CN104297718A - Interferometer array integrated correction method - Google Patents

Abstract

The invention provides an interferometer array integrated correction method. The method includes the steps of firstly, parameterizing a target signal initial incidence direction, a processing and installing comprehensive error and a feeder line passageway comprehensive error; secondly, obtaining a measuring equation set according to a known track rotation antenna array, and obtaining error parameters and incidence signal directions through parameter estimation; thirdly, modifying the error parameters into an interference angle measurement formula to obtain a precisely-corrected angle through the iteration technology. By means of the method, the incidence signal directions do not need to be accurately calibrated, the basic known quantities of the method are the rotation angle and the phase difference measurement value, the interferometer array processing and installing comprehensive error and the feeder line passageway comprehensive error can be obtained at the same time through parameter estimation, the problem that the direction error and the pitching error are coupled can be solved through the iteration technology when the angle measurement error correction is executed, and finally the precisely-corrected angle is obtained. The interferometer array integrated correction method is accurate in error model, simple in execution process, high in correction precision and capable of improving the correction efficiency and the angle measurement accuracy of an interferometer.

Description

A kind of interferometer array integrated correction method

Technical field

The present invention relates to a kind of interferometer array integrated correction method, be applied in the direction finding of radiation source with in locating, belong to radio direction finding (RDF) field.This technology is widely applied in fields such as radar, sonar, mobile communication, geophysical surveys, and particularly in electronic countermeasure, interferometer can timely and accurately to target localization.

Background technology

The ultimate principle of interferometer direction finding is the incident angle being calculated information source by the difference of the different array element of measuring radiation source arrival interferometer.The current raising along with radiation source working frequency range, in order to ensure the precision of interferometry, to the processing of the phase equalization of each array element of interferometer, array and installation accuracy, strict requirement must be proposed, and the passage consistency of array element rear end is strictly controlled, to reduce each interchannel Sensor gain and phase perturbations to greatest extent, but be limited to the impact of processing installation accuracy, calibration measure must be taked to calibrate processing composition error, feeder line passage composition error are installed.

By Wanfang Database, domestic open academic journal, academic dissertation, meeting paper, patent, standard, regulation etc. are retrieved, search condition is: cql: // interfere and (angle measurement or direction finding) and (calibration or corrects), retrieve the document that 45 sections of conditions are relevant altogether; By to defense S & T information Resource service system (DTIRSS, Defence Technology Information Resources Service System) retrieve, this service system comprises IEL, Elsevier, EI, Springer, AD database, NASA database, DE database etc., search condition is interferometer+ quadratic search (Direction Finding or angle measuring)+quadratic search calibration, retrieves 7 sections of condition pertinent literatures altogether.

Recognize from domestic and international open source literature retrieval, interferometer array calibration steps is broadly divided into following a few class:

1) only consider passage sensor gain and phase uncertainties, or regard center of antenna position deviation and the error synthesis of passage amplitude phase unbalance as passage sensor gain and phase uncertainties and carry out measuring or estimating, form calibration parameter or correction card.Concrete, the method comprises and arranges reference channel and compare method, Measurement and calibration table method, the width phase parameter estimation technique, and wherein the width phase parameter estimation technique comprises again correlation method, FFT method, least square method etc.Although above-mentioned concrete grammar is different, but common ground only considers channel amplitude and phase information, when antenna misalignment ideal position and after can not ignore, inter-channel phase error can change along with the change of signal incident angle, now, this method only considering calibration of amplitude and phase is just no longer accurate; These class methods can not assess the processing installation composition error of bay in addition.Typical case's document is as follows:

[1] Cui Yuxin. multi-channel digital interferometer direction finding receiver phase Design of Calibration System [J]. marine electronic resists, and 2010,33 (1)

[2] Ding Yikai. interferometer channel error corrects and signal acquisition circuit design [D]. Xian Electronics Science and Technology University, 2010.

[3] Zhang Haiyan. the research of Five-channel phase-interfer-ometer direction-finding and realization [D] (correlation method calibration, the calibration of FFT method, the calibration of LS method). Chengdu University of Technology, 2004.

[4] Chen Junhua. circle battle array interferometer direction finding technology [D]. Shanghai Communications University, 2008.

[5] season weighs. the realization [J] of reconnaissance system for radar near filed phase bearing calibration. and aerospace electronic warfare, 2013,29 (5)

[6] Wen Fuzhong, Li Bo. the phase equalization bearing calibration [J] of Multi-channel interferometer direction finding. electronic information countermeasure techniques, 2012,27 (2)

[7] hair tiger, Yang Jianbo, Liu Peng. the interferometer direction finding state of the art and developmental research [J]. electronic information countermeasure techniques, 2010,25 (6)

[8] Guo Fang. many channel receivers broadband alignment technique research and implementation [D]. University of Electronic Science and Technology, 1999.

[9]Schneider,Stephen?W.The?Calibration?of?Four-Arm?Spiral?Modal?Measurements?for?Angle-of-Arrival?Determination?(Preprint).AD?Report，2006?JUL.

[10]HAN?Yue-tao.Multi-baseline?interferometer?broadband?real-time?phase?calibration?method.2011?4th?International?Congress?on?Image?and?Signal?Processing.

2) center of antenna and passage amplitude phase unbalance error are demarcated respectively.First to antenna phase center independent measurement, obtain the position of its phase center, then postpone to calibrate to channel phases.These class methods depend on the Accurate Calibration to bay phase center, and after antenna array completes, the relative position of each antenna also depends on its installation site, if group is after battle array completes, then demarcate, are often limited by antenna feeder and passage, are unfavorable for implementing.Typical case's document is as follows:

[1] Feng Xiaoyu. the Research on Calibration Technology [D] of interferometer direction finding. Xian Electronics Science and Technology University, 2012.

[2] Wang Yuwen. wide-band ratio width adds interferometer direction finding antenna array [D]. University of Electronic Science and Technology, 1999.

3) signal source that incident direction is known is set, calculates lubber line error, realize calibrating interferometer.The background of pertinent literature revises the baseline vector error in the application of Long baselines (km magnitude) interferometer, and method is by arranging fixing derived reference signal, and this method needs the incident direction by miscellaneous equipment or means precision calibration signal.Typical case's document is as follows:

[1] Zhong Danxing, Yang Zhengbin, Monday the .LBI direction detecting positioning system such as space many calibrations source correcting algorithm [J]. systems engineering and electronic technology, 2008,30 (5)

[2] Li Yuxing, Li Yanjie, Wang Pei. interferometer system error analysis and correction [A]. the tenth academic nd Annual Meeting collection [C] .2008. of national radar

4) a kind of special linear array interferometer is described in the document of the people such as Kawase, this interferometer is made up of three pairs of antennas, first pair of astronomical cycle is on rotating mechanism, for echo signal being reflexed to middle second pair of antenna, signal reflex is entered last on receiving antenna by second pair of antenna again, rotate first pair of antenna with certain stepping, rotate a circle the phase difference measurements system of equations that just can obtain containing error, can obtain interferometer system error by solving it.When document method implements calibration, first need the position angle and the angle of pitch that are obtained incident target by optical telescope; Secondly the difference error that document is considered comprises the droop error of the error in length of first pair of antenna pivot arm, anglec of rotation error and the surfaces of revolution, due to three pairs of antennas successively will be experienced, incoming signal transmission path model is different from general interferometer, and therefore its error model is not suitable for general interferometer; Do not provide further angle measurement correction algorithm after Access to publication error term, do not point out how to eliminate orientation and pitch error coupled problem in interference angle measuring algorithm.Pertinent literature is as follows:

[1]Kawase,Seiichiro.Radio-interferometer?for?monitoring?orbital-resource?congestion.ICSSC.Japan,April?15-19,2003.

5) based on the array calibration technology of Estimation of Spatial Spectrum, obtain in " Estimation of Spatial Spectrum theoretical and algorithm " book that this technology is shown at Wang Yongliang etc. and comparatively comprehensively sum up, these calibration algorithms include source calibration, self calibration and the collimation technique based on auxiliary array element, these algorithms can by Ro-vibrational population, phase position error and array element mutual coupling error etc. are brought in Estimation of Spatial Spectrum model, subspace and signal space characteristic etc. is utilized to carry out estimation calibration, these collimation technique basic theories are Estimation of Spatial Spectrum technology, the data used are sampling snaps of fixing information source incident direction, in addition for non-homogeneous array element of structuring the formation, Power estimation technology could be used after generally needing pre-service.Typical case's document is as follows:

[1] work such as Wang Yongliang, Chen Hui. Estimation of Spatial Spectrum theory and algorithm. publishing house of Tsing-Hua University, 2004.

[2] Chen Juan. based on modeling and interferometer direction finding algorithm research (passive calibration) [D] of the satellite reconaissance link of ADS. University of Electronic Science and Technology, 2009.

[3] Wang Lei. based on the radio communication reconnaissance system key technology research [D] of Array Signal Processing. China Science & Technology University, 2005.

[4] first duckweed. based on the passive radar direction finding technology [D] of broadband system. Harbin Engineering University, 2011.

[5] burnt strong. satellite communication system interference source DOA estimation method research [D]. Harbin Institute of Technology, 2008.

[6] Zhang Weihua. communication direction finding modeling and simulation research [D]. the National University of Defense Technology, 2005.

[7] Zhang Yaguang. array received signal imitation and DOA algorithm for estimating are studied [D]. University of Electronic Science and Technology, 2009.

Summary of the invention

The technical matters that the present invention solves is: install composition error and feeder line passage composition error to obtain interferometer array processing simultaneously, seek a kind of without Accurate Calibration incoming signal direction, without the interferometer array calibration steps of Estimation of Spatial Spectrum technology; Meanwhile, also need to seek a kind of angle calibration system method that effectively can utilize interferometer array calibration result, the method needs to overcome azimuthal error and pitch error when angle measurement is resolved and to intercouple problem, eliminates interferometer array processing and installs composition error and feeder line passage composition error to the impact of angle measurement accuracy.The invention provides a kind of interferometer array integrated correction method, can solve the technical problem, the present invention does not need the incident direction of accurate known signal, do not need to adopt Estimation of Spatial Spectrum technology yet, the present invention is basic known quantity with the anglec of rotation, first by signal original incident direction, composition error and feeder line passage composition error parametrization are simultaneously installed in processing, secondly rotary antenna battle array obtains and measures system of equations, then error parameter and incoming signal direction is obtained by parameter estimation, finally error parameter correction is entered to interfere angle measurement formula, pass through iterative technique, overcome azimuthal error and pitch error to intercouple problem, thus obtain the angle after close adjustment.

The technical scheme that the present invention solves is: a kind of interferometer array integrated correction method, comprises the error model stage of setting up, obtains the measurement equation stage, solve the error parameter stage and obtain the angle measurement calibration result stage;

It is described that to set up error model stage etch as follows:

(1) on interferometer front, set up surving coordinate system, to choose on interferometer front an array element as interferometer measurement coordinate origin O, using desirable azimuth reference datum as Y-axis, using desirable pitching baseline as Z axis, by right-hand rule determination X-axis; The angle in objective definition incident direction and XOY face is pitching angle theta, and the angle in the projection of objective definition incident direction in XOY plane and XOZ face is position angle φ;

(2) in the interferometer measurement coordinate system set up in described step (1), if target original incident position angle is φ ₀, the original incident angle of pitch is θ ₀; If total M array element in interferometer array, 0th array element is positioned at initial point O place, i-th array element is arranged in desirable orientation baseline, and a jth array element is arranged in desirable pitching baseline, i, j=1,2 ..., M-1 and i ≠ j, there is the processing installation composition error in X-axis, Y-axis, Z axis three directions relative to ideal position in the i-th array element, is respectively Δ x _i, Δ y _i, Δ z _i, jth array element relative to ideal position exist X-axis, Y-axis, Z axis three directions processing install composition error be respectively Δ x _j, Δ y _j, Δ z _j; In addition, the Received signal strength of each array element enters interferometer signal processor by respective feeder line passage, strictly not isometric between feeder line passage, if with the feeder line passage of the 0th array element for reference length, then by i-th, the feeder line passage of j array element is set to Δ d respectively relative to the feeder line passage composition error of the 0th array element _i, Δ d _j; Respectively by Δ x _i, Δ y _i, Δ z _i, Δ d _i, θ ₀, φ ₀, Δ x _j, Δ y _j, Δ z _j, Δ d _j, θ ₀, φ ₀as six unknown parameters of azimuth reference datum, pitching baseline, set up the phase eikonal equation of interferometer azimuth reference datum, pitching baseline:

In formula, i, j=1,2 ..., M-1 and i ≠ j, L _ibe the i-th array element azimuth reference datum design length, L _jfor jth array element pitching baseline design length, for the interferometer phase aberration measurements of azimuth reference datum, for the interferometer phase aberration measurements of pitching baseline, λ is the wavelength of incoming signal;

(3) interferometer be arranged on elaborate servo mechanism or be erected on precise rotating platform, by adjusting the position of interferometer, the Z axis of the interferometer measurement coordinate system that described step (1) is set up overlaps with the direction rotating shaft of elaborate servo mechanism or precise rotating platform, the Y-axis of interferometer measurement coordinate system that described step (1) is set up and the pitching shaft parallel of elaborate servo mechanism or precise rotating platform; Keep target incident direction constant, make interferometer respectively around surving coordinate system Z axis and Y-axis anglec of rotation δ φ, δ θ, after coordinate conversion, by the interferometer azimuth reference datum phase eikonal equation in described step (2) and pitching baseline phase eikonal equation, by rotation of coordinate, obtaining take rotation amount δ φ, δ θ as azimuth reference datum, the pitching baseline six parameter phase difference model of basic known quantity:

In formula, i, j=1,2 ..., M-1 and i ≠ j;

It is as follows that equation stage etch is measured in described acquisition:

(4) control servo control mechanism or turntable rotate δ φ successively _k, δ θ _kaccurate step angle, k represents that kth time rotates, and 0≤k≤N-1, N represents number of revolutions, N>=0, resident certain hour on each step angle, gathers the interferometer phase aberration measurements that described current accurate step angle is corresponding;

(5) the interferometer phase aberration measurements gathered in every section of residence time in described step (4) is averaged, obtain corresponding step angle upper position baseline phase aberration measurements pitching baseline phase aberration measurements

(6) described step (5) is processed the phase aberration measurements obtained substitute into azimuth reference datum, pitching baseline six parameter phase difference model in described step (3), obtain azimuth reference datum, the non-linear six parameter phase difference measurements system of equations of pitching baseline:

In formula, i, j=1,2 ..., M-1 and i ≠ j, x _i=[Δ x _i, Δ y _i, Δ z _i, Δ d _i, θ ₀, φ ₀] ^trepresent the parameter that the i-th array element is to be asked, x _j=[Δ x _j, Δ y _j, Δ z _j, Δ d _j, θ ₀, φ ₀] ^trepresent the parameter that jth array element is to be asked, w _ik, w _jkrepresent the measurement noises that difference collection is introduced; represent respectively and walk postrotational azimuth reference datum, pitching baseline six parameter phase eikonal equation through k, form is as follows:

In formula, 0≤k≤N-1, l represents the l time rotation, 0≤l≤k, δ φ _lbe the l time orientation to accurate step angle, δ θ _lbe that the l time pitching is to accurate step angle;

It is described that to solve error parameter stage etch as follows:

(7) non-linear six parameter phase difference measurements system of equations step (6) obtained, at initial value x _i0, x _j0place's linearization, to x in the i-th array element _iinitialize x _i0, x _i0=[Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, θ ₀₀, φ ₀₀] ^t, wherein Δ x _i0, Δ y _i0, Δ z _i0the initial value of composition error is installed in processing for X-axis, Y-axis, Z axis three directions, Δ d _i0for the initial value of feeder line passage composition error, θ ₀₀for the initial value of pitching initial incidence angle, φ ₀₀for the initial value of orientation initial incidence angle, at initial value x _i0place carries out first order Taylor expansion to the non-linear six parameter phase difference measurements system of equations of azimuth reference datum in described step (6), obtains azimuth reference datum lienarized equation group, is write as vector form:

Α in formula _ifor first-order partial derivative matrix, form is as follows:

for difference residual error, form is as follows:

Dx _ifor initial value x _i0correction; w _i=[w _i0, w _i1... w _iN-1] ^tfor measurement noises;

In like manner, to x in jth array element _jinitialize x _j0, x _j0=[Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, θ ₀₀, φ ₀₀] ^t, wherein Δ x _j0, Δ y _j0, Δ z _j0the initial value of composition error is installed in processing for X-axis, Y-axis, Z axis three directions, Δ d _j0for the initial value of feeder line passage composition error, θ ₀₀for the initial value of pitching initial incidence angle, φ ₀₀for the initial value of orientation initial incidence angle, at x _j0place carries out first order Taylor expansion to the non-linear six parameter phase difference measurements system of equations of pitching baseline in described step (6), obtains pitching baseline lienarized equation group, is write as vector form:

In formula, Α _jfor first-order partial derivative matrix, form is as follows:

for difference residual error, form is as follows:

Dx _jfor initial value x _j0correction, i, j=1,2 ..., M-1 and i ≠ j; w _j=[w _j0, w _j1... w _jN-1] ^tfor measurement noises;

(8) obtain the least square solution of azimuth reference datum, pitching baseline lienarized equation group in step (7) according to weighted least-squares method, this solution is initial value x _i0, x _j0correction dx _i, dx _j:

P in formula _i, P _jfor least square weighting matrix, i, j=1,2...M-1 and i ≠ j;

(9) according to the linearization six parameter phase difference measurements solution of equations that described step (8) obtains, judge to resolve end condition, if the absolute value of least square solution | dx _i|, | dx _j| be less than the interferometer array calibration accuracy of setting, then initial value x _i0, x _j0be non-linear six parameter phase difference measurements solution of equations; If the absolute value of least square solution | dx _i|, | dx _j| be more than or equal to the interferometer array calibration accuracy of setting, utilize least square solution to initial value x _i0, x _j0revise, obtain correction x ' _i0, x ' _j0, utilize revised x ' _i0, x ' _j0x in replacement step (7) _i0, x _j0, re-execute described step (7), (8), (9), until dx _i, dx _jmeet the requirement of interferometer array calibration accuracy, initial value x _i0, x _j0correction formula as follows:

x′ _i0＝x _i0+dx _i

x′ _j0＝x _j0+dx _j

I, j=1 in formula, 2 ..., M-1 and i ≠ j;

This step finally obtains composition error item corresponding to i-th array element

X _i0=[Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, θ ₀₀, φ ₀₀] ^t, the composition error item that a jth array element is corresponding

X _j0=[Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, θ ₀₀, φ ₀₀] ^t, namely the processing of the i-th array element in X-axis, Y-axis, Z axis three directions is installed composition error and is respectively Δ x _i0, Δ y _i0, Δ z _i0, feeder line passage composition error is Δ d _i, the processing of jth array element in X-axis, Y-axis, Z axis three directions is installed composition error and is respectively Δ x _j0, Δ y _j0, Δ z _j0, feeder line passage composition error is Δ d _j;

Described acquisition angle measurement calibration result stage etch is as follows:

(10) the whole composition error item Δ x will obtained in step (9) _i0, Δ y _i0, Δ z _i0, Δ d _i0, Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, substitute into the phase difference measurements equation of the orientation of described step (3), pitching baseline, introduce noise item w during azimuth reference datum interferometry simultaneously _i, noise item w when pitching base line interference is measured _j, obtaining being with noisy take rotation amount δ φ, δ θ as azimuth reference datum, the pitching baseline six parameter phase eikonal equation of basic known quantity:

In formula, for band noisy orientation difference, pitching difference that interferometry obtains;

(11) by carrying out computing to base line interference phase level difference measurements multiple in step (10), synthesize a virtual baseline and interfere phase level difference measurements, virtual baseline after synthesis is generally not more than half wavelength lambda/2 of incoming signal, utilize the phase level difference measurements after synthesis, realize resolving without fuzzy angle measurement, for azimuth reference datum phase difference measurements equation in step (10), if i=m and i=n, m<n, 1≤m≤M-1, during 1≤n≤M-1, synthesize a short virtual baseline by computing, computing operator is H _i(), then corresponding orientation virtual baseline phase difference measurements equation is written as:

Δ x _n0, Δ y _n0, Δ z _n0, Δ d _n0, L _n, w _nrespectively during corresponding i=n Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, L _i, w _i;

Δ x _m0, Δ y _m0, Δ z _m0, Δ d _m0, L _m, w _mrespectively during corresponding i=m Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, L _i, w _i;

In like manner, for pitching baseline phase difference measurements equation in described step (10), if j=p and j=q, p<q, synthesize a short virtual baseline when 1≤p≤M-1,1≤q≤M-1, computing operator is H _j(), then write out pitching virtual baseline phase difference measurements equation:

Δ x _q0, Δ y _q0, Δ z _q0, Δ d _q0, L _q, w _qrespectively during corresponding j=q Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, L _j, w _j;

Δ x _p0, Δ y _p0, Δ z _p0, Δ d _p0, L _p, w _prespectively during corresponding j=p Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, L _j, w _j;

(12) in the orientation that step (11) obtains, pitching virtual baseline phase difference measurements equation, differ from orientation pitching differs middlely deduct 2 π H respectively _i(Δ d _n0, Δ d _m0)/λ, 2 π H _j(Δ d _q0, Δ d _p0)/λ, and will subtract each other result reduction to (-π, π] principal value interval, obtain following without integral circumference ambiguity orientation, pitching baseline phase difference measurements system of equations:

In formula <> symbol represent that reduction is arrived (-π, π] principal value interval; w ₁=H _i(w _n, w _m), w ₂=H _j(w _q, w _p); F in formula ₁(θ, φ), f ₂(θ, φ) is defined as follows:

$f_1(\mathrm{\&theta;},\mathrm{\&phi;})=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(H_i(\mathrm{\&Delta;}{x}_{n0},\mathrm{\&Delta;}{x}_{m0})\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}+(H_i(L_n,L_m)+H_i(\mathrm{\&Delta;}{y}_{n0},\mathrm{\&Delta;}{y}_{m0}))\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}+H_i(\mathrm{\&Delta;}{z}_{n0},\mathrm{\&Delta;}{z}_{m0})\sin \mathrm{\&theta;})$

$f_2(\mathrm{\&theta;},\mathrm{\&phi;})=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(H_j(\mathrm{\&Delta;}{x}_{q0},\mathrm{\&Delta;}{x}_{p0})\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}+H_j(\mathrm{\&Delta;}{y}_{q0},\mathrm{\&Delta;}{y}_{p0})\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}+(H_j(L_q,L_p)+H_j(\mathrm{\&Delta;}{z}_{q0},\mathrm{\&Delta;}{z}_{p0}))\sin \mathrm{\&theta;})$

(13) vector y=[θ, φ] is defined ^t, to y initialize y ₀, herein for angle of pitch initial value, for position angle initial value, at y ₀near to carrying out first order Taylor expansion without integral circumference ambiguity orientation, pitching baseline phase difference measurements system of equations in step (12), obtain linearization without fuzzy phase difference measurements system of equations, write as vector form:

$u\&ap;B{|}_{y=y_0}\mathrm{dy}+w$

In formula, u is that form is as follows without fuzzy phase difference measurements residual error:

B is that form is as follows without fuzzy phase difference measurements system of equations first-order partial derivative matrix:

$B=\left[\begin{array}{cc}\frac{\&PartialD;f_1\left(y\right)}{\&PartialD;\mathrm{\&theta;}}& \frac{\&PartialD;f_1\left(y\right)}{\&PartialD;\mathrm{\&phi;}}\\ \frac{\&PartialD;f_2\left(y\right)}{\&PartialD;\mathrm{\&theta;}}& \frac{\&PartialD;f_2\left(y\right)}{\&PartialD;\mathrm{\&phi;}}\end{array}\right]$

Dy=[d θ, d φ] ^trepresent y ₀correction variable; W=[w ₁, w ₂] ^tfor measurement noises;

(14) what obtain described step (13) directly inverts without fuzzy phase difference measurements system of equations, can obtain initial value y in step (13) ₀correction variable dy:

dy＝B ^-1u

(15) linearization obtained according to described step (14) is without fuzzy phase difference measurements solution of equations, judge to resolve end condition, if linearization is without the absolute value of fuzzy phase difference measurements solution of equations | dy| is less than the Interferometer angle measurement precision of permission, then initial value y ₀be non-linear without fuzzy phase difference measurements solution of equations; If linearization is without the absolute value of fuzzy phase difference measurements solution of equations | dy| is more than or equal to the Interferometer angle measurement precision of setting, utilizes dy to initial value y ₀revise, obtain modified value y ' ₀, with y ' ₀replace the initial value y in described step (13) ₀, re-execute described step (13), (14), (15), until dy meets the Interferometer angle measurement precision of setting, to initial value y ₀correction formula as follows:

y′ ₀＝y ₀+dy

This step finally obtains the Interferometer angle measurement value after calibrating namely the angle of pitch after Interferometer angle measurement calibration is position angle after calibration is

The present invention's advantage is compared with prior art:

(1) the present invention is in array error item, using array element phase heart deviation and installation deviation as a composition error item, using array element feeder line error and channel error as a composition error item, carry out parametrization simultaneously, by measuring and parameter estimation in interferometer phase, calculate composition error item, for the interferometer that frequency range is higher, as millimeter wave interferometer, its wavelength is shorter, composition error item on angle measurement accuracy impact significantly, is ignored approximate calibration method that is some or certain several error component if adopt again, can not be met the requirement of angle measurement accuracy;

(2) the present invention only needs to be arranged on turntable or servo control mechanism when starting by interferometer front, then by by certain track angle measuring interferometer front, obtains phase difference measurements equation, finally carries out mathematics manipulation and obtain composition error; This process does not need to carry out independent measurement to target incident direction, phase heart position, installation site, feeder line time delay and channel time delay etc., and manual intervention rate is low, is easy to be designed to interferometer array auto-calibration device, improves the efficiency of calibration;

(3) the present invention avoids when array calibration using nonuniform noise Estimation of Spatial Spectrum technology, and theory and the computation complexity of the array calibration technology of Estimation of Spatial Spectrum are all higher;

(4) the present invention is in order to improve angle measurement accuracy, do not need to form look-up table, but processing is installed in composition error, feeder line passage composition error substitution interference angle measurement equation, utilize alternative manner, overcome azimuthal error and pitch error to intercouple problem, and then eliminate composition error item to the impact of angle measurement accuracy.

Accompanying drawing explanation

Fig. 1 is interferometer array integrated correction method flow diagram of the present invention;

Fig. 2 is that composition error schematic diagram is installed in a kind of L-type interferometer array processing of the present invention;

Fig. 3 is a kind of L-type interferometer array of the present invention feeder line passage composition error schematic diagram;

Fig. 4 (a) is front angle Error Graph for the present invention calibrates;

Fig. 4 (b) is rear angle Error Graph for the present invention calibrates.

Embodiment

Be example below in conjunction with 5 array elements " L " the type interferometer shown in accompanying drawing 2, Fig. 3, the present invention is described in further detail, a kind of interferometer array integrated correction method as shown in Figure 1 comprises the error model stage of setting up, obtains the measurement equation stage, solves the error parameter stage and obtain the angle measurement calibration result stage, and concrete embodiment is described below:

Set up error model stage etch as follows:

(1) on interferometer front, surving coordinate system is set up.In " L " type interferometer shown in Fig. 2, to choose on interferometer front array element 0 as interferometer measurement coordinate origin O, using desirable azimuth reference datum O2 as Y-axis, using desirable pitching baseline O4 as Z axis, by right-hand rule determination X-axis; The angle in objective definition incident direction and XOY face is pitching angle theta, and the angle in the projection of objective definition incident direction in XOY plane and XOZ face is position angle φ;

(2) set up containing all orientation of composition error item, the phase eikonal equation of pitching baseline.In the interferometer measurement coordinate system that step (1) is set up, if target original incident position angle is φ ₀, the original incident angle of pitch is θ ₀; In " L " type interferometer array shown in Fig. 2, total M=5 array element, the 0th array element is positioned at initial point O place, and i-th array element is arranged in the azimuth reference datum of Theoretical Design, and a jth array element is arranged in the pitching baseline of Theoretical Design, i=1,2, j=3,4.The i-th, there is the processing installation composition error in X-axis, Y-axis, Z axis three directions in j array element relative to Theoretical Design position, be respectively Δ x _i, Δ y _i, Δ z _i, Δ x _j, Δ y _j, Δ z _j; In addition, as shown in Figure 3, the Received signal strength of each array element enters interferometer signal processor by respective feeder line passage, strictly not isometric between feeder line passage, if with the feeder line passage of the 0th array element for reference length, then can by i-th, the feeder line passage of j array element is designated as Δ d respectively relative to the feeder line passage composition error of the 0th array element _i, Δ d _j, then can set up the phase eikonal equation of interferometer azimuth reference datum, pitching baseline:

In formula, i=1,2, j=3,4, L _ibe the i-th array element azimuth reference datum design length, L _jfor jth array element pitching baseline design length, for the interferometer phase aberration measurements of azimuth reference datum, for the interferometer phase aberration measurements of pitching baseline, λ is the wavelength of incoming signal;

(3) foundation take rotation amount as six parameter phase difference models of basic known quantity.Certain interferometer shown in Fig. 2 is arranged in elaborate servo mechanism, by adjusting the position of interferometer, the Z axis of the interferometer measurement coordinate system that step (1) is set up overlaps with elaborate servo mechanism direction rotating shaft, the Y-axis of the interferometer measurement coordinate system that step (1) is set up and elaborate servo mechanism pitching shaft parallel; Keep target incident direction constant, make interferometer respectively around surving coordinate system Z axis and Y-axis anglec of rotation δ φ, δ θ, after coordinate conversion, according to the interferometer azimuth reference datum phase eikonal equation described in step (2) and pitching baseline phase eikonal equation, obtaining take rotation amount δ φ, δ θ as azimuth reference datum, the pitching baseline six parameter phase difference model of basic known quantity:

In formula, i=1,2 j=3,4.

Obtain measurement equation stage etch as follows:

(4) control servo control mechanism or turntable rotate δ φ successively _k, δ θ _kaccurate step angle, k represents that kth time rotates, and 0≤k≤N-1, N represents number of revolutions, N>=0, resident certain hour on each step angle, gathers the interferometer phase aberration measurements that described current accurate step angle is corresponding;

(5) to phase aberration measurements average value processing.The interferometer phase aberration measurements gathered in every section of residence time in step (4) is averaged, obtains corresponding step angle upper position baseline phase aberration measurements pitching baseline phase aberration measurements

(6) non-linear six parameter phase difference measurements system of equations are obtained.Step (5) is processed the phase aberration measurements obtained substitute into azimuth reference datum, pitching baseline six parameter phase difference model in step (3), obtain azimuth reference datum, the non-linear six parameter phase difference measurements system of equations of pitching baseline:

In formula, i=1,2 j=3,4, x _i=[Δ x _i, Δ y _i, Δ z _i, Δ d _i, θ ₀, φ ₀] ^trepresent the parameter that the i-th array element is to be asked, x _j=[Δ x _j, Δ y _j, Δ z _j, Δ d _j, θ ₀, φ ₀] ^trepresent the parameter that jth array element is to be asked, w _ik, w _jkrepresent the measurement noises that difference collection is introduced; represent respectively and walk postrotational azimuth reference datum, pitching baseline six parameter phase eikonal equation through k, form is as follows:

In formula, 0≤k≤N-1, l represents the l time rotation, 0≤l≤k, δ φ _lbe the l time orientation to accurate step angle, δ θ _lbe that the l time pitching is to accurate step angle;

It is described that to solve error parameter stage etch as follows:

(7) at initial value x _i0, x _j0place is by non-linear six parameter phase difference measurements system of equations linearizations.Non-linear six parameter phase difference measurements system of equations step (6) obtained, at initial value x _i0, x _j0place's linearization, to x in the i-th array element _iinitialize x _i0, x _i0=[Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, θ ₀₀, φ ₀₀] ^t, wherein Δ x _i0, Δ y _i0, Δ z _i0the initial value of composition error is installed in processing for X-axis, Y-axis, Z axis three directions, Δ d _i0for the initial value of feeder line passage composition error, θ ₀₀for the initial value of pitching initial incidence angle, φ ₀₀for the initial value of orientation initial incidence angle, at initial value x _i0place carries out first order Taylor expansion to the non-linear six parameter phase difference measurements system of equations of azimuth reference datum in described step (6), obtains azimuth reference datum lienarized equation group, is write as vector form:

Α in formula _ifor first-order partial derivative matrix, form is as follows:

for difference residual error, form is as follows:

Dx _ifor initial value x _i0correction; w _i=[w _i0, w _i1... w _iN-1] ^tfor measurement noises.

In like manner, to x in jth array element _jinitialize x _j0, x _j0=[Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, θ ₀₀, φ ₀₀] ^t, wherein Δ x _j0, Δ y _j0, Δ z _j0the initial value of composition error is installed in processing for X-axis, Y-axis, Z axis three directions, Δ d _j0for the initial value of feeder line passage composition error, θ ₀₀for the initial value of pitching initial incidence angle, φ ₀₀for the initial value of orientation initial incidence angle, at x _j0place carries out first order Taylor expansion to the non-linear six parameter phase difference measurements system of equations of pitching baseline in described step (6), obtains pitching baseline lienarized equation group, is write as vector form:

In formula, Α _jfor first-order partial derivative matrix, form is as follows:

for difference residual error, form is as follows:

Dx _jfor initial value x _j0correction, w _j=[w _j0, w _j1... w _jN-1] ^tfor measurement noises, i=1,2j=3 in formula, 4;

(8) least square solution of linearization six parameter phase difference measurements system of equations is asked.Initial value x in (7) is obtained according to weighted least-squares method _i0, x _j0correction dx _i, dx _j:

P in formula _i, P _jfor least square weighting matrix, i=1,2 j=3,4.

(9) if the absolute value of least square solution | dx _i|, | dx _j| be less than the interferometer array calibration accuracy of setting, then initial value x _i0, x _j0be non-linear six parameter phase difference measurements solution of equations; If the absolute value of least square solution | dx _i|, | dx _j| be more than or equal to the interferometer array calibration accuracy of setting, utilize least square solution to initial value x _i0, x _j0revise, obtain correction x ' _i0, x ' _j0, utilize revised x ' _i0, x ' _j0x in replacement step (7) _i0, x _j0, re-execute described step (7), (8), (9), until dx _i, dx _jmeet the requirement of interferometer array calibration accuracy.Initial value x _i0, x _j0correction formula as follows:

x′ _i0＝x _i0+dx _i

x′ _j0＝x _j0+dx _j

In formula, i=1,2 j=3,4;

This step finally obtains composition error item x corresponding to i-th array element _i0=[Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, θ ₀₀, φ ₀₀] ^t, the composition error item x that a jth array element is corresponding _j0=[Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, θ ₀₀, φ ₀₀] ^t, namely the processing of the i-th array element in X-axis, Y-axis, Z axis three directions is installed composition error and is respectively Δ x _i0, Δ y _i0, Δ z _i0, feeder line passage composition error is Δ d _i, the processing of jth array element in X-axis, Y-axis, Z axis three directions is installed composition error and is respectively Δ x _j0, Δ y _j0, Δ z _j0, feeder line passage composition error is Δ d _j;

Described calibration angle measurement result stage etch is as follows:

(10) the whole composition error item Δ x will obtained in step (9) _i0, Δ y _i0, Δ z _i0, Δ d _i0, Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, substitute into the phase difference measurements equation of the orientation of described step (3), pitching baseline, introduce noise item w during azimuth reference datum interferometry simultaneously _i, noise item w when pitching base line interference is measured _j, obtaining being with noisy take rotation amount δ φ, δ θ as azimuth reference datum, the pitching baseline six parameter phase eikonal equation of basic known quantity:

In formula, for orientation difference, pitching difference that interferometry obtains;

(11) orientation, pitching virtual baseline phase difference measurements system of equations is obtained.By interfering phase level difference measurements to carry out arithmetical operation to multiple Long baselines, synthesizing a Short baseline and interfering phase level difference measurements, utilizing this result, can realize resolving without fuzzy angle measurement.

As shown in Figure 2, for azimuth reference datum, if by arithmetical operation H when i=m and i=n, m=1, n=2 _i(L _n, L _m) a synthesis short virtual baseline L _n-2L _m, now can according to operator H _i() writes out orientation virtual baseline phase difference measurements equation:

In like manner, for pitching baseline, if by arithmetical operation H when j=p and j=q, p=3, q=4 _j(L _q, L _p) a synthesis short virtual baseline L _q-2L _p, now can according to operator H _j() writes out pitching virtual baseline phase difference measurements equation:

(12) deduct the impact of feeder line channel error, and will differ reduction to (-π, π] principal value interval, obtain non-linear without fuzzy phase difference measurements system of equations.From the phase difference measurements equation of the orientation that step (11) obtains, pitching baseline, deduction feeder line passage composition error Δ d _n0, Δ d _m0, Δ d _q0, Δ d _p0impact, namely differ from orientation pitching differs middlely deduct 2 π (Δ d respectively _n0-2 Δ d _m0)/λ, 2 π (Δ d _q0-2 Δ d _p0)/λ, and by result of calculation reduction to (-π, π] principal value interval, obtain following without integral circumference ambiguity orientation, pitching baseline phase difference measurements system of equations:

In formula <> symbol represent that reduction is arrived (-π, π] principal value interval; w ₁=w _n-2w _m, w ₂=w _q-2w _p; F in formula ₁(θ, φ), f ₂(θ, φ) is defined as follows:

$f_1(\mathrm{\&theta;},\mathrm{\&phi;})=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}((\mathrm{\&Delta;}{x}_{n0}-2\mathrm{\&Delta;}{x}_{m0})\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}+((L_n-2L_m)+(\mathrm{\&Delta;}{y}_{n0}-2\mathrm{\&Delta;}{y}_{m0}))\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}++(\mathrm{\&Delta;}{z}_{n0}-2\mathrm{\&Delta;}{z}_{m0})\sin \mathrm{\&theta;})$

$f_2(\mathrm{\&theta;},\mathrm{\&phi;})=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}((\mathrm{\&Delta;}{x}_{q0}-2\mathrm{\&Delta;}{x}_{p0})\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}+(\mathrm{\&Delta;}{y}_{q0}-2\mathrm{\&Delta;}{y}_{p0})\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}+((L_q-2L_p)+(\mathrm{\&Delta;}{z}_{q0}-2\mathrm{\&Delta;}{z}_{p0}))\sin \mathrm{\&theta;})$

(13) vector y=[θ, φ] is defined ^t, to y initialize y ₀, herein for angle of pitch initial value, for position angle initial value, at y ₀near to carrying out first order Taylor expansion without integral circumference ambiguity orientation, pitching baseline phase difference measurements system of equations in step (12), obtain linearization without fuzzy phase difference measurements system of equations, write as vector form:

$u\&ap;B{|}_{y=y_0}\mathrm{dy}+w$

In formula, u is that form is as follows without fuzzy phase difference measurements residual error:

B is that form is as follows without fuzzy phase difference measurements system of equations first-order partial derivative matrix:

$B=\left[\begin{array}{cc}\frac{\&PartialD;f_1\left(y\right)}{\&PartialD;\mathrm{\&theta;}}& \frac{\&PartialD;f_1\left(y\right)}{\&PartialD;\mathrm{\&phi;}}\\ \frac{\&PartialD;f_2\left(y\right)}{\&PartialD;\mathrm{\&theta;}}& \frac{\&PartialD;f_2\left(y\right)}{\&PartialD;\mathrm{\&phi;}}\end{array}\right]$

Dy=[d θ, d φ] ^trepresent y ₀correction variable; W=[w ₁, w ₂] ^tfor measurement noises;

(14) what obtain described step (13) directly inverts without fuzzy phase difference measurements system of equations, can obtain initial value y in step (13) ₀correction variable dy:

dy＝B ^-1u

(15) linearization obtained according to described step (14) is without fuzzy phase difference measurements solution of equations, judge to resolve end condition, if linearization is without the absolute value of fuzzy phase difference measurements solution of equations | dy| is less than the Interferometer angle measurement precision of permission, then initial value y ₀be non-linear without fuzzy phase difference measurements solution of equations; If linearization is without the absolute value of fuzzy phase difference measurements solution of equations | dy| is more than or equal to the Interferometer angle measurement precision of setting, utilizes dy to initial value y ₀revise, obtain modified value y ' ₀, with y ' ₀replace the initial value y in described step (13) ₀, re-execute described step (13), (14), (15), until dy meets the Interferometer angle measurement precision of setting.To initial value y ₀correction formula as follows:

y′ ₀＝y ₀+dy

This step finally obtains the Interferometer angle measurement value after calibrating namely the angle of pitch after Interferometer angle measurement calibration is position angle after calibration is

The random survey phase error of certain millimeter wave interferometer is about 20 °, the data phase aberration measurements of each stepping point being performed to about 5 seconds are average, the difference is smoothly utilized to carry out array calibration, after obtaining interferometer composition error item, utilize described angle measurement calibration algorithm, eliminate array element processing and composition error, systematic error caused by passage feeder line disparity error are installed, interfered angle measurement result accurately.When not calibrating interferometer, as shown in accompanying drawing 4a, there is obvious system deviation (1 ° of magnitude) in angle measurement result, this angle measurement result cannot be applied in real work; After calibrating interferometer as depicted in fig. 4b, angle measurement result is without obvious system deviation, and show as very little stochastic error (0.01 ° of magnitude), this angle measurement accuracy can meet interferometer real work demand.

Non-elaborated part of the present invention belongs to techniques well known.

Claims (1)

1. an interferometer array integrated correction method, is characterized in that: comprise the error model stage of setting up, obtain the measurement equation stage, solve the error parameter stage and obtain the angle measurement calibration result stage;

It is described that to set up error model stage etch as follows:

(1) on interferometer front, set up surving coordinate system, to choose on interferometer front an array element as interferometer measurement coordinate origin O, using desirable azimuth reference datum as Y-axis, using desirable pitching baseline as Z axis, by right-hand rule determination X-axis; The angle in objective definition incident direction and XOY face is pitching angle theta, and the angle in the projection of objective definition incident direction in XOY plane and XOZ face is position angle φ;

(2) in the interferometer measurement coordinate system set up in described step (1), if target original incident position angle is φ ₀, the original incident angle of pitch is θ ₀; If total M array element in interferometer array, 0th array element is positioned at initial point O place, i-th array element is arranged in desirable orientation baseline, and a jth array element is arranged in desirable pitching baseline, i, j=1,2 ..., M-1 and i ≠ j, there is the processing installation composition error in X-axis, Y-axis, Z axis three directions relative to ideal position in the i-th array element, is respectively Δ x _i, Δ y _i, Δ z _i, jth array element relative to ideal position exist X-axis, Y-axis, Z axis three directions processing install composition error be respectively Δ x _j, Δ y _j, Δ z _j; In addition, the Received signal strength of each array element enters interferometer signal processor by respective feeder line passage, strictly not isometric between feeder line passage, if with the feeder line passage of the 0th array element for reference length, then by i-th, the feeder line passage of j array element is set to Δ d respectively relative to the feeder line passage composition error of the 0th array element _i, Δ d _j; Respectively by Δ x _i, Δ y _i, Δ z _i, Δ d _i, θ ₀, φ ₀, Δ x _j, Δ y _j, Δ z _j, Δ d _j, θ ₀, φ ₀as six unknown parameters of azimuth reference datum, pitching baseline, set up the phase eikonal equation of interferometer azimuth reference datum, pitching baseline:

In formula, i, j=1,2 ..., M-1 and i ≠ j, L _ibe the i-th array element azimuth reference datum design length, L _jfor jth array element pitching baseline design length, for the interferometer phase aberration measurements of azimuth reference datum, for the interferometer phase aberration measurements of pitching baseline, λ is the wavelength of incoming signal;

(3) interferometer be arranged on elaborate servo mechanism or be erected on precise rotating platform, by adjusting the position of interferometer, the Z axis of the interferometer measurement coordinate system that described step (1) is set up overlaps with the direction rotating shaft of elaborate servo mechanism or precise rotating platform, the Y-axis of interferometer measurement coordinate system that described step (1) is set up and the pitching shaft parallel of elaborate servo mechanism or precise rotating platform; Keep target incident direction constant, make interferometer respectively around surving coordinate system Z axis and Y-axis anglec of rotation δ φ, δ θ, after coordinate conversion, by the interferometer azimuth reference datum phase eikonal equation in described step (2) and pitching baseline phase eikonal equation, by rotation of coordinate, obtaining take rotation amount δ φ, δ θ as azimuth reference datum, the pitching baseline six parameter phase difference model of basic known quantity:

In formula, i, j=1,2 ..., M-1 and i ≠ j;

It is as follows that equation stage etch is measured in described acquisition:

(4) control servo control mechanism or turntable rotate δ φ successively _k, δ θ _kaccurate step angle, k represents that kth time rotates, and 0≤k≤N-1, N represents number of revolutions, N>=0, resident certain hour on each step angle, gathers the interferometer phase aberration measurements that described current accurate step angle is corresponding;

(5) the interferometer phase aberration measurements gathered in every section of residence time in described step (4) is averaged, obtain corresponding step angle upper position baseline phase aberration measurements pitching baseline phase aberration measurements

(6) described step (5) is processed the phase aberration measurements obtained substitute into azimuth reference datum, pitching baseline six parameter phase difference model in described step (3), obtain azimuth reference datum, the non-linear six parameter phase difference measurements system of equations of pitching baseline:

In formula, i, j=1,2 ..., M-1 and i ≠ j, x _i=[Δ x _i, Δ y _i, Δ z _i, Δ d _i, θ ₀, φ ₀] ^trepresent the parameter that the i-th array element is to be asked, x _j=[Δ x _j, Δ y _j, Δ z _j, Δ d _j, θ ₀, φ ₀] ^trepresent the parameter that jth array element is to be asked, w _ik, w _jkrepresent the measurement noises that difference collection is introduced; represent respectively and walk postrotational azimuth reference datum, pitching baseline six parameter phase eikonal equation through k, form is as follows:

In formula, 0≤k≤N-1, l represents the l time rotation, 0≤l≤k, δ φ _lbe the l time orientation to accurate step angle, δ θ _lbe that the l time pitching is to accurate step angle;

It is described that to solve error parameter stage etch as follows:

(7) non-linear six parameter phase difference measurements system of equations step (6) obtained, at initial value x _i0, x _j0place's linearization, to x in the i-th array element _iinitialize x _i0, x _i0=[Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, θ ₀₀, φ ₀₀] ^t, wherein Δ x _i0, Δ y _i0, Δ z _i0the initial value of composition error is installed in processing for X-axis, Y-axis, Z axis three directions, Δ d _i0for the initial value of feeder line passage composition error, θ ₀₀for the initial value of pitching initial incidence angle, φ ₀₀for the initial value of orientation initial incidence angle, at initial value x _i0place carries out first order Taylor expansion to the non-linear six parameter phase difference measurements system of equations of azimuth reference datum in described step (6), obtains azimuth reference datum lienarized equation group, is write as vector form:

Α in formula _ifor first-order partial derivative matrix, form is as follows:

for difference residual error, form is as follows:

dx _ifor initial value x _i0correction;

W _i=[w _i0, w _i1... w _iN-1] ^tfor measurement noises;

In like manner, to x in jth array element _jinitialize x _j0, x _j0=[Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, θ ₀₀, φ ₀₀] ^t, wherein Δ x _j0, Δ y _j0, Δ z _j0the initial value of composition error is installed in processing for X-axis, Y-axis, Z axis three directions, Δ d _j0for the initial value of feeder line passage composition error, θ ₀₀for the initial value of pitching initial incidence angle, φ ₀₀for the initial value of orientation initial incidence angle, at x _j0place carries out first order Taylor expansion to the non-linear six parameter phase difference measurements system of equations of pitching baseline in described step (6), obtains pitching baseline lienarized equation group, is write as vector form:

In formula, Α _jfor first-order partial derivative matrix, form is as follows:

for difference residual error, form is as follows:

Dx _jfor initial value x _j0correction, i, j=1,2 ..., M-1 and i ≠ j; w _j=[w _j0, w _j1... w _jN-1] ^tfor measurement noises;

(8) obtain the least square solution of azimuth reference datum, pitching baseline lienarized equation group in step (7) according to weighted least-squares method, this solution is initial value x _i0, x _j0correction dx _i, dx _j:

P in formula _i, P _jfor least square weighting matrix, i, j=1,2...M-1 and i ≠ j;

(9) according to the linearization six parameter phase difference measurements solution of equations that described step (8) obtains, judge to resolve end condition, if the absolute value of least square solution | dx _i|, | dx _j| be less than the interferometer array calibration accuracy of setting, then initial value x _i0, x _j0be non-linear six parameter phase difference measurements solution of equations; If the absolute value of least square solution | dx _i|, | dx _j| be more than or equal to the interferometer array calibration accuracy of setting, utilize least square solution to initial value x _i0, x _j0revise, obtain correction x ' _i0, x ' _j0, utilize revised x ' _i0, x ' _j0x in replacement step (7) _i0, x _j0, re-execute described step (7), (8), (9), until dx _i, dx _jmeet the requirement of interferometer array calibration accuracy, initial value x _i0, x _j0correction formula as follows:

x′ _i0＝x _i0+dx _i

x′ _j0＝x _j0+dx _j

I, j=1 in formula, 2 ..., M-1 and i ≠ j;

This step finally obtains composition error item corresponding to i-th array element

X _i0=[Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, θ ₀₀, φ ₀₀] ^t, the composition error item that a jth array element is corresponding

X _j0=[Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, θ ₀₀, φ ₀₀] ^t, namely the processing of the i-th array element in X-axis, Y-axis, Z axis three directions is installed composition error and is respectively Δ x _i0, Δ y _i0, Δ z _i0, feeder line passage composition error is Δ d _i, the processing of jth array element in X-axis, Y-axis, Z axis three directions is installed composition error and is respectively Δ x _j0, Δ y _j0, Δ z _j0, feeder line passage composition error is Δ d _j;

Described acquisition angle measurement calibration result stage etch is as follows:

(10) the whole composition error item Δ x will obtained in step (9) _i0, Δ y _i0, Δ z _i0, Δ d _i0, Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, substitute into the phase difference measurements equation of the orientation of described step (3), pitching baseline, introduce noise item w during azimuth reference datum interferometry simultaneously _i, noise item w when pitching base line interference is measured _j, obtaining being with noisy take rotation amount δ φ, δ θ as azimuth reference datum, the pitching baseline six parameter phase eikonal equation of basic known quantity:

In formula, for band noisy orientation difference, pitching difference that interferometry obtains;

(11) by carrying out computing to base line interference phase level difference measurements multiple in step (10), synthesize a virtual baseline and interfere phase level difference measurements, virtual baseline after synthesis is generally not more than half wavelength lambda/2 of incoming signal, utilize the phase level difference measurements after synthesis, realize resolving without fuzzy angle measurement, for azimuth reference datum phase difference measurements equation in step (10), if i=m and i=n, m<n, 1≤m≤M-1, during 1≤n≤M-1, synthesize a short virtual baseline by computing, computing operator is H _i(), then corresponding orientation virtual baseline phase difference measurements equation is written as:

Δ x _n0, Δ y _n0, Δ z _n0, Δ d _n0, L _n, w _nrespectively during corresponding i=n Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, L _i, w _i;

Δ x _m0, Δ y _m0, Δ z _m0, Δ d _m0, L _m, w _mrespectively during corresponding i=m Δ x _i0, Δ y _i0, Δ z _i0, Δ d _i0, L _i, w _i;

In like manner, for pitching baseline phase difference measurements equation in described step (10), if j=p and j=q, p<q, synthesize a short virtual baseline when 1≤p≤M-1,1≤q≤M-1, computing operator is H _j(), then write out pitching virtual baseline phase difference measurements equation:

Δ x _q0, Δ y _q0, Δ z _q0, Δ d _q0, L _q, w _qrespectively during corresponding j=q Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, L _j, w _j;

Δ x _p0, Δ y _p0, Δ z _p0, Δ d _p0, L _p, w _prespectively during corresponding j=p Δ x _j0, Δ y _j0, Δ z _j0, Δ d _j0, L _j, w _j;

(12) in the orientation that step (11) obtains, pitching virtual baseline phase difference measurements equation, differ from orientation pitching differs middlely deduct 2 π H respectively _i(Δ d _n0, Δ d _m0)/λ, 2 π H _j(Δ d _q0, Δ d _p0)/λ, and will subtract each other result reduction to (-π, π] principal value interval, obtain following without integral circumference ambiguity orientation, pitching baseline phase difference measurements system of equations:

In formula <> symbol represent that reduction is arrived (-π, π] principal value interval; w ₁=H _i(w _n, w _m), w ₂=H _j(w _q, w _p); F in formula ₁(θ, φ), f ₂(θ, φ) is defined as follows:

$f_1(\mathrm{\&theta;},\mathrm{\&phi;})=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(H_i({\mathrm{\&Delta;x}}_{n0},{\mathrm{\&Delta;x}}_{m0})\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}+(H_i(L_n,L_m)+H_i({\mathrm{\&Delta;y}}_{n0},{\mathrm{\&Delta;y}}_{m0}))\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}+H_i({\mathrm{\&Delta;z}}_{n0},{\mathrm{\&Delta;z}}_{m0})\sin \mathrm{\&theta;})$

$f_2(\mathrm{\&theta;},\mathrm{\&phi;})=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(H_j({\mathrm{\&Delta;x}}_{q0},{\mathrm{\&Delta;x}}_{p0})\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}+H_j({\mathrm{\&Delta;y}}_{q0},{\mathrm{\&Delta;y}}_{p0})\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}+(H_j(L_q,L_p)+H_j({\mathrm{\&Delta;z}}_{q0},{\mathrm{\&Delta;z}}_{p0}))\sin \mathrm{\&theta;})$

(13) vector y=[θ, φ] is defined ^t, to y initialize y ₀, herein for angle of pitch initial value, for position angle initial value, at y ₀near to carrying out first order Taylor expansion without integral circumference ambiguity orientation, pitching baseline phase difference measurements system of equations in step (12), obtain linearization without fuzzy phase difference measurements system of equations, write as vector form:

u≈B| _y＝y0dy+w

In formula, u is that form is as follows without fuzzy phase difference measurements residual error:

B is that form is as follows without fuzzy phase difference measurements system of equations first-order partial derivative matrix:

$B=\left[\begin{array}{cc}\frac{{\&PartialD;f}_1\left(y\right)}{\&PartialD;\mathrm{\&theta;}}& \frac{{\&PartialD;f}_1\left(y\right)}{\&PartialD;\mathrm{\&phi;}}\\ \frac{{\&PartialD;f}_2\left(y\right)}{\&PartialD;\mathrm{\&theta;}}& \frac{{\&PartialD;f}_2\left(y\right)}{\&PartialD;\mathrm{\&phi;}}\end{array}\right]$

Dy=[d θ, d φ] ^trepresent y ₀correction variable; W=[w ₁, w ₂] ^tfor measurement noises;

(14) what obtain described step (13) directly inverts without fuzzy phase difference measurements system of equations, can obtain initial value y in step (13) ₀correction variable dy:

dy＝B ^-1u

(15) linearization obtained according to described step (14) is without fuzzy phase difference measurements solution of equations, judge to resolve end condition, if linearization is without the absolute value of fuzzy phase difference measurements solution of equations | dy| is less than the Interferometer angle measurement precision of permission, then initial value y ₀be non-linear without fuzzy phase difference measurements solution of equations; If linearization is without the absolute value of fuzzy phase difference measurements solution of equations | dy| is more than or equal to the Interferometer angle measurement precision of setting, utilizes dy to initial value y ₀revise, obtain modified value y ' ₀, with y ' ₀replace the initial value y in described step (13) ₀, re-execute described step (13), (14), (15), until dy meets the Interferometer angle measurement precision of setting, to initial value y ₀correction formula as follows:

y′ ₀＝y ₀+dy

This step finally obtains the Interferometer angle measurement value after calibrating namely the angle of pitch after Interferometer angle measurement calibration is position angle after calibration is