CN103793614B - A kind of mutation filtering method - Google Patents
A kind of mutation filtering method Download PDFInfo
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- CN103793614B CN103793614B CN201410061632.9A CN201410061632A CN103793614B CN 103793614 B CN103793614 B CN 103793614B CN 201410061632 A CN201410061632 A CN 201410061632A CN 103793614 B CN103793614 B CN 103793614B
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Abstract
The present invention relates to a kind of mutation filtering algorithm, has substantial amounts of state suddenly change, just becomes particularly significant to the signal transacting of this kind of system in nature.Coupling system characteristic and status information, system noise and observation noise are regarded as two STOCHASTIC CONTROL amounts, set up mutation potential function, Singular Set is obtained, and Characteristics of Mutation is evaluated by catastrophe progression method, and then calculates state mutation normalization degree of membership, represent the degree of state mutation, if state is undergone mutation completely, then once status predication value on not considering in this filtering is calculated, but state estimation is carried out with reference to sample point data predicted value and current measurement value；If fractional mutations, use state predicted value size is calculated according to mutation degree of membership, state estimation is carried out in conjunction with sample point data predicted value and current measurement value.It is an advantage of the current invention that Mathematical Modeling and system noise and measurement noise statistical property accurately need not be known, the signal transacting of strong nonlinearity and strong random sexual system is particularly well-suited to.
Description
Technical field
The present invention relates to a kind of filtering method of estimation of jump signal, is particularly well-suited to strong nonlinearity and strong randomness
The signal transacting of system.
Background technology
In nature, in addition to gradual change and continuous and derivable variation phenomenon, substantial amounts of mutation and jump is also there is
Move phenomenon, such as Modeling of Gyro Drift Signal, make the output signal of radio altimeter when the aircraft of horizontal flight leaps mountain area, inertial navigation
Error signal in output error signal, Transfer Alignment, SA error signals of GPS etc., this kind of signal has catastrophe characteristicses.By
Do not have deterministic frequency spectrum in signal, it is impossible to useful signal is extracted with conventional filtering method.
Using more, especially UKF filtering accuracies are high, convergence rate for existing KF, EKF and UKF and its improved filtering method
Hurry up, its essence is non-linear density function to be approached using a number of sampled point, carry out the state and error of nonlinear model
The prediction of covariance, and then recursion and renewal, but UKF algorithms belong to the expansion of classical KF filtering, and with accurate mathematics
Based on known to model and system noise and measurement noise statistical property, and when system or environment acute variation, noise is united
Meter characteristic will be varied widely, and now filter accuracies and stability will decline, or even diverging.This in order to improve
UKF lacks the adaptive ability to being mutated, and occurs in that Sage Husa are filtered, and Robust filtering, Strong tracking filter, fading factor are calculated
Method etc., however these algorithms be all based on strict mathematical reasoning and harshness hypothesis condition, and in systems in practice these
Part is often difficult to meet.
Content of the invention
It is an object of the invention to proposing a kind of filtering estimating processing method of jump signal.
In order to realize that the mutation to signal is estimated, it is impossible to again as selecting some random values in UKF and PF filtering methods, it should
RightMoment arrivesSampled data between moment is made full use of, and designs mutation filtering method (Catastrophe for this
Filter Method), abbreviation CF.
As inertial navigation system, high-speed sampling can be accomplished, but not accomplish to resolve at a high speed, fromThe resolving moment arrivesSolution
The moment is calculated, mass data, i.e. sample point data can be gathered.
For system noiseAnd measurement noiseThrough certain emulation or experiment, it is possible to obtain partial information, if
Without any prior information, can first assume that system noise and measurement noise are white Gaussian noise.
Set up system state equation and measurement equation：
In formula,Battle array is shifted for a step,For measuring battle array,For system noise,For measurement noise.
When, calculate a step status predication.
Due to system modeThe estimate at momentWith a step status predication value, measured value, system noiseAnd measurement noiseFour amounts have direct relation, with this 4 variables as controlled quentity controlled variable, set up state mutation potential function：
In formula,The state variable of expression systemPotential function,For measured value,One step status predication value,Amount
Survey noise,For system noise.
For state mutation potential functionFirst derivation is carried out, and is made, you can obtain critical point set
Into profile of equilibrium.
By to potential functionSecond dervative is carried out, and is made, combine single order and second dervative equation, disappear
Go state variable, you can obtain the Bifurcation equation for reflecting the decomposed form of relation between state variable and control variables.
The bifurcation set equation of abruptly-changing system decomposed form is：
,,,
Normalizing formula is derived by the bifurcation set equation of decomposed form：
,,,
When each control variables in Bifurcation equation meets bifurcation set equation, illustrate that system mode there occurs mutation.
In order to calculate the mutation content for doing well, state is calculated with " incomplementarity " principle using " complementation ", i.e.,, by normalized, mutation value of the state variable in [0,1] scope is calculated, that is, is normalized
Mutation degree of membership, represent the degree of state mutation.
If state is undergone mutation completely, illustrate that system state equation has been not suitable for descriptive system, then in this filtering
A step status predication value is not considered in calculating, but carries out state estimation with reference to sample point data predicted value and current measurement value：
(1) utilize fromArriveSampled data between moment, calculate sampled dataVariance；(2) root
Sampled data predicted value is calculated according to measurement equation or is predicted using sampled data matched curve；(3) the increasing for trusting predicted value is calculated
Beneficial coefficient；(4) calculateMoment state estimation.
If fractional mutations, according to mutation degree of membershipTo calculate the size using a step status predication value, in conjunction with sampling
Point data predicted value and current measurement value carry out state estimation：(1) the size for believing one-step prediction value is calculated；(2) computation and measurement value variance；(3) calculate and believe survey
Value and the size of sample point data predicted value；(4) calculateMoment shape
State estimate .
Calculate state estimation variance.
WithWithUsed as the initial value of state estimation next time, and then recurrent state is estimated.
It is an advantage of the current invention that (1) need not accurately know that Mathematical Modeling and system noise and amount noise statisticses are special
Property；(2) according to the mutation content of state and noise, this method is estimated that system state change is more obvious, and filtering is estimated
Effect is better；(3) the Signal estimation of strong nonlinearity and strong random sexual system is particularly well-suited to；(4) can be discontinuous directly processing
Phenomenon, and any special inherent mechanism is not contacted, it is particularly well-suited to be still unknown internal action systematic research, and is suitable for
In the situation that discontinuity can be observed, it is not necessary to know the differential equation for being described that system state variables is followed in advance.
Description of the drawings
Fig. 1 is the state mutation structure of the present invention；
Fig. 2 is the CF mutation filtering method flow processs of the present invention；
Fig. 3 is that course angle error filtering of the present invention in inertial navigation system Transfer Alignment is estimated.
Specific embodiment
Illustrate below in conjunction with the accompanying drawings and the present invention is described in more detail.
So that the error filtering of inertial navigation Transfer Alignment is estimated as an example, and work as carrier with carrier aircraft in flight course, environmental change
Acutely, flight dynamics characteristic is complicated, it will it may not be gradually from a state to another state to cause carrier movement state
Become, but be once mutated, the Transfer Alignment model that sets up in this case has strong nonlinearity, and the statistical property of noise will
Vary widely, the Transfer Alignment error equation for setting up attitude is：
In formula,Battle array is shifted for one step of attitude,For measuring battle array,For system noise,For measurement noise.Such as
Fruit does not have any prior information, can first be assumed to white noise, andWith .
System initialization state-transition matrixAnd measurement matrix, state estimation initial value, estimate that initial value is missed
Difference.
When, calculate a step status predication value.
Due to system state variablesWith a step status predication value, measured value, system noiseMake an uproar with measurement
Sound4 variables have direct relation, set up butterfly mutation potential function：
In formula,The state variable of expression systemPotential function, a, b, c, d represent the state variable control become
Amount.
Potential function for mutation Mathematical ModelingFirst derivative is sought, and is made, you can obtain critical point
The profile of equilibrium for assembling, the Singular Set of profile of equilibrium.By to potential functionSecond dervative is sought, and is made,
Joint single order and second dervative equation, erased condition variable, you can obtain reflecting relation between state variable and control variables
The Bifurcation equation of decomposed form.
The bifurcation set equation of butterfly abruptly-changing system decomposed form is：
,,,
Normalizing formula is derived by the bifurcation set equation of decomposed form：
,,,
When each control variables in Bifurcation equation meets bifurcation set equation, illustrate that system mode there occurs mutation.In order to
The mutation content for doing well is calculated, state is calculated with " incomplementarity " principle using " complementation ", i.e.,
, by normalized, mutation value of the state variable in [0,1] scope can be calculated, i.e. normalization mutation degree of membership, represent shape
The degree of state mutation.
If state is undergone mutation completely, illustrate that system state equation has been not suitable for descriptive system, then calculate in this filtering
In do not consider a step status predication value, but carry out state estimation with reference to sample point data predicted value and current measurement value：(1) utilize
FromArriveSample point data between moment, calculate sample point dataVariance；(2) basis
Measurement equation is calculated sample point data predicted value or is predicted using sampled data matched curve；(3) the increasing for trusting predicted value is calculated
Beneficial coefficient；(4) calculateMoment state estimation.
If fractional mutations, according to mutation degree of membershipTo calculate the size using a step status predication value, in conjunction with sampling
Point data predicted value and current measurement value carry out state estimation：(1) the size for believing one-step prediction value is calculated；(2) computation and measurement value variance；(3) calculate and believe survey
Value and the size of sample point data predicted value；(4) calculateMoment shape
State estimate .
Calculate state estimation variance.
WithWithUsed as the initial value of state estimation next time, and then recurrent state is estimated.
Sub- inertial navigation and main inertial navigation course angle estimation error, such as Fig. 3 are carried out using mutation filtering method, evaluated error is
0.3o, and the error of KF filtering is adopted for 0.9o.
The present invention is proposed for abruptly-changing system, and its core content is the mutation content according to system mode, estimates shape
State value；If system is not mutated, and also is linear, using general Linear Estimation or conventional filtering method；If
System is strong nonlinearity or strong randomness, there occurs mutation equivalent to state, can be filtered estimation using the present invention.
Finally illustrated is that above case study on implementation is merely to illustrate technical scheme and unrestricted, can be to this
Bright modify or change, without deviating from the scope of the technical program, its all should cover scope of the presently claimed invention work as
In.
Claims (1)
1. one kind is mutated filtering method, it is characterised in that the step of being mutated filtering method includes：FromThe resolving moment arrives
The moment is resolved, mass data, i.e. sample point data is gathered；(2) for system noiseAnd measurement noiseThrough emulation or test, it is possible to obtain prior information, if without any prior information, first can assume system noise and
Measurement noise is white Gaussian noise；(3) system state equation and measurement equation are set up, in formulaBattle array is shifted for a step,For measuring battle array,For system noise,For measurement noise；⑷When, calculate a step shape
State is predicted；(5) due to system modeThe estimate at momentWith a step status predication value, measured value, system noiseAnd measurement noiseFour amounts have direct relation, with this 4 variables as controlled quentity controlled variable,
Set up state mutation potential function, in formulaThe state variable of expression systemPotential function,For measured value,One step status predication value,Measurement noise,For system noise；(6) for state mutation
Potential functionFirst derivation is carried out, and is made, you can obtain the profile of equilibrium that critical point is assembled；(7) by right
Potential functionSecond dervative is carried out, and is made, joint single order and second dervative equation, erased condition variable, i.e.,
The Bifurcation equation for reflecting the decomposed form of relation between state variable and control variables can be obtained；(8) abruptly-changing system decomposed form
Bifurcation set equation is,,,, by the bifurcation set equation of decomposed form
Derive normalizing formula：,,,, when each control variables in Bifurcation equation meets
During bifurcation set equation, illustrate that system mode there occurs mutation；(9) in order to calculate the mutation content for doing well, using " complementation " and
" incomplementarity " principle calculates state, i.e.,, by normalized, calculate state variable and exist
The mutation value of [0,1] scope, i.e. normalization mutation degree of membership, represent the degree of state mutation；If (10) state occurs completely
Mutation, illustrates that system state equation has been not suitable for descriptive system, then in this filtering is calculated do not consider a step status predication
Value, but state estimation is carried out with reference to sample point data predicted value and current measurement value：1. utilize fromArriveBetween moment
Sampled data, calculate sampled dataVariance；2. sampled data is calculated according to measurement equation
Predicted value is predicted using sampled data matched curve；3. the gain coefficient for trusting predicted value is calculated；4. calculateMoment state estimation；(11) such as
Fruit part is mutated, according to mutation degree of membershipTo calculate the size using a step status predication value, pre- in conjunction with sample point data
Measured value and current measurement value carry out state estimation：1. the size for believing one-step prediction value is calculated；2. computation and measurement value variance；3. calculate and believe survey
Value and the size of sample point data predicted value；4. calculateMoment shape
State estimate ；(12) shape is calculated
State estimate variance；WithWithUsed as the initial value of state estimation next time, and then recurrent state is estimated.
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| INS/GPS组合导航系统模糊卡尔曼滤波算法研究;姚文国等;《弹箭与制导学报》;20070831;第27卷(第3期);4-10页 * |
| Kalman滤波在井下人员跟踪定位中的应用;罗宇锋等;《工矿自动化》;20130930;第39卷(第9期);54-57页 * |
| 基于航弹的动基座传递对准研究;杨金显;《弹箭与制导学报》;20091231;第29卷(第6期);76-80页 * |
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