:

[0026]

[0027] δ mn The noise figure, after simplification, is expressed as:

[0028]

[0029] The element in the m-th row and n-th column of the extended matrix T is:

[0030]

[0031] Where β represents the range of variation of the incident angle of the interference signal.

[0032] Furthermore, step S3 specifically includes:

[0033] Perform spectral decomposition on the sampling covariance matrix, arrange the eigenvalues ​​according to their magnitude, and the eigenvectors corresponding to the top Q largest eigenvalues ​​constitute the interference subspace U. j Based on the properties of the characteristic subspace, the projection matrix P of the disturbance subspace j for:

[0034]

[0035] Projecting the array-received signal onto the interference subspace yields the interference signal component. This component is then weighted and added to the original sampled signal to obtain the enhanced data.

[0036] X d (t)=X(t)+gP j X(t)=(I+gP j X(t)

[0037] The reconstructed sampling covariance matrix R d for:

[0038]

[0039] Where g represents the intensification coefficient, which is a constant, and P j The projection matrix represents the interference subspace. This is the sampling covariance matrix.

[0040] Furthermore, the tapering process in step S4 specifically involves: Here, ⊙ represents element-wise multiplication.

[0041] Furthermore, step S5 specifically includes:

[0042] Substituting the tapered sampling covariance matrix into the power-inverted PI algorithm yields the weight vector w for widening and deepening the null depression under a uniform circular matrix: Where, δ M Given an M×1 dimensional vector, the output signal after interference suppression is: y(n) = w H X(n).

[0043] This invention proposes a high-dynamic GNSS null widening and deepening anti-interference method based on triangular distribution, abbreviated as T-NWD. This method widens and deepens the null by enhancing the interference components to reconstruct the covariance matrix and combining it with a power inversion algorithm. Compared with traditional interference suppression algorithms based on uniform circular arrays, it can still effectively suppress interference under high dynamic conditions. Compared with other covariance matrix tapering algorithms, it forms deeper nulls without changing the contribution of noise terms in the covariance matrix. The null width and depth of this invention can be adjusted by parameters to adapt to different interference environments, significantly improving the anti-interference performance of navigation receivers. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart of a high-dynamic GNSS null widening and deepening anti-interference method based on triangular distribution provided by an embodiment of the present invention;

[0046] Figure 2 This is a comparison of the beam patterns of T-NWD and PI provided in the embodiments of the present invention; wherein, (a) is the PI beam pattern; (b) is the T-NWD beam pattern; (c) is a top view of the PI beam pattern; (d) is a top view of the T-NWD beam pattern; (e) is a side view of the PI beam pattern; and (f) is a side view of the T-NWD beam pattern.

[0047] Figure 3This is a comparison diagram of the influence of different parameters β on the T-NWD null width provided in the embodiments of the present invention; wherein, (a) is the null widening of the T-NWD algorithm at the interference pitch angle, (b) is a local magnified view of (a), (c) is the null widening of T-NWD at the interference azimuth angle, and (d) is a local magnified view of (c).

[0048] Figure 4 This is a comparison diagram of the effects of different deepening coefficients g on the null depth of T-NWD provided in the embodiments of the present invention; wherein, (a) is the null deepening of T-NWD at the interference azimuth angle, and (b) is a local magnified view of (a);

[0049] Figure 5 This is a comparison chart of the output signal-to-interference-plus-noise ratio (SNR) of T-NWD provided in this embodiment of the invention under different input SNR ratios with other methods;

[0050] Figure 6 This is a comparison chart of the output signal-to-interference-plus-noise ratio (SNR) of the T-NWD provided in this embodiment of the invention under different input SNRs with other methods. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] This invention proposes a high-dynamic GNSS null widening and deepening anti-interference method based on triangular distribution, such as... Figure 1 As shown, the method includes:

[0053] Step S1: Estimate the covariance matrix of the received signal

[0054] Set up a uniform circular array with M elements. One element is located at the center of the circle, and the remaining M-1 elements are evenly distributed on the circumference of a circle in a certain plane. The radius of the circular array is... λ is the carrier wavelength. Assume that L satellite signals and Q interference signals arrive at the array simultaneously. This represents the elevation and azimuth angles at which the signal from the l-th satellite arrives at the circular array. Let represent the elevation and azimuth angles at which the q-th interfering signal arrives at the circular array. Then, the received signal of the uniform circular array is expressed as:

[0055]

[0056] Among them, s l (t) represents the satellite signal, s qw(t) represents the interference signal, and w(t) represents the noise. Let P be the steering vector of the incident signal. The position matrix of the array element and the direction of arrival of the signal are represented as follows:

[0057]

[0058] p0 = [0,0,0] T

[0059] p m =d[cos r m ,sin r m ,0] T m = 1, 2, ..., M-1

[0060]

[0061] Therefore, the sampling covariance matrix of the received signal is:

[0062]

[0063] Where N represents the number of sampling points, and X(n) represents the signal after sampling X(t).

[0064] Step 2: Derive the extended matrix based on the perturbation model

[0065] Assume the change in the incident angle of the q-th interference signal is the pitch angle Δθ. q and azimuth Δθ q and If the distribution conforms to a triangle within the interval [-β, β], then Δθ q and The probability density functions are as follows:

[0066]

[0067]

[0068] Where β represents the range of the incident angle of the interference signal, the average covariance matrix of the signal received by the uniform circular array is expressed as:

[0069]

[0070] in, Let I represent the interference power of the q-th interference signal, and I be the identity matrix. express The joint probability density function, Indicates noise power.

[0071] The element in the m-th row and n-th column is represented as:

[0072]

[0073] Where, δ nn The noise figure can be represented by the following:

[0074]

[0075] The element in the m-th row and n-th column of the extended matrix T is:

[0076]

[0077] Where β represents the range of variation of the incident angle of the interference signal.

[0078] Step 3: Enhance the interference components and reconstruct the covariance matrix

[0079] Perform spectral decomposition on the sampling covariance matrix, arrange the eigenvalues ​​according to their magnitude, and the eigenvectors corresponding to the top Q largest eigenvalues ​​constitute the interference subspace U. j Based on the properties of the characteristic subspace, the projection matrix P of the disturbance subspace j for:

[0080]

[0081] Ideally, the interference subspace and the noise subspace are orthogonal. Projecting the array-received signal onto the interference subspace yields the interference signal component. Weighting this component and adding it to the original sampled signal results in data with enhanced interference components.

[0082] X d (t)=X(t)+gP j X(t)=(I+gP j X(t)

[0083] The reconstructed sampling covariance matrix R d for:

[0084]

[0085] Where g represents the intensification coefficient, which is a constant, and P j The projection matrix represents the interference subspace. This is the sampling covariance matrix.

[0086] Step 4: Taper the reconstructed sampling covariance matrix:

[0087]

[0088] Here, ⊙ represents element-wise multiplication.

[0089] Step 5: Widening and Deepening Nulls to Suppress Interference

[0090] Substituting the tapered sampled covariance matrix into the Power Inversion (PI) algorithm yields the weight vector w for widening and deepening nulls under a uniform circular matrix:

[0091]

[0092] Where, δ M Given an M×1 dimensional vector, the output signal after interference suppression is:

[0093] y(n)=w H X(n).

[0094] The effectiveness and superiority of the invention are illustrated through simulation comparisons. In all simulations, a 7-element uniform circular array with a central element is used, and the element spacing is half a wavelength.

[0095] A satellite signal is incident on the array from the direction (10°, 120°), and two single-tone interferences are incident on the array from (60°, 60°) and (60°, 260°) respectively. The input signal-to-noise ratio (SNR) is -20dB, and the input interference-to-signal ratio (JSR) is 60dB. In the T-NWD algorithm, β = 2 and g = 10 are used respectively. The results are as follows. Figure 2 As shown in the figure, (a), (c), and (e) are the beam diagram, top view, and side view of the beam diagram of the traditional PI algorithm, respectively; (b), (d), and (f) are the beam diagram, top view, and side view of the beam diagram of the T-NWD algorithm, respectively. It can be seen from the figure that the T-NWD algorithm can generate nulls in both directions of interference, and the nulls are wider than those of the PI algorithm. Moreover, the nulls are not shallower and the deepest nulls are even deeper than those of the PI algorithm, which proves the effectiveness of the T-NWD algorithm.

[0096] An incident angle of a satellite signal is set at (12°, 105°), and a single-tone interference is incident on the array from (53°, 174°). The signal-to-noise ratio (SNR) is -20 dB, the signal-to-interference ratio (JSR) is 60 dB, and the deepening factor g is 10. Different parameters β are set to investigate their impact on the null width of the T-NWD method. The results are as follows: Figure 3 As shown in the figure, (a) shows the null width of the T-NWD algorithm at the pitch angle of the interference, (b) is a magnified view of (a), (c) shows the null width of T-NWD at the azimuth angle of the interference, and (d) is a magnified view of (c). It can be seen from the figure that as β increases, the null width also increases.

[0097] The simulation conditions were set as follows: a satellite signal and a single-tone interference were incident on a circular array from (12°, 105°) and (53°, 174°) respectively, with β = 2°, SNR = -20dB, and JSR = 60dB. The influence of the deepening coefficient g on the null depth of the T-NWD method was analyzed, and the results are as follows: Figure 4 As shown in the figure, (a) shows the null depth of T-NWD in the interference azimuth angle, and (b) is a magnified view of (a). It can be seen from the figure that as the deepening coefficient g increases, the null depth also increases.

[0098] An incident angle of a satellite signal is set to (10°, 120°). During the weight update period, the incident angle of a single-tone interference changes from (60°, 170°) to (62°, 172°). The signal-to-noise ratio (SNR) is -20dB, the interference-to-signal ratio (JSR) is set to 40dB to 70dB, and the number of snapshots is 512. Weights calculated from sampled data where the interference is incident at (60°, 170°) are used to perform anti-interference processing on the data after the interference angle perturbation. Using the array output SNR as the indicator, T-NWD is compared with traditional PI, PI null broadening based on uniform distribution (U-NW), and PI null broadening based on Laplace distribution (L-NW). The T-NWD parameters are set to β = 1°, g = 10; the U-NW parameter is set to τ = 1°; and the L-NW parameter is set to ξ = 0.8. The results are as follows: Figure 5 As shown in the figure, it can be seen that with the disturbance of the interference angle, the output SINR of the T-NWD array does not change with the increase of the interference signal power, and the output signal-to-interference-plus-noise ratio is higher than the other three comparison methods, demonstrating good anti-interference performance in high dynamic environment.

[0099] A satellite signal is set to an incident angle of (12°, 105°), and a single-tone interference (STO) is incident on the array from (53°, 174°). The input interference-to-signal ratio (JSR) is 60dB, and the input signal-to-noise ratio (SNR) is increased from -25dB to -15dB. Using the initial incident angle data of the interference, the optimal weights are calculated, and the data after the interference angle perturbation is processed. The array output SINR is compared with that of the T-NWD method under different input SNRs, using the PI, L-NW, and U-NW methods. Figure 6 As shown in the figure, the array output SINR of T-NWD increases continuously with the increase of the input SNR, and is significantly better than other methods.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-dynamic GNSS null widening and deepening anti-interference method based on triangular distribution, characterized in that, The method includes: Step S1: Set the change of the incident angle of the interference signal to follow a triangular probability distribution model, and estimate the sampling covariance matrix of the received signal; Step S2: Based on the perturbation model, determine the transformation matrix, i.e. the extended matrix, between the average covariance matrix and the sampled covariance matrix, which is used for null widening; Step S3: Extract the interference components in the array received signal through orthogonal projection transformation, enhance the interference components through weighting coefficients, and reconstruct the sampling covariance matrix for null deepening; Step S4: Taper the reconstructed sampling covariance matrix; Step S5: Use the PI algorithm to suppress interference while widening and deepening the null trap; Step S1 further includes: Set a with A uniform circular array of elements, with one element located at the center, and the remaining elements... The array elements are uniformly distributed on the circumference of a circle on a certain plane, and the radius of the circular array is... , Let the carrier wavelength be , and assume that there is satellite signals and Multiple interference signals arrive at the array simultaneously. Indicates the first The elevation and azimuth angles at which satellite signals arrive at the circular array Indicates the first Given the elevation and azimuth angles at which several interfering signals arrive at the circular array, the received signal of the uniform circular array can be expressed as: in, Indicates satellite signal, Indicates interference signal. Indicates noise. , is the steering vector of the incident signal. This indicates the elevation and azimuth angles at which the satellite signal arrives at the circular array. and The position matrix of the array element and the direction of arrival of the signal are represented as follows: The sampling covariance matrix of the received signal is then: in, Indicates the number of sampling points. Indicates to The signal after sampling; Step S2 further includes: Set the first The change in the incident angle of each interference signal is the pitch angle. and azimuth , and In the interval If all elements within the triangle conform to a probability distribution, then... and The probability density functions are as follows: in, The mean covariance matrix of the signal received by the uniform circular array, representing the range of the incident angle of the interference signal, is expressed as: in, Indicates the first The interference power of each interference signal. It is the identity matrix. ,express The joint probability density function, , , Indicates noise power; The Line 1 Column elements are represented as: The noise figure, after simplification, is expressed as: Among them, the extended matrix The Line 1 The column elements are: in, This indicates the range of variation in the incident angle of the interference signal; Step S3 further includes: Perform spectral decomposition on the sampling covariance matrix, and arrange the samples according to their eigenvalues. The eigenvectors corresponding to the large eigenvalues ​​constitute the interference subspace. Based on the properties of the feature subspace, the projection matrix of the interference subspace for: Projecting the array-received signal onto the interference subspace yields the interference signal component. This component is then weighted and added to the original sampled signal to obtain the enhanced data. Reconstructed sampling covariance matrix for: in, This represents the intensification factor, which is a constant. The projection matrix represents the interference subspace. This is the sampling covariance matrix.

2. The method according to claim 1, characterized in that, The tapering process in step S4 is specifically as follows: ,in, This represents element-wise product.

3. The method according to claim 2, characterized in that, Step S5 further includes: Substituting the tapered sampling covariance matrix into the power-inverted PI algorithm yields the weight vector for widening and deepening nulls under a uniform circular matrix. : ,in, for The 3D vector, after interference suppression, output signal is: .

Images