CN113866796B - Navigation receiver anti-interference method based on airspace filtering and wave beam forming - Google Patents
Navigation receiver anti-interference method based on airspace filtering and wave beam forming Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/21—Interference related issues ; Issues related to cross-correlation, spoofing or other methods of denial of service
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- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
- H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
- H04B7/0842—Weighted combining
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Abstract
The invention provides an anti-interference method of a navigation receiver based on spatial filtering and beam forming, which aims to improve the anti-interference capability of the navigation receiver and reduce the complexity of operation, and comprises the following implementation steps: an anti-interference system of the satellite navigation receiver is constructed, an array antenna receives radio frequency analog signals, a radio frequency module converts each radio frequency analog signal into a digital intermediate frequency signal, a spatial filtering module performs spatial filtering on each digital intermediate frequency signal based on an improved power inversion algorithm, a despreading module performs despreading processing on the digital intermediate frequency signals after interference suppression, and a beam forming module performs power enhancement on the despread navigation signals based on an adaptive beam forming algorithm to obtain an anti-interference result of the navigation receiver. The invention can inhibit strong interference and weak interference, improves the anti-interference capability of the navigation receiver, adopts the self-adaptive wave beam forming algorithm without knowing the layout of the array antenna and the number and incoming directions of the navigation satellites, and has low operation complexity.
Description
Technical Field
The invention belongs to the technical field of satellite navigation, relates to an anti-interference technology of a satellite navigation receiver, in particular to a combined anti-interference algorithm of spatial filtering and beam forming, and can be used for receiving navigation signals when broadband interference exists.
Background
Satellite navigation receivers are increasingly widely used, and for navigation receivers, due to the long transmission distance, navigation signals are very easy to submerge in electromagnetic interference of surrounding environment when reaching the ground, so that the positioning calculation result of the navigation receiver is affected.
The anti-interference technology of the satellite navigation receiver is mainly divided into a time-frequency domain filtering technology and a space domain filtering technology, but the time-frequency domain filtering technology can only inhibit narrow-band interference, satellite navigation signals are received through an array antenna, null is adaptively generated on the direction of an interference signal source by using a space domain filtering mode, broadband interference is inhibited, the prior knowledge such as the arrival direction of a desired signal and the arrival direction of the interference signal is not required to be known by using the most power inversion algorithm, the weighting vector of the antenna array is calculated through covariance matrix inversion of the received signals, and interference inhibition is carried out on digital intermediate frequency signals through the weighting vector, but the algorithm has the defects that the null cannot be aligned to the arrival direction of weak interference under the condition that strong interference and weak interference exist simultaneously, weak interference cannot be effectively inhibited, and meanwhile, the power of the desired signal can be reduced.
For example, patent application publication number CN105301606 a, entitled "method and apparatus for anti-interference of navigation receiver with cascade structure", discloses a method for anti-interference of navigation receiver, which uses cascade mode, i.e. the first stage selects each antenna one by one as reference antenna, adopts power inversion algorithm to inhibit interference, then despreads output signal of each branch of the first stage, uses despread data to obtain space feature vector for information of one or several satellites in the agreed signal, and sends the space feature vector to the second stage adaptive filter processor. According to the method, a plurality of adaptive airspace or space-time filtering processing modules are adopted to connect one adaptive airspace filtering processing module in cascade, so that the influence of selection of a reference antenna on the anti-interference performance of a system is avoided, but the method has the defects that when interference is restrained on a digital intermediate frequency signal in a first stage, a power inversion algorithm is adopted, weak interference cannot be restrained effectively by the algorithm, and when the power of a desired signal is enhanced by second-stage beam forming, satellite incoming information needs to be known, and the operation complexity is high.
Disclosure of Invention
The invention aims at solving the technical problems of the technology, and provides an anti-interference method of a navigation receiver based on spatial filtering and beam forming, which aims at improving the anti-interference capability of the navigation receiver and reducing the complexity of operation.
In order to achieve the above purpose, the technical scheme adopted by the invention comprises the following steps:
(1) Building an anti-interference system of a satellite navigation receiver:
Constructing an anti-interference system of a satellite navigation receiver comprising an array antenna, a radio frequency module, a spatial filtering module, a despreading module and a beam forming module, wherein:
the array antenna comprises M array elements which are periodically arranged, wherein M is more than or equal to 4 and is used for receiving radio frequency analog signals of the navigation satellite;
The radio frequency module comprises a frequency converter and an AD chip, the frequency converter is used for carrying out down-conversion on radio frequency analog signals, and the AD chip is used for carrying out analog-to-digital conversion on the conversion result of the frequency converter;
the spatial filtering module is used for performing spatial filtering on the digital intermediate frequency signals converted by the radio frequency module;
the despreading module is used for despreading the digital intermediate frequency signal subjected to interference suppression by the spatial filtering module;
the beam forming module is used for carrying out power enhancement on the despread navigation signals;
(2) The array antenna receives radio frequency analog signals:
each array element in the array antenna receives a radio frequency analog signal at the t-th moment, A (t) = [ A 1(t),A2(t),...,Am(t),...,AM(t)]T ], wherein [ (DEG ] T represents transposition operation, A m (t) represents the radio frequency analog signal at the t-th moment received by the m-th array element, N m(t)、jm (t) respectively represents a navigation signal of an nth navigation satellite at a nth moment, noise at the nth moment and an interference signal at the nth moment, which are received by an mth array element; n represents the number of navigation satellites, N is more than or equal to 2;
(3) The radio frequency module converts each radio frequency analog signal into a digital intermediate frequency signal:
The radio frequency module performs down-conversion on each path of radio frequency analog signal A m (t) through a frequency converter, and performs analog-to-digital conversion on each path of analog intermediate frequency signal after down-conversion through an AD chip to obtain M paths of digital intermediate frequency signals B:
wherein K represents the number of sampling points, K is more than or equal to 1, b m (K) represents a digital intermediate frequency signal for carrying out kth sampling on an mth intermediate frequency analog signal;
(4) The spatial filtering module performs spatial filtering on each digital intermediate frequency signal based on an improved power inversion algorithm:
(4a) The spatial filtering module calculates R XX of a covariance matrix of the digital intermediate frequency signal B;
(4b) The spatial filtering module performs feature decomposition on the covariance matrix R XX to obtain M feature values and M feature vectors, and recombines the feature values which are less than or equal to the noise power P noise and the corresponding feature vectors into a new covariance inverse matrix
Wherein J is the number of interference sources, J is less than M-1, lambda m is the M-th eigenvalue, q m is the M-th eigenvector corresponding to lambda m, and q m H is the conjugate transpose result of q m;
(4c) The airspace filtering module takes each array element as a reference array element and passes through a new covariance inverse matrix And calculating a weight vector W m of each reference array element by using a constraint vector alpha m of the reference array element to obtain a weight vector W of the array antenna:
W＝[W1,W2,...,Wm,...,WM]T；
(4d) The spatial filtering module performs interference suppression on the digital intermediate frequency signal B through a weight vector W of the array antenna to obtain M paths of digital intermediate frequency signals S after interference suppression:
(5) The despreading module performs despreading processing on the digital intermediate frequency signal S after interference suppression:
the despreading module despreads the digital intermediate frequency signal S= [ S 1,s2,...,sm,...,sM]T ] after interference suppression to obtain navigation signals of N navigation satellites received by the array antenna, wherein the navigation signals of the nth navigation satellite received by the array antenna are:
(6) Obtaining an anti-interference result of a navigation receiver:
the beam forming module respectively carries out power enhancement on the navigation signals of each navigation satellite based on the self-adaptive beam forming algorithm, so as to realize the constraint on the weight vector and obtain N navigation signals received by the array antenna after the navigation satellite power enhancement.
Compared with the prior art, the invention has the following advantages:
1. The spatial filtering module performs spatial filtering on each digital intermediate frequency signal based on an improved power inversion algorithm, namely, firstly calculates a covariance matrix of the digital intermediate frequency signal, then performs characteristic decomposition on the covariance matrix, selects characteristic values meeting conditions and corresponding characteristic vectors thereof to be combined into a new covariance inverse matrix, and calculates a weight vector of a reference array element through the new covariance inverse matrix and a constraint vector of each reference array element, thereby avoiding the defect that the weight vector of the reference array element can only realize strong interference suppression by directly adopting the covariance inverse matrix of the digital intermediate frequency signal in the prior art, realizing the common suppression of strong interference and weak interference, and effectively improving the anti-interference capability of a navigation receiver.
2. The despreading module performs despreading processing on the digital intermediate frequency signals after interference suppression, and then the beam forming module performs power enhancement on the navigation signals of each navigation satellite based on the adaptive beam forming algorithm, so that the constraint on weight vectors is realized, finally, the anti-interference result of the navigation receiver is obtained, the reduction of signal power caused by interference suppression on the digital intermediate frequency signals based on the improved power inversion algorithm is made up, and meanwhile, in the process of performing power enhancement on the navigation signals of each navigation satellite based on the adaptive beam forming algorithm, only iteration is needed without knowing the layout of an array antenna and the number sum of the navigation satellites, so that the operation complexity is reduced.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a diagram showing the effect of spatial domain filtering in an embodiment of the present invention;
fig. 3 is an effect diagram of prior art spatial filtering.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and to specific examples:
Referring to fig. 1, the present invention includes the steps of:
Step 1) constructing an anti-interference system of a satellite navigation receiver:
Constructing a satellite navigation receiving anti-interference system comprising an array antenna, a radio frequency module, a spatial filtering module, a despreading module and a beam forming module, wherein:
The array antenna comprises 7 array elements which are distributed in a Y shape and is used for receiving radio frequency analog signals of the navigation satellite;
the radio frequency module comprises a frequency converter and an AD chip, the frequency converter is used for carrying out down-conversion on radio frequency analog signals to an intermediate frequency of 50MHz, and the AD chip is used for carrying out analog-to-digital conversion on the conversion result of the frequency converter;
the spatial filtering module is used for performing spatial filtering on the digital intermediate frequency signals converted by the radio frequency module;
the despreading module is used for despreading the digital intermediate frequency signal subjected to interference suppression by the spatial filtering module;
the beam forming module is used for carrying out power enhancement on the despread navigation signals;
(2) The array antenna receives radio frequency analog signals:
each array element in the array antenna receives a radio frequency analog signal a (t) = [ a 1(t),A2(t),...,Am(t),...,A7(t)]T ] at the t-th moment, wherein [ · ] T represents a transposed operation, and a m (t) represents a radio frequency analog signal at the t-th moment received by the m-th array element, including two navigation satellite signals, noise and two interference signals
Step 3) the radio frequency module converts each radio frequency analog signal into a digital intermediate frequency signal:
The radio frequency module performs down-conversion on each path of radio frequency analog signal A m (t) through a frequency converter, and performs analog-to-digital conversion on each path of analog intermediate frequency signal 50MHz after down-conversion under the condition that the sampling frequency is f s and 150MHz through an AD chip, so as to obtain M paths of digital intermediate frequency signals B:
Wherein K represents the number of sampling points, and k=f s·T≥1,bm (K) represents a digital intermediate frequency signal for kth sampling of the mth intermediate frequency analog signal;
Step 4) the spatial filtering module performs spatial filtering on each digital intermediate frequency signal based on an improved power inversion algorithm:
(4a) The spatial filtering module calculates a covariance matrix R XX of the digital intermediate frequency signal B, and the calculation formula is as follows:
RXX＝E(BBH)
Wherein B H represents the conjugate transpose of B;
(4b) The spatial filtering module performs feature decomposition on the covariance matrix R XX to obtain 7 feature values and 7 feature vectors:
Recombining the eigenvalue of less than or equal to the noise power P noise and the corresponding eigenvector into a new covariance inverse matrix
Wherein J is the number of interference sources being 2, lambda m is the m-th eigenvalue, q m is the m-th eigenvector corresponding to lambda m, and q m H is the conjugate transpose result of q m;
(4c) The airspace filtering module takes each array element as a reference array element and passes through a new covariance inverse matrix And calculating a weight vector W m of each reference array element by using a constraint vector alpha m of the reference array element to obtain a weight vector W of the array antenna:
W＝[W1,W2,...,Wm,...,W7]T；
(4d) The spatial filtering module performs interference suppression on the digital intermediate frequency signal B through a weight vector W of the array antenna to obtain M paths of digital intermediate frequency signals S after interference suppression:
The invention is utilized when calculating the weight vector W of the array antenna In order to eliminate the eigenvalue and eigenvector corresponding to interference, the system only consists of the eigenvalue and eigenvector of the noise subspace, and the noise subspace is orthogonal to the interference subspace by subspace theory, so that the improved power inversion algorithm can form deeper nulls at strong interference and weak interference, the digital intermediate frequency signal at the moment is considered to contain no interference signal, and the signal-to-interference-and-noise ratio of the navigation signal is improved to the signal-to-noise ratio level.
Step 5) the despreading module performs despreading processing on the digital intermediate frequency signal S after interference suppression:
The despreading module despreads the digital intermediate frequency signal S= [ S 1,s2,...,sm,...,s7]T ] after interference suppression to obtain navigation signals of 2 navigation satellites received by the array antenna, wherein the navigation signals of the nth navigation satellite received by the array antenna are:
The despreading adopts a general technology of a spread spectrum system, and the signal-to-interference-plus-noise ratio SINR of the navigation signal of the nth navigation satellite is improved through despreading.
Step 6), the beam forming module obtains the anti-interference result of the navigation receiver:
The beam forming module respectively carries out power enhancement on navigation signals of each navigation satellite based on a self-adaptive beam forming algorithm, so as to realize the constraint on the weight vector W of the array antenna, and the realization steps are as follows:
(6a) Initializing a weight vector of an array antenna as W= [ W 1,w2,…,wM]T＝[1,1,...,1]T ], and setting the iteration step length as mu and k=1;
(6b) The beam forming module synthesizes M paths of navigation signals X n of the nth navigation satellite received by the array antenna to obtain a synthesized digital intermediate frequency signal y n (k):
yn(k)＝WHXn(k)；
(6c) The beam forming module performs conjugate transposition on the synthesized digital intermediate frequency signal y n (k), and updates W through a conjugate transposition result y n(k)H of y n (k), so as to obtain updated W *:
W*＝W(k)+μXr(k)yn(k)H；
(6d) Let the weight W 1 =1 of the first array element, normalize the weights of the remaining M-1 array elements, realize the constraint of the weight vector w= [ W 1,w2,…,wM]T, wherein the formula for normalizing the weights of the remaining M-1 array elements is:
(6e) Judging whether k=k is true, if yes, obtaining a navigation signal after the power of the nth navigation satellite received by the array antenna is enhanced, otherwise, making k=k+1, and executing the step (6 b).
The beam forming module respectively carries out power enhancement on the navigation signals of each navigation satellite based on the self-adaptive beam forming algorithm, so that the constraint on weight vectors is realized, the anti-interference result of the navigation receiver is finally obtained, the reduction of signal power caused by interference suppression on the digital intermediate frequency signals based on the improved power inversion algorithm is made up, meanwhile, the self-adaptive beam forming obtains the weight vectors through iteration, only the iteration times and the iteration step length are required to be set, the layout of an antenna array, the number of navigation signals and the navigation signals are not required to be known, and the operation complexity is low; finally, the navigation signals with the 2 navigation satellite power enhanced received by the array antenna are obtained, and the signal-to-interference-and-noise ratio of the 2 navigation signals is further improved.
The effects of the present invention are further described below in conjunction with simulation experiments:
1. simulation conditions and content:
the simulation adopts Windows 10 operating system and MATLAB R2020a; the simulation parameters were set as follows: the simulation adopts a 7-array element Y-type array antenna, and the expected signals received by the two Beidou navigation satellites are Beidou B3I signals, the ranging code numbers (PRN) are respectively 1 and 2, the directions are respectively (10 degrees, 30 degrees) and (20 degrees, 40 degrees), and the signal-to-noise ratio (SNR) is-25 dB; 2 broadband interference signals are set, wherein the incoming direction of weak interference signals is (70 degrees, 80 degrees), the Interference Signal Ratio (ISR) is 35dB, the incoming direction of strong interference signals is (50 degrees, 190 degrees), the ISR is 70dB, namely the signal-to-interference and noise ratio (SINR) before the anti-interference treatment is-70 dB.
The anti-interference capability of the navigation receiver anti-interference method with a cascade structure in the invention is compared and simulated, and the results are shown in fig. 2 and 3.
2. Simulation result analysis:
Referring to fig. 2, the spatial filtering module performs spatial filtering on each digital intermediate frequency signal based on an improved power inversion algorithm, wherein fig. 2 (a) - (g) are spatial filtering results obtained by taking a first array element as a reference array element and a seventh array element as a reference array element, and it can be seen that null is formed in the directions of (70 °,80 °) and (50 °,190 °) of interference signals when each array element is taken as a reference signal, so that the suppression of strong interference and weak interference is realized. After the spatial filtering module of the invention, the signal-to-interference-plus-noise ratio SINR of the Beidou B3I signal is shown in table 1.
TABLE 1
As can be seen from table 1, the spatial filter module suppresses both strong and weak interference signals, and the SINR is approximately equal to the SNR, which is considered to be no longer containing interference signals.
The digital intermediate frequency signals after passing through the spatial filtering module are sent to a despreading module, 7 paths of signals with interference removed are despread, the despreading adopts a general technology of a spread spectrum signal system, each path of signals is obtained by two Beidou B3I signals with the ranging code numbers of 1 and 2 after despreading, and after passing through the despreading module, the signal-to-interference-and-noise ratio SINR of the Beidou signals is shown in a table 2.
TABLE 2
As seen from table 2, the SINR of the beidou signal is further improved by the despreading module.
And (3) forming a new 7-path signal by using the signals with the same PRN number in each path after despreading to obtain 7-path signals of PRN1 and 7-path signals of PRN2, respectively performing self-adaptive beamforming on 2 paths of Beidou satellite signals, improving the power of the Beidou signals, and after passing through a beamforming module, obtaining the final SINR (Signal-to-interference and noise ratio) of the Beidou signals as shown in Table 3.
TABLE 3 Table 3
The signal to interference plus noise ratio (SINR) of the Beidou satellite PRN1 and the Beidou satellite PRN2 before the anti-interference treatment is-70 dB, and the signal to interference plus noise ratio of the Beidou satellite PRN1 and the Beidou satellite PRN2 after the anti-interference treatment is improved by 90dB.
Referring to fig. 3, the prior art spatial filtering module performs spatial filtering by using a power inversion algorithm, where fig. 3 (a) - (g) are spatial filtering results obtained by using a first element as a reference element to a seventh element as a reference element, respectively, and it can be seen that null is formed in a direction (50 °,190 °) of a strong interference signal, but no significant null is formed in a direction (70 °,80 °) of a weak interference signal, so that weak interference cannot be effectively suppressed.
Claims (3)
1. The navigation receiver anti-interference method based on spatial filtering and beam forming is characterized by comprising the following steps:
(1) Building an anti-interference system of a satellite navigation receiver:
Constructing an anti-interference system of a satellite navigation receiver comprising an array antenna, a radio frequency module, a spatial filtering module, a despreading module and a beam forming module, wherein:
the array antenna comprises M array elements which are periodically arranged, wherein M is more than or equal to 4 and is used for receiving radio frequency analog signals of the navigation satellite;
The radio frequency module comprises a frequency converter and an AD chip, the frequency converter is used for carrying out down-conversion on radio frequency analog signals, and the AD chip is used for carrying out analog-to-digital conversion on the conversion result of the frequency converter;
the spatial filtering module is used for performing spatial filtering on the digital intermediate frequency signals converted by the radio frequency module;
the despreading module is used for despreading the digital intermediate frequency signal subjected to interference suppression by the spatial filtering module;
the beam forming module is used for carrying out power enhancement on the despread navigation signals;
(2) The array antenna receives radio frequency analog signals:
each array element in the array antenna receives a radio frequency analog signal A (t) = [ A 1(t),A2(t),...,Am(t),...,AM(t)]T ] at the t-th moment, wherein [ (DEG ] T represents transposition operation, A m (t) represents the radio frequency analog signal at the t-th moment received by the m-th array element, N m(t)、jm (t) respectively represents a navigation signal of an nth navigation satellite at a nth moment, noise at the nth moment and an interference signal at the nth moment, which are received by an mth array element; n represents the number of navigation satellites, N is more than or equal to 2;
(3) The radio frequency module converts each radio frequency analog signal into a digital intermediate frequency signal:
The radio frequency module performs down-conversion on each path of radio frequency analog signal A m (t) through a frequency converter, and performs analog-to-digital conversion on each path of analog intermediate frequency signal after down-conversion through an AD chip to obtain M paths of digital intermediate frequency signals B:
wherein K represents the number of sampling points, K is more than or equal to 1, b m (K) represents a digital intermediate frequency signal for carrying out kth sampling on an mth intermediate frequency analog signal;
(4) The spatial filtering module performs spatial filtering on each digital intermediate frequency signal based on an improved power inversion algorithm:
(4a) The spatial filtering module calculates R XX of a covariance matrix of the digital intermediate frequency signal B;
(4b) The spatial filtering module performs feature decomposition on the covariance matrix R XX to obtain M feature values and M feature vectors, and recombines the feature values which are less than or equal to the noise power P noise and the corresponding feature vectors into a new covariance inverse matrix
Wherein J is the number of interference sources, J is less than M-1, lambda m is the M-th eigenvalue, q m is the M-th eigenvector corresponding to lambda m, and q m H is the conjugate transpose result of q m;
(4c) The airspace filtering module takes each array element as a reference array element and passes through a new covariance inverse matrix And calculating a weight vector W m of each reference array element by using a constraint vector alpha m of the reference array element to obtain a weight vector W of the array antenna:
W＝[W1,W2,...,Wm,...,WM]T；
(4d) The spatial filtering module performs interference suppression on the digital intermediate frequency signal B through a weight vector W of the array antenna to obtain M paths of digital intermediate frequency signals S after interference suppression:
(5) The despreading module performs despreading processing on the digital intermediate frequency signal S after interference suppression:
the despreading module despreads the digital intermediate frequency signal S= [ S 1,s2,...,sm,...,sM]T ] after interference suppression to obtain navigation signals of N navigation satellites received by the array antenna, wherein the navigation signals of the nth navigation satellite received by the array antenna are:
(6) The beam forming module obtains an anti-interference result of the navigation receiver:
The beam forming module respectively carries out power enhancement on the navigation signals of each navigation satellite based on the self-adaptive beam forming algorithm, so as to realize the constraint on the weight vector W of the array antenna and obtain N navigation satellite power enhanced navigation signals received by the array antenna.
2. The method for resisting interference of navigation receiver based on spatial filtering and beam forming according to claim 1, wherein the covariance matrix R XX of the digital intermediate frequency signal B calculated in the step (4 a) is calculated by the following formula:
RXX＝E(BBH)
Wherein B H represents the conjugate transpose of B.
3. The method for resisting interference of navigation receiver based on spatial filtering and beam forming according to claim 1, wherein the beam forming module in step (6) respectively performs power enhancement on the navigation signal of each navigation satellite based on the adaptive beam forming algorithm, and the implementation steps are as follows:
(6a) Initializing a weight vector of an array antenna as W= [ W 1,w2,…,wM]T＝[1,1,...,1]T ], and setting the iteration step length as mu and k=1;
(6b) The beam forming module synthesizes M paths of navigation signals X n of the nth navigation satellite received by the array antenna to obtain a synthesized digital intermediate frequency signal y n (k):
yn(k)＝WHXn(k)；
(6c) The beam forming module performs conjugate transposition on the synthesized digital intermediate frequency signal y n (k), and updates W through a conjugate transposition result y n(k)H of y n (k), so as to obtain updated W *:
W*＝W(k)+μXr(k)yn(k)H；
(6d) Let the weight W 1 =1 of the first array element, normalize the weights of the remaining M-1 array elements, realize the constraint of the weight vector w= [ W 1,w2,…,wM]T, wherein the formula for normalizing the weights of the remaining M-1 array elements is:
(6e) Judging whether k=k is true, if yes, obtaining a navigation signal after the power of the nth navigation satellite received by the array antenna is enhanced, otherwise, making k=k+1, and executing the step (6 b).
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