CN110361760B - GNSS receiver multi-beam pointing anti-interference method based on subspace tracking - Google Patents
GNSS receiver multi-beam pointing anti-interference method based on subspace tracking Download PDFInfo
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Abstract
The invention discloses a GNSS receiver multi-beam pointing anti-interference method based on subspace tracking, which eliminates strong interference signals by using a noise subspace tracking technology, then estimates the guide vector of each satellite navigation signal by using the correlation between signals after multi-channel periodic delay and satellite navigation signals and adopting a DOA estimation method based on the Clean idea, and finally forms a weight vector matrix for each satellite construction beam by using the guide vector to realize the enhancement of the satellite signal incoming direction. The invention does not need to know the transmitted navigation symbol and the satellite orientation, is a blind self-adaptive algorithm, effectively improves the signal-to-interference-and-noise ratio of the navigation signal while inhibiting the complex interference signal, and can improve the receiving capability of the system to the satellite navigation signal in the complex environment to a certain extent.
Description
Technical Field
The invention belongs to the field of satellite navigation signal anti-interference, relates to the technical content of self-adaptive blind beam forming anti-interference for a satellite navigation receiver, and particularly relates to a multi-beam pointing anti-interference method for a GNSS receiver based on subspace tracking.
Background
Navigation satellites typically operate in high altitudes several tens of thousands of kilometers from the ground, and the signals received by ground receivers are relatively weak, usually submerged in receiver thermal noise. Thus, when the receiver is subjected to various unintentional and intentional radio frequency interference, the satellite signals cannot be extracted from the noise, eventually resulting in reduced positioning accuracy or loss of lock of the tracking loop, sometimes even failure to function properly. The satellite navigation signal power is very weak, and the interference is very easy to happen, so that the research on the satellite navigation anti-interference technology is particularly urgent. In order to ensure the effectiveness of a satellite navigation system in increasingly complex electromagnetic interference environments, anti-interference receiver technical research is carried out, and the method has great national defense safety and national economic significance.
Research work has been carried out for many years in satellite navigation anti-jamming aspect in China. In terms of the commercialization of the time-frequency domain anti-interference technology, mayflower Communication Company (U.S. Mayflower Communication Company) has applied for a patent in 1993 and 1997, and a time domain adaptive anti-interference algorithm is applied to a GPS receiver, so that a good anti-interference effect is obtained through the test of an actual interference environment. In 1998, the american scholars r.l.fante conducted relatively deep theoretical research in the space-time field of the anti-interference technology of the satellite navigation receiver, and conducted many experiments on the basis of the research to verify the specific problems in the theory. The specific problems include selection of a space-time anti-interference criterion, influence of multipath interference and the like. One year later, american scholars w.l.myrik also started research in the space-time domain of satellite navigation receiver anti-jamming technology. The main result is that a multi-stage wiener filtering technology is successfully introduced in the space-time anti-interference process, so that the calculation amount required in the space-time process is reduced to a great extent, and the practical performance of the space-time anti-interference technology is greatly increased.
In addition, M.G.Amin also carries out extensive research on the anti-interference problem of the satellite navigation receiver and obtains better research results including time domain anti-interference, frequency domain anti-interference, array anti-interference and space-time anti-interference. In 2000, r.l.fante gives a relatively complete discussion of an anti-interference navigation receiver based on Space Time Adaptive Processing (STAP), and this technology represents a new development direction of anti-interference technology of navigation receivers. Since then, in order to promote the practicability of the STAP technology in the field of satellite navigation anti-interference, various researchers have conducted long-term research on problems such as rank reduction processing and STAP in a non-uniform environment. At present, space-time adaptive filtering has become a research focus in the field of satellite navigation anti-interference, and is widely concerned.
The anti-interference technology field of satellite navigation starts late in China, and a mature product used by a large amount of equipment does not exist at present. In recent years, with the rapid development of the satellite navigation industry in China, many scientific research units and universities in China begin to research the satellite navigation anti-interference technology. The satellite navigation anti-interference algorithm and the implementation thereof of the high school such as the western's safety electronic technology university, the Chinese civil aviation university, the national defense technology university, the air force engineering university, the Harbin industrial university and the like and the scientific research institutions such as the middle-electric group, the space 504 station, the space 704 station and the like do a lot of work, and mainly comprise the existing models for anti-interference improvement and the development of digital anti-interference receivers. In the aspect of the existing type anti-interference improvement, the anti-interference improvement technology adopted in China at present mainly utilizes an antenna array to receive signals, realizes the anti-interference in an airspace in an anti-interference processor, can adaptively resist various noise suppression type interferences of continuous wave type, pulse type and other waveforms, has anti-interference performance meeting the requirement of the type index, but has the anti-interference number limited by the number of antenna array elements; in the aspect of digital anti-interference receiver development, a plurality of digital anti-interference receiver development projects are provided in China, various circuit optimization and anti-interference processing schemes are provided by various development units, the anti-interference capability is improved compared with a basic scheme, but the application requirements under a complex electromagnetic environment cannot be met.
From the current research situation at home and abroad, research on the satellite navigation anti-compression system interference problem can be summarized into the following three aspects:
(1) Time domain/frequency domain adaptive filtering technique
The time domain filtering method is to design an adaptive time domain filter to suppress the interference signal. The frequency domain filter method is to change the signal to the frequency domain for processing, and suppress the interference signal by setting a threshold and performing the zeroing operation on the frequency spectrum value larger than the threshold. Compared with a time domain filter algorithm, frequency domain processing is easy to realize by engineering, and the method is a commonly adopted technical means for an anti-interference receiver of early satellite navigation. Badke B, ouyang X M, ZHao L and the like successively research the time-frequency domain satellite navigation anti-interference technology based on short-time Fourier transform, subspace technology and the like, and certain results are obtained.
(2) Spatial filtering technique
The spatial filtering method utilizes array signal processing and beam forming theory to perform discrete parallel sampling on spatial signals in a spatial domain, and distinguishes the incoming direction of signals and interference from the space to achieve the purpose of interference suppression. Typical algorithms include minimum power algorithm proposed by Gecan a et al, self-coherent recovery anti-interference algorithm using C/a code periodicity proposed by professor Moeness of villannova university, usa, least square despreading and despreading multi-target array algorithm using known spreading code information proposed by Rong Z et al, and the like.
(3) Space-time domain joint filtering technology
Space Time Adaptive Processing (STAP) was proposed in 1973 by schoolers such as Brenna and the like and is used for solving the problem of ground clutter suppression in Space-Time two-dimensional coupling distribution in an airborne radar. The essence of the method is that a one-dimensional spatial filtering technology is popularized to a time and space two-dimensional domain to form a space-time two-dimensional processing structure. Considering that in airborne/missile-borne receiver applications, the array antenna aperture is often limited, when the number of interferers is large and the types are complex, pure spatial domain processing cannot achieve good interference suppression performance because it cannot provide enough degrees of freedom. Therefore, fante et al apply STAP technique to GPS anti-interference, greatly improving the degree of freedom of the adaptive system.
From the prior art, the time domain/frequency domain filtering techniques have the advantages of low cost, simplicity and feasibility, but they cannot produce effective interference suppression effect when there are multiple narrowband interferences or a single wideband interference (time domain wideband signal). The spatial filtering technology is a common anti-interference means at present, and effectively suppresses narrowband interference and broadband interference (array broadband signals) through a self-adaptive antenna array, however, a degree of freedom needs to be sacrificed when a narrowband interference is suppressed by a pure spatial filtering technology, and if broadband interference needs to be suppressed, the number of antenna array elements needs to be increased, which increases the cost of the satellite navigation receiver and is difficult to implement in occasions where the antenna aperture is limited (such as airborne and missile-borne). The space-time adaptive processing originated from ground clutter suppression of the airborne early warning radar can be used for solving the problems, and the technology can increase the degree of freedom of an adaptive filtering system by adding a time tap on the premise of not increasing the array element number. However, most of the existing space-time adaptive anti-interference methods focus on how to design and generate deeper nulls in the interference direction, only concern about the suppression capability of interference signals, and ignore the influence of the anti-interference processing process on satellite signals.
Disclosure of Invention
The invention aims to: in order to overcome the defects in the prior art, the method for preventing the GNSS receiver from being interfered by the multi-beam pointing based on the noise subspace tracking is provided, the method can overcome the influence of a complex interference environment on the GNSS signal receiving to a certain extent, and a beam forming weight vector matrix is constructed in a self-adaptive mode according to the characteristics of an interference source in the signal processing process, so that the receiving capacity of a system on satellite navigation signals in the complex environment is effectively improved.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for anti-jamming by multi-beam pointing of GNSS receiver based on subspace tracking, comprising the following steps:
s1: setting the baseband signal received by the antenna array of the satellite navigation receiver with M (M is more than 1, M belongs to N) array elements at the time N as X (N), and calculating the corresponding covariance matrix R xx ；
S2: iterative solution is carried out on the standard orthogonal basis of the noise subspace projection of the covariance matrix by utilizing a fast data projection method to obtain the characteristic vector estimation w corresponding to the noise subspace sub ；
S3: using the noise subspace feature vector w obtained in step S2 sub Projecting the calibrated baseband signal X (n) received by an antenna array of the satellite navigation receiver at the time n to obtain the optimal projection Y of the baseband signal X (n) in the noise subspace sub ；
S4: respectively to the projected data Y sub Delaying the data of each channel by one C/A code period, and estimating the direction of arrival parameters of each satellite navigation signal one by utilizing the clear idea
L is the number of satellite signals received by the receiver;
s5: according to the direction of arrival parameters of each satellite antenna
Constructing corresponding arrival vectors
The optimal array weighting vector for each satellite can be obtained according to the minimum mean square error criterion as
Wherein
Weighting the vector for the optimal array corresponding to the ith satellite;
s6: respectively carrying out optimal projection Y on the L optimal array weighting vectors obtained in the step S5 sub And performing weighted accumulation to obtain an observation output signal Y (n) of each satellite.
Further, the expression of the baseband signal X (n) in step S1 is as follows:
wherein, T s Is the sampling interval; l is the number of satellite signal sources; for the l satellite, s l (n)，c l And τ l (n) the satellite effective signal, the C/A code and the signal delay corresponding to the satellite effective signal, the C/A code and the signal delay are respectively; a (theta) l ) Is the steering vector of the l-th satellite, theta l Is the angle parameter of the direction of arrival; k is the number of interference sources; j. the design is a square k (n) is an interference signal, d k A vector is directed thereto; v (n) is additive white Gaussian noise.
The expression for the baseband signal X (n) is rewritten using a data vector form:
X(n)＝s(n)+u(n)+V(n)
and calculating a covariance matrix of signals x (n) received by the satellite navigation receiver antenna array at the time n
R xx ＝E{X(n)X H (n)}＝R s +R u +R v
Wherein E {. Is statistical expectation, (. C) H For the conjugate transpose process of matrices, R s ，R u And R V Covariance matrices of GNSS signals, interference signals and noise respectively defined as
Further, the specific step of performing iterative solution on the orthonormal basis of the noise subspace projection of the covariance matrix by using the fast data projection method in step S2 is as follows:
s2-1: initializing an iterative counter n =0, setting a preset threshold delta =0.001, and initializing a noise subspace projection matrix by adopting a random orthogonal initialization method to obtain an orthogonal matrix U 0 ；
S2-2: for the nth iteration, calculating the current subspace signal projection
S2-3: the calculation of the Householder reflection matrix has
Wherein e is 1 ＝[1，0，...，0] T ，
Is a vector r n First elementA corresponding argument value;
s2-4: computing orthonormal matrices
Wherein
Beta is more than or equal to 0 and is used as the learning step length;
s2-5: to z n Regularizing and assigning to U n+1 I.e. by
U n+1 ＝z n D
Wherein, the first and the second end of the pipe are connected with each other,
s2-6: incrementing an iteration counter, n = n +1;
if | | | U n+1 -U n || 2 If the value is larger than or equal to delta, repeating the steps S2-1 to S2-5, otherwise, outputting an optimal projection matrix U opt 。
Further, the optimal projection in step S3
Further, in the step S4, the projected data Y are respectively aligned sub If the data of each channel is delayed by one C/A code period, the ith channel is provided, and the delayed signal is expressed as
Wherein, a i (θ l ) Is a (theta) l ) The ith element of (v) i ( n ) The noise signal of the ith channel after projection; considering the C/A code as a periodic signal, there is thus C l (nT s -τ l (n)-T)＝c l (nT s -τ l (n)), the above formula is represented by
Since the C/A codes of each satellite are independent of each other, the projected signal
With delayed signal u i (n) the cross-correlation vector is represented as
Wherein the content of the first and second substances,
is a complex constant of the number of the first and second,
the power of the first satellite signal; constructing new vectors
The above formula can be represented as
Wherein, the first and the second end of the pipe are connected with each other,
is the product of Kronecker
The above formula is represented as
Order to
The above formula can be expressed in a matrix form
Wherein the content of the first and second substances,
using sample cross-correlation vectors
Instead of the former
And is estimated by minimizing the objective function as follows
And theta.
Estimation using a minimization objective function
The specific flow of and θ is:
s4-1: let L =1, order
Estimating using the following equation
S4-2: for L =2, the residual is calculated
Estimate using the following equation
S4-3: for L = k, the residual is calculated
Estimate using the following equation
S4-4: repeating the above steps until L is equal to the preset satellite number, thereby obtaining the DOA parameters of all satellite signals
The method firstly eliminates strong interference signals by using a noise subspace tracking technology, then estimates the guide vector of each satellite navigation signal by using the correlation between the signal after the multi-channel periodic delay and the satellite navigation signal and adopting a DOA estimation method based on the Clean idea, and finally forms a weight vector matrix for each satellite construction beam by using the guide vector to realize the enhancement of the satellite signal incoming direction.
Has the beneficial effects that: compared with the prior art, the method effectively inhibits the suppression type strong interference signals by utilizing a noise subspace tracking algorithm with low computation complexity aiming at the problem of receiving the satellite navigation signals in the complex electromagnetic environment, and simultaneously constructs the weight matrix formed by the array wave beams through satellite signal direction of arrival estimation (DOA) based on the spread spectrum code period autocorrelation and clear idea, thereby effectively enhancing the satellite navigation communication signals. The invention does not need to know the transmitted navigation symbol and the satellite orientation, is a blind self-adaptive algorithm, effectively improves the signal-to-interference-and-noise ratio of the navigation signal while inhibiting the complex interference signal, improves the capturing and tracking capacity of the satellite navigation receiver in the interference environment, can improve the receiving capacity of the system to the satellite navigation signal in the complex environment to a certain extent, and improves the signal receiving quality of the satellite navigation receiver.
Drawings
FIG. 1 is a schematic diagram of a multi-beam pointing anti-jamming principle of a GNSS receiver based on subspace tracking;
FIG. 2 is a flowchart of a subspace tracking based strong interference suppression method;
FIG. 3 is a flowchart of a satellite signal source direction parameter estimation process based on Clean idea;
fig. 4 is a distribution diagram of uniform linear array elements.
Detailed Description
The invention is further elucidated with reference to the drawings and the embodiments.
In this embodiment, the method of the present invention is applied to a GNSS system, as shown in fig. 1, and includes the following specific steps:
s1: the number of antenna array elements of the satellite navigation receiver is M, M is a natural number greater than 1, the baseband signal received by the antenna array of the satellite navigation receiver at the time n is recorded as x (n), and if the baseband signal is x (n), the baseband signal has
Wherein, T s Is a sampling interval; l is the number of satellite signal sources; for the l satellite, s l (n)，c l And τ l (n) delaying the satellite effective signal, the C/A code and the signal corresponding to the satellite effective signal; a (theta) l ) Is the steering vector of the l-th satellite, theta l Is the angle parameter of the direction of arrival; k is the number of interference sources; j. the design is a square k (n) is an interference signal, d k A vector is directed thereto; v (n) is additive white Gaussian noise. Can be rewritten into by formally using data vector
X(n)＝s(n)+u(n)+V(n)
Calculating covariance matrix R of signals X (n) received by satellite navigation receiver antenna array at n time xx Then there is
R xx ＝E{X(n)X H (n)}＝R s +R u +R v
Wherein E {. Is statistical expectation, (. C) H For the conjugate transpose process of matrices, R s ，R u And R V Covariance matrices of GNSS signals, interference signals and noise respectively defined as
S2: using Fast Data Projection (FDPM) on covariance matrix R xx The standard orthogonal basis of the noise subspace projection is subjected to iterative solution to obtain a characteristic vector estimation w corresponding to the noise subspace sub This step is explained in detail below:
in a strong interference environment, further assuming that signals of different interference sources are uncorrelated with each other, and interference, noise and navigation satellite signals are uncorrelated with each other, the covariance matrix of signals received by the satellite navigation system can be approximately described as
R xx ＝R u +R′ s
Wherein R' s ＝R s +R V For a component composed of both signal and noise components, since the power of a strong interference signal is generally much stronger than the noise level of the receiver, and the power of a GNSS signal without autocorrelation processing is generally 20-30dB lower than the noise level, the interference signal power is dominant in the whole received signal, and the GNSS signal and the receiver thermal noise can be considered as noise signals. At this time, if to R xx By performing eigenvalue decomposition, the received signal can be decomposed into a union of two subspaces, i.e.
Therein, sigma I ＝diag{λ 1 ，…，λ K The matrix is a K multiplied by K dimension diagonal matrix formed by K maximum eigenvalues, and the corresponding K eigenvectors form an M multiplied by K dimension matrix U I An interference signal subspace is formed; and sigma V ＝diag{λ K+1 ，…，λ M-K The M-K characteristic values are contained, and the corresponding M-K characteristic vectors form an M x (M-K) dimensional matrix U V A noise signal subspace is developed containing the GNSS signal and the receiver thermal noise.
Conventional methods typically project the received signal into a noise signal subspace to suppress the effects of strong interference by performing eigenvalue decomposition on the covariance matrix of the received signal. However, these methods are not suitable for time-varying scenes with more antenna elements and motion of the receiving platform, and require multiple snapshots to obtain a better result, which results in extremely high computation complexity.
The method introduces a data projection model into strong interference suppression processing, can complete estimation of the subspace projection matrix by using the sampling data of a single snapshot through repeated iteration of the orthogonal projection matrix, avoids calculation and matrix inversion of a plurality of snapshot data autocorrelation matrices, and reduces the calculation complexity.
As shown in fig. 2, the specific implementation steps are as follows:
s2-1: initializing an iterative counter n =0, setting a preset threshold delta =0.001, and initializing a noise subspace projection matrix by adopting a random orthogonal initialization method to obtain an orthogonal matrix U 0 ；
S2-2: for the nth iteration, calculating the current subspace signal projection
S2-3: calculate Householder reflection matrix has
Wherein e is 1 ＝[1，0，...，0] T ，
Is a vector r n Argument value corresponding to the first element;
s2-4: computing orthonormal matrices
Wherein
Beta is more than or equal to 0 and is used as the learning step length;
s2-5: to z n Regularizing and assigning value to U n+1 I.e. by
U n+1 ＝z n D
Wherein, the first and the second end of the pipe are connected with each other,
s2-6: incrementing an iteration counter, n = n +1;
if | | | U n+1 -U n || 2 If the value is larger than or equal to delta, repeating the steps S2-1 to S2-5, otherwise, outputting an optimal projection matrix U opt 。
S3: utilizing the noise subspace feature vector w obtained in the step S2 sub Projecting the calibrated baseband signal X (n) received by an antenna array of the satellite navigation receiver at the time n to obtain the optimal projection of the baseband signal X (n) in the noise subspace
And the suppression of strong interference is realized.
S4: as shown in fig. 3, the projected data are separately aligned
If the data of each channel is delayed by one C/A code period T, the ith channel is provided, and the delayed signal can be expressed as
Wherein, a i (θ l ) Is a (theta) l ) The ith element of (v) i (n) is the noise signal of the i-th channel after projection, considering that the C/A code is a periodic signal, so that there is C l (nT s -τ l (n)-T)＝c l (nT s -τ l (n)), and the above formula can be represented as
Since the C/A codes of each satellite are independent of each other, the projected signals
With delayed signal u i The cross-correlation vector of (n) may representIs composed of
Wherein, the first and the second end of the pipe are connected with each other,
is a complex constant which is a function of the time,
constructing a new vector for the power of the l-th satellite signal
The above formula can be expressed as
Wherein the content of the first and second substances,
is the product of Kronecker. Order to
The above formula can then be expressed as
Order to
The above formula can be expressed in a matrix form
Wherein the content of the first and second substances,
using sample interactionsRelation vector
Instead of the former
And is estimated by minimizing the objective function as follows
And theta.
Referring to FIG. 3, estimating
And θ the specific method steps are as follows:
s4-1: let L =1, order
Estimating using the following equation
S4-2: for L =2, the residual is calculated
Estimating using the following equation
S4-3: for L = k, the residual is calculated
Estimate using the following equation
S4-4: repeating the above steps until L is equal to the preset satellite number, thereby obtaining DOA parameters of all satellite signals
S5: according to the direction of arrival parameters of each satellite antenna
Constructing a steering vector matrix
Wherein
Is the steering vector of the l-th satellite signal determined by the antenna array structure.
In this embodiment, taking the simple uniform linear array shown in fig. 4 as an example, if the distance between each array element is d, the corresponding steering vector matrix is
Order to
The steering vector of the first satellite signal is the corresponding array weighting vector according to the minimum mean square error criterion
The output signal of the l-th beam is then
S6: respectively performing weighted accumulation on the input signals by using the L optimal array weighted vectors obtained in the step S5 to obtain observation output signals Y (n) = [ z ] of each satellite 1 (n)，z 2 (n)，…，z L (n)]。
In the embodiment, the subspace tracking-based multi-beam pointing anti-interference method is applied to a satellite navigation receiving system, so that the satellite navigation signal can be enhanced while the forced pressure type interference is suppressed, and the anti-interference capability of the GNSS system is effectively improved.
Claims (6)
1. A GNSS receiver multi-beam pointing anti-interference method based on subspace tracking is characterized in that: the method comprises the following steps:
s1: setting a baseband signal received by an antenna array of a satellite navigation receiver with M array elements at time N as X (N), wherein M is more than 1, M belongs to N, and calculating a corresponding covariance matrix R xx ；
S2: iterative solution is carried out on the standard orthogonal basis of the noise subspace projection of the covariance matrix by utilizing a fast data projection method, and the characteristic vector estimation w corresponding to the noise subspace is obtained sub ；
S3: using the noise subspace feature vector w obtained in step S2 sub Carrying out projection processing on a calibrated baseband signal X (n) received by an antenna array of a satellite navigation receiver at a time n to obtain an optimal projection Y of the baseband signal X (n) in a noise subspace sub ；
S4: respectively to the projected data Y sub Delaying one C/A code period of each channel data, estimating the direction of arrival parameters of each satellite navigation signal one by one
L is the number of satellite signal sources;
s5: according to the direction of arrival parameters of each satellite antenna
Constructing corresponding arrival vectors
The optimal array weighting vector for each satellite can be obtained according to the minimum mean square error criterion as
Wherein
Weighting the vector for the optimal array corresponding to the ith satellite;
s6: respectively carrying out optimal projection Y on the L optimal array weighting vectors obtained in the step S5 sub Carrying out weighted accumulation to obtain an observation output signal Y (n) of each satellite;
the specific steps of using the fast data projection method to iteratively solve the orthonormal basis of the noise subspace projection of the covariance matrix in the step S2 are as follows:
s2-1: initializing an iterative counter n =0, setting a preset threshold delta =0.001, and initializing a noise subspace projection matrix by adopting a random orthogonal initialization method to obtain an orthogonal matrix U 0 ；
S2-2: for the nth iteration, calculating the current subspace signal projection
S2-3: the calculation of the Householder reflection matrix has
Wherein e is 1 ＝[1，0，...，0] T ，
Is a vector r n Argument value corresponding to the first element;
s2-4: computing orthonormal matrices
Wherein
Beta is more than or equal to 0 and is used as the learning step length;
s2-5: to z n Regularizing and assigning to U n+1 I.e. by
Un +1 ＝z n D
Wherein, the first and the second end of the pipe are connected with each other,
s2-6: incrementing an iteration counter, n = n +1;
if | | | U n+1 -U n || 2 If not less than delta, repeating the step S2-1ES2-5, otherwise, outputting an optimal projection matrix U opt 。
2. The method of claim 1, wherein the method is characterized in that: the expression of the baseband signal X (n) in step S1 is as follows:
wherein, T s Is the sampling interval; l is the number of satellite signal sources; for the ith satellite, s l (n)，c l And τ l (n) the satellite effective signal, the C/A code and the signal delay corresponding to the satellite effective signal, the C/A code and the signal delay are respectively; a (theta) l ) Is the steering vector of the l-th satellite, theta l Is the angle parameter of the direction of arrival; k is the number of interference sources; j is a unit of k (n) is an interference signal, d k A vector is directed thereto; v (n) is additive white Gaussian noise.
3. The method according to claim 2, wherein the GNSS receiver based on subspace tracking has multi-beam pointing anti-jamming capability, and the method comprises: the expression for the baseband signal X (n) is rewritten using a data vector form:
X(n)＝s(n)+u(n)+V(n)
and calculating a covariance matrix of signals X (n) received by the satellite navigation receiver antenna array at the n moment
R xx ＝E{X(n)X H (n)}＝R s +R u +R V
Wherein E {. Is the statistical expectation, (. Cndot.) H For the conjugate transpose process of matrices, R s ，R u And R V Covariance matrices of GNSS signals, interference signals and noise respectively defined as
4. The method of claim 3, wherein the method is characterized in that: the optimal projection in the step S3
5. The method according to claim 1, wherein the method comprises: in the step S4, the data Y after projection are respectively aligned sub If the data of each channel is delayed by one C/A code period, the ith channel is provided, and the delayed signal is expressed as
Wherein, a i (θ l ) Is a (theta) l ) The ith element of (v) i (n) is the noise signal of the ith channel after projection; considering the C/A code as a periodic signal, there is thus C l (nT s -τ l (n)-T)＝c l (nT s -τ l (n)), the above formula is represented by
Since the C/A codes of each satellite are independent of each other, the projected signals
With delayed signal u i (n) the cross-correlation vector is represented as
Wherein, the first and the second end of the pipe are connected with each other,
is a complex constant which is a function of the time,
the power of the first satellite signal; constructing new vectors
The above formula can be expressed as
Wherein, the first and the second end of the pipe are connected with each other,
is the product of Kronecker
The above formula is represented as
Order to
The above formula can be expressed in a matrix form
Wherein, the first and the second end of the pipe are connected with each other,
using sample cross-correlation vectors
Substitute for
And is estimated by minimizing the objective function as follows
And theta
6. The method of claim 5, wherein the method is characterized in that: the step S4 utilizes the minimized objective function to estimate
The specific flow of and θ is:
s4-1: let L =1, order
Estimating using the following equation
S4-2: for L =2, the residual is calculated
Estimating using the following equation
S4-3: for L = k, the residual is calculated
Estimate using the following equation
S4-4: repeating the above steps until L is equal to the preset satellite number, thereby obtaining the DOA parameters of all satellite signals
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| CN113281788B (en) * | 2021-05-26 | 2022-01-18 | 国网江苏省电力有限公司电力科学研究院 | Beidou navigation system interference source direct positioning method based on propagation operator |
| CN114325600B (en) * | 2021-12-22 | 2023-09-26 | 广东邦盛北斗科技股份公司 | Anti-interference method, system and device for Beidou navigation system and cloud platform |
| CN115372998B (en) * | 2022-08-22 | 2023-04-07 | 中国矿业大学 | Low-complexity robust wide-linear beam forming method for satellite navigation receiver |
| CN115549709B (en) * | 2022-11-29 | 2023-03-24 | 富景慧智(北京)科技有限公司 | Satellite communication system and method for inhibiting multi-channel mutual interference |
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