CN103792550A - United anti-interference method based on array antennas and GPS/SINS - Google Patents

Abstract

The invention provides a united anti-interference method based on array antennas and a GPS/SINS. The method includes the steps that after the position and the posture of a carrier are initialized, a GPS/SINS integrated navigation state equation and a measurement equation are built; the position and the posture of the carrier are provided in real time through GPS/SINS integrated navigation, and the current position of a satellite is calculated according to satellite ephemeris information to obtain a guiding vector from the satellite to the carrier; the guiding vector serves as prior information of a multi-constraint minimum variance space-time self-adaptive processing algorithm and suppresses broadband interference and narrow-band interference in a space domain and a time domain at the same time. According to the united anti-interference method, wave beams can be formed in the direction of a plurality of visual satellites at the same time, and null steering is formed in the interference direction, so that interference signals are suppressed while satellite signals are enhanced. An antenna array of a round structure is adopted, the position and the posture of the carrier are provided for forming the wave beams of the array antennas through GPS/SINS integrated navigation, the position of satellite is provided by the adoption of a satellite ephemeris, and therefore the prior information is provided for forming the wave beams.

Description

A kind of associating anti-interference method based on array antenna and GPS/SINS

Technical field

What the present invention relates to is a kind of integrated navigation technology, specifically a kind of array antenna and GPS(GPS)/SINS(strapdown inertial navigation system) integrated navigation technology.

Background technology

GPS navigation system can be round-the-clock for its user provides exact position, speed and temporal information covering the whole world, and its using value is more and more higher.But along with the raising of artificial interference technology, satellite only relies on its spread spectrum system to carry out anti-interferencely can not meeting consumers' demand.According to ICD-200, the anti-jamming margin of commercial GPS receiver is no more than 24dB(and depends on noise level).If jamming-to-signal ratio is greater than 24dB, commercial GPS C/A code receiver just cannot keep the tracking to signal.Test shows, the jammer that power is 1W can make 85 kilometers cannot work with interior C/A code receiver.In addition, existing gps signal is launched in well-known frequency, and its modulation signature is widely known by the people, and signal to noise ratio (S/N ratio) is lower again, thereby is easy to disturb or cheat.Therefore, research GPS Anti-Jamming Technique has become focus and emphasis.

At present, the anti-interference method based on signal processing is to study the most active field, and common technology comprises time-domain filtering technology and airspace filter technology.Adaptive temporal filter technology is a kind of narrow-band interference rejection method, and it makes required cost function minimize to remove undesired signal by adaptive algorithm the useful signal receiving, interference and noise.Time-domain filtering is very stable when for BOUNDED DISTURBANCES source, and this is because it can provide complicated rejection filter criterion simultaneously, and it is counted as the independent embedded part before embedded part or the GPS receiver of GPS receiver pre-process and post-process.Very little to size impact in the situation that, the inhibition that this technology is disturbed arrowband is greater than 30dB.Disturb for eliminating arrowband, time-domain filtering technology can be used for complicated arrowband and continuous wave interference source, but this can be subject to again the restriction of remaining computation bandwidth, and this remaining computation bandwidth can hinder effective gps signal processing.Airspace filter technology is to realize by adaptive array, and it can effectively suppress coherent interference and broadband interference.Adaptive antenna and self-adaptive filters in time area are somewhat similar, also to make certain cost function minimize, if it has a very large defect is exactly the incident direction of useful signal and undesired signal time close to each other, adaptive antenna also can impact useful signal in suppressing undesired signal.Its realization needs power, the more cost that consumption rate is larger, and needs a larger workbench.Airspace filter mainly contains two types: zero falls into and wave beam formation.Zero sunken technology is minimum to the demand of useful signal quantity of information, and it is more easily realized than beam-forming technology.Zero falls into the output power of technology minimum signal, and it can be divided into arrowband and two kinds, broadband situation.Beam-forming technology requires the information of many relevant useful signals, and implements also more complicated.The output signal-to-noise ratio of beam-forming technology maximum signal, beam-forming technology is also divided into arrowband and two kinds, broadband situation.

Simple time-domain filtering and simple spatial domain have relative merits separately, but the quality of these two kinds of disposal routes just can be complementary, can be by the two in conjunction with application, and then form a kind of associating Anti-Jamming Technique, i.e. space-time two-dimension Combined Treatment (STAP) Anti-Jamming Technique.The airspace filter that the spatial processing energy force rate of space-time two-dimensional Combined Treatment is simple is stronger.When needs carry out zero sunken time to broadband signal, because signal bandwidth be can not ignore, can in space, cause what is called " to disperse " phenomenon.General airspace filter means all need the space of this broadband initiation " to disperse " and consider especially, and this is also that simple spatial domain method is processed the reason that broadband signal is difficult to obtain promising result.Space-time two-dimensional Combined Treatment is combined with frequency information and spatial information (si), naturally can be in the time of sky in plane by complete the showing of each component of signal of dispersing, thereby can eliminate and suppress disturbing to greatest extent.And STAP technology also has the plurality of advantages such as signal equalization and inherent anti-multipath interference performance of inherent wave beam formation, inherence, thereby can realize anti-interference process in strengthening signal.

In addition, GPS/SINS integrated navigation also can improve the antijamming capability of GPS receiver.The loop bandwidth of receiver need to be between antijamming capability and performance of dynamic tracking tradeoff design, be that receiver is in order to improve the ability that self suppresses interference and noise, loop bandwidth need to be reduced, and need loop bandwidth to increase in order to follow the tracks of the dynamic property of carrier.And introduce after inertia information, SINS can accurately estimate the speed of carrier, calculates the Doppler shift of carrier with respect to satellite, thereby reduces the loop bandwidth of receiver, increases the antijamming capability of receiver.

But all there is certain defect in above traditional anti-interference method.Simple time domain disposal route can not suppress broadband interference, and zero in airspace filter falls into method can not provide gain in satellite-signal direction, and satellite-signal is also likely suppressed.Beamforming Method in airspace filter and space-time adaptive are processed the angle that often needs satellite to arrive receiver.GPS/SINS combination anti-interference method needs GPS receiver can correctly export pseudorange, pseudorange rates or position, velocity information.

Summary of the invention

The object of the present invention is to provide a kind of associating anti-interference method based on array antenna and GPS/SINS that interference performance is strong that suppresses.

The object of the present invention is achieved like this:

After the position and attitude of initialization carrier, set up GPS/SINS integrated navigation state equation and measurement equation; GPS/SINS integrated navigation provides position and the attitude of carrier in real time, calculates the position of current satellite according to satellite ephemeris information simultaneously, thereby obtains satellite to the steering vector between carrier, and satellite arrives deflection and the angle of pitch of carrier; Then, described steering vector is as the prior imformation of multiple constraint minimum variance space-time adaptive processing (MCMV-STAP) algorithm, in spatial domain, time domain suppresses broadband interference and arrowband disturbs simultaneously.Specifically comprise the steps:

Step 1: initialization carrier positions, speed and attitude information

In earth coordinates, set the coordinate of carrier initial time: latitude L, longitude λ and height h; Initialization carrier is the speed in day coordinate system northeastward: east orientation speed V _e, north orientation speed V _nwith sky to speed V _u; The attitude angle of initialization carrier, comprises pitching angle theta, roll angle γ and position angle ψ; Then set the flight path of carrier, can be set as the tracks such as static, rectilinear motion or circular motion.Thereby obtain the output of desirable gyroscope and accelerometer, f _e, f _nand f _ube expressed as accelerometer east orientation, north orientation and day to output.

Step 2: the parameter information of initialization Navigation Filter

In GPS/SINS integrated navigation wave filter, adopt feedback compensation mode.The quantity of state of Navigation Filter is attitude error, velocity error, site error, gyro error and accelerometer error.φ _e, φ _nand φ _ube expressed as carrier angle of pitch error, roll angle error and azimuth angle error, δ V _e, δ V _nwith δ V _ube expressed as east orientation velocity error, north orientation velocity error and the sky of carrier to velocity error, δ L, δ λ and δ h are expressed as latitude error, longitude error and the height error of carrier.ε _e, ε _nand ε _ube expressed as gyroscope east orientation, north orientation and day to drift.

with

be expressed as accelerometer east orientation, north orientation and day to output error.

Step 3: the error rate of computing gyroscope and accelerometer

Step 4: according to the parameter in step 1-3, calculate attitude of carrier angle error rate of change, velocity error rate of change and site error rate of change

Step 5: introduce GPS pseudo range measurement information, adopt feedback compensation mode to proofread and correct SINS output information, obtain current position accurately and attitude.

Calculate satellite to the pseudorange between carrier according to the measured code phase error of GPS receiver tracking loop circuit, pseudorange upgrades the quantity of state of Navigation Filter as measurement information, thereby dopes the error of current SINS institute state quantity measurement amount.Then adopt feedback compensation mode to proofread and correct SINS output information, obtain current position accurately and attitude.

Step 6: calculate the coordinate of carrier in the body-fixed coordinate system of the earth's core

The carrier positions being calculated by step 5 is arranged in earth coordinates, i.e. (L, λ, h) is translated in the body-fixed coordinate system of the earth's core its position coordinates

can be expressed as

$X_p^e={[(R+h)\cos L\cos \mathrm{\λ},(R+h)\cos L\sin \mathrm{\λ},(R+h)\sin L]}^T---\left(1\right)$

In formula (1), R is earth radius.

Step 7: calculating carrier coordinate system (b system) is tied to the transition matrix of the earth's core body-fixed coordinate system (e system) to transition matrix, the navigation coordinate of navigation coordinate system (n system)

The attitude of carrier angle being calculated by step 5, can calculate the transition matrix of carrier coordinate system to navigation coordinate system

for

$C_b^n=\left[\begin{array}{ccc}\cos \mathrm{\γ}\cos \mathrm{\ψ}-\sin \mathrm{\ψ}\sin \mathrm{\θ}\sin \mathrm{\γ}& -\sin \mathrm{\ψ}\cos \mathrm{\θ}& \sin \mathrm{\γ}\cos \mathrm{\ψ}+\cos \mathrm{\γ}\sin \mathrm{\θ}\sin \mathrm{\ψ}\\ \cos \mathrm{\γ}\sin \mathrm{\ψ}+\sin \mathrm{\γ}\sin \mathrm{\θ}\cos \mathrm{\ψ}& \cos \mathrm{\ψ}\cos \mathrm{\θ}& \sin \mathrm{\γ}\sin \mathrm{\ψ}-\cos \mathrm{\γ}\sin \mathrm{\θ}\cos \mathrm{\ψ}\\ -\sin \mathrm{\γ}\cos \mathrm{\θ}& \sin \mathrm{\θ}& \cos \mathrm{\θ\γ}\cos \end{array}\right]---\left(2\right)$

The carrier positions being calculated by step 5, can calculate navigation coordinate and be tied to the transition matrix of the earth's core body-fixed coordinate system

for

$C_n^e=\left[\begin{array}{ccc}-\sin \mathrm{\λ}& -\sin L\cos \mathrm{\λ}& \cos L\cos \mathrm{\λ}\\ \cos \mathrm{\λ}& -\sin L\sin \mathrm{\λ}& \cos L\sin \mathrm{\λ}\\ 0& \cos L& \sin L\end{array}\right]---\left(3\right)$

Step 8: calculate carrier to the steering vector between satellite

By (2) in step 7, (3) can be in the hope of carrier coordinate system the transformed matrix to the earth's core body-fixed coordinate system

$C_b^e=C_n^e{C}_b^n---\left(4\right)$

Utilize satellite ephemeris to calculate the position of satellite in the body-fixed coordinate system of the earth's core

and in conjunction with formula (1) (4), can be in the hope of carrier to the steering vector between satellite

${\stackrel{\→}{r}}^b={\left(C_b^e\right)}^T(X_s^e-X_p^e)---\left(5\right)$

Step 9: in carrier coordinate system, calculate position angle and the angle of pitch of satellite arrival antenna

If will

coordinate in carrier coordinate system is defined as

azimuth angle alpha and the angle of pitch β of satellite arrival antenna can be expressed as respectively

$\mathrm{\α}=\arctan (\hat{x},\hat{y})---\left(6\right)$

$\mathrm{\β}=\arctan (\hat{z},\sqrt{{\hat{x}}^2+{\hat{y}}^2})---\left(7\right)$

Step 10: design circular array antenna structure

In order to control beam position satellites in view direction at position angle and angle of pitch direction simultaneously, the present invention adopts circular array antenna structure.6 array elements are uniformly distributed in the circle battle array on circumference, and making radius of circle is r, and on circumference, the interval between adjacent array element is also r.Choosing of array element interval, to meet Nyquist's theorem the same with time-domain sampling interval, and Space domain sampling interval d should be less than 1/2 of satellite carrier wavelength X.By satellite frequency f=1575.42 × 10 ⁶mHz, so array element distance is

$d\&le;\frac{\mathrm{\&lambda;}}{2}=\frac{1}{2}\&CenterDot;\frac{\mathrm{<figure-callout\; id="1"\; label="c\; f\; l"\; filenames="HDA0000465116030000021.png"\; state="\{\{state\}\}">c</figure-callout>}}{f_l}=\frac{1}{2}\&CenterDot;\frac{3\&times;{10}^8}{1575.42\&times;{10}^6}=\frac{1}{2}\&CenterDot;0.19=0.095m=9.5\mathrm{cm}---\left(8\right)$

In formula (8), c is the light velocity.

In order to make main beam width narrower, secondary lobe is lower, and resolution is high, and what need to make that array element interval tries one's best is large, so get radius of circle r=d=9.5cm, the diameter of whole array antenna is about 19cm.

Step 11: calculate satellite-signal and arrive the time delay between the each array element of antenna

According to (6) (7) in step 9, can be by α and β representation unit vector

e(α,β)=(sinαcosβ,cosαcosβ,sinβ) ^T (9)

Therefore, satellite-signal arrives i bay and arrives the mistiming τ between first reference array element _ican be expressed as

τ _i=e ^T·(x _i-x ₁)/c i=1,2,…M-1 (10)

In formula (10), M representative antennas array element number.

Step 12: set up array antenna received signals model

User generally can receive 4 above satellite-signals, therefore, need to form the satellite that multiple beam positions are corresponding.Suppose that array antenna received has arrived P satellite-signal, Q undesired signal, antenna reception to signal model can be expressed as

$U\left(t\right)=\underset{k=1}{\overset{P}{\mathrm{\&Sigma;}}}a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)s_k\left(t\right)+\underset{k=P+1}{\overset{P+Q}{\mathrm{\&Sigma;}}}a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)j_{k-P}\left(t\right)+n\left(t\right)---\left(11\right)$

In formula (11), s (t) and j (t) represent respectively the satellite-signal and the undesired signal that receive, a (α _k, β _k, T _s) be the steering vector of k echo signal (satellite-signal or undesired signal).T _stime domain lag line interval, α _kand β _kbe expressed as position angle and the angle of pitch that k echo signal arrives array antenna.N (t) represents white Gaussian noise, and its power spectrum density is expressed as N ₀/ 2.

In formula (11), a (α _k, β _k, T _s) expression space-time two-dimensional target vector, i.e. time vector a _s(T _s) and direction in space vector a _s(α _k, β _k) Crow Neck long-pending (Kronecker Product), and can be expressed as:

$a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)=a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k)\&CircleTimes;a_s\left(T_s\right)---\left(12\right)$

The time delay unit number that makes each radio-frequency channel is N,

$a_s({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k)=\left[\begin{array}{cccc}1& e^{-j2\mathrm{\&pi;f}{\mathrm{\&tau;}}_1}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;f}{\mathrm{\&tau;}}_{M-1}}\end{array}\right]---\left(13\right)$

$a_t=\left[\begin{array}{cccc}1& e^{-j2\mathrm{\&pi;fT}}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;f}(N-1)T_s}\end{array}\right]---\left(14\right)$

In formula (13), f represents satellite frequency, τ _i(i=1,2 ... M-1) provided by formula (10).In formula (14), T _sin the time interval that represents delay cell, its value should be less than signal bandwidth.

Step 13: calculate aerial array weighted vector

Adopt multiple constraint minimum variance space-time adaptive processing (MCMV-STAP) algorithm to retrain satellites in view signal, then make array output power minimum, thereby suppress undesired signal when protecting satellite-signal.This algorithm need to be tried to achieve the optimum weights of array, is expressed as follows:

$\left\{\begin{array}{c}\mathrm{\&omega;}=\arg \min {\mathrm{\&omega;}}^H{R}_U\mathrm{\&omega;}\\ \mathrm{subjectto}:{\mathrm{\&omega;}}^{H}A=F^T\end{array}\right.---\left(15\right)$

In formula (15), ω represents the weighted vector of array, the conjugate transpose of H representing matrix, R _ube the array covariance matrix of input signal, can be expressed as

R _U=E{UU ^H} (16)

In formula (15), A represents the constraint matrix of satellite-signal, and F represents the constraint vector corresponding with A, and A and F are expressed as

A=[a(α ₁,β ₁,T _s),a(α ₂,β ₂,T _s)…a(α _P,β _P,T _s)] (17)

F ^t=[1,1 ... 1] _{1 × p}(18) adopt method of Lagrange multipliers, array weighted vector ω can be expressed as

$\mathrm{\&omega;}=R_U^{-1}A{\left(A^H{R}_U^{-1}A\right)}^{-1}f---\left(19\right)$

After obtaining array weights, the output that can obtain array express be for

y(t)=ω ^HU(t)。

Traditional space-time adaptive processing method, adopts Blind adaptive beamforming algorithm conventionally, does not need to know that satellite arrives position angle and the angle of pitch of array antenna, just simply using a certain bay as carrying out weights constraint with reference to array element.But, owing to not retraining in satellite-signal direction, can not form wave beam in satellite-signal direction.Therefore, such blind beamforming algorithm also will weaken the satellite-signal of expecting in suppressing undesired signal, and satellite-signal power will be weakened, and can not obtain the maximum Signal to Interference plus Noise Ratio of signal.

Carrier positions and attitude that the present invention mainly utilizes GPS/SINS integrated navigation system to provide, the satellite position that GPS ephemeris provides, thus obtain satellite to the steering vector between carrier, satellite arrives deflection and the angle of pitch of carrier.Then, this steering vector is as the prior imformation of multiple constraint minimum variance space-time adaptive processing (MCMV-STAP) algorithm, in spatial domain, time domain suppresses broadband interference and arrowband disturbs simultaneously.

Calculating satellite of the present invention is to the steering vector method between carrier, the position that it is characterized in that carrier that GPS/SINS calculates is arranged in earth coordinates, attitude is arranged in sky, northeast coordinate system, utilize satellite position that satellite ephemeris resolves in the body-fixed coordinate system of the earth's core, should under carrier coordinate system, provide and wave beam forms required steering vector.The present invention after changes in coordinates, obtains deflection and the angle of pitch of satellite arrival carrier by tried to achieve prior imformation (position of satellite, the position of carrier and attitude) in carrier coordinate system.

The mode that the present invention adopts array antenna to combine with GPS/SINS improves the antijamming capability of navigation neceiver.In array antenna, adopt the space-time adaptive beamforming algorithm (MCMV-STAP) of multiple constraint minimum variance criterion, this algorithm can form wave beam in many satellites in view directions, forms zero and falls into, thereby suppress undesired signal when strengthening satellite-signal at interference radiating way.In order to obtain the peak power of satellite-signal, this algorithm need to know that satellite-signal arrives position angle and the angle of pitch of carrier.Therefore, the present invention adopts circular array antenna structure, introduce the wave beam that GPS/SINS integrated navigation is array antenna and form position and attitude that carrier is provided, adopt satellite ephemeris that the position of satellite is provided, thereby provide prior imformation for wave beam forms, satellites in view arrives position angle and the angle of pitch of carrier.

Accompanying drawing explanation

Fig. 1 is the implementing procedure figure of the associating anti-interference method based on array antenna and GPS/SINS;

Fig. 2 is the schematic diagram of array antenna, sky, northeast coordinate system and carrier coordinate system;

Fig. 3 is the structural drawing of multiple constraint minimum variance space-time two-dimensional self-adaptive processing (MCMV-STAP).

Embodiment

Below in conjunction with accompanying drawing, the present invention is further elaborated.

Step 1: initialization carrier positions, speed and attitude information

As shown in Figure 1, need position and the attitude of first initialization carrier.In earth coordinates, set the coordinate of carrier initial time: latitude L=45 °, longitude λ=126 ° and height h=200m.The attitude angle of initialization carrier, comprises pitching angle theta=0 °, roll angle γ=0 ° and ψ=45 °, position angle.Then set the flight path of carrier, can be set as the tracks such as static, rectilinear motion or circular motion.Carrier flight path is as requested set the east orientation speed V of carrier _e, north orientation speed V _nwith sky to speed V _u.Thereby obtain the output of desirable gyroscope and accelerometer, f _e, f _nand f _ube expressed as accelerometer east orientation, north orientation and day to output.

Step 2: the parameter information of initialization Navigation Filter

In GPS/SINS integrated navigation wave filter, adopt feedback compensation mode.The quantity of state of Navigation Filter is attitude error, velocity error, site error, gyro error and accelerometer error.At initial time, carrier angle of pitch error φ _e=0.1 °, roll angle error φ _n=0.1 ° and azimuth angle error φ _u=1 °.The east orientation velocity error δ V of carrier _e=0.2m/s, north orientation velocity error δ V _n=0.2m/s and sky are to velocity error δ V _u=0.5m/s.The latitude error δ L=0 of carrier °, longitude error δ λ=0 ° and height error δ h=20m.Gyro drift ε _b=0.1 °/h, white noise ε _g=0.05 °/h, accelerometer constant error

white noise w _a=5 × 10 ^-4g, g is acceleration of gravity.Gyro error ε east orientation, north orientation and day to drift be expressed as ε _e, ε _nand ε _u.Accelerometer east orientation, north orientation and day to output error can be expressed as respectively

with

Step 3: the error rate of computing gyroscope and accelerometer

Gyrostatic constant value drift can be to be described as with arbitrary constant

${\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}_b=0---\left(1\right)$

Gyrostatic noise ε _gcan describe with Dirac function.Therefore, gyro error rate of change

can be expressed as

$\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}={\stackrel{\&CenterDot;}{\mathrm{\&epsiv;}}}_b+{\mathrm{\&epsiv;}}_g---\left(2\right)$

For accelerometer error rate of change

can be thought of as first-order Markov process, error model is taken as

$\stackrel{\&CenterDot;}{\&dtri;}=-\frac{1}{T_a}\&dtri;+w_a---\left(3\right)$

Wherein, T _arepresent correlation time, w _afor white-noise process.

Step 4: according to the parameter in step 1-3, calculate attitude of carrier angle error rate of change, velocity error rate of change and site error rate of change

1, calculate attitude of carrier angle error rate of change

with

be expressed as the rate of change of carrier angle of pitch error, roll angle error and azimuth angle error, attitude of carrier angle error rate of change can be expressed as

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_E=-\frac{{\mathrm{\&delta;V}}_N}{R+h}+({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E}{R+h}\tan L){\mathrm{\&phi;}}_N-({\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R+h}\tan L){\mathrm{\&phi;}}_U+{\mathrm{\&epsiv;}}_E\\ {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_N=\frac{{\mathrm{\&delta;V}}_E}{R+h}-{\mathrm{\&omega;}}_{\mathrm{ie}}\sin \mathrm{L\&delta;L}-({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E}{R+h}\tan L){\mathrm{\&phi;}}_E-\frac{V_E}{R+h}{\mathrm{\&phi;}}_U+{\mathrm{\&epsiv;}}_N\\ {\stackrel{\&CenterDot;}{\mathrm{\&phi;}}}_U=\frac{{\mathrm{\&delta;V}}_E}{R+h}\tan L+({\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R+h}{\sec }^{2}L)\mathrm{\&delta;L}+({\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R+h}){\mathrm{\&phi;}}_E+\frac{V_N}{R+h}{\mathrm{\&phi;}}_N+{\mathrm{\&epsiv;}}_U\end{array}---\left(4\right)$

In formula (4), R represents earth radius, ω _ierepresent earth rotation angular speed.

2, calculate the rate of change of bearer rate error

with

be expressed as east orientation velocity error, north orientation velocity error and the sky of carrier to the rate of change of velocity error, bearer rate error rate can be expressed as

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&delta;V}}}_E=(\frac{V_N}{R+h}\tan L-\frac{V_U}{R+h}){\mathrm{\&delta;V}}_E+({2\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E}{R+h}\tan L){\mathrm{\&delta;V}}_N\\ -(-{\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R+h}){\mathrm{\&delta;V}}_U+({2\mathrm{\&omega;}}_{\mathrm{ie}}{V}_N\cos L+\frac{V_E{V}_N}{R+h}{\sec }^{2}L+2{\mathrm{\&omega;}}_{\mathrm{ie}}{V}_U\sin L)\mathrm{\&delta;L}\\ +{\&dtri;}_E+f_N{\mathrm{\&phi;}}_U-f_U{\mathrm{\&phi;}}_N\\ {\stackrel{\&CenterDot;}{\mathrm{\&delta;V}}}_N=-2({\mathrm{\&omega;}}_{\mathrm{ie}}\sin L+\frac{V_E}{R+h}\tan L){\mathrm{\&delta;V}}_E-\frac{V_U}{R+h}{\mathrm{\&delta;V}}_N-\frac{V_N}{R+h}{\mathrm{\&delta;V}}_U\\ -(2{\mathrm{\&omega;}}_{\mathrm{ie}}{V}_E\cos L+\frac{V_E^2{\sec }^{2}L}{R+h})\mathrm{\&delta;L}+{\&dtri;}_N-f_E{\mathrm{\&phi;}}_U+f_U{\mathrm{\&phi;}}_E\\ {\stackrel{\&CenterDot;}{\mathrm{\&delta;V}}}_U=(2{\mathrm{\&omega;}}_{\mathrm{ie}}\cos L+\frac{V_E}{R+h}){\mathrm{\&delta;V}}_E+\frac{{2V}_N}{R+h}{\mathrm{\&delta;V}}_N-2{\mathrm{\&omega;}}_{\mathrm{ie}}{V}_E\sin \mathrm{L\&delta;L}+{\&dtri;}_U+f_E{\mathrm{\&phi;}}_N-f_N{\mathrm{\&phi;}}_E\end{array}---\left(5\right)$

3, calculate the rate of change of carrier positions error

with

be expressed as the rate of change of latitude error, longitude error and the height error of carrier.Carrier positions error rate can be expressed as

$\begin{array}{c}\mathrm{\&delta;}\stackrel{\&CenterDot;}{L}=\frac{{\mathrm{\&delta;V}}_N}{R+h}\\ \mathrm{\&delta;}\stackrel{\&CenterDot;}{\mathrm{\&lambda;}}=\frac{{\mathrm{\&delta;V}}_E}{R+h}\\ \mathrm{\&delta;}\stackrel{\&CenterDot;}{h}=\mathrm{\&delta;}{V}_U\end{array},\sec L+\frac{V_E}{R+h}\sec \mathrm{LtgL\&delta;L}---\left(6\right)$

Step 5: introduce GPS pseudo range measurement information, adopt feedback compensation mode to proofread and correct SINS output information, obtain current

Position and attitude accurately.

Calculate satellite to the pseudorange between carrier according to the measured code phase error of GPS receiver tracking loop circuit, pseudorange upgrades the quantity of state of Navigation Filter as measurement information, thereby dope site error (the δ L that current SINS measures, δ λ, δ h) and attitude error (δ θ, δ γ, δ ψ).Then adopt feedback compensation mode to proofread and correct position (L, λ, h) and the attitude (θ, γ, ψ) of SINS output, obtain current position accurately and attitude.

L=L+δL

λ=λ+δλ

h=h+δh

θ=θ+δθ (7)

γ=γ+δγ

ψ=ψ+δψ

Step 6: calculate the coordinate of carrier in the body-fixed coordinate system of the earth's core

The carrier positions being calculated by step 5 is arranged in earth coordinates, i.e. (L, λ, h) is translated in the body-fixed coordinate system of the earth's core its position coordinates

can be expressed as

$X_p^e={[(R+h)\cos L\cos \mathrm{\&lambda;},(R+h)\cos L\sin \mathrm{\&lambda;},(R+h)\sin L]}^T---\left(8\right)$

Step 7: calculating carrier coordinate system (b system) is tied to the transition matrix of the earth's core body-fixed coordinate system (e system) to transition matrix, the navigation coordinate of navigation coordinate system (n system)

The attitude of carrier being calculated by step 5 can calculate the transition matrix of carrier coordinate system to navigation coordinate system

for

$C_b^n=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}-\sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&gamma;}& -\sin \mathrm{\&psi;}\cos \mathrm{\&theta;}& \sin \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}\\ \cos \mathrm{\&gamma;}\sin \mathrm{\&psi;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&psi;}\cos \mathrm{\&theta;}& \sin \mathrm{\&gamma;}\sin \mathrm{\&psi;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}\\ -\sin \mathrm{\&gamma;}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;\&gamma;}\cos \end{array}\right]---\left(9\right)$

The carrier positions being calculated by step 5, can calculate navigation coordinate and be tied to the transition matrix of the earth's core body-fixed coordinate system

for

$C_n^e=\left[\begin{array}{ccc}-\sin \mathrm{\&lambda;}& -\sin L\cos \mathrm{\&lambda;}& \cos L\cos \mathrm{\&lambda;}\\ \cos \mathrm{\&lambda;}& -\sin L\sin \mathrm{\&lambda;}& \cos L\sin \mathrm{\&lambda;}\\ 0& \cos L& \sin L\end{array}\right]---\left(10\right)$

Step 8: calculate carrier to the steering vector between satellite

By (9) in step 7, (10) can be in the hope of carrier coordinate system the transformed matrix to the earth's core body-fixed coordinate system

$C_b^e=C_n^e{C}_b^n---\left(11\right)$

Utilize satellite ephemeris to calculate the position of satellite in the body-fixed coordinate system of the earth's core

and in conjunction with formula (8) (11), can be in the hope of carrier to the steering vector between satellite

${\stackrel{\&RightArrow;}{r}}^b={\left(C_b^e\right)}^T(X_s^e-X_p^e)---\left(12\right)$

Step 9: in carrier coordinate system, calculate position angle and the angle of pitch of satellite arrival antenna

If will

coordinate in carrier coordinate system is defined as azimuth angle alpha and the angle of pitch β of satellite arrival antenna can be expressed as respectively

$\mathrm{\&alpha;}=\arctan (\hat{x},\hat{y})---\left(13\right)$

$\mathrm{\&beta;}=\arctan (\hat{z},\sqrt{{\hat{x}}^2+{\hat{y}}^2})---\left(14\right)$

Step 10: design circular array antenna structure

In order to control beam position satellites in view direction at position angle and angle of pitch direction simultaneously, the present invention adopts circular array antenna structure, as shown in Figure 2.6 array elements are uniformly distributed in the circle battle array on circumference, and making radius of circle is r, and on circumference, the interval between adjacent array element is also r.Choosing of array element interval, to meet Nyquist's theorem the same with time-domain sampling interval, and Space domain sampling interval d should be less than 1/2 of satellite carrier wavelength X.By satellite frequency f=1575.42 × 10 ⁶mHz, so array element distance is

$d\&le;\frac{\mathrm{\&lambda;}}{2}=\frac{1}{2}\&CenterDot;\frac{\mathrm{<figure-callout\; id="1"\; label="c\; f\; l"\; filenames="HDA0000465116030000021.png"\; state="\{\{state\}\}">c</figure-callout>}}{f_l}=\frac{1}{2}\&CenterDot;\frac{3\&times;{10}^8}{1575.42\&times;{10}^6}=\frac{1}{2}\&CenterDot;0.19=0.095m=9.5\mathrm{cm}---\left(15\right)$

In formula (15), c is the light velocity.

In order to make main beam width narrower, secondary lobe is lower, and resolution is high, and what need to make that array element interval tries one's best is large, so get radius of circle r=d=9.5cm, the diameter of whole array antenna is about 19cm.

Take antenna array place plane as xoy plane, take true origin as reference, x axle array element is No. 1 array element, the polar coordinates of 6 array elements are respectively: (r, 0), (r, π/3), (r, 2 π/3), (r, π), (r, 4 π/3), (r, 5 π/3).

Step 11: calculate satellite-signal and arrive the time delay between the each array element of antenna

According to (13) (14) in step 9, can be by α and β representation unit vector

e(α,β)=(sinαcosβ,cosαcosβ,sinβ) ^T (16)

Therefore, satellite-signal arrives i bay and can be expressed as to the mistiming τ i between first reference array element

τ _i=e ^t(x _i-x ₁)/c i=1,2 ... in M-1 (17) formula (17), M representative antennas array element number.

Step 12: set up array antenna received signals model

User generally can receive 4 above satellite-signals, therefore, need to form the satellite that multiple beam positions are corresponding.Suppose that array antenna received has arrived P satellite-signal, Q undesired signal, antenna reception to signal model can be expressed as

$U\left(t\right)=\underset{k=1}{\overset{P}{\mathrm{\&Sigma;}}}a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)s_k\left(t\right)+\underset{k=P+1}{\overset{P+Q}{\mathrm{\&Sigma;}}}a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)j_{k-P}\left(t\right)+n\left(t\right)---\left(18\right)$

In formula (18), s (t) and j (t) represent respectively the satellite-signal and the undesired signal that receive, a (α _k, β _k, T _s) be the steering vector of k echo signal (satellite-signal or undesired signal).T _stime domain lag line interval, α _kand β _kbe expressed as position angle and the angle of pitch that k echo signal arrives array antenna.N (t) represents white Gaussian noise, and its power spectrum density is expressed as N ₀/ 2.

In formula (18), a (α _k, β _k, T _s) expression space-time two-dimensional target vector, i.e. time vector a _s(T _s) and direction in space vector a _s(α _k, β _k) Crow Neck long-pending (Kronecker Product), and can be expressed as:

$a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)=a_s({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k)\&CircleTimes;a_s\left(T_s\right)---\left(19\right)$

The time delay unit number that makes each radio-frequency channel is N,

$a_s({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k)=\left[\begin{array}{cccc}1& e^{-j2\mathrm{\&pi;f}{\mathrm{\&tau;}}_1}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;f}{\mathrm{\&tau;}}_{M-1}}\end{array}\right]---\left(20\right)$

$a_t=\left[\begin{array}{cccc}1& e^{-j2\mathrm{\&pi;fT}}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;f}(N-1)T_s}\end{array}\right]---\left(21\right)$

In formula (20), f represents satellite frequency, τ _i(i=1,2 ... M-1) provided by formula (17).In formula (21), T _sin the time interval that represents delay cell, its value should be less than signal bandwidth.

Step 13: calculate aerial array weighted vector

The structural drawing that accompanying drawing 3 is multiple constraint minimum variance space-time two-dimensional self-adaptive processing (MCMV-STAP).From the passage of each array element, time delays at different levels have formed FIR wave filter, can remove and disturb in time domain; From identical time delay node, different array element has formed the auto adapted filtering in spatial domain, can differentiate space interference source and then form on Ling Xiancong spatial domain, spatial domain and suppress to disturb.And the processing in spatial domain also can further utilize time domain feedback information after treatment, when empty, process and also therefore there is the ability of simultaneously rejecting interference in space-time two-dimensional territory.

Adopt MCMV-STAP algorithm to retrain satellites in view signal, then make array output power minimum, thereby suppress undesired signal when protecting satellite-signal.This algorithm need to be tried to achieve the optimum weights of array, is expressed as follows:

$\left\{\begin{array}{c}\mathrm{\&omega;}=\arg \min {\mathrm{\&omega;}}^H{R}_U\mathrm{\&omega;}\\ \mathrm{subjectto}:{\mathrm{\&omega;}}^{H}A=F^T\end{array}\right.---\left(22\right)$

In formula (22), ω represents the weighted vector of array, the conjugate transpose of H representing matrix, R _ube the array covariance matrix of input signal, can be expressed as

R _U=E{UU ^H} (23)

In formula (23), A represents the constraint matrix of satellite-signal, and F represents the constraint vector corresponding with A, and A and F are expressed as

A=[a(α ₁,β ₁,T _s),a(α ₂,β ₂,T _s)…a(α _P,β _P,T _s)] (24)

F ^t=[1,1 ... 1] _{1 × p}(25) adopt method of Lagrange multipliers, array weighted vector ω can be expressed as

$\mathrm{\&omega;}=R_U^{-1}A{\left(A^H{R}_U^{-1}A\right)}^{-1}f---\left(26\right)$

After obtaining array weights, the output that can obtain array express be for

y(t)=ω ^HU(t)。(27) 。

Claims (2)

1. the associating anti-interference method based on array antenna and GPS/SINS, is characterized in that: after the position and attitude of initialization carrier, set up GPS/SINS integrated navigation state equation and measurement equation; GPS/SINS integrated navigation provides position and the attitude of carrier in real time, calculates the position of current satellite according to satellite ephemeris information simultaneously, thereby obtains satellite to the steering vector between carrier, and satellite arrives deflection and the angle of pitch of carrier; Then, described steering vector is as the prior imformation of multiple constraint minimum variance space-time adaptive Processing Algorithm, in spatial domain, time domain suppresses broadband interference and arrowband disturbs simultaneously.

2. the associating anti-interference method based on array antenna and GPS/SINS according to claim 1, is characterized in that specifically comprising the steps:

Step 1: initialization carrier positions, speed and attitude information;

In earth coordinates, set the coordinate of carrier initial time: latitude L, longitude λ and height h; Initialization carrier is the speed in day coordinate system northeastward: east orientation speed V _e, north orientation speed V _nwith sky to speed V _u; The attitude angle of initialization carrier, comprises pitching angle theta, roll angle γ and position angle ψ; Then the flight path of setting carrier is the one in static, rectilinear motion or circular motion track; Thereby obtain the output of gyroscope and accelerometer, f _e, f _nand f _ube expressed as accelerometer east orientation, north orientation and day to output;

Step 2: the parameter information of initialization Navigation Filter;

In GPS/SINS integrated navigation wave filter, adopt feedback compensation mode; The quantity of state of Navigation Filter is attitude error, velocity error, site error, gyro error and accelerometer error, φ _e, φ _nand φ _ube expressed as carrier angle of pitch error, roll angle error and azimuth angle error, δ V _e, δ V _nwith δ V _ube expressed as east orientation velocity error, north orientation velocity error and the sky of carrier to velocity error, δ L, δ λ and δ h are expressed as latitude error, longitude error and the height error of carrier, ε _e, ε _nand ε _ube expressed as gyroscope east orientation, north orientation and day to drift,

with

be expressed as accelerometer east orientation, north orientation and day to output error;

Step 3: the error rate of computing gyroscope and accelerometer;

Step 4: according to the parameter in step 1-3, calculate attitude of carrier angle error rate of change, velocity error rate of change and site error rate of change;

Step 5: introduce GPS pseudo range measurement information, adopt feedback compensation mode to proofread and correct SINS output information, obtain current position accurately and attitude;

Calculate satellite to the pseudorange between carrier according to the measured code phase error of GPS receiver tracking loop circuit, pseudorange upgrades the quantity of state of Navigation Filter as measurement information, thereby dope the error of current SINS institute state quantity measurement amount, then adopt feedback compensation mode to proofread and correct SINS output information, obtain current position accurately and attitude;

Step 6: calculate the coordinate of carrier in the body-fixed coordinate system of the earth's core;

The carrier positions being calculated by step 5 is arranged in earth coordinates, i.e. (L, λ, h) is translated in the body-fixed coordinate system of the earth's core its position coordinates be expressed as

$X_p^e={[(R+h)\cos L\cos \mathrm{\&lambda;},(R+h)\cos L\sin \mathrm{\&lambda;},(R+h)\sin L]}^T$

Wherein, R is earth radius;

Step 7: calculating carrier coordinate system and be b, to be tied to navigation coordinate system be that transition matrix, the navigation coordinate of n system is tied to the transition matrix that the earth's core body-fixed coordinate system is e system;

The attitude of carrier angle being calculated by step 5, calculates the transition matrix of carrier coordinate system to navigation coordinate system

for

$C_b^n=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}-\sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&gamma;}& -\sin \mathrm{\&psi;}\cos \mathrm{\&theta;}& \sin \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}\\ \cos \mathrm{\&gamma;}\sin \mathrm{\&psi;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&psi;}\cos \mathrm{\&theta;}& \sin \mathrm{\&gamma;}\sin \mathrm{\&psi;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}\\ -\sin \mathrm{\&gamma;}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;\&gamma;}\cos \end{array}\right]$

The carrier positions being calculated by step 5, calculates navigation coordinate and is tied to the transition matrix of the earth's core body-fixed coordinate system for

$C_n^e=\left[\begin{array}{ccc}-\sin \mathrm{\&lambda;}& -\sin L\cos \mathrm{\&lambda;}& \cos L\cos \mathrm{\&lambda;}\\ \cos \mathrm{\&lambda;}& -\sin L\sin \mathrm{\&lambda;}& \cos L\sin \mathrm{\&lambda;}\\ 0& \cos L& \sin L\end{array}\right];$

Step 8: calculate carrier to the steering vector between satellite;

By the transition matrix in step 7

transition matrix

try to achieve the transformed matrix of carrier coordinate system to the earth's core body-fixed coordinate system

$C_b^e=C_n^e{C}_b^n$

Utilize satellite ephemeris to calculate the position of satellite in the body-fixed coordinate system of the earth's core

and in conjunction with formula $X_p^e={[(R+h)\cos L\cos \mathrm{\&lambda;},(R+h)\cos L\sin \mathrm{\&lambda;},(R+h)\sin L]}^T$ With $C_b^e=C_n^e{C}_b^n,$ Try to achieve carrier to the steering vector between satellite

${\stackrel{\&RightArrow;}{r}}^b={\left(C_b^e\right)}^T(X_s^e-X_p^e)$

Step 9: in carrier coordinate system, calculate position angle and the angle of pitch of satellite arrival antenna;

If will

coordinate in carrier coordinate system is defined as

azimuth angle alpha and the angle of pitch β of satellite arrival antenna can be expressed as respectively

$\mathrm{\&alpha;}=\arctan (\hat{x},\hat{y})$

$\mathrm{\&beta;}=\arctan (\hat{z},\sqrt{{\hat{x}}^2+{\hat{y}}^2})$

Step 10: design circular array antenna structure;

6 array elements are uniformly distributed in the circle battle array on circumference, making radius of circle is r, on circumference, the interval between adjacent array element is also r, choosing of array element interval, to meet Nyquist's theorem the same with time-domain sampling interval, Space domain sampling interval d should be less than 1/2 of satellite carrier wavelength X, by satellite frequency f=1575.42 × 10 ⁶mHz, so array element distance is

$d\&le;\frac{\mathrm{\&lambda;}}{2}=\frac{1}{2}\&CenterDot;\frac{c}{f_{l1}}=\frac{1}{2}\&CenterDot;\frac{3\&times;{10}^8}{1575.42\&times;{10}^6}=\frac{1}{2}\&CenterDot;0.19=0.095m=9.5\mathrm{cm}$

Wherein, c is the light velocity;

Step 11: calculate satellite-signal and arrive the time delay between the each array element of antenna;

According in step 9 $\mathrm{\&alpha;}=\arctan (\hat{x},\hat{y}),$ $\mathrm{\&beta;}=\arctan (\hat{z},\sqrt{{\hat{x}}^2+{\hat{y}}^2}),$ By α and β representation unit vector

e(α,β)=(sinαcosβ,cosαcosβ,sinβ) ^T

Therefore, satellite-signal arrives i bay and arrives the mistiming τ between first reference array element _ican be expressed as

τ _i=e ^T·(x _i-x ₁)/c i=1,2,…M-1

Wherein, M representative antennas array element number;

Step 12: set up array antenna received signals model

If array antenna received has arrived P satellite-signal, Q undesired signal, antenna reception to signal model be expressed as

$U\left(t\right)=\underset{k=1}{\overset{P}{\mathrm{\&Sigma;}}}a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)s_k\left(t\right)+\underset{k=P+1}{\overset{P+Q}{\mathrm{\&Sigma;}}}a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)j_{k-P}\left(t\right)+n\left(t\right)$

Wherein, s (t) and j (t) represent respectively the satellite-signal and the undesired signal that receive, a (α _k, β _k, T _s) be the steering vector of k echo signal, T _stime domain lag line interval, α _kand β _kbe expressed as position angle and the angle of pitch that k echo signal arrives array antenna, n (t) represents that white Gaussian noise, its power spectrum density are expressed as N ₀/ 2;

A (α _k, β _k, T _s) expression space-time two-dimensional target vector, i.e. time vector a _s(T _s) and direction in space vector a _s(α _k, β _k) Crow Neck long-pending, and be expressed as:

$a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k,T_s)=a({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k)\&CircleTimes;a_s\left(T_s\right)$

The time delay unit number that makes each radio-frequency channel is N,

$a_s({\mathrm{\&alpha;}}_k,{\mathrm{\&beta;}}_k)=\left[\begin{array}{cccc}1& e^{-j2\mathrm{\&pi;f}{\mathrm{\&tau;}}_1}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;f}{\mathrm{\&tau;}}_{M-1}}\end{array}\right]$

$a_t=\left[\begin{array}{cccc}1& e^{-j2\mathrm{\&pi;fT}}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-j2\mathrm{\&pi;f}(N-1)T_s}\end{array}\right]$

F represents satellite frequency, T _sthe time interval, its value of representing delay cell should be less than signal bandwidth;

Step 13: calculate aerial array weighted vector;

Adopt multiple constraint minimum variance space-time adaptive Processing Algorithm to retrain satellites in view signal, then make array output power minimum, being expressed as follows of the optimum weights of array:

$\left\{\begin{array}{c}\mathrm{\&omega;}=\arg \min {\mathrm{\&omega;}}^H{R}_U\mathrm{\&omega;}\\ \mathrm{subjectto}:{\mathrm{\&omega;}}^{H}A=F^T\end{array}\right.$

Its) in, ω represents the weighted vector of array, the conjugate transpose of H representing matrix, R _ube input signal array covariance matrix, be expressed as

R _U=E{UU ^H}

A represents the constraint matrix of satellite-signal, and F represents the constraint vector corresponding with A, and A and F are expressed as

A=[a(α ₁,β ₁,T _s),a(α ₂,β ₂,T _s)…a(α _P,β _P,T _s)]

f ^T=[1,1…1] _1×p

Adopt method of Lagrange multipliers, array weighted vector ω is expressed as

$\mathrm{\&omega;}=R_U^{-1}A{\left(A^H{R}_U^{-1}A\right)}^{-1}f$

After obtaining array weights, the output that obtains array express be for

y(t)=ω ^HU(t)。

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