CN105787265A - Atomic spinning top random error modeling method based on comprehensive integration weighting method - Google Patents

Abstract

The invention provides an atomic spinning top random error modeling method based on a comprehensive integration weighting method and belongs to the technical field of top data processing.According to the method, weak steadiness and the weak linear characteristic of real-time output data of a top are comprehensively considered, linear characteristics and non-linear characteristics are fitted based on the comprehensive integration weighting method, and the modeling method which is more comprehensive and more accurate is provided.The weak linear characteristic is also considered while weak steadiness is considered, and meanwhile a method for using the residual sequence of a model to establish another model is abandoned.By means of the modeling method, the defect that a single model cannot embody linear and non-linear composite characteristics of random errors of the top is overcome, and modeling precision is improved.Accuracy of model establishment directly influences the subsequent reprocessing course, and therefore the atomic spinning top random error modeling method based on the comprehensive integration weighting method plays a crucial role in improving top precision.

Description

Atomic spin Gyro Random error modeling method based on meta-synthesis methodology

Technical field

The present invention proposes a kind of atomic spin Gyro Random error modeling method based on meta-synthesis methodology, belongs to gyro data processing technology field.

Background technology

Development along with quantum regulation and control technology, manipulation atomic spin is in without exchange relaxation (SpinExchangeRelaxationFree, SERF) state, the electricity spin close coupling of the nuclear spin of intert-gas atoms and alkali metal atom, carry out the measurement of angular movement, be called the atomic spin gyroscope based on SERF.By theory analysis, this New type atom spin gyroscope has the feature of superhigh precision, small size.Therefore, atomic spin gyroscope is considered as the developing direction of superhigh precision gyroscope of future generation, has important scientific research and engineering practice is worth.

Gyro error includes static error, dynamic error and random error.First two error is relevant with the kinematic parameter of carrier, can be compensated by Experimental Calibration, and what really affect gyro performance is the random drift of gyro.Modelling of Random Drift of Gyroscopes is weakly stationary, line of weakness, not easily extracts the actual signal of gyro exactly.Therefore Gyro random error model is set up accurately to be filtered in filtering and just to seem extremely important.

The free Series Modeling of Gyroscope Random Drift modeling method, neural net model establishing and the wavelet series Nonlinear Modeling etc. comparatively commonly used at present.Time series modeling Application comparison in model prediction is extensive, wherein autoregression (AR) modeling method is conventional time series modeling method, but the premise of its application is data must be steady, linear, and namely it can not be applied in the Accurate Model of non-stationary, Nonlinear Time Series.The non-linear modeling method such as neutral net, support vector machine is continuously available application in recent years, and achieves good effect.But neutral net can not provide the concrete mathematic(al) representation between the input and output needing modeling, and substantial amounts of experimental data must be relied on just to complete, " crossing study " of neutral net, the problems such as " local minimums " that is easily absorbed in also limit the practicality of the method.Support vector machine (SVM) intelligent algorithm, it is specific to the machine learning method of finite sample situation, peculiar advantage in Function Fitting and recurrence, adopt structural risk minimization, practical problem is transformed into by nonlinear transformation the feature space of higher-dimension, higher dimensional space constructs linear decision and realizes the non-linear decision function in former space, solve problem of dimension dexterously, there is small-sample learning, global optimizing, feature that generalization ability is strong.Meanwhile, genetic planning (GP) have also been obtained continuous application in Nonlinear Modeling.Genetic planning is a kind of very effective adaptable search modeling method, and the method does not need any priori, has good objectivity and great versatility, compares odds ratio with additive method more prominent, therefore obtains the favor of a lot of people.

Being single consider line of weakness or weakly stationary based on traditional modeling method, the present invention takes into account weak linear characteristic while considering weakly stationary.First gyro is exported data and set up the linear model based on ARIMA and the nonlinear model based on support vector machine (SVM) respectively, then the weight of linear processes model is determined again through game theoretic meta-synthesis methodology, and then simulate the built-up pattern of higher precision, play most important effect for improving Gyro Precision.

Summary of the invention

Goal of the invention: the invention aims to solve the unicity that classical spinning top stochastic error modeling method considers: weakly stationary or line of weakness.A kind of atomic spin Gyro Random error modeling method based on meta-synthesis methodology is provided.

Technical scheme: the technical solution used in the present invention is: based on the atomic spin Gyro Random error modeling method of meta-synthesis methodology, comprise the following steps:

(1) the original output data of gyro are obtained, selected sample length n, obtain time series y (n)；

(2) time series y (n) is set up the linear model y based on ARIMA₁(n)；

(3) time series y (n) is set up the nonlinear model y based on SVM₂(n)；

(4) the weight c of linear processes model is determined by game theoretic synthesized integration method₁、c₂, make the linear processes feature of sequence combine；

(5) two kinds of models of weighted array, i.e. y (n)=c₁y₁(n)+c₂y₂N (), obtains high-precision built-up pattern.

Preferentially, the described ARIMA of foundation linear model includes following content:

First gyro is exported data and carry out stationary test, common method is based on augmentation Dickey-fowler (ADF) method of inspection of unit root, the method principle is: for an autoregressive process, if all characteristic roots of its characteristic equation are all in unit circle, then and sequence stationary；If having characteristic root to exist and being 1, then sequence non-stationary, and autoregressive coefficient sum is exactly equal to 1.If stationary sequence, then directly set up arma modeling；Otherwise, then data are carried out first difference, then carry out stationary test, until after d jump divides, data are stationary sequences.Draw auto-correlation and the partial autocorrelation figure of stationary sequence, thoroughly do away with hangover and order p and the q of the tentatively selected arma modeling of truncation situation.Optimize p and q according to AIC or BIC criterion, obtain best order.After determining model order, model parameter being estimated, stationary sequence is finally set up ARMA, and (namely former sequence is set up ARIMA (p, d, q) model by p, q) model.

Preferentially, described SVM is a learning model having supervision, is commonly used to carry out pattern recognition, classification and regression analysis.Its core concept is: by nonlinear mapping ρ, non-linear variable x is mapped to a higher dimensional space, and then carries out linear regression at higher dimensional space.Here nonlinear mapping is realized dexterously by kernel function, and the generation of result is affected bigger by the selection of kernel function.

Preferentially, described ARIMA and SVM model is all the linear processes model directly former sequence set up, and the method that the traditional residual sequence with a kind of model of non-usage goes to set up another kind of model.

Preferentially, described theory of games is:

Theory of games is used for Index Weights evaluation, owing to time series y (n) has linear processes compound characteristics, therefore the present invention adopts meta-synthesis methodology, by game theoretic meta-synthesis methodology, linear weight and nonlinear integrated are got up, make the respective deviation between possible weight and each basic weight minimum, retain information linear, nonlinear weight weight values as far as possible.

Beneficial effect: the proposition of the present invention solves the unicity that classical spinning top stochastic error modeling method considers: weakly stationary or line of weakness.Provide a kind of atomic spin gyroscope stochastic error modeling method based on meta-synthesis methodology, the method has taken into account weakly stationary and the line of weakness of gyro Static output data, first gyro is exported data and set up the linear model based on ARIMA and the nonlinear model based on support vector machine (SVM) respectively, then again through the game theoretic weight determining linear processes model, and then the built-up pattern of higher precision is simulated.Solve the shortcoming that single model cannot embody the linear processes compound characteristics of Gyro Random error, improve the precision of modeling.The accuracy that model is set up directly influences follow-up reprocessing process, and the atomic spin gyroscope stochastic error modeling method based on meta-synthesis methodology that therefore present invention proposes has vital effect for improving Gyro Precision.

Accompanying drawing explanation

Fig. 1 is the overall modeling method flow chart of atomic spin Gyro Random error；

Fig. 2 is linear modeling approach flow chart；

Fig. 3 is non-linear modeling method flow chart.

Detailed description of the invention

In conjunction with the drawings and specific embodiments, the present invention is further illustrated.

Fig. 1 show the overall modeling method flow chart of atomic spin Gyro Random error, specifically, comprises the following steps:

Obtain the original output data of gyro, selected sample length n, obtain time series y (n)；Respectively time series y (n) is set up the linear model y based on ARIMA₁(n) and the nonlinear model y based on SVM₂(n)；The weight c of linear processes model is determined by game theoretic synthesized integration method₁、c₂, make the linear processes feature of sequence combine；Two kinds of models of last weighted array, i.e. y (n)=c₁y₁(n)+c₂y₂N (), obtains high-precision built-up pattern.

Game theory asks the method for weight as follows:

If m weight vectors $W_i^T={\{w_{k1},w_{k2},\mathrm{...}{w}_{km}\}}^T,$ Have L kind method that it is composed to weigh, k=1,2 ..., L, then any linear combination of this L vector is:

$W={\Σ}_{k=1}^L{\mathrm{\γ}}_k{W}_k^T,({\mathrm{\γ}}_k\≥0)---\left(1\right)$

In formula: γ_kFor linear combination coefficient, for making w and each w_kDeviation minimization, need to γ_kIt is optimized.Thus derive game model:

$\min =\left|\right|{\Σ}_{i=1}^m{\mathrm{\γ}}_i{w}_i^T-w_j^T|{|}_2,(j=1,2,\mathrm{...}m)---\left(2\right)$

This game model is one group of Interaction programming model containing multiple object function, can obtain a comprehensive weight result by solving.The matrix form of the system of linear equations that formula (2) optimized first derivative condition is corresponding is:

$\left[\begin{array}{cccc}{w}_1{w}_1^T& w_1{w}_2^T& \mathrm{...}& w_1{w}_L^T\\ w_2{w}_1^T& w_2{w}_2^T& \mathrm{...}& w_2{w}_L^T\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ w_L{w}_1^T& w_L{w}_2^T& \mathrm{...}& w_L{w}_L^T\end{array}\right]---\left(3\right)$

Use Matlab software can solving equation (3) easily, by value of calculation γ_kBring formula (2) into, comprehensive weight vector W can be obtained.

Fig. 2 is linear modeling approach flow chart, specifically, including following technical proposal:

Gyro is exported sample sequence y (n) and carries out stationary test.Common method is based on augmentation Dickey-fowler (ADF) method of inspection of unit root, and the method principle is: for an autoregressive process, if all characteristic roots of its characteristic equation are all in unit circle, then and sequence stationary；If having characteristic root to exist and being 1, then sequence non-stationary, and autoregressive coefficient sum is exactly equal to 1.Matlab can directly use stationary test function dfARtest, determine whether stationary sequence according to return value.If sample y (n) is non-stationary series, then data is carried out first difference, then carries out stationary test, until d jump obtains stationary sequence x (n) after dividing, then have (1-B)^dY (n)=x (n), wherein B is One-step delay operator, i.e. By (n)=y (n-1).Calculate correlation Coefficient Function figure and the PARCOR coefficients functional arrangement drawing of sample sequence x (n), thoroughly do away with hangover and order p and the q of the tentatively selected arma modeling of truncation situation, thenWherein ε_nIt it is independent identically distributed sequence of random variables.Then optimize p and q according to AIC or BIC criterion, obtain best order.If q=0, x (n) are AR (P) model,Then former sequenceIf p=0, x (n) are MA (q) model, $x\left(n\right)={\mathrm{\ϵ}}_n+{\Σ}_{j=1}^q{\mathrm{\β}}_j{\mathrm{\ϵ}}_{n-j},$ Then former sequence ${(1-B)}^{d}y\left(n\right)=({\mathrm{\ϵ}}_n+{\Σ}_{j=1}^q{\mathrm{\β}}_j{\mathrm{\ϵ}}_{n-j});$ If p, q be not all 0, x (n) for ARMA (p, q) model, then obtain former sequences y (n) ARIMA (p, d, q) model, namelyAfter determining model, to model parameterAnd β_jEstimating, model is set up and is terminated.For obtaining optimal models, it is necessary to model applicability is tested, assay better then application model, otherwise continues Optimized model.

Fig. 3 is non-linear modeling method flow chart, specifically, including following technical proposal:

The core concept of SVM modeling is: by nonlinear mapping ρ, non-linear variable y is mapped to a higher dimensional space, and then carries out linear regression at higher dimensional space, be i.e. f (y)=σ^Tρ (y)+b, wherein σ is weight vector, and b is constant.The analytic expression of the linear regression hyperplane that support vector machines determines is: $f\left(y\right)={\Σ}_{i=1}^n({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)K(y_i,y)+b,$ Wherein n is the number of training sample, $K(y_i,y)=\exp \left(\frac{\left|\right|y-y_i|{|}^2}{{\mathrm{\σ}}^2}\right)$ For gaussian radial basis function kernel function, α^*, α is Lagrange multiplier.Concrete modeling procedure is: first choose the time sequence of a segment length as input vector；Then input vector data are normalized so that all data are between [-1,1]；Select SVM kernel function, found the punishment parameter e and nuclear parameter g of optimum SVM by cross validation；Train SVM regression machine with optimized parameter, set up SVM nonlinear model.

Claims (4)

1. based on the atomic spin Gyro Random error modeling method of meta-synthesis methodology, it is characterised in that: comprise the following steps:

(1) the original output data of gyro are obtained, selected sample length n, obtain time series y (n)；

(2) time series y (n) is set up the linear model y based on ARIMA₁(n)；

(3) time series y (n) is set up the nonlinear model y based on SVM₂(n)；

(4) the weight c of linear processes model is determined by game theoretic meta-synthesis methodology₁、c₂, make the linear processes feature of sequence combine；

(5) two kinds of models of weighted array, i.e. y (n)=c₁y₁(n)+c₂y₂N (), obtains high-precision built-up pattern.

2. modeling method according to claim 1, it is characterised in that: step 2 comprises the following steps:

(1) adopt the augmentation Dickey-fowler method of inspection based on unit root that gyro is exported data and carry out stationary test, namely for an autoregressive process, if all characteristic roots of its characteristic equation are all in unit circle, then sequence stationary；If having characteristic root to exist and being 1, then sequence non-stationary, and autoregressive coefficient sum is exactly equal to 1；

(2) if stationary sequence, then draw auto-correlation and the partial autocorrelation figure of stationary sequence, thoroughly do away with hangover and order p and the q of the tentatively selected arma modeling of truncation situation；Otherwise, then data are carried out first difference, then carry out stationary test, until after d jump divides, data are stationary sequences x (n), then have (1-B)^dY (n)=x (n), wherein B is One-step delay operator, i.e. By (n)=y (n-1)；

(3) optimize p and q according to AIC or BIC criterion, obtain best order, if q=0, x (n) they are AR (P) model,Then former sequenceIf p=0, x (n) are MA (q) model,Then former sequenceIf p, q be not all 0, x (n) for ARMA (p, q) model, then obtain former sequences y (n) ARIMA (p, d, q) model, namely

3. modeling method according to claim 1, it is characterised in that: SVM described in step 3 is modeled as, by nonlinear mapping ρ, non-linear variable y is mapped to a higher dimensional space, and then carries out linear regression at higher dimensional space, i.e. f (y)=σ^τρ (y)+b, wherein σ is weight vector, and b is constant；The analytic expression of the linear regression hyperplane that support vector machines determines is:Wherein n is the number of training sample,For gaussian radial basis function kernel function, α^*, α is Lagrange multiplier.

4. modeling method according to claim 1, it is characterised in that: step 4 comprises the steps:

(1) m weight vectors is setHave L kind method that it is composed to weigh, k=1,2 ..., L, then any linear combination of this L vector is:

$\begin{array}{cc}W={\Σ}_{k=1}^L{\mathrm{\γ}}_k{W}_k^T& ({\mathrm{\γ}}_k\≥0)\end{array}---\left(1\right)$

In formula: γ_kFor linear combination coefficient；

(2) for making w and each w_kDeviation minimization, need to γ_kIt is optimized, thus derives game model:

$\begin{array}{cc}\min =\left|\right|{\Σ}_{i=1}^m{\mathrm{\γ}}_i{w}_i^T-w_j^T|{|}_2& (j=1,2,\mathrm{...}m)\end{array}---\left(2\right)$

This game model is one group of Interaction programming model containing multiple object function, can obtain a comprehensive weight result by solving, and the matrix form of the system of linear equations that formula (2) optimized first derivative condition is corresponding is:

$\left[\begin{array}{cccc}{w}_1{w}_1^T& w_1{w}_2^T& \mathrm{...}& w_1{w}_L^T\\ w_2{w}_1^T& w_2{w}_2^T& \mathrm{...}& w_2{w}_L^T\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ w_L{w}_1^T& w_L{w}_2^T& \mathrm{...}& w_L{w}_L^T\end{array}\right]---\left(3\right)$

(3) Matlab software solving equation (3) is used, by value of calculation γ_kBring formula (2) into, comprehensive weight vector W can be obtained.