A real-time suppression method for fast time-varying interference suppression in high-precision anti-interference navigation

Abstract

The present invention relates to the technical field of high-precision anti-interference satellite navigation, and specifically discloses a method for real-time suppression of fast time-varying suppression interference of high-precision anti-interference navigation, including: passing a spatial signal through M radio frequency-intermediate frequency-digital channels to obtain M digital intermediate frequency signals; performing serial / parallel conversion and FFT on each digital intermediate frequency signal in turn, dividing it into two paths, one path is sent to a FIFO cache, and the other path is subjected to multi-beam-noise subspace projection processing to obtain an optimal weight vector; performing time matching and weighted summation on the optimal weight vector and cached data to suppress interference therein; performing IFFT and parallel / serial conversion on the data after suppressing interference in turn to obtain a digital intermediate frequency signal after suppressing interference. The present invention comprehensively utilizes the strong channel mismatch adaptability of space-frequency joint, the ability to reduce the covariance matrix and the order of the weight vector, and the orthogonal complementary characteristics of the noise subspace and the interference subspace, etc., to achieve real-time suppression of fast time-varying suppression interference.

Description

Technical Field

[0001] The present invention relates to the technical field of high-precision anti-interference satellite navigation, and in particular to a method for real-time suppression of fast time-varying interference in high-precision anti-interference navigation. Background Art

[0002] The outstanding features of high-precision anti-interference satellite navigation applications such as precision approach and landing of aircraft, landing of aircraft on aircraft carriers, formation flying and automatic aerial refueling, rapid direction finding and autonomous north seeking of missile launchers / aircraft are complex interference environments and high requirements for positioning and orientation.

[0003] The complexity of the interference environment is mainly manifested in the variety of interference types and changes. From the perspective of interference mechanism, the interference types are divided into suppression interference, deception interference, and suppression and deception combined interference. Deception interference is further divided into regeneration and forwarding types. Interference changes mainly include the number, direction, modulation, frequency, intensity, etc. of interference that changes rapidly or slowly over time. Positioning and orientation requirements include real-time or near real-time positioning services at the decimeter / centimeter level and orientation services better than 1 degree / 0.5 degree.

[0004] High-precision positioning and orientation in complex interference environments requires solving three strongly coupled problems: complex interference detection and real-time suppression, satellite signal distortion tracing and control, and high-precision positioning and orientation with low distortion.

[0005] Through theoretical deduction, simulation analysis and experimental verification, the inventors decoupled the above three problems into three categories, seven subcategories and 10 sequential topics as shown in the table below.

[0006] Based on this, 10 high-precision anti-interference navigation invention patents corresponding to the above topics are planned and laid out, as shown in Table 1.

[0007] Table 1 List of decoupling and disassembly of high-precision positioning and orientation problems in complex interference environments

[0008]

[0009] In the present invention, the first category, the first subcategory, and the first invention listed in Table 1 - a real-time suppression method for fast time-varying suppression interference are analyzed and explained.

[0010] The key to real-time suppression of fast time-varying interference lies in: strong adaptability to channel mismatch (i.e., the fluctuation amount that changes with frequency in the amplitude and phase inconsistency between channels), strong estimation ability of anti-interference degree of freedom occupancy (anti-interference degree of freedom reserve), small amount of calculation of anti-interference weight vector and fast convergence speed.

[0011] Existing solutions similar to the fast time-varying suppression interference real-time suppression method of high-precision anti-interference navigation of the present invention include: space-time joint-multi-beam-SMI method, space-frequency joint-multi-beam-LMS method.

[0012] Space-time joint-multi-beam-SMI method: The anti-interference weight vector converges quickly, but has poor adaptability to channel mismatch and lacks the ability to estimate the occupancy of the anti-interference degrees of freedom. The anti-interference weight vector has a large amount of computation and does not meet the requirements of real-time suppression of fast time-varying interference.

[0013] Space-frequency joint-multi-beam-LMS method: It has strong adaptability to channel mismatch and small amount of computation of anti-interference weight vector, but it does not have the ability to estimate the occupancy of anti-interference degrees of freedom, the convergence speed of anti-interference weight vector is slow, and it does not meet the requirements of real-time suppression of fast time-varying interference.

[0014] Based on this technical background, the present invention studies a real-time suppression method for fast time-varying interference suppression of high-precision anti-interference navigation. Summary of the invention

[0015] In view of the deficiencies in the prior art, the present invention provides a method for real-time suppression of fast time-varying suppression interference for high-precision anti-interference navigation, which adopts a space-frequency joint-multi-beam-noise subspace projection method, comprehensively utilizes the strong channel mismatch adaptation ability, covariance matrix and weight vector order reduction ability of the space-frequency joint, and the orthogonal complementary characteristics of the noise subspace and the interference subspace, etc., to achieve real-time suppression of fast time-varying suppression interference; it has the advantages of strong channel mismatch adaptability, strong anti-interference freedom degree occupancy estimation ability, small amount of calculation and fast convergence speed.

[0016] In order to achieve the above object, the present invention provides a method for real-time suppression of fast time-varying interference in high-precision anti-interference navigation, comprising:

[0017] The spatial signal passes through M RF-IF-digital channels to obtain M digital IF signals;

[0018] Each digital intermediate frequency signal is sequentially subjected to serial / parallel conversion and N-point FFT and then divided into two paths, one of which is sent to the FIFO memory for buffering, and the other is sent as an input vector to the weight vector calculation unit for multi-beam-noise subspace projection processing to obtain the optimal weight vector;

[0019] Performing time matching and weighted sum processing on the optimal weight vector and the cached data to suppress interference therein and obtain interference-suppressed data;

[0020] The interference-suppressed data is sequentially subjected to IFFT and parallel / serial conversion to obtain L digital intermediate frequency signals after interference suppression.

[0021] The beneficial effects of the present invention include:

[0022] (1) The method for real-time suppression of fast time-varying suppression interference for high-precision anti-interference navigation proposed in the present invention adopts a space-frequency joint-multi-beam-noise subspace projection method, which comprehensively utilizes the strong channel mismatch adaptability, covariance matrix and weight vector order reduction capabilities of the space-frequency joint, and the orthogonal complementary characteristics of the noise subspace and the interference subspace, to achieve real-time suppression of fast time-varying suppression interference; it has the unique advantage of strong anti-interference freedom occupancy estimation capability, strong channel mismatch adaptability, small amount of calculation, and fast convergence speed.

[0023] (2) The fast time-varying interference real-time suppression method for high-precision anti-interference navigation proposed in the present invention separates the channel mismatch within the satellite signal bandwidth into slight channel mismatches within N narrow bands through M channels, serial / parallel conversion, N-point FFT, etc. The channel mismatch adaptability is as strong as that of the space-frequency joint-multi-beam-LMS method.

[0024] (3) The fast time-varying suppression interference real-time suppression method for high-precision anti-interference navigation proposed in the present invention obtains an estimate of the anti-interference degree of freedom occupancy while obtaining the noise subspace projection matrix, which makes up for the shortcomings of the existing space-time joint-multi-beam-SMI method and space-frequency joint-multi-beam-LMS method.

[0025] (4) The fast time-varying suppression interference real-time suppression method for high-precision anti-interference navigation proposed in the present invention reduces an MN-order weight vector to N M-order weight vectors through M-channels, serial / parallel conversion, N-point FFT, etc. The convergence speed of the weight vector is as fast as that of the space-time joint-multi-beam-SMI method, but the amount of calculation is only a fraction of the latter. .

[0026] (5) The fast time-varying suppression interference real-time suppression method for high-precision anti-interference navigation proposed in the present invention matches the weighted data with the optimal weight vector, that is, the weighted data is also the training data of the weight vector, ensuring that the null position and depth of the directional pattern match the direction and intensity of the interference; avoiding the problem that the interference cannot be effectively suppressed due to the mismatch between the data and the weight vector (that is, the data to be weighted is different from the training data of the weight vector) in the existing methods.

[0027] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention with reference to the accompanying drawings.

[0029] Figure 1 It is a flow chart of the method for real-time suppression of fast time-varying interference for high-precision anti-interference navigation proposed by the present invention.

[0030] Figure 2This is a schematic diagram of the processing structure in a specific implementation of the method for real-time suppression of fast time-varying interference in high-precision anti-interference navigation proposed by the present invention. DETAILED DESCRIPTION

[0031] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0032] The present invention provides a method for real-time suppression of fast time-varying interference in high-precision anti-interference navigation. Figure 1 As shown, including:

[0033] The spatial signal passes through M RF-IF-digital channels to obtain M digital IF signals;

[0034] Each digital intermediate frequency signal is sequentially subjected to serial / parallel conversion and N-point FFT and then divided into two paths, one of which is sent to the FIFO memory for buffering, and the other is sent as an input vector to the weight vector calculation unit for multi-beam-noise subspace projection processing to obtain the optimal weight vector;

[0035] Performing time matching and weighted sum processing on the optimal weight vector and the cached data to suppress interference therein and obtain interference-suppressed data;

[0036] The interference-suppressed data is sequentially subjected to IFFT and parallel / serial conversion to obtain L digital intermediate frequency signals after interference suppression.

[0037] In the present invention, the interference suppression method can be decomposed into space-time joint adaptive processing (STAP) and space-frequency joint adaptive processing (SFAP) from the perspective of array signal processing. STAP includes M antenna array elements and M transverse filters, where the transverse filter is composed of a delay interval of The covariance matrix is ​​composed of N taps, and the order of the covariance matrix is ​​MN×MN. SFAP contains M antenna elements, M FFTs, N taps, 1 IFFT, etc. The covariance matrix is ​​N M×M matrices. Usually M is 4~16 and N is 10~15.

[0038] In the present invention, from the perspective of whether there is a gain constraint on the satellite signal, it can be decomposed into two levels: adaptive nulling anti-interference and multi-beam anti-interference. The number of beams L in the multi-beam anti-interference depends on the number of visible satellites, usually 12 to 16. Both adaptive nulling anti-interference and multi-beam anti-interference can make the array antenna form a null in the interference direction, but the latter takes into account the gain of L satellites upward, so the signal-to-noise ratio loss is smaller, which is more conducive to high-precision positioning and orientation.

[0039] In the present invention, from the perspective of updating and applying frequency of anti-interference weight vector, it can be decomposed into three levels: continuous adaptation (also called point-by-point sampling adaptation) and block adaptation; linear least mean square (LMS) and recursive least squares belong to continuous adaptation, and the anti-interference weight vector is updated and applied once each time a snapshot data is received; sampling matrix inversion (SMI) belongs to block adaptation, and the covariance matrix (statistical characteristics) of the received data is estimated using a data block composed of K snapshots, and the anti-interference weight vector is updated and applied once every K snapshot data.

[0040] In the present invention, a space-frequency joint-multi-beam-noise subspace projection method is adopted, which comprehensively utilizes the strong channel mismatch adaptability, covariance matrix and weight vector order reduction capability of the space-frequency joint, and the orthogonal complementary characteristics of the noise subspace and the interference subspace, so as to realize the real-time suppression of fast time-varying suppression interference; it has the unique advantages of strong anti-interference freedom degree occupancy estimation capability, strong channel mismatch adaptability, small amount of calculation and fast convergence speed.

[0041] In the present invention, the channel mismatch within the satellite signal bandwidth is separated into slight channel mismatches within N narrowbands through M channels, serial / parallel conversion, N-point FFT, etc. The channel mismatch adaptability is as strong as that of the space-frequency joint-multi-beam-LMS method.

[0042] In the present invention, while obtaining the noise subspace projection matrix, an estimate of the anti-interference freedom degree occupancy is obtained, which makes up for the shortcomings of the existing space-time joint-multi-beam-SMI method and space-frequency joint-multi-beam-LMS method.

[0043] In the present invention, a MN-order weight vector is reduced to N M-order weight vectors by space-frequency combination. The convergence speed of the weight vector is as fast as that of the space-time combination-multi-beam-SMI method, but the amount of calculation is only a fraction of the latter. .

[0044] According to the present invention, obtaining M digital intermediate frequency signals through M radio frequency-intermediate frequency-digital channels of the spatial signal includes:

[0045] The spatial signal is sequentially received, amplified, down-converted, filtered, and processed by analog-to-digital conversion units to obtain M digital intermediate frequency signals.

[0046] According to the present invention, the weight vector calculation unit The input vector consists of M, frequency components, and its expression is:

[0047] ;

[0048] in, .

[0049] According to the present invention, the expression of the optimal weight vector is:

[0050] ;

[0051] in, For the beam, Array element, The weight corresponding to the frequency, , .

[0052] According to the present invention, another path is sent as an input vector to a weight vector calculation unit for multi-beam-noise subspace projection processing to obtain an optimal weight vector, which includes:

[0053] Modeling multi-beam anti-interference as a constrained optimization problem of weight vectors;

[0054] The Lagrange multiplier method is used to solve the weight vector constraint optimization problem and the optimal weight vector expression in the form of inverse covariance matrix is ​​obtained;

[0055] The optimal weight vector expression in the form of inverse covariance matrix is ​​simplified to obtain the optimal weight vector expression in the form of noise subspace projection matrix.

[0056] According to the present invention, the formula used to model multi-beam anti-interference as a constrained optimization problem of a weight vector is:

[0057] ;

[0058] in, The expected satellite signal direction, The steering vector of the frequency; is the covariance matrix;

[0059] The expression of the covariance matrix is:

[0060] ;

[0061] in, For the Satellite signals, The power of a frequency, For the Satellite signals, The steering vector of the frequency, is the noise power, is the interference steering vector matrix, , , For the Interference, frequency components;

[0062] The expression of the interference steering vector matrix is:

[0063] ;

[0064] in, For the Interference, The steering vector of the frequency.

[0065] According to the present invention, the expression of the optimal weight vector in the form of an inverse covariance matrix is:

[0066] ;

[0067] in, It is the inverse matrix of the covariance matrix, referred to as the inverse covariance matrix.

[0068] According to the present invention, the expression of the optimal weight vector in the form of a noise subspace projection matrix is:

[0069] ;

[0070] Simplification of the optimal weight vector expression in the form of the inverse covariance matrix includes:

[0071] Ignoring the satellite signals which are weak relative to interference and noise, the expression of the covariance matrix is:

[0072] ;

[0073] According to the matrix inversion lemma, we get:

[0074]

[0075] ;

[0076] Under the condition of suppressing interference, the interference power is much greater than the noise power. , simplify the above formula to get:

[0077] ;

[0078] Substituting this into the expression for the optimal weight vector in the form of the inverse covariance matrix yields:

[0079]

[0080] ;

[0081] The first bracket contains a scalar, which is used to normalize the magnitude of the weight vector. It does not need to be calculated specifically. After obtaining the vector in the curly brackets, it is normalized automatically. is the projection of the desired satellite steering vector in the noise subspace, is the noise subspace projection matrix.

[0082] According to the present invention, the noise subspace projection matrix is ​​obtained by eigenvalue decomposition of the covariance matrix, singular value decomposition of the data matrix, or multi-stage Wiener filtering;

[0083] The initialization and iteration process of the noise subspace projection matrix obtained by multi-level Wiener filtering is:

[0084] (1) Initialization: , ;

[0085] (2) Iteration Second-rate: ;

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] Pick middle The corresponding large value The projection matrix that forms the noise subspace ;in, ;

[0091] The expression of the optimal weight vector of the noise subspace projection matrix obtained based on multi-level Wiener filtering is:

[0092] .

[0093] In the present invention, a space-frequency joint-multi-beam-noise subspace projection method is adopted, which comprehensively utilizes the strong channel mismatch adaptability, covariance matrix and weight vector order reduction capability of the space-frequency joint, and the orthogonal complementary characteristics of the noise subspace and the interference subspace, so as to suppress fast time-varying suppression interference in real time; it has the unique advantages of strong anti-interference freedom degree occupancy estimation capability, strong channel mismatch adaptability, small amount of calculation and fast convergence speed.

[0094] The present invention will be described in more detail below by way of examples.

[0095] Embodiment 1:

[0096] like Figure 1 As shown, this embodiment proposes a method for real-time suppression of fast time-varying interference in high-precision anti-interference navigation, and its processing structure is as follows Figure 2As shown, the specific steps include:

[0097] 1) The spatial signal is received, amplified, down-converted, filtered, and processed by the M antenna array elements, down-conversion channels, and analog-to-digital conversion units, and then outputs M digital intermediate frequency signals;

[0098] 2) Each digital intermediate frequency signal is divided into two paths after serial / parallel conversion (S / P) and N-point FFT, one path is sent to the first-in-first-out (FIFO) buffer, and the other path is sent to the weight vector calculation unit; the weight vector calculation unit The input vector consists of M, frequency components, namely ,in ;

[0099] 3) The weight vector calculation unit uses the multi-beam-noise subspace projection method to obtain the optimal weight vector ,in For the beam, Array element, The weight corresponding to the frequency, , ; After the optimal weight vector is matched with the time of the FIFO cache data, weighted processing is performed to suppress interference and obtain data after interference suppression;

[0100] 4) Perform IFFT and parallel / serial conversion (P / S) on the L groups and N channels of interference suppressed data to obtain L digital intermediate frequency signals with suppressed interference, i.e., L desired satellite signals with high received signal-to-noise ratio (good reception quality);

[0101] In this embodiment, the multi-beam-noise subspace projection method in step 3) includes:

[0102] The solution of the multi-beam anti-interference weight vector can be modeled as the following constrained optimization problem:

[0103] ;

[0104] in, is the direction of the desired satellite signal and the steering vector of the kth frequency; is the covariance matrix, and its expression is:

[0105] ;

[0106] In the formula, For the Satellite signals, The power of a frequency, For the Satellite signals, The steering vector of the frequency; is the noise power; is the interference steering vector matrix, For the Interference, The steering vector of the frequency; , , For the Interference, frequency components;

[0107] Using the Lagrange multiplier method, the optimal solution to the above constrained optimization problem can be obtained as:

[0108] (1);

[0109] Next, equation (1) is transformed into the product of the desired satellite steering vector and the noise subspace projection matrix, thereby avoiding the inversion of the covariance matrix and reducing the amount of calculation;

[0110] Considering that the satellite signal reaching the ground is quite weak, 20-30 dB lower than the thermal noise, ignoring the satellite signal, the inverse matrix of the covariance matrix can be obtained as follows:

[0111] ;

[0112] By the matrix inversion lemma, we can get:

[0113]

[0114]

[0115] Under interference suppression conditions, the interference power is much greater than the noise power , then the above formula can be simplified to:

[0116] (2);

[0117] Substituting (2) into (1), we can get:

[0118]

[0119] ;

[0120] The first bracket on the right side of the equation contains a scalar, which is used to normalize the magnitude of the weight vector. It does not need to be calculated specifically, and it can be normalized after obtaining the vector in the brackets.

[0121] In this way, we only need to solve ; This item is The projection on the noise subspace (i.e., the orthogonal subspace of the interference subspace) is is the projection matrix; the projection matrix can be obtained by eigenvalue decomposition of the covariance matrix, singular value decomposition of the data matrix, and multi-level Wiener filtering (MWF);

[0122] Taking MWF as an example, its initialization and iteration process is as follows:

[0123] (1) Initialization: , ;

[0124] (2) Iteration Second-rate: ;

[0125] ;

[0126] ;

[0127] ;

[0128] ;

[0129] Pick middle The corresponding large value The projection matrix that forms the noise subspace ,in ;

[0130] Then the optimal weight vector is:

[0131] ;

[0132] In this way, beam, The amount of computation for the optimal weight vector corresponding to a frequency is , then the optimal weight vector calculation amount corresponding to N frequencies is , is the computational complexity of the space-time joint-multi-beam-SMI method , the amount of calculation is significantly reduced;

[0133] In this embodiment, the estimation of the anti-interference freedom occupancy is , the anti-interference freedom reserve is Based on this, the number of virtual interferences in the strong short-delay deception interference detection and suppression method of high-precision anti-interference navigation, as well as the number of virtual interferences in the detection and suppression method of suppressing deception combined interference, are coordinated.

[0134] The embodiment of the present invention proposes a real-time suppression method for fast time-varying suppression interference of high-precision anti-interference navigation, which adopts a space-frequency joint-multi-beam-noise subspace projection method, and comprehensively utilizes the strong channel mismatch adaptability, covariance matrix and weight vector order reduction capabilities of the space-frequency joint, and the orthogonal complementary characteristics of the noise subspace and the interference subspace, etc., to achieve real-time suppression of fast time-varying suppression interference; it has the unique advantage of strong anti-interference freedom degree occupancy estimation capability, strong channel mismatch adaptability, small amount of calculation, and fast convergence speed.

[0135] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for real-time suppression of fast time-varying interference in high-precision anti-interference navigation, characterized in that: include: The spatial signal passes through M RF-IF-digital channels to obtain M digital IF signals; Each digital intermediate frequency signal is sequentially subjected to serial / parallel conversion and N-point FFT and then divided into two paths, one of which is sent to the FIFO memory for buffering, and the other is sent as an input vector to the weight vector calculation unit for multi-beam-noise subspace projection processing to obtain the optimal weight vector; Performing time matching and weighted sum processing on the optimal weight vector and the cached data to suppress interference therein and obtain interference-suppressed data; The interference-suppressed data is sequentially subjected to IFFT and parallel / serial conversion to obtain L digital intermediate frequency signals after interference suppression.

2. The method according to claim 1, characterized in that The spatial signal passes through M RF-IF-digital channels to obtain M digital IF signals including: The spatial signal is sequentially received, amplified, down-converted, filtered, and processed by analog-to-digital conversion units to obtain M digital intermediate frequency signals.

3. The method according to claim 1, characterized in that The weight vector calculation unit The input vector consists of M, frequency components, and its expression is: ； in, .

4. The method according to claim 1, characterized in that: The expression of the optimal weight vector is: ； in, For the beam, Array element, The weight corresponding to the frequency, , .

5. The method according to claim 4, characterized in that The other path is sent as an input vector to the weight vector calculation unit for multi-beam-noise subspace projection processing to obtain the optimal weight vector including: Modeling multi-beam anti-interference as a constrained optimization problem of weight vectors; The Lagrange multiplier method is used to solve the weight vector constraint optimization problem and the optimal weight vector expression in the form of inverse covariance matrix is ​​obtained; The optimal weight vector expression in the form of the inverse covariance matrix is ​​simplified to obtain the optimal weight vector expression in the form of the noise subspace projection matrix.

6. The method according to claim 5, characterized in that The formula used to model multi-beam anti-interference as a constrained optimization problem of weight vectors is: ； in, The expected satellite signal direction, The steering vector of the frequency; is the covariance matrix; The expression of the covariance matrix is: ； in, For the Satellite signals, The power of a frequency, For the Satellite signals, The steering vector of the frequency, is the noise power, is the interference steering vector matrix, , , For the Interference, frequency components; The expression of the interference steering vector matrix is: ； in, For the Interference, The steering vector of the frequency.

7. The method according to claim 5, characterized in that The expression of the optimal weight vector in the form of the inverse covariance matrix is: ； in, It is the inverse matrix of the covariance matrix, referred to as the inverse covariance matrix.

8. The method according to claim 5, characterized in that The expression of the optimal weight vector in the form of the noise subspace projection matrix is: ； Simplifying the optimal weight vector expression in the form of the inverse covariance matrix includes: Ignoring the satellite signals which are weak relative to interference and noise, the expression of the covariance matrix is: ； According to the matrix inversion lemma, we get: ； Under the condition of suppressing interference, the interference power is much greater than the noise power. , simplify the above formula to get: ； Substituting this into the expression of the optimal weight vector in the inverse covariance matrix form yields: ； The first bracket contains a scalar, which is used to normalize the magnitude of the weight vector. It does not need to be calculated specifically. After obtaining the vector in the curly brackets, it is normalized automatically. is the projection of the desired satellite steering vector in the noise subspace, is the noise subspace projection matrix.

9. The method according to claim 8, characterized in that The noise subspace projection matrix is ​​obtained by eigenvalue decomposition of the covariance matrix, singular value decomposition of the data matrix, or multi-stage Wiener filtering; The initialization and iteration process of the noise subspace projection matrix obtained by multi-stage Wiener filtering is: (1) Initialization: , ; (2) Iteration Second-rate: ; ； ； ； ； Pick middle The corresponding large value The projection matrix that forms the noise subspace ;in, ; The expression of the optimal weight vector of the noise subspace projection matrix obtained based on multi-level Wiener filtering is: 。

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