CN106022212A - Gyroscope temperature drift modeling method - Google Patents
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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
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~IMFN;
(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~IMFNAnd IMFpre-all;Wherein,
(22) the relative entropy of each decomposed component is calculated;Wherein, i-th decomposed component IMFiRelative entropy beIn formula, i=2 ..., N, P (IMFpre-all) represent IMFpre-allGeneral
Rate value, P (IMFi) represent IMFiProbit;
(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 answeredk;
(24) decomposed component IMF is calculated1~IMFkSum, obtain noise signal
Further, step (3) specifically includes:
To described noise signal fnoiseCarry out Quadric Spline matching, obtain matching noise signal fnoise(d) be:In formula, j is integer and j >=3, diRepresent the i-th data of residual error, N0,3(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 MSEth;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,2m], step-length SLFor:
SL=n, standard deviation threshold values MSEthFor: MSEth=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:
In formula, MSE [] expression is averaged,Representing useful signal, s represents support in SVM
The number of vector, aiWithFor Lagrange multiplier, xiRepresent SVM matching fpureSupport vector, x is fpure'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:
In formula, fnoiseRepresenting noise signal, j is integer and j >=3, giRepresent i-th kernel functional parameter, N0,4(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 fnoise(d), the mathematical model setting up the drift of gyro temperature is:
In formula, d is that gyro temperature floats noise data, dkFor supporting vector, aiWithFor 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~IMFN。
(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~IMFNAnd IMFpre-all, IMFpre-allWith reference to formula
1;(22) the relative entropy of each decomposed component is calculated;Wherein, i-th decomposed component IMFiRelative entropy HiPublic 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 Diank;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 IMFk, IMFkIt
Front decomposed component is noise component(s), and component afterwards is component of signal;(24) decomposed component IMF is calculated1~IMFk's
With, obtain noise signal fnoise, fnoiseWith reference to formula 3, useful signal fpureWith reference to formula 4.
In formula, P (IMFpre-all) represent IMFpre-allProbit, P (IMFi) represent IMFiProbit.
(3) described noise signal is carried out Quadric Spline matching, obtain matching noise signal.
This step specifically includes: to described noise signal fnoiseCarrying out Quadric Spline matching, obtaining matching noise signal is:
In formula, j is integer and j >=3, diRepresent the i-th data of residual error, N0,3(t-i) base of Quadric Spline is represented
Function, concrete formula is:
In formula, ti、ti+1、ti+2、ti+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,2m], step-length SL
For: SL=n, standard deviation threshold values MSEthFor: MSEth=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, aiWithFor Lagrange multiplier, xiRepresent SVM matching fpureSupport vector, x is fpure'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, fnoiseRepresenting noise signal, j is integer and j >=3, giRepresent i-th kernel functional parameter, N0,4(g-i)
Representing cubic uniform B-spline basic function, concrete formula is:
In formula, gi、gi+1、gi+2、gi+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 MSEth;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 fnoise(d), the mathematical model setting up the drift of gyro temperature is:
In formula, d is that gyro temperature floats data, dkFor supporting vector, aiWithFor 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~IMFN;
(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~IMFNAnd IMFpre-all;Wherein,
(22) the relative entropy of each decomposed component is calculated;Wherein, i-th decomposed component IMFiRelative entropy beIn formula, i=2 ..., N, P (IMFpre-all) represent IMFpre-allGeneral
Rate value, P (IMFi) represent IMFiProbit;
(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 IMFk;
(24) decomposed component IMF is calculated1~IMFkSum, 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 fnoiseCarry out Quadric Spline matching, matching noise signal f obtainednoise(d) be:In formula, j is integer and j >=3, diRepresent the i-th data of residual error, N0,3(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 MSEth;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 SLFor:
SL=n, standard deviation threshold values MSEthFor: MSEth=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 MSElComputing formula be:
In formula, MSE [] expression is averaged,Representing useful signal, s represents support in SVM
The number of vector, aiWithFor Lagrange multiplier, xiRepresent SVM matching fpureSupport vector, x is fpure'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:
In formula, fnoiseRepresenting noise signal, j is integer and j >=3, giRepresent i-th kernel functional parameter, N0,4(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 fnoise(d), the mathematical model setting up the drift of gyro temperature is:
In formula, s represents the number supporting vector in SVM, aiWithFor Lagrange multiplier, d is that gyro temperature floats noise
Data, dkFor supporting vector, aiWithFor Lagrange multiplier, C is penalty coefficient optimal value, and g is kernel functional parameter
Optimal value, b is hyperplane intercept constant.
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