CN106022212A - Gyroscope temperature drift modeling method - Google Patents

Abstract

The invention provides a gyroscope temperature drift modeling method. The method comprises the steps that EEMD and relative entropy are used as a separation method of signal and noise of a gyroscope temperature drift signal; a mean square error threshold of SVM fitting is set; a three-times uniform B-spline and mesh searching method is used to finely search the parameters C and g of SVM; if a search value is less than the threshold, parameter optimization is stopped; and finally, parameters acquired through optimization are substituted into an SVM formula to acquire the gyroscope temperature drift mathematical modeling. According to the invention, gyroscope temperature drift modeling is realized, and the requirements of high precision and miniaturization of a gyroscope are met.

Description

A kind of gyro Temperature Drift Modeling

Technical field

The present invention relates to digital signal processing method, particularly relate to a kind of gyro Temperature Drift Modeling.

Background technology

Optical fibre gyro is usually operated under complex environment, and complex environment temperature can cause gyro to produce non-heterogeneite phase Move, thus bring the drift that gyro exports.For the gyroscopic drift caused by temperature, two kinds of methods are had to be modified at present, A kind of is to use the method for physics to carry out abatement impact, and another kind of method is to use algorithm to carry out drift compensation.Compared to thing Reason method, compensation method will not bring the raising of cost and volume.Along with the improvement of algorithm, drift compensation method the most more comes More disclosure satisfy that gyro high accuracy, the requirement of miniaturization.

Set Empirical Mode Decomposition (Ensemble Empirical Mode Decomposition, EEMD) is a kind of based on making an uproar The data analysing method of sound auxiliary, it can carry out adaptive decomposition in time domain, need not any basic function.EEMD makes an uproar The selection of acoustic amplitude is particularly significant, and this is related to the quality of signal decomposition.If it is improper that noise amplitude selects, it will band Carry out the problems such as mode mixing, false mode and useful signal can not properly separate.When applying EEMD, traditional auxiliary The amplitude of noise needs to be added based on experience value, typically takes the standard deviation of primary signal 0.1-0.4 times, use exist with Machine, discomposing effect can not be guaranteed.But in actual use, the amplitude of aid in noise is far above this model Enclose, according to the difference of signal frequency domain, often take less value effect more preferable.

Support vector machine (Support Vector Machine, SVM) is a kind of learning model having supervision, extensively applies Classification, prediction and matching in data.In support vector regression algorithm for estimating, radially base (Radial basis function, RBF) kernel functional parameter g and penalty coefficient C directly affects the quality of SVM fitting effect.Kernel functional parameter g determines The lower dimensional space mapping mode to higher dimensional space, penalty coefficient C is used for balance error and model complexity, therefore must Must be by being calculated parameter C and the g of optimum.For the parameter optimization of SVM regression model, mainly by minimum Change root-mean-square error (Mean Square Error, MSE) and obtain optimized parameter.Stress and strain model (grid search) comes Finding optimal parameter C and g, it is a kind of ergodic algorithm, although computational efficiency is the highest, but can be in CV meaning Under obtain the highest classification accuracy.But traditional grid data service is both for discrete C's and g, and in order to The efficiency calculated, often step-length all select relatively big, this cannot ensure in global scope optimum.

B-spline is a kind of fitting algorithm flexible, efficient, and wherein Quadric Spline has preferable details and portrays ability, Cubic B-spline then has more preferable low frequency signal to follow the tracks of, capability of fitting.For the feature of B-spline function, secondary is permissible For matching high-frequency signal, can be used to follow the tracks of relatively low frequency signal three times.

Summary of the invention

Goal of the invention: the present invention is directed to the problem that prior art exists, it is provided that a kind of gyro Temperature Drift Modeling.Should Method can realize gyro temperature drift modeling, meets gyro high accuracy, the requirement of miniaturization.

Technical scheme: gyro Temperature Drift Modeling of the present invention, including:

(1) use EEMD method that gyro temperature drift signal f is decomposed, obtain N number of decomposed component: IMF₁～IMF_N；

(2) calculate the relative entropy of each decomposed component, and isolate from gyro temperature drift signal according to relative entropy Noise signal；

(3) described noise signal is carried out Quadric Spline matching, obtain matching noise signal；

(4) cubic uniform B-spline and trellis search method are used, the penalty coefficient of search SVM and kernel functional parameter Optimal value；

(5) optimal value searched is substituted into SVM, combine described matching noise signal, set up the mathematics of gyro temperature drift Model.

Further, step (2) specifically includes:

(21) decomposed component IMF is calculated₂～IMF_NAnd IMF_pre-all；Wherein,

(22) the relative entropy of each decomposed component is calculated；Wherein, i-th decomposed component IMF_iRelative entropy beIn formula, i=2 ..., N, P (IMF_pre-all) represent IMF_pre-allGeneral Rate value, P (IMF_i) represent IMF_iProbit；

(23) draw relative entropy curve according to the relative entropy of each decomposed component, and the conversion flex point institute finding out curve is right The decomposed component IMF answered_k；

(24) decomposed component IMF is calculated₁～IMF_kSum, obtain noise signal

Further, step (3) specifically includes:

To described noise signal f_noiseCarry out Quadric Spline matching, obtain matching noise signal f_noise(d) be:In formula, j is integer and j >=3, d_iRepresent the i-th data of residual error, N_0,3(t-i) Represent the basic function of Quadric Spline.

Further, step (4) specifically includes:

(41) the definition penalty coefficient C of SVM and the scope of kernel functional parameter g and step-length, and standard deviation threshold values is set；

(42) minima as defined in the range of by penalty coefficient C value being；

(43) by kernel functional parameter g as defined in the range of increase respectively value defining step-length, combine current penalty coefficient C value carries out SVM matching respectively, is calculated SVM matching mean square error during different g value；

(44) SVM matching mean square error during described different g value is carried out cubic uniform B-spline matching, connected Continuous B-spline matching mean square error, and therefrom choose minima；

(45) judge that whether the minima of B-spline matching mean square error is less than described standard deviation threshold values MSE_th；If it is not, Then the value of penalty coefficient C is increased a step-length, and return execution (43), the most current penalty coefficient C It is optimal value with the value of kernel functional parameter g.

Further, step (41) specifically includes:

The penalty coefficient C and kernel functional parameter g of definition SVM are in the range of C&g ∈ [-2^-m,2^m], step-length S_LFor: S_L=n, standard deviation threshold values MSE_thFor: MSE_th=p, wherein, m >=8, n≤0.5, p value allows by mistake according to system Difference is defined.

Further, SVM matching mean square error MSE in step (43)_lComputing formula be:

${\mathrm{MSE}}_l=MSE\[f_{pure}-\underset{i=1}{\overset{s}{\Σ}}(a_i-a_i^{*})C*\exp (-g||x_i-x|{|}^2)+b\]$

In formula, MSE [] expression is averaged,Representing useful signal, s represents support in SVM The number of vector, a_iWithFor Lagrange multiplier, x_iRepresent SVM matching f_pureSupport vector, x is f_pure's Value, b represents hyperplane intercept constant, and C represents current penalty coefficient value, and g represents current kernel functional parameter value.

Further, in step (44), the computing formula of B-spline matching mean square error is:

${\mathrm{MSE}}_{\left\{c\right\}}\left(g\right)=MSE\[f_{noise}-\underset{i=j-3}{\overset{j}{\Σ}}{g}_i{N}_{0,4}(g-i)\]$

In formula, f_noiseRepresenting noise signal, j is integer and j >=3, g_iRepresent i-th kernel functional parameter, N_0,4(g-i) Represent cubic uniform B-spline basic function.

Further, step (5) specifically includes:

The optimal value of the penalty coefficient C searched and kernel functional parameter g is substituted into SVM, combines described matching noise letter Number f_noise(d), the mathematical model setting up the drift of gyro temperature is:

$f\left(d\right)=\[\underset{i=1}{\overset{k}{\Σ}}(a_i-a_i^{*})C*\exp (-g||d-d_k|{|}^2)-b\]+f_{noise}\left(d\right)$

In formula, d is that gyro temperature floats noise data, d_kFor supporting vector, a_iWithFor Lagrange multiplier, C is punishment Coefficient optimal value, g is kernel functional parameter optimal value, and b is hyperplane intercept constant.

Beneficial effect: compared with prior art, its remarkable advantage is the present invention: the present invention is first by EEMD and relative entropy As signal and the separation method of noise of gyro temperature drift signal, then set the mean square error threshold values of SVM matching, And use cubic uniform B-spline and trellis search method that parameter C and the g of SVM are carried out fine search, work as search value Less than stopping parameter optimization during threshold values, the parameter finally optimizing obtained substitutes into SVM formula, obtains the number of gyro temperature drift Learn modeling.The present invention can realize gyro temperature drift modeling, meets gyro high accuracy, the requirement of miniaturization.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of the present invention.

Detailed description of the invention

As it is shown in figure 1, the present embodiment comprises the following steps:

(1) use EEMD method that gyro temperature drift signal f is decomposed, obtain N number of decomposed component: IMF₁～IMF_N。

(2) calculate the relative entropy of each decomposed component, and isolate from gyro temperature drift signal according to relative entropy Noise signal.

This step specifically includes: (21) calculate decomposed component IMF₂～IMF_NAnd IMF_pre-all, IMF_pre-allWith reference to formula 1；(22) the relative entropy of each decomposed component is calculated；Wherein, i-th decomposed component IMF_iRelative entropy H_iPublic affairs Formula is with reference to formula 2；(23) draw relative entropy curve according to the relative entropy of each decomposed component, and the conversion finding out curve is turned Decomposed component IMF corresponding to Dian_k；Wherein, the conversion flex point of relative entropy curve is the maximum of slope of curve conversion, This flex point is the separation of component of signal and noise component(s), and the decomposed component that this separation is corresponding is IMF_k, IMF_kIt Front decomposed component is noise component(s), and component afterwards is component of signal；(24) decomposed component IMF is calculated₁～IMF_k's With, obtain noise signal f_noise, f_noiseWith reference to formula 3, useful signal f_pureWith reference to formula 4.

In formula, P (IMF_pre-all) represent IMF_pre-allProbit, P (IMF_i) represent IMF_iProbit.

(3) described noise signal is carried out Quadric Spline matching, obtain matching noise signal.

This step specifically includes: to described noise signal f_noiseCarrying out Quadric Spline matching, obtaining matching noise signal is:

In formula, j is integer and j >=3, d_iRepresent the i-th data of residual error, N_0,3(t-i) base of Quadric Spline is represented Function, concrete formula is:

In formula, t_i、t_i+1、t_i+2、t_i+3Represent 4 continuous centrifugal pumps of matching discrete objects respectively.

(4) cubic uniform B-spline and trellis search method are used, the penalty coefficient of search SVM and kernel functional parameter Optimal value.

This step specifically includes:

(41) the definition penalty coefficient C of SVM and the scope of kernel functional parameter g and step-length, and standard deviation threshold values is set. Particularly as follows: the penalty coefficient C and kernel functional parameter g of definition SVM are in the range of C&g ∈ [-2^-m,2^m], step-length S_L For: S_L=n, standard deviation threshold values MSE_thFor: MSE_th=p, wherein, m and n according to signal self-defining, for The temperature drift data of gyro often take m >=8, and the value of n≤0.5, p value is defined according to system allowable error.

(42) minima as defined in the range of by penalty coefficient C value being.

(43) by kernel functional parameter g as defined in the range of increase respectively value defining step-length, combine current penalty coefficient C value carries out SVM matching respectively, is calculated SVM matching mean square error during different g value.Wherein, SVM intends The computing formula closing mean square error is

In formula, MSE [] expression is averaged,Representing useful signal, s represents support in SVM The number of vector, a_iWithFor Lagrange multiplier, x_iRepresent SVM matching f_pureSupport vector, x is f_pure's Value, b represents hyperplane intercept constant, and C represents current penalty coefficient value, and g represents current kernel functional parameter value.

(44) SVM matching mean square error during described different g value is carried out cubic uniform B-spline matching, connected Continuous B-spline matching mean square error, and therefrom choose minima.Wherein, the computing formula of B-spline matching mean square error For:

In formula, f_noiseRepresenting noise signal, j is integer and j >=3, g_iRepresent i-th kernel functional parameter, N_0,4(g-i) Representing cubic uniform B-spline basic function, concrete formula is:

$N_{0,4}(g-i)=\frac{1}{6}\[\begin{array}{cccc}1& t& t^2& t^3\end{array}\]\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{g}_i\\ g_{i+1}\\ g_{i+2}\\ g_{i+3}\end{array}\right],t\∈\[0,1\]$

In formula, g_i、g_i+1、g_i+2、g_i+3Represent 4 continuous centrifugal pumps of matching discrete objects respectively.

(45) judge that whether the minima of B-spline matching mean square error is less than described standard deviation threshold values MSE_th；If it is not, Then the value of penalty coefficient C is increased a step-length, and return execution (43), the most current penalty coefficient C It is optimal value with the value of kernel functional parameter g.

(5) optimal value searched is substituted into SVM, combine described matching noise signal, set up the mathematics of gyro temperature drift Model.

This step specifically includes: the optimal value of the penalty coefficient C searched and kernel functional parameter g substitutes into SVM, connection Close described matching noise signal f_noise(d), the mathematical model setting up the drift of gyro temperature is:

In formula, d is that gyro temperature floats data, d_kFor supporting vector, a_iWithFor Lagrange multiplier, C is penalty coefficient Optimal value, g is kernel functional parameter optimal value, and b is hyperplane intercept constant.

Claims (8)

1. a gyro Temperature Drift Modeling, it is characterised in that the method includes:

(1) use EEMD method that gyro temperature drift signal f is decomposed, obtain N number of decomposed component: IMF₁～IMF_N；

(2) calculate the relative entropy of each decomposed component, and isolate from gyro temperature drift signal according to relative entropy Noise signal；

(3) described noise signal is carried out Quadric Spline matching, obtain matching noise signal；

(4) cubic uniform B-spline and trellis search method are used, the penalty coefficient of search SVM and kernel functional parameter Optimal value；

(5) optimal value searched is substituted into SVM, combine described matching noise signal, set up the mathematics of gyro temperature drift Model.

Gyro Temperature Drift Modeling the most according to claim 1, it is characterised in that: step (2) is specifically wrapped Include:

(21) decomposed component IMF is calculated₂～IMF_NAnd IMF_pre-all；Wherein,

(22) the relative entropy of each decomposed component is calculated；Wherein, i-th decomposed component IMF_iRelative entropy beIn formula, i=2 ..., N, P (IMF_pre-all) represent IMF_pre-allGeneral Rate value, P (IMF_i) represent IMF_iProbit；

(23) draw relative entropy curve according to the relative entropy of each decomposed component, and find out the conversion flex point institute of this curve Corresponding decomposed component IMF_k；

(24) decomposed component IMF is calculated₁～IMF_kSum, obtain noise signal

Gyro Temperature Drift Modeling the most according to claim 1, it is characterised in that: step (3) is specifically wrapped Include:

To described noise signal f_noiseCarry out Quadric Spline matching, matching noise signal f obtained_noise(d) be:In formula, j is integer and j >=3, d_iRepresent the i-th data of residual error, N_0,3(t-i) Represent the basic function of Quadric Spline.

Gyro Temperature Drift Modeling the most according to claim 1, it is characterised in that: step (4) is specifically wrapped Include:

(41) the definition penalty coefficient C of SVM and the scope of kernel functional parameter g and step-length, and standard deviation threshold values is set；

(42) minima as defined in the range of by penalty coefficient C value being；

(43) by kernel functional parameter g as defined in the range of increase respectively value defining step-length, combine current penalty coefficient C value carries out SVM matching respectively, is calculated SVM matching mean square error during different g value；

(44) SVM matching mean square error during described different g value is carried out cubic uniform B-spline matching, connected Continuous B-spline matching mean square error, and therefrom choose minima；

(45) judge that whether the minima of B-spline matching mean square error is less than described standard deviation threshold values MSE_th；If it is not, Then the value of penalty coefficient C is increased a step-length, and return execution (43), the most current penalty coefficient C It is optimal value with the value of kernel functional parameter g.

Gyro Temperature Drift Modeling the most according to claim 4, it is characterised in that: step (41) is concrete Including:

The penalty coefficient C and kernel functional parameter g of definition SVM are in the range of C&g ∈ [-2-m, 2m], step-length S_LFor: S_L=n, standard deviation threshold values MSE_thFor: MSE_th=p, wherein, m >=8, n≤0.5, p value allows by mistake according to system Difference is defined.

Gyro Temperature Drift Modeling the most according to claim 4, it is characterised in that: SVM in step (43) Matching mean square error MSE_lComputing formula be:

${\mathrm{MSE}}_l=MSE\[f_{pure}-\underset{i=1}{\overset{s}{\Σ}}(a_i-a_i^{*})C*\exp (-g||x_i-x|{|}^2)+b\]$

In formula, MSE [] expression is averaged,Representing useful signal, s represents support in SVM The number of vector, a_iWithFor Lagrange multiplier, x_iRepresent SVM matching f_pureSupport vector, x is f_pure's Value, b represents hyperplane intercept constant, and C represents current penalty coefficient value, and g represents current kernel functional parameter value.

Gyro Temperature Drift Modeling the most according to claim 4, it is characterised in that: B in step (44) The computing formula of spline-fit mean square error is:

${\mathrm{MSE}}_{\left\{c\right\}}\left(g\right)=MSE\[f_{noise}-\underset{i=j-3}{\overset{j}{\Σ}}{g}_i{N}_{0,4}(g-i)\]$

In formula, f_noiseRepresenting noise signal, j is integer and j >=3, g_iRepresent i-th kernel functional parameter, N_0,4(g-i) Represent cubic uniform B-spline basic function.

Gyro Temperature Drift Modeling the most according to claim 1, it is characterised in that: step (5) is specifically wrapped Include:

The optimal value of the penalty coefficient C searched and kernel functional parameter g is substituted into SVM, combines described matching noise letter Number f_noise(d), the mathematical model setting up the drift of gyro temperature is:

$f\left(d\right)=\[\underset{i=1}{\overset{s}{\Σ}}(a_i-a_i^{*})C*\exp (-g||d-d_k|{|}^2)-b\]+f_{noise}\left(d\right)$

In formula, s represents the number supporting vector in SVM, a_iWithFor Lagrange multiplier, d is that gyro temperature floats noise Data, d_kFor supporting vector, a_iWithFor Lagrange multiplier, C is penalty coefficient optimal value, and g is kernel functional parameter Optimal value, b is hyperplane intercept constant.