CN106338742B - Dimensionality reduction self-adaptive multiple-beam gps signal anti-interference method based on cross-spectrum criterion - Google Patents

Dimensionality reduction self-adaptive multiple-beam gps signal anti-interference method based on cross-spectrum criterion Download PDF

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CN106338742B
CN106338742B CN201610953208.4A CN201610953208A CN106338742B CN 106338742 B CN106338742 B CN 106338742B CN 201610953208 A CN201610953208 A CN 201610953208A CN 106338742 B CN106338742 B CN 106338742B
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covariance matrix
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CN106338742A (en
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贺顺
徐淼
严剑
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Hunan Ding Fang Electronic Technology Co Ltd
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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
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Abstract

The invention belongs to communication technical field, it is related to the dimensionality reduction self-adaptive multiple-beam gps signal anti-interference method based on cross-spectrum criterion.Including：Estimate interference plus noise signals covariance matrix in GPS receiver signal；Calculate each gps satellite relative GPS receiver deflection；Estimate each nominal spatial domain steering vector of gps satellite relative GPS receiver；Each gps satellite correspondence dimensionality reduction matrix of construction；Using the sample data vector after each gps satellite correspondence dimensionality reduction matrix computations correspondence dimensionality reduction；Calculate the self adaptation weight vector after each gps satellite correspondence dimensionality reduction；Each gps satellite correspondence dimensionality reduction self adaptation weight vector is made into Matrix Multiplication operation with the sample data vector after corresponding dimensionality reduction respectively, anti-interference gps signal output result is obtained.Invention can more preferably construct Data Dimensionality Reduction matrix, as far as possible useful information in retention data, effectively reduce anti-interference process computational complexity, solves the problems, such as that prior art computational complexity is high, be difficult to real-time processing and useful data information loss during dimension-reduction treatment is operated.

Description

Dimensionality reduction self-adaptive multiple-beam gps signal anti-interference method based on cross-spectrum criterion
Technical field
The invention belongs to communication technical field, a kind of drop based on cross-spectrum criterion of satellite navigation system is further related to Dimension self-adaptive multiple-beam gps signal anti-interference method.
Background technology
Global positioning system (GPS) is a kind of high-precision navigation positioning system, can be with round-the-clock, real-time, continuous high-precision Degree provides the user the information such as longitude, latitude, height, speed and time, is satellite navigation most advanced, most widely used at present Alignment system.
At present, the Anti-Jamming Technique of the receiver of traditional satellite navigation system is broadly divided into three classes, is filtered using self adaptation Wave technology is filtered treatment to the echo-signal for receiving, wherein mainly comprising frequency domain filtering, time-domain filtering and envelope amplitude limit etc. Technology.Anti-interference process is carried out to the echo-signal for receiving using array subsignal treatment technology, wherein mainly being adjusted including spatial domain Zero-sum Polarization technique.The method filtered using forward and backward related anti-interference process and INS integrated navigations is entered to the echo-signal for receiving Row is anti-interference.
Dong Li Mei et al. is in document《GPS Research on anti-interference technique with beam position》(navigator fix and time service, Navigation Positioning＆Timing, 2016,3 (2)) in propose that a kind of minimum variance principle using constraint is realized Anti-interference algorithm.Using space where signal and where interference, the difference in space carries out adaptive matched filter to the algorithm so that Wave beam can farthest suppress interference signal when satellite-signal is pointed to.The weak point of the algorithm is, in actual environment It is difficult to obtain enough independent identically distributed training samples carry out interference plus noise covariance matrix estimation, and is carrying out certainly Needs are inverted to interference plus noise covariance matrix when adapting to matched filtering, and computational complexity is very high, it is difficult to realize place in real time Reason.
The content of the invention
It is an object of the invention to overcome above-mentioned the deficiencies in the prior art, there is provided a kind of dimensionality reduction based on cross-spectrum criterion is adaptive Multi-beam gps signal anti-interference method is answered, Data Dimensionality Reduction matrix, the useful letter as far as possible in retention data can be preferably constructed Breath, while effectively reducing the computational complexity of anti-interference process, to solve, prior art computational complexity is high, be difficult to real-time processing And dimension-reduction treatment operation in useful data information loss problem.
A kind of dimensionality reduction self-adaptive multiple-beam gps signal anti-interference method based on cross-spectrum criterion, comprises the following steps：
S1 utilizes maximum Likelihood, estimates the covariance matrix of the interference plus noise signals in GPS receiver signal；
S2 calculates each gps satellite relative to GPS according to gps satellite and the geometrical relationship of ground receiver Deflection；
S3 estimates nominal spatial domain steering vector of each gps satellite relative to GPS；
Deflection of each gps satellite relative to GPS that S3.1 is calculated according to S2, estimates each Deflection set of the gps satellite relative to GPS；
S3.2 utilizes covariance matrix reconstruction formula, and each gps satellite of construction is oriented to relative to the spatial domain of GPS Covariance matrix；
S3.3 utilizes Eigenvalue Decomposition formula, and association is oriented to relative to the spatial domain of GPS to each gps satellite Variance matrix carries out Eigenvalues Decomposition operation, obtains each feature that each spatial domain of gps satellite is oriented to covariance matrix Value and corresponding characteristic vector.
Be oriented in each spatial domain of gps satellite corresponding to the characteristic value of maximum in the characteristic value of covariance matrix by S3.4 Nominal spatial domain steering vector of the characteristic vector as each gps satellite relative to GPS；
S4 constructs the corresponding dimensionality reduction matrix of each gps satellite；
S4.1 utilizes Eigenvalue Decomposition formula, and the interference plus noise covariance matrix in GPS receiver signal is carried out Eigenvalues Decomposition is operated, and obtains the characteristic value and characteristic vector of interference plus noise covariance matrix；
It is each relative to the interference plus noise covariance matrix in GPS receiver signal that S4.2 calculates each gps satellite The mutual spectrum of individual characteristic vector；
S4.3 believes miscellaneous noise ratio criterion according to maximum output, screens each principal eigenvector set of gps satellite；
S4.4 constructs the corresponding dimensionality reduction matrix of each gps satellite using the principal eigenvector set of each gps satellite；
S5 calculates the sample after the corresponding dimensionality reduction of each gps satellite using the corresponding dimensionality reduction matrix of each gps satellite Data vector；
S6 is according to linearly constrained minimum variance, the self adaptation power arrow after the corresponding dimensionality reduction of each gps satellite of calculating Amount；
S7 is by the corresponding dimensionality reduction self adaptation weight vector of each gps satellite dimensionality reduction corresponding with each gps satellite respectively Sample data vector afterwards makees Matrix Multiplication operation, obtains the corresponding jamproof gps signal output result of each gps satellite.
The invention has the advantages that：
1) compared to directly dimension complete to interference plus noise covariance matrix is inverted in the prior art, there is computational complexity high Problem, the present invention will tie up matrix, generate the data vector after dimensionality reduction and the self adaptation weight vector after dimensionality reduction by construction, can Computational complexity is effectively reduced, real-time processing is easy to implement.
2) compared to in the prior art also with cross-spectrum criterion self adaptation each gps satellite of selected characteristic vectorial structure Corresponding dimensionality reduction matrix method, the present invention is made using each gps satellite relative to the nominal spatial domain steering vector of GPS Guiding constraint, can be more sane to direction angle error, and further reduces output Signal to Interference plus Noise Ratio loss.
Brief description of the drawings
Fig. 1 is flow chart of the invention；
Fig. 2 is the array element arrangement schematic diagram of the uniform circular array in the specific embodiment of the invention；
Fig. 3 is the descending row of the interference plus noise covariance matrix characteristic value estimated in the specific embodiment of the invention List intention；
Fig. 4 is the corresponding normalization cross-spectrum analogous diagram of the signal of gps satellite of the present invention 1 difference spatial domain steering vector；
Fig. 5 is the real spatial domain steering vector dimensionality reduction Wave beam forming directional diagram of gps satellite of the invention 1；
Fig. 6 is the spatial domain steering vector dimensionality reduction Wave beam forming directional diagram that gps satellite of the invention 1 is estimated；
Fig. 7 is the nominal spatial domain steering vector dimensionality reduction Wave beam forming directional diagram of gps satellite of the invention 1；
Fig. 8 is the dimensionality reduction Wave beam forming directional diagram of the Power-inversion algorithm of gps satellite of the invention 1.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
The step of reference picture 1, present invention implementation, is as follows：
S1 utilizes maximum Likelihood, estimates the covariance matrix of the interference plus noise signals in GPS receiver signal.
The covariance matrix of the interference plus noise signals in GPS receiver signal is estimated according to equation below：
Wherein, RJNThe covariance matrix of the interference plus noise signals in GPS receiver signal is represented, K represents that GPS connects The gps signal snap sum of receipts, k represents k-th snap, and ∑ represents sum operation, XkRepresent kth time snap echo data arrow Amount, Xk=[x1(k), x2(k) ..., xN(k)]T, xnK () represents the kth time that n-th array element is received in GPS array Snapshot data, n=1,2 ..., N, N represent array element sum in GPS array, T represents that transposition is operated, and H represents conjugation Transposition is operated.
S2 calculates each gps satellite relative to GPS according to gps satellite and the geometrical relationship of ground receiver Deflection.
Each gps satellite is calculated relative to the deflection of GPS according to equation below：
Wherein,Deflection of the l gps satellite relative to GPS is represented, l=1 ..., L, L are represented Gps satellite sum,Azimuth of the l gps satellite relative to GPS is represented,Represent the l gps satellite relative to The angle of pitch of GPS, arctan represents that arc tangent is operated, Δ Nl、ΔElWith Δ HlRepresent respectively the l gps satellite with The north of the difference of GPS position in the northeast day coordinate system with GPS as origin to, east to day direction Coordinate components, arccos represents that anticosine is operated.
S3 estimates nominal spatial domain steering vector of each gps satellite relative to GPS.
Deflection of each gps satellite relative to GPS that S3.1 is calculated according to S2, estimates each Deflection set of the gps satellite relative to GPS.
Each gps satellite is estimated relative to the deflection set of GPS according to equation below：
Wherein, ΩlDeflection set of the l gps satellite relative to GPS is represented, l=1 ..., L, L are represented Gps satellite sum,Represent the l gps satellite relative to an element in the deflection set of GPS, θ tables Show azimuth,Represent the angle of pitch,WithThe l azimuth of the gps satellite relative to GPS and pitching are represented respectively Angle, △ θ andRepresent the root-mean-square error value of azimuth and pitching angular estimation respectively, △ θ ＞ 0,
S3.2 utilizes covariance matrix reconstruction formula, and each gps satellite of construction is oriented to relative to the spatial domain of GPS Covariance matrix.
Each gps satellite is oriented to covariance matrix and is constructed according to equation below relative to the spatial domain of GPS：
Wherein, RlRepresent the l gps satellite relative to GPS spatial domain be oriented to covariance matrix, l=1 ..., L, L represent gps satellite sum, and ∫ represents integration operation, ΩlRepresent deflection collection of the l gps satellite relative to GPS Close,The l gps satellite is represented relative to an element in the deflection set of GPS,Represent root According toThe spatial domain steering vector of construction,Exp is represented with e The index operation at bottom, j represents imaginary unit, there is j2=-1 sets up, and λ represents the wavelength of satellite navigation signals；R represents GPS receiver The radius of machine uniform circular array array, sin represents sinusoidal operation, and cos represents that cosine is operated, and N represents GPS uniform circular array battle array The array element sum of row, T represents that transposition is operated.
S3.3 utilizes Eigenvalue Decomposition formula, and association is oriented to relative to the spatial domain of GPS to each gps satellite Variance matrix carries out Eigenvalues Decomposition operation, obtains each feature that each spatial domain of gps satellite is oriented to covariance matrix Value and corresponding characteristic vector.
Each gps satellite is oriented to covariance matrix Eigenvalues Decomposition result relative to the spatial domain of GPS：
Wherein, RlRepresent the l gps satellite relative to GPS spatial domain be oriented to covariance matrix, l=1 ..., L, L represent gps satellite sum, and N represents the array element sum in GPS array, and ∑ represents sum operation, ρrIt is the l GPS Satellite is oriented to r-th characteristic value of covariance matrix, r=1 ..., N, v relative to the spatial domain of GPSrRepresent and the l Gps satellite is oriented to the corresponding characteristic vector of r-th characteristic value of covariance matrix relative to the spatial domain of GPS, and H is represented altogether Yoke transposition is operated.
Be oriented in each spatial domain of gps satellite corresponding to the characteristic value of maximum in the characteristic value of covariance matrix by S3.4 Nominal spatial domain steering vector of the characteristic vector as each gps satellite relative to GPSL represents that the l GPS is defended Star, l=1 ..., L, L represent gps satellite sum.
S4 constructs the corresponding dimensionality reduction matrix of each gps satellite.
S4.1 utilizes Eigenvalue Decomposition formula, and the interference plus noise covariance matrix in GPS receiver signal is carried out Eigenvalues Decomposition is operated, and obtains the characteristic value and characteristic vector of interference plus noise covariance matrix.
It is to the result that the interference plus noise covariance matrix in GPS receiver signal makees Eigenvalues Decomposition
Wherein, RJNThe interference plus noise covariance matrix in GPS receiver signal is represented, N represents the total number of characteristic value, ∑ Represent sum operation, λiRepresent the ith feature value of the interference plus noise covariance matrix in GPS receiver signal, uiRepresent with The ith feature of the interference plus noise covariance matrix in GPS receiver signal is worth corresponding characteristic vector, and H represents conjugate transposition Operation.
It is each relative to the interference plus noise covariance matrix in GPS receiver signal that S4.2 calculates each gps satellite The mutual spectrum of individual characteristic vector.
Each Characteristic Vectors of each gps satellite relative to the interference plus noise covariance matrix in GPS receiver signal The mutual spectrum of amount is calculated according to the following formula：
Wherein, γL, iRepresent the l gps satellite relative to the interference plus noise covariance matrix in GPS receiver signal The mutual spectrum of ith feature vector, l=1 ..., L, L represent gps satellite sum, and i=1 ..., N, N represent the total of characteristic value Number, | | | | the operation of 2 norms is represented,Nominal spatial domain steering vector of the l gps satellite relative to GPS is represented, H represents conjugate transposition operation, uiRepresent the ith feature value pair with the interference plus noise covariance matrix in GPS receiver signal The characteristic vector answered, λiRepresent the ith feature value of the interference plus noise covariance matrix in GPS receiver signal.
S4.3 believes miscellaneous noise ratio criterion according to maximum output, screens each principal eigenvector set of gps satellite.
Screening each principal eigenvector set of gps satellite is comprised the following steps that：
All spies of the S4.3.1 to the l gps satellite relative to the interference plus noise covariance matrix in GPS receiver signal The mutual spectrum for levying vector is arranged according to descending order, obtains the cross-spectrum value sequence after the l gps satellite sequence；
S4.3.2 sets iteration variable m=1, energy threshold Q, Q be one more than 0 less than the l gps satellite sequence after it is mutual The constant of spectrum summation；
S4.3.3 obtains the l GPS to preceding m mutually spectrum summation in the cross-spectrum value sequence after the l gps satellite sequence Preceding m energy mutually corresponding to spectrum of satellite；
S4.3.4 compares the l preceding m of gps satellite energy mutually corresponding to spectrum and energy threshold Q sizes, if l Preceding m energy mutually corresponding to spectrum of gps satellite is more than energy threshold Q, then by the cross-spectrum after the l gps satellite sequence M characteristic vector of the interference plus noise covariance matrix in value sequence in the preceding m corresponding GPS receiver signal of mutual spectrum Set is used as the l principal eigenvector set of gps satellite；Otherwise, iteration variable adds 1, repeats S4.3.3 and S4.3.4.
S4.4 constructs the corresponding dimensionality reduction matrix of each gps satellite using the principal eigenvector set of each gps satellite.
The corresponding dimensionality reduction matrix B of each gps satellitelConstruct according to the following formula：
Bl=[u1, u2..., uM]
M represents the l number of the element of the principal eigenvector set of gps satellite.
S5 is using the sample after the corresponding dimensionality reduction of the corresponding each gps satellite of dimensionality reduction matrix computations of each gps satellite Data vector.
Sample data vector after the corresponding dimensionality reduction of each gps satellite is calculated according to the following formula：
Wherein, YL, kRepresent the sample data vector after the dimensionality reduction of the l kth of gps satellite time snap, l=1 ..., L, L represents gps satellite sum, and k=1 ..., K, K represent the gps signal snap sum that GPS is received, BlRepresent each The corresponding dimensionality reduction matrix of gps satellite, H represents that conjugation means are operated, XkRepresent kth time snap echo data vector.
S6 is according to linearly constrained minimum variance, the self adaptation power arrow after the corresponding dimensionality reduction of each gps satellite of calculating Amount.
Self adaptation weight vector after the corresponding dimensionality reduction of each gps satellite is calculated according to the following formula：
Wherein, wlThe self adaptation weight vector after the corresponding dimensionality reduction of the l gps satellite is represented, l=1 ..., L, L represent GPS The population of satellite,Sample data covariance matrix after the corresponding dimensionality reduction of the l gps satellite,∑ Sum operation is represented, k=1 ..., K, K represent the gps signal snap sum that GPS is received, YL, kRepresent that the l GPS is defended Sample data vector after the dimensionality reduction of the kth time snap of star, H represents that conjugation means are operated, ()-1Representing matrix inversion operation, BlThe corresponding dimensionality reduction matrix of each gps satellite of expression,For the l gps satellite is led relative to the nominal spatial domain of GPS To vector.
S7 is by the corresponding dimensionality reduction self adaptation weight vector of each gps satellite dimensionality reduction corresponding with each gps satellite respectively Sample data vector afterwards makees Matrix Multiplication operation, obtains the corresponding jamproof gps signal output result of each gps satellite.
Effect of the invention can be illustrated by following emulation experiments：
1) simulated conditions
The GPS operation principle of the uniform circular array of 8 array elements is simulated, array element arrangement mode is referring to Fig. 2, wherein signal source S-phase pair includes azimuth and the angle of pitch with the deflection of the northeast day coordinate system of receiver.In order that between adjacent array element Away from the relation for meeting half-wavelength, the radius for taking the circle battle array is R=0.653.=0.1904m is the L of GPS navigation signal1Carrier frequency The corresponding wavelength of rate.Assuming that a total of 4 gps satellites are observed, the incident direction angle of satellite navigation signals be respectively (45 °, 45 °), (70 °, 30 °), (150 °, 50 °) and (270 °, 60 °), input signal-to-noise ratio be respectively -30dB, -28dB, -35dB and - 35dB.The incident direction angle of 4 wide-band interferers be respectively (50 °, 70 °), (60 °, 65 °), (120 °, 60 °) and (250 °, 65 °), it is input into dry making an uproar than being respectively 50dB, 55dB, 75dB and 60dB.1000 snapshot datas are received altogether.Orientation angle and The root-mean-square error of pitching angular estimation be respectively Δ θ=- 5 ° and
2) emulation content and result
Interference plus noise covariance matrix is estimated according to 1000 reception sample datas of snap, then to interference plus noise Covariance matrix carries out feature decomposition, shown in the descending arrangement reference picture 3 of characteristic value.In Fig. 3, abscissa represents characteristic value Number, ordinate represents the size of characteristic value, and 4 big characteristic values can be observed by Fig. 3, and correspondence is because there is 4 strong jammings Signal.
Illustrated by taking gps satellite 1 as an example, first to being provided according to the inertial navigation of satellite ephemeris parameter and receiver Receiver rough position estimates incident orientation angle of the satellite relative to receiver；Then nominal spatial domain steering vector, and profit are solved The cross-spectrum of the nominal spatial domain steering vector of the signal of gps satellite 1 is calculated with the characteristic vector of interference plus noise covariance matrix.Fig. 4 Give the signal of gps satellite 1 difference spatial domain steering vector the corresponding mutual spectrum of normalization.In Fig. 4, abscissa represents mutual spectrum Number, ordinate represents the size for normalizing mutual spectrum, as seen from Figure 4, for the nominal steering vector estimated, mark Claim steering vector the corresponding mutual spectrum of normalization, can be mutual with the normalization of faint advantage closer to true spatial domain steering vector Spectrum, illustrates that nominal spatial domain steering vector is more sane to Wave beam forming.Dimensionality reduction matrix is constituted finally according to the selection of mutual spectrum Characteristic vector, and carry out Wave beam forming using the data after dimensionality reduction.Fig. 5 is represented using the true spatial domain steering vector of satellite 1 Dimensionality reduction Wave beam forming directional diagram, in Fig. 5, x coordinate represents azimuth, the y coordinate representation angle of pitch, and z coordinate represents that aerial array increases Benefit.Fig. 6 represents the dimensionality reduction Wave beam forming directional diagram using the estimation spatial domain steering vector of satellite 1, and in Fig. 6, x coordinate represents orientation Angle, the y coordinate representation angle of pitch, z coordinate represents antenna array gain.Fig. 7 is represented using the nominal spatial domain steering vector of satellite 1 Dimensionality reduction Wave beam forming directional diagram, in Fig. 7, x coordinate represents azimuth, the y coordinate representation angle of pitch, and z coordinate represents that aerial array increases Benefit.Fig. 8 represents that in Fig. 8, x coordinate represents azimuth, y-coordinate using the dimensionality reduction Wave beam forming directional diagram after Power-inversion algorithm The angle of pitch is represented, z coordinate represents antenna array gain.With reference to Fig. 5, Fig. 6, Fig. 7 and Fig. 8, it is clear that as can be seen that four kinds of mode structures The self adaptation weight vector made can form deeper null in interference position, can effectively suppress interference.Estimate Fig. 5~8 Output Signal to Interference plus Noise Ratio SINR is respectively：- 25.5968dB, -25.6020dB, -25.6019dB and -30.4695dB.It follows that The seizing signal energy loss of nominal spatial domain steering vector illustrates nominal spatial domain steering vector less than the spatial domain steering vector estimated Robustness is had more to direction angle error, and the method specific power inversion algorithm with guiding constraint is to the energy loss of signal It is smaller.
In sum, under for the anti-interference application background of gps signal, directly matrix inversion process is computationally intensive asks for full dimension Topic, the present invention selects characteristic vector and constitutes the corresponding dimensionality reduction matrix of each gps satellite and can not only realize using cross-spectrum criterion Dimensionality reduction Adaptive beamformer, effectively suppresses the interference of broadband pressing type, and ensures the output Signal to Interference plus Noise Ratio loss reduction after dimensionality reduction, Being constrained by nominal spatial domain steering vector can preferably reduce signal energy loss.Emulation experiment also indicates that the present invention in numeral In the anti-interference background of gps signal of multi-beam Formation Technologies, by dimension-reduction treatment, can Fast Convergent formed adaptive beam, There is good rejection ability to the interference of broadband pressing type and useful GPS satellite navigation signal effect can be effectively protected.
Obviously, those skilled in the art can carry out various changes and modification without deviating from essence of the invention to the present invention God and scope.So, if these modifications of the invention and modification belong to the scope of the claims in the present invention and its equivalent technologies Within, then the present invention is also intended to comprising these changes and modification.

Claims (1)

1. a kind of dimensionality reduction self-adaptive multiple-beam gps signal anti-interference method based on cross-spectrum criterion, it is characterised in that the method bag Include following steps：
S1 utilizes maximum Likelihood, estimates the covariance matrix of the interference plus noise signals in GPS receiver signal；
The covariance matrix of the interference plus noise signals in GPS receiver signal is estimated according to equation below：
R J N ≈ 1 K Σ k = 1 K X k X k H
Wherein, RJNThe covariance matrix of the interference plus noise signals in GPS receiver signal is represented, K represents what GPS was received Gps signal snap sum, k represents k-th snap, and ∑ represents sum operation, XkRepresent kth time snap echo data vector, Xk= [x1(k), x2(k) ..., xN(k)]T, xnK () represents the fast umber of beats of kth time that n-th array element is received in GPS array According to, n=1,2 ..., N, N represent array element sum in GPS array, T represents that transposition is operated, and H represents that conjugate transposition is grasped Make；
S2 calculates side of each gps satellite relative to GPS according to gps satellite and the geometrical relationship of ground receiver To angle；
Each gps satellite is calculated relative to the deflection of GPS according to equation below：
Wherein,Deflection of the l gps satellite relative to GPS is represented, l=1 ..., L, L represent that GPS is defended Star sum,Azimuth of the l gps satellite relative to GPS is represented,Represent that the l gps satellite connects relative to GPS The angle of pitch of receipts machine, arctan represents that arc tangent is operated, Δ Nl、ΔElWith Δ HlL gps satellite and GPS receiver are represented respectively The north of the difference that seat in the plane is put in the northeast day coordinate system with GPS as origin is to, east to the coordinate with day direction point Amount, arccos represents that anticosine is operated；
S3 estimates nominal spatial domain steering vector of each gps satellite relative to GPS；
Deflection of each gps satellite relative to GPS that S3.1 is calculated according to S2, estimates that each GPS is defended Deflection set of the astrology for GPS；
Each gps satellite is estimated relative to the deflection set of GPS according to equation below：
Wherein, ΩlRepresent deflection set of the l gps satellite relative to GPS, l=1 ..., L,Represent the L gps satellite represents azimuth relative to an element in the deflection set of GPS, θ,Represent the angle of pitch, Δ θ andRepresent the root-mean-square error value of azimuth and pitching angular estimation respectively, Δ θ ＞ 0,
S3.2 utilizes covariance matrix reconstruction formula, and each gps satellite of construction is oriented to association side relative to the spatial domain of GPS Difference matrix；
Each gps satellite is oriented to covariance matrix and is constructed according to equation below relative to the spatial domain of GPS：
Wherein, RlRepresent that the l gps satellite is oriented to covariance matrix, l=1 ..., L, ∫ table relative to the spatial domain of GPS Show integration operation,Represent basisThe spatial domain steering vector of construction,Exp is represented with e The index operation at bottom, j represents imaginary unit, there is j2=-1 sets up, and λ represents the wavelength of satellite navigation signals；R represents GPS receiver The radius of machine uniform circular array array, sin represents sinusoidal operation, and cos represents that cosine is operated；
S3.3 utilizes Eigenvalue Decomposition formula, and covariance is oriented to relative to the spatial domain of GPS to each gps satellite Matrix carries out Eigenvalues Decomposition operation, obtain each gps satellite spatial domain be oriented to covariance matrix each characteristic value and Corresponding characteristic vector；
Each gps satellite is oriented to covariance matrix Eigenvalues Decomposition result relative to the spatial domain of GPS：
R l = Σ r = 1 N ρ r v r v r H
Wherein, RlRepresent that the l gps satellite is oriented to covariance matrix, l=1 ..., L, ρ relative to the spatial domain of GPSrFor The l gps satellite is oriented to r-th characteristic value of covariance matrix, r=1 ..., N, v relative to the spatial domain of GPSrTable Show Characteristic Vectors corresponding relative to r-th characteristic value of the spatial domain guiding covariance matrix of GPS with the l gps satellite Amount；
The each spatial domain of gps satellite is oriented to S3.4 the feature corresponding to the characteristic value of maximum in the characteristic value of covariance matrix Nominal spatial domain steering vector of the vector as each gps satellite relative to GPS
S4 constructs the corresponding dimensionality reduction matrix of each gps satellite；
S4.1 utilizes Eigenvalue Decomposition formula, and feature is carried out to the interference plus noise covariance matrix in GPS receiver signal Value operation splitting, obtains the characteristic value and characteristic vector of interference plus noise covariance matrix；
It is to the result that the interference plus noise covariance matrix in GPS receiver signal makees Eigenvalues Decomposition
R J N = Σ i = 1 N λ i u i u i H
Wherein, λiRepresent the ith feature value of the interference plus noise covariance matrix in GPS receiver signal, uiExpression connects with GPS The ith feature of the interference plus noise covariance matrix in the collection of letters number is worth corresponding characteristic vector；
S4.2 calculates each spy of each gps satellite relative to the interference plus noise covariance matrix in GPS receiver signal Levy the mutual spectrum of vector；
Each gps satellite is relative to each characteristic vector of the interference plus noise covariance matrix in GPS receiver signal Mutual spectrum is calculated according to the following formula：
γ l , i = | | a ‾ l H u i | | 2 λ i
Wherein, γL, iRepresent i-th of the l gps satellite relative to the interference plus noise covariance matrix in GPS receiver signal The mutual spectrum of characteristic vector, | | | | the operation of 2 norms is represented,Represent that the l gps satellite is nominal relative to GPS Spatial domain steering vector；
S4.3 believes miscellaneous noise ratio criterion according to maximum output, screens each principal eigenvector set of gps satellite；
Screening each principal eigenvector set of gps satellite is comprised the following steps that：
All Characteristic Vectors of the S4.3.1 to the l gps satellite relative to the interference plus noise covariance matrix in GPS receiver signal The mutual spectrum of amount is arranged according to descending order, obtains the cross-spectrum value sequence after the l gps satellite sequence；
S4.3.2 sets iteration variable m=1, and energy threshold Q, Q are one and the mutual spectrum after the l gps satellite sorts is less than more than 0 The constant of summation；
S4.3.3 obtains the l gps satellite to preceding m mutually spectrum summation in the cross-spectrum value sequence after the l gps satellite sequence The energy mutual corresponding to spectrum of preceding m；
S4.3.4 compares the l preceding m of gps satellite energy mutually corresponding to spectrum and energy threshold Q sizes, if the l GPS Preceding m energy mutually corresponding to spectrum of satellite is more than energy threshold Q, then by the cross-spectrum value sequence after the l gps satellite sequence In preceding m interference plus noise covariance matrix mutually in the corresponding GPS receiver signal of spectrum m characteristic vector collection cooperation It is the l principal eigenvector set of gps satellite；Otherwise, iteration variable adds 1, repeats S4.3.3 and S4.3.4；
S4.4 constructs the corresponding dimensionality reduction matrix of each gps satellite using the principal eigenvector set of each gps satellite；
The corresponding dimensionality reduction matrix B of each gps satellitelConstruct according to the following formula：
Bl=[u1, u2..., uM]
M represents the l number of the element of the principal eigenvector set of gps satellite；
S5 is using the sample data after the corresponding dimensionality reduction of the corresponding each gps satellite of dimensionality reduction matrix computations of each gps satellite Vector；
Sample data vector after the corresponding dimensionality reduction of each gps satellite is calculated according to the following formula：
Y l , k = B l H X k
Wherein, YL, kRepresent the sample data vector after the dimensionality reduction of the l kth of gps satellite time snap；
S6 is according to linearly constrained minimum variance, the self adaptation weight vector after the corresponding dimensionality reduction of each gps satellite of calculating；
Self adaptation weight vector after the corresponding dimensionality reduction of each gps satellite is calculated according to the following formula：
w l = R Y l - 1 · ( B l H a ‾ l )
Wherein, wlRepresent the self adaptation weight vector after the corresponding dimensionality reduction of the l gps satellite, l=1 ..., L,The l GPS is defended Sample data covariance matrix after the corresponding dimensionality reduction of star,(·)-1Representing matrix inversion operation；
S7 is by after the corresponding dimensionality reduction self adaptation weight vector of each gps satellite respectively dimensionality reduction corresponding with each gps satellite Sample data vector makees Matrix Multiplication operation, obtains the corresponding jamproof gps signal output result of each gps satellite.
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