CN103926561B - A kind of parameter estimation weights method for designing eliminated for the singular value of ultra-short baseline alignment error calibration - Google Patents

Abstract

The present invention relates to the parameter estimation weights method for designing in the alignment error calibration of a kind of ultra-short baseline.In order to be applied in the calibration of ultra short base line alignment error and effectively eliminate singular value, to improve the installation positioning precision of ultra-short baseline equipment.The coefficient matrix utilizing ultra-short baseline alignment error calibration observational equation calculates the eigenmatrix of singular value, extracts the eigenvalue of singular value from singularity characteristics matrix, and whether the data that judging characteristic value is corresponding accordingly exist unusual.Set two decision thresholds of height, quantify to be mapped as the trapezoidal weights of unusual elimination by eigenvalue, be further combined and become singular value weights elimination weight matrix.Weights are introduced in conventional ultra-short baseline alignment error calibration calculations and can effectively reduce the impact that alignment error is calibrated by singular value, improve the accuracy of calibration calculations.It is applicable to the calculating that calibrates for error of ultra-short baseline installation site deviation and setting angle deviation.

Description

A kind of parameter estimation weights method for designing eliminated for the singular value of ultra-short baseline alignment error calibration

Technical field

The present invention relates to a kind of parameter estimation weights method for designing eliminated for the singular value of ultra-short baseline alignment error calibration.

Background technology

Ultra-short baseline equipment has to pass through the systematic error that alignment error calibration correction produces due to basic matrix installation before use, it is ensured that The positioning precision of system.The alignment error calibration calculations of ultra-short baseline utilizes GPS, three kinds of data of compass and acoustics location to complete, Measurement data in reality often produces the singular value of observation because of environmental effect or equipment self-noise, such as outlier or gross error.Very The existence of different value can make the result of alignment error parameter estimation produce deviation with actual value, has a strong impact on equipment precision, therefore necessary Singular value is effectively differentiated and removes.Outlier deviation true value substantially can artificially be removed, but the hands when point wild in observation is more Dynamic removal workload is huge；Gross error is close with true value, and observation directly perceived cannot differentiate removal.Automatically differentiate so that a kind of The method differentiated and remove singular value.

Summary of the invention

It is an object of the invention to provide a kind of parameter estimation weights design eliminated for the singular value of ultra-short baseline alignment error calibration Method, can be applied in the calibration of ultra short base line alignment error and effectively to eliminate singular value, to improve ultra-short baseline equipment Installation positioning precision.

The present invention solves that above-mentioned technical problem adopts the technical scheme that:

(1) ultra-short baseline alignment error calibration observation data and observational equation thereof is utilized to calculate singularity characteristics matrix Ω, Γ；

(2) singular eigenvalue problem is calculated according to the eigenmatrix in step (1)；

(3) calculate each group of singular value corresponding to observation data according to singular eigenvalue problem in step (2) and eliminate weights；

(4) each weighed combination in step (3) becomes singular value eliminate weight matrix, introduces the calibration of ultra-short baseline alignment error In calculating, eliminate the singular value impact on calibration result.

In step (1), the method for described calculating singularity characteristics matrix is:

WhereinFor the coefficient matrix after ultra-short baseline alignment error observational equation linearisation,See for ultra-short baseline alignment error Survey the parameter matrix after equation linearisation,It is the singularity characteristics matrix of observational equation.

In step (2), described singularity characteristics value calculating method is:

${\mathrm{\θ}}_i={\mathrm{\Γ}}_i^2{(1-{\mathrm{\ω}}_{\mathrm{ii}})}^{-1},i=\mathrm{1,2}...n$

Wherein θ_iFor singular eigenvalue problem, Γ_iSingularity characteristics matrix for observational equationMiddle i-th element, ω_iiUnusual for observational equation EigenmatrixI-th element on middle leading diagonal, according to singular eigenvalue problem θ_iValue judge whether these group data exist very Different.

In step (3), the singular value that each group of described calculating observation data are corresponding eliminates the process of weights:

Set two decision threshold θ High and θ Low of height；

First determine whether θ_iWhether less than low threshold θ Low, if it is singular eigenvalue problem θ_iParameter estimation weights be 0 weights, Unusual for existing less than low threshold judgement；

Otherwise continue to judge θ_iWhether higher than high threshold θ High, if it is singular eigenvalue problem θ_iParameter estimation weights be 1 power Value, higher than high threshold judgement for without unusual；If otherwise singular eigenvalue problem θ_iParameter estimation weights be trapezoidal weights；

According to singular eigenvalue problem θ_iQuantify mapping calculation trapezoidal weights K_ii:

$K_{\mathrm{ii}}=\left\{\begin{array}{cc}0& {\mathrm{\&theta;}}_i<{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}\\ 1& {\mathrm{\&theta;}}_i>{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}\\ ({\mathrm{\&theta;}}_i-{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}){({\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}-{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}})}^{-1}& {\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}<{\mathrm{\&theta;}}_i<{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}\end{array}\right..$

In step (4), singular value eliminates the process of weight matrix introducing ultra-short baseline alignment error calibration calculations and is:

Estimate to solve in formula at ultra-short baseline alignment error calibration iterative least square, (k_iδ(i-j))_n×nIt it is the tables of data of expansion Reach formula, add weight matrixThe trapezoidal weights K wherein tried to achieve in claim_iiConstituteOn leading diagonal I element,In remaining element be 0:

The beneficial effects of the present invention is: disclosed invention using by the counted singular eigenvalue problem of singularity characteristics matrix as unusual The criterion of value, quantifies to map formation trapezoidal weights singular value in ultra-short baseline alignment error is calibrated and eliminates eigenvalue, Can effectively differentiate and reject the singular value in calibration observation data, improve calibration accuracy.

The inventive method utilizes the coefficient matrix of ultra-short baseline alignment error calibration observational equation to calculate the eigenmatrix of singular value, from Extracting the eigenvalue of singular value in singularity characteristics matrix, whether the data that judging characteristic value is corresponding accordingly exist unusual.By setting Two decision thresholds of fixed height, quantify to be mapped as the trapezoidal weights of unusual elimination by eigenvalue, are further combined and become singular value weights Eliminate weight matrix.Weights are introduced in conventional ultra-short baseline alignment error calibration calculations and can effectively reduce singular value to installing by mistake The impact of difference calibration, improves the accuracy of calibration calculations.The present invention is applicable to ultra-short baseline installation site deviation and setting angle The calculating that calibrates for error of deviation.

Accompanying drawing explanation

Fig. 1 is the FB(flow block) of the inventive method.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is described further.

A kind of parameter estimation weights method for designing eliminated for the singular value of ultra-short baseline alignment error calibration, the reality of described method Existing process is:

Step one, utilize ultra-short baseline alignment error calibration observation data and observational equation calculate singularity characteristics matrix Ω, Γ；

Step 2, according in step one eigenmatrix calculate singular eigenvalue problem；

Step 3, calculate each group of observation singular value corresponding to data according to singular eigenvalue problem in step 2 and eliminate weights；

Step 4, each weighed combination in step 3 is become singular value eliminate weight matrix, introduce ultra-short baseline alignment error calibration In calculating, eliminate the singular value impact on calibration result.

In step one, the method for described calculating singularity characteristics matrix is:

WhereinFor the coefficient matrix after ultra-short baseline alignment error observational equation linearisation,See for ultra-short baseline alignment error Survey the parameter matrix after equation linearisation,It is the singularity characteristics matrix of observational equation.

In step 2, described singularity characteristics value calculating method is:

${\mathrm{\&theta;}}_i={\mathrm{\&Gamma;}}_i^2{(1-{\mathrm{\&omega;}}_{\mathrm{ii}})}^{-1},i=\mathrm{1,2}...n$

Wherein θ_iFor singular eigenvalue problem, Γ_iSingularity characteristics matrix for observational equationMiddle i-th element, ω_iiUnusual for observational equation EigenmatrixI-th element on middle leading diagonal.According to singular eigenvalue problem θ_iValue judge whether these group data exist very Different.

In step 3, the process of the singular value elimination weights that each group of described calculating observation data are corresponding is:

Set two decision threshold θ of height_HighAnd θ_Low；

First determine whether θ_iWhether less than low threshold θ_Low, if it is singular eigenvalue problem θ_iParameter estimation weights be 0 weights, low Unusual for existing in low threshold judgement；

Otherwise continue to judge θ_iWhether higher than high threshold θ_High, if it is singular eigenvalue problem θ_iParameter estimation weights be 1 power Value, higher than high threshold judgement for without unusual；If otherwise singular eigenvalue problem θ_iParameter estimation weights be trapezoidal weights；

According to singular eigenvalue problem θ_iQuantify mapping calculation trapezoidal weights K_ii:

$K_{\mathrm{ii}}=\left\{\begin{array}{cc}0& {\mathrm{\&theta;}}_i<{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}\\ 1& {\mathrm{\&theta;}}_i>{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}\\ ({\mathrm{\&theta;}}_i-{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}){({\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}-{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}})}^{-1}& {\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}<{\mathrm{\&theta;}}_i<{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}\end{array}\right..$

In step 4, singular value eliminates the process of weight matrix introducing ultra-short baseline alignment error calibration calculations and is:

The formula that solves ((k in formula (5) is estimated at ultra-short baseline alignment error calibration iterative least square_iδ(i-j))_n×nOne is exactly The date expression of its expansion) in, add the weight matrix that claim 4 obtainsWherein in claim The trapezoidal weights K tried to achieve_iiConstituteI-th element on leading diagonal,In remaining element be 0:

The invention has the beneficial effects as follows: can effectively reject the unusual observation data of more than 70%, ultra-short baseline alignment error school Quasi-result multiplicity improves maximum 0.05 °, and system accuracy improves the highest 0.1% oblique distance.

The present invention differentiates singular value by the singular eigenvalue problem of calculating observation data, quantifies to be mapped as trapezoidal weights by singular eigenvalue problem, Substitute into the impact that can effectively eliminate singular value in the calibration of ultra-short baseline alignment error.

Estimate as it is shown in figure 1, present embodiment is the parameter eliminating the described singular value for the calibration of ultra-short baseline alignment error The process of weighted value method for designing is described in more detail:

Ultra-short baseline alignment error calibration overdetermined equation is built first with ultra-short baseline, GPS, n measurement data of compass equipment Group, its installation site or setting angle deviation calibration equation have all following form:

(1) formula is the Solving Nonlinear Equation formula of ultra-short baseline calibration observational equation, and wherein m is number of parameters to be solved (n ＞ m),For the coefficient matrix after ultra-short baseline alignment error observational equation linearisation,For ultra-short baseline alignment error observation side Parameter matrix after journey linearisation.

And then the coefficient matrix in (1) formula of utilizationWith parameter matrixThe singularity characteristics matrix of calculating observation data

Followed byN element on leading diagonal and n-dimensional vectorThe n calculating n group observation data the most corresponding is individual strange Different eigenvalue θ:

${\mathrm{\&theta;}}_i={\mathrm{\&Gamma;}}_i^2{(1-{\mathrm{\&omega;}}_{\mathrm{ii}})}^{-1},i=\mathrm{1,2}...n---\left(3\right)$

Singular eigenvalue problem θ_iValue characterize i-th group of data and there is unusual probability: θ_iThe least, there is the possibility of singular value in i-th group of data Property is the biggest, and vice versa.

Set thresholding θ_Thresh-LowWith θ_Thresh-High, it is respectively used to differentiate singular value and normal data: singular eigenvalue problem θ_iIt is higher than θ_Thresh-HighThen judge that i-th group of data, as normal data, and arranges all-pass weights to normal data；Singular eigenvalue problem θ_iIt is less than θ_Thres-hLowThen judge that i-th group of data, as singular value, and arranges complete only weights to normal data；Strange between two thresholdings Different eigenvalue, it is determined that for part singular value, and excessive weights are set, it may be assumed that

$K_{\mathrm{ii}}=\left\{\begin{array}{cc}0& {\mathrm{\&theta;}}_i<{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}\\ 1& {\mathrm{\&theta;}}_i>{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}\\ ({\mathrm{\&theta;}}_i-{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}){({\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}-{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}})}^{-1}& {\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{Low}}<{\mathrm{\&theta;}}_i<{\mathrm{\&theta;}}_{\mathrm{Thresh}-\mathrm{High}}\end{array}\right.---\left(4\right)$

The feature being distributed according to ultra-short baseline alignment error calibration observation data source error in reality, typically chooses two threshold values and is respectively θ_Thresh-High=2.7 | | Γ | |²/ rank (Ω), θ_Thresh-Low=0.3 | | Γ | |²/rank(Ω)。

So quantify singular eigenvalue problem to be mapped as estimating weights k_i, and three kinds of weights have tapered in form as shown in Figure 1. Weights k will be estimated_iCorresponding observation data der group diagonally battle array is singular value and eliminates matrix:

Unit impact response function during wherein δ () represents mathematics.

The least square that singular value elimination matrix substitution in (5) formula finally solves (1) formula ultra-short baseline Calibration equation solves In formula, weighted least-squares realizes the elimination of singular value.

Claims (3)

1. the parameter estimation weights method for designing eliminated for the singular value of ultra-short baseline alignment error calibration, it is characterised in that:

(1) ultra-short baseline alignment error calibration observation data and observational equation thereof is utilized to calculate singularity characteristics matrix

(2) singular eigenvalue problem is calculated according to the eigenmatrix in step (1)；

(3) calculate each group of singular value corresponding to observation data according to singular eigenvalue problem in step (2) and eliminate weights；

(4) each weighed combination in step (3) becomes singular value eliminate weight matrix, introduces in ultra-short baseline alignment error calibration calculations, eliminate the singular value impact on calibration result；

In step (1), the method for described calculating singularity characteristics matrix is:

WhereinFor the coefficient matrix after ultra-short baseline alignment error observational equation linearisation,For the parameter matrix after ultra-short baseline alignment error observational equation linearisation,It is the singularity characteristics matrix of observational equation；

In step (4), singular value eliminates the process of weight matrix introducing ultra-short baseline alignment error calibration calculations and is:

Estimate to solve in formula at ultra-short baseline alignment error calibration iterative least square, (k_iδ(i-j))_{n × n}It is the date expression of expansion, adds weight matrixThe trapezoidal weights K wherein tried to achieve in claim_iiConstituteI-th element on leading diagonal,In remaining element be 0:

A kind of parameter estimation weights method for designing eliminated for the singular value of ultra-short baseline alignment error calibration the most according to claim 1, it is characterised in that: in step (2), described singularity characteristics value calculating method is:

WhereinFor singular eigenvalue problem, Γ_iSingularity characteristics matrix for observational equationMiddle i-th element, ω_iiSingularity characteristics matrix for observational equationI-th element on middle leading diagonal, according to singular eigenvalue problemValue judge whether these group data exist unusual.

A kind of parameter estimation weights method for designing eliminated for the singular value of ultra-short baseline alignment error calibration the most according to claim 2, it is characterized in that: in step (3), the process of the singular value elimination weights that each group of described calculating observation data are corresponding is:

Set two decision threshold θ High and θ Low of height；

First determine whetherWhether less than low threshold θ Low, if it is singular eigenvalue problemParameter estimation weights be 0 weights, less than low threshold judgement unusual for existing；

Otherwise continue to judgeWhether higher than high threshold θ High, if it is singular eigenvalue problemParameter estimation weights be 1 weights, higher than high threshold judgement for without unusual；If otherwise singular eigenvalue problemParameter estimation weights be trapezoidal weights；

According to singular eigenvalue problemQuantify mapping calculation trapezoidal weights K_ii: