High-dynamic GNSS null widening and deepening anti-interference method based on triangular distribution

Abstract

The invention provides a high-dynamic GNSS null widening and deepening anti-interference method based on triangular distribution, and the method comprises the steps: setting the change of an interference signal incident angle to follow a triangular probability distribution model, and estimating a sampling covariance matrix of a received signal; determining a conversion matrix, namely an expansion matrix, between an average covariance matrix and a sampling covariance matrix on the basis of a disturbance model for null widening, extracting interference components in array receiving signals through orthogonal projection transformation, enhancing the interference components through weighting coefficients, reconstructing the sampling covariance matrix for null deepening, and extracting the interference components from the array receiving signals through orthogonal projection transformation. And performing tapering processing on the reconstructed sampling covariance matrix, and realizing null widening and deepening while performing interference suppression by using a PI algorithm. The null width and the null depth can be adjusted through parameters so as to adapt to different interference environments, and the anti-interference performance of the navigation receiver is remarkably improved.

Description

Technical Field

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

[0002] In view of the wide use of GNSS (Global Navigation Satellite System), and the satellite signals are extremely vulnerable to interference, the anti-interference technology of navigation receivers plays an important role in providing stable PNT (Positioning, Navigation, Timing) services.

[0003] In a high-dynamic environment, the nulls generated by conventional satellite navigation receiver anti-interference algorithms are relatively narrow, and the direction of interference changes too fast and is easily out of the null, resulting in poor anti-interference effect. An effective means to solve the problem that interference is easily out of the null in a high-dynamic environment is to broaden the null. The existing null broadening algorithms can be divided into two categories: differential constraint and covariance matrix tapering. The former cannot flexibly control the width of the null broadening, while the latter may cause the null to become shallower. Summary of the Invention

[0004] Aiming at the null mismatch problem of traditional navigation receivers under high-dynamic conditions, the present invention proposes a high-dynamic GNSS null broadening and deepening anti-interference method based on triangular distribution. This method sets the perturbation angle of the interference to follow a triangular distribution, derives the tapering matrix. In order to overcome the problem that the null becomes shallower in the covariance matrix tapering algorithm, the covariance matrix is reconstructed by enhancing the interference component, and finally the null broadening and deepening are realized by combining the power inversion algorithm, so as to solve the null mismatch problem in a high-dynamic environment.

[0005] To achieve the above objectives, the specific technical solutions of the present invention include 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, determine the conversion matrix, i.e., the expansion matrix, between the average covariance matrix and the sampling covariance matrix based on the perturbation model for null broadening;

[0008] Step S3, extract the interference component in the array received signal through orthogonal projection transformation, and enhance the interference component through the weighting coefficient to reconstruct the sampling covariance matrix for null deepening;

[0009] Step S4, perform tapering processing on the reconstructed sampling covariance matrix;

[0010] Step S5, while using the PI algorithm for interference suppression, achieve null broadening and deepening.

[0011] Further, the specific steps of step S1 include:

[0012] Set up a uniform circular array with M array elements, where one array element is located at the center of the circle, and the remaining M - 1 array elements are evenly distributed on the circumference of 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. represents the elevation angle and azimuth angle of the l-th satellite signal arriving at the circular array. represents the elevation angle and azimuth angle of the q-th interference signal arriving 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 (t) represents the interference signal, and w(t) represents the noise. is the steering vector of the incident signal, and P and respectively represent the position matrix of the array elements and the direction of arrival of the signal, which are expressed as follows:

[0015]

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

[0017]

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

[0019] Further, the specific steps of step S2 include:

[0020] Set the change amount of the incident angle of the q-th interference signal as the elevation angle Δθ q and the azimuth angle Δθ q and Both conform to the triangular probability distribution within the interval [-β, β]. Then the probability density functions of Δθ q and are respectively:

[0021]

[0022] Among them, β represents the change range of the incident angle of the interference signal. The average covariance matrix of the received signal of the uniform circular array is expressed as:

[0023]

[0024] Among them, represents the interference power of the q-th interference signal, I is the identity matrix, represents the joint probability density function of represents the noise power;

[0025] The element in the m-th row and n-th column of

[0026]

[0027] δ mn represents the noise figure, and after simplification, it is expressed as:

[0028]

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

[0030]

[0031] Among them, β represents the change range of the incident angle of the interference signal.

[0032] Furthermore, the specific steps of step S3 include:

[0033] Perform spectral decomposition on the sampled covariance matrix, arrange it according to the eigenvalue size, and the eigenvectors corresponding to the first Q large eigenvalues form the interference subspace U j , based on the properties of the eigen-subspace, the projection matrix P j of the interference subspace is:

[0034]

[0035] Project the array received signal onto the interference subspace to obtain the interference signal component, perform weighting processing on it and add it to the original sampled signal to obtain the data with enhanced interference component:

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

[0037] The reconstructed sampled covariance matrix R d is:

[0038]

[0039] Among them, g represents the deepening coefficient, which is a constant, and P j represents the projection matrix of the interference subspace, is the sampling covariance matrix.

[0040] Further, in step S4, the tapering process specifically is: wherein, ⊙ represents element-wise multiplication.

[0041] Further, step S5 specifically includes:

[0042] Bring the tapered sampling covariance matrix into the power inversion PI algorithm to obtain the weight vector w with widened and deepened nulls under a uniform circular array: wherein, δ M is an M×1 vector, and the output signal after interference suppression is: y(n) = w H X(n).

[0043] The present invention proposes a high-dynamic GNSS null-widening and deepening anti-jamming method based on triangular distribution, abbreviated as T-NWD. This method reconstructs the covariance matrix by enhancing the interference component and combines the power inversion algorithm to achieve null widening and deepening. Compared with the traditional interference suppression algorithm based on a uniform circular array, it can still effectively suppress interference under high-dynamic conditions. Compared with other covariance matrix tapering-based algorithms, the formed null is deeper, and it will not change the contribution of the noise term in the covariance matrix. The null width and depth of the present invention can both be adjusted by parameters to adapt to different interference environments, significantly improving the anti-jamming performance of the navigation receiver. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following-described drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

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

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

[0047] Figure 3It is a comparison chart of the influence of different parameters β on the null width of T-NWD provided by the embodiments of the present invention; wherein, (a) shows the null broadening situation of the T-NWD algorithm at the interference elevation angle, (b) is the partial enlarged view of (a), (c) shows the null broadening situation of T-NWD at the interference azimuth angle, and (d) is the partial enlarged view of (c);

[0048] Figure 4 It is a comparison chart of the influence of different deepening coefficients g on the null depth of T-NWD provided by the embodiments of the present invention; wherein, (a) shows the null deepening situation of T-NWD at the interference azimuth angle, and (b) is the partial enlarged view of (a);

[0049] Figure 5 It is a comparison chart of the output signal-to-interference-plus-noise ratio of T-NWD under different input signal-to-interference ratios and other methods provided by the embodiments of the present invention;

[0050] Figure 6 It is a comparison chart of the output signal-to-interference-plus-noise ratio of T-NWD under different input signal-to-noise ratios and other methods provided by the embodiments of the present invention. Detailed implementation manners

[0051] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0052] The present invention proposes a high-dynamic GNSS null broadening and deepening anti-interference method based on triangular distribution, as Figure 1 shown, the method includes:

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

[0054] Set a uniform circular array with M array elements, with one array element located at the center of the circle, and the remaining M - 1 array elements are evenly distributed on the circumference of a certain plane. The radius of the circular array is λ is the carrier wavelength. Assume that there are L satellite signals and Q interference signals arriving at the array simultaneously, represents the elevation angle and azimuth angle of the l-th satellite signal arriving at the circular array, represents the elevation angle and azimuth angle of the q-th interference signal arriving at the circular array. Then the received signal of the uniform circular array is expressed as:

[0055]

[0056] wherein, s l (t) represents the satellite signal, s q(t) represents the interference signal, and w(t) represents the noise. is the steering vector of the incident signal, P and respectively represent the position matrix of the array elements and the direction of arrival of the signal, which are expressed as follows:

[0057]

[0058] p 0 =[0, 0, 0] T

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

[0060]

[0061] Then, the sample 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 that the change in the incident angle of the q-th interference signal is the pitch angle Δθ q and the azimuth angle Δθ q and both follow a triangular distribution within the interval [-β, β]. Then, the probability density functions of Δθ q and are respectively:

[0066]

[0067]

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

[0069]

[0070] where, represents the interference power of the q-th interference signal, I is the identity matrix, represents 's joint probability density function, represents the noise power.

[0071] The element in the m-th row and n-th column of

[0072]

[0073] is expressed as: nn where δ

[0074]

[0075] represents the noise factor. After arrangement and derivation, it can be obtained that:

[0076]

[0077] where β represents the change range of the incident angle of the interference signal.

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

[0079] Perform spectral decomposition on the sampled covariance matrix, arrange it according to the eigenvalue size, and the eigenvectors corresponding to the first Q large eigenvalues form the interference subspace U j , based on the properties of the eigen-subspace, the projection matrix P j of the interference subspace is:

[0080]

[0081] In the ideal case, the interference subspace and the noise subspace are orthogonal. Projecting the array received signal onto the interference subspace can obtain the interference signal component. Perform weighted processing on it and add it to the original sampled signal to obtain the data with enhanced interference component:

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

[0083] The reconstructed sampled covariance matrix R d is:

[0084]

[0085] where g represents the deepening coefficient, which is a constant, and P j represents the projection matrix of the interference subspace, is the sampled covariance matrix.

[0086] Step 4: Perform tapering processing on the reconstructed sampled covariance matrix:

[0087]

[0088] Among them, ⊙ represents the element-wise product.

[0089] Step 5: Null broadening and deepening interference suppression

[0090] Substitute the tapered sampling covariance matrix into the Power Inversion (PI) algorithm to obtain the weight vector w for null broadening and deepening under a uniform circular array:

[0091]

[0092] where δ M is an M×1 vector, and the output signal after interference suppression is:

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

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

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

[0096] Set the incident angle of a satellite signal to be (12°, 105°), and a single-tone interference is incident on the array from (53°, 174°). The signal-to-noise ratio SNR = -20 dB, the signal-to-interference ratio JSR = 60 dB, and the deepening coefficient g = 10. Different parameters β are set respectively to investigate its influence on the null width of the T-NWD method. The results are as Figure 3 shown. Among them, (a) is the null broadening situation of the T-NWD algorithm in the elevation angle of the interference, (b) is the partial enlarged view of (a), (c) is the null broadening situation of the T-NWD in the azimuth angle of the interference, and (d) is the partial enlarged view of (c). It can be seen from the figure that as β increases, the null width also increases continuously.

[0097] Set the simulation conditions such that a satellite signal and a single-tone interference are incident on the circular array from (12°, 105°) and (53°, 174°) respectively, β = 2°, signal-to-noise ratio SNR = -20 dB, jammer-to-signal ratio JSR = 60 dB, and analyze the influence of the deepening coefficient g on the null depth of the T-NWD method. The results are as Figure 4 shown. Among them, (a) shows the null deepening of T-NWD at the interference azimuth angle, and (b) is a partial enlarged view of (a). It can be seen from the figure that as the deepening coefficient g increases, the null depth also continuously deepens.

[0098] Set the incident angle of a satellite signal to (10°, 120°). During the weight update period, the incident angle of a single-tone interference changes from (60°, 170°) to (62°, 172°), SNR = -20 dB, JSR is set from 40 dB to 70 dB, and the number of snapshots is 512. The weights calculated using the sampling data when the interference is incident at (60°, 170°) are used to perform anti-jamming processing on the data after the interference angle perturbation. Taking the array output signal-to-jammer-plus-noise ratio SINR as an index, compare T-NWD with the traditional PI, PI null broadening based on uniform distribution (U-NW), and PI null broadening based on Laplace distribution (L-NW) methods. Set the T-NWD parameter β = 1°, g = 10, the U-NW parameter τ = 1°, and the L-NW parameter ξ = 0.8. The results are as Figure 5 shown. It can be seen from the figure that with the perturbation of the interference angle, the array output SINR of T-NWD does not change with the increase of the interference signal power, and the output signal-to-jammer-plus-noise ratio is higher than the other three comparison methods, showing good anti-jamming performance in a high-dynamic environment.

[0099] Set the incident angle of a satellite signal to (12°, 105°), and a single-tone interference is incident on the array from (53°, 174°). The input jammer-to-signal ratio JSR = 60 dB, and the input signal-to-noise ratio SNR increases from -25 dB to -15 dB. After still using the data of the initial incident angle of the interference to calculate the optimal weights, process the data after the interference angle perturbation. Compare the array output SINR of T-NWD with PI, L-NW, and U-NW methods under different input signal-to-noise ratios SNR, as Figure 6 shown. It can be seen from the figure that the array output SINR of T-NWD continuously increases with the increase of the input SNR, and is significantly better than the other methods.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements 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 comprises: Step S1, setting the change of the interference signal incident angle to follow the triangular probability distribution model, and estimating the sampling covariance matrix of the received signal; Step S2, determining a conversion matrix between the average covariance matrix and the sampling covariance matrix, i.e., an expansion matrix, based on the disturbance model, for null widening; Step S3, extracting interference components in the array receiving signal through orthogonal projection transformation, enhancing the interference components through weighted coefficients, and reconstructing the sampling covariance matrix for null deepening; Step S4, performing tapering processing on the reconstructed sampling covariance matrix; Step S5, using the PI algorithm to suppress interference while achieving widening and deepening of the null.

2. The method according to claim 1, characterized in that The step S1 further comprises: Set up a uniform circular array with M array elements, one array element is located at the center of the circle, and the remaining M-1 array elements are evenly distributed on the circumference of a plane. The radius of the circular array is λ is the carrier wavelength. Assuming that L satellite signals and Q interference signals arrive at the array at the same time, Indicates the elevation angle and azimuth angle of the lth satellite signal arriving at the circular array, represents the elevation angle and azimuth angle of the qth interference signal arriving at the circular array, and the uniform circular array receiving signal is expressed as: Among them, s l (t) represents the satellite signal, s q (t) represents the interference signal, w(t) represents the noise, is the steering vector of the incident signal, P and They represent the position matrix of the array element and the direction of arrival of the signal, respectively, as follows: p0＝[0,0,0] T p m =d[cosr m ,sinr m ,0] T ,m=1,2,…,M-1 Then the sampling covariance matrix of the received signal is: Wherein, M represents the number of sampling points, and X(n) represents the signal after sampling X(t).

3. The method according to claim 2, characterized in that The step S2 further comprises: Set the change in the incident angle of the qth interference signal to the pitch angle Δθ q and azimuth Δθ q and In the interval [-β, β], the probability distribution of triangles is consistent, then Δθ q and The probability density functions are: Among them, β represents the range of the interference signal incident angle, and the average covariance matrix of the uniform circular array received signal is expressed as: in, represents the interference power of the qth interference signal, I is the unit matrix, express The joint probability density function, θ q (t) = θ q +Δθ q , represents the noise power; The element in the mth row and nth column of is represented as: δ mn represents the noise factor, which can be simplified as: Among them, the element in the mth row and nth column of the extended matrix T is: Wherein, β represents the range of variation of the interference signal incident angle.

4. The method according to claim 3, characterized in that The step S3 further comprises: Perform spectral decomposition on the sampling covariance matrix and arrange it according to the size of the eigenvalues. The eigenvectors corresponding to the first Q large eigenvalues ​​constitute the interference subspace U j , based on the properties of the feature subspace, the projection matrix P of the interference subspace j for: The interference signal component is obtained by projecting the array received signal onto the interference subspace, which is weighted and added to the original sampled signal to obtain the data after the interference component is enhanced: X d (t)=X(t)+ g P j X(t)=(I+ g P j )X(t) The reconstructed sampling covariance matrix R d for: Among them, g represents the deepening coefficient, which is a constant, P j represents the projection matrix of the interference subspace, is the sampling covariance matrix.

5. The method according to claim 4, characterized in that The tapering process in step S4 is specifically as follows: where ⊙ represents the element-wise product.

6. The method according to claim 5, characterized in that The step S5 further comprises: Substituting the sampling covariance matrix after tapering into the power inversion PI algorithm, we can obtain the weight vector w of the null widening and deepening under the uniform circular array: Among them, δ M is an M×1 dimensional vector, and the output signal after interference suppression is: y(n)=w H X(n).

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