CN104112079A - Fuzzy adaptive variational Bayesian unscented Kalman filter method - Google Patents
Fuzzy adaptive variational Bayesian unscented Kalman filter method Download PDFInfo
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Abstract
The invention provides a fuzzy adaptive variational Bayesian unscented Kalman filter method. The method comprises the steps of estimating a one-step prediction target state as shown in the description and a covariance matrix thereof as shown in the description, iteratively estimating the variance as shown in the description of the measured noise, calculating the true value as shown in the description, the estimate value as shown in the description, the matching degree index as shown in the description and the adjustment quantity as shown in the description of a residual variance matrix at the current moment, and the adjusted measured noise variance as shown in the description, and calculating the estimated value as shown in the description of the target state and the error covariance matrix thereof. The method is capable of estimating the statistic variance capacity of the measured noise on line, and therefore, the filter error caused by unknown time variant of the noise statistical property is reduced and nonlinear filter estimation accuracy is improved. Meanwhile, the fuzzy logic method based on the innovated covariance matching technique is used for adjusting the measured noise variance estimated by the variational Bayesian method in real time, inhibiting the divergence of the filter and enhancing the robustness of the filter method.
Description
Technical field
What the present invention relates to is the method in a kind of signal processing technology field, is specifically related to a kind of fuzzy self-adaption variation Bayes Unscented kalman filtering method.
Background technology
Non-linear stochastic dynamic system is the type systematic extensively running in practical application, such as guidance and the control system of rocket, the inertial navigation system on aircraft and naval vessel, the estimation of satellite orbit/attitude, integrated navigation, detection of radar or sonar etc. all belongs to this type systematic.Even for linear system, when needs while estimated state and parameter, also there will be Nonlinear Filtering Problem.And Nonlinear Filtering Problem is extensively present in numerous scientific domains, thereby the state estimation of nonlinear system in theory or in engineering, be all very important.
The most frequently used in nonlinear system filtering method is EKF (extended Kalman filter, EKF).EKF, by nonlinear model is carried out to the linearization process based on Taylor series expansion, obtains first approximation item as the approximate expression form of previous status equation and measurement equation.Although EKF is simply easy to realize, still exist linearization meeting to make system produce larger error, cause wave filter to be difficult to stablize, also exist Jacobian matrix to calculate the defects and the restriction of using such as difficult simultaneously, this also impels people constantly to seek new nonlinear filtering algorithm.The nineties in 20th century, the people such as Julier have proposed Unscented kalman filtering (unscented Kalman filter, UKF) algorithm, have solved the deficiency of EKF by the method for deterministic sampling.The core of UKF is Unscented conversion (UT), it carefully selects the set of a minimum sampled point by the surrounding in stochastic variable, then by these sampled point substitution nonlinear models, the weighted sum of way utilize to(for) the discrete point newly obtaining just can be so that average and covariance matrix that posteriority is estimated be accurate to even more high-order (can be as accurate as three rank for Gaussian noise) of second order, and EKF can only obtain the precision of single order.
No matter it should be noted that in filtering application process, be UKF or EKF, all must accurately oneself knows the statistical property of noise.For real application systems, it is unknown that measuring noise square difference becomes always time, this is because measurement system is subject to the interference of inside and outside various factors, comprises measuring error and environmental perturbation, and the uncertainty of this noise statistics often causes existing filtering method to lose efficacy.Therefore, introducing auto-adaptive filtering technique carries out algorithm improvement and seems particularly important, as maximum posteriori (MAP) estimation, fuzzy logic technology, strong tracking technique and variation Bayes (VB) method etc.
Summary of the invention
In order to solve the above problems, in the present invention, take Unscented kalman filtering (UKF) as basic wave filter, adopt variational Bayesian method to estimate in real time the unknown variance of measuring noise, and in conjunction with fuzzy logic method, the measurement noise variance of estimating is compensated to adjustment, obtain a kind of fuzzy self-adaption variation Bayes Unscented kalman filtering (FAVB-UKF) method.
The present invention is the improved form of UKF, comprises and estimates one-step prediction dbjective state
and covariance matrix
(in the present invention
for discrete time mark,
represent to use
target information constantly estimates the
target information constantly); Iterative estimate is measured the variance of noise
; Calculate the actual value of the residual error variance battle array of current time
, estimated value
, matching degree index
, adjustment amount
and the measurement noise variance after adjusting
; Calculate the estimation of dbjective state
(
represent that this value is
optimal estimation value constantly) and error covariance
.Particular content is as follows:
step 1filtering starting condition is set, comprises:
(1.1) original state
and covariance matrix
;
(1.2) size of the moving window in fuzzy logic method W;
(1.3) VB iterations N, initiation parameter
,
;
.
step 2the variation Bayes Unscented kalman filtering (VB-UKF) carrying out in moving window calculates, and specifically comprises:
(2.1) loop control variable is set
initial value, order
, iterative loop starts;
(2.2) time upgrades, and estimates one-step prediction dbjective state
and covariance matrix
;
(2.3) measure and upgrade, specifically comprise:
(2.3.1) the prediction estimated value of computation and measurement value
(2.3.2) Cross-covariance of computing mode and measured value
(2.3.3) adopt variational Bayesian method iterative computation to measure noise variance matrix
, root mean square newly ceases covariance matrix
, gain battle array
, optimal estimation
and error covariance
, iterative process is as follows:
(I) loop control variable is set
tinitial value, order
t=1, according to the value of iterations N, iterative loop starts
(II) computation and measurement noise variance matrix
, subscript wherein
trepresent the
tvalue during inferior iteration
(III) calculate root mean square and newly cease covariance matrix
with gain battle array
.
(IV) calculate optimal estimation
and error covariance
(V) if
, order
; Then return to (II), otherwise carry out (VI)
(VI) finish VB iterative process, try to achieve
,
,
.
(2.4) if
, order
, then return
step 2; Otherwise VB-UKF calculates in end moving window, carry out
step 3.
step 3utilize fuzzy logic method dynamically to adjust
, specifically comprise:
(3.1) calculate the actual value of the residual error variance battle array of current time
, estimated value
and matching degree index
.
(3.2) with
for the input parameter of fuzzy inference system (FIS), the adjustment amount of computation and measurement noise variance matrix
, and the measurement noise variance of VB method being estimated with this
adjust, obtain current time and measure noise variance
.
step 4measurement noise variance after whole for readjustment
, at current time, carry out a standard UKF algorithm, obtain the estimation of dbjective state
and error covariance
.
Beneficial effect of the present invention: on the one hand, measure the statistical variance of noise by introducing VB method On-line Estimation, become the filtering error causing while having reduced due to noise statistics the unknown, improved nonlinear filtering estimated accuracy.On the other hand, utilize the fuzzy logic method of the covariance matching technology based on new breath, adjust in real time the measuring noise square difference that VB method is estimated, dispersing of suppression filter, has strengthened the robustness of FAVB-UKF.
Accompanying drawing explanation
Fig. 1 is structured flowchart of the present invention;
Fig. 2 is matching degree parameter
with adjustment amount
graph of a relation.
Embodiment
Below in conjunction with drawings and Examples, the present invention will be further described.
With reference to Fig. 1, the state-space model of establishing nonlinear dynamic system is:
(1)
Wherein,
expression system state (
for n dimensional vector complete or collected works),
to measure vector,
with
all differentiable function,
with
be all that average is zero white Gaussian noise, its variance is respectively
with
, and measure noise variance
while being, become unknown.
The original state of supposing the system is:
,
, and
be independent of respectively
with
.
Below, based on system model in detail, the concrete implementation step of FAVB-CKF is described in detail:
step 1filtering starting condition is set, comprises:
(1.1) original state
and covariance matrix
;
(1.2) size of the moving window in fuzzy logic method W;
(1.3) VB iterations N, initiation parameter
,
;
.
step 2the VB-UKF carrying out in moving window calculates, and specifically comprises:
(2.1) loop control variable is set
initial value, order
, iterative loop starts;
(2.2) time upgrades, and specifically comprises:
(2.2.1) calculate sigma point and weights coefficient
(2)
Wherein,
for state vector
dimension;
with
be respectively
state estimation value and error covariance matrix thereof constantly;
for scale parameter;
determined the degree of sigma point away from average, conventionally removed a very little positive number, in the present embodiment, got
.
be made as 0.
represent the of root mean square matrix
jrow.
The weights coefficient calculations of average and variance is as follows:
(3)
Wherein,
be used for portraying distributed intelligence, in Gauss's situation, value is 2.
(2.2.2) calculate the sigma point after propagating
(4)
(2.2.3) estimate one-step prediction dbjective state
and covariance matrix
;
(5)
(6)
Wherein, subscript "
" the transposition computing of representing matrix.
(2.3) measure and upgrade, specifically comprise:
(2.3.1) calculate sigma point
(7)
(2.3.2) calculate the sigma point after propagating
(8)
(2.3.3) the prediction estimated value of computation and measurement value
(9)
(2.3.4) Cross-covariance of computing mode and measured value
(10)
(2.3.5) iterative computation is measured noise variance
(I) calculate
parameter prediction value
(11)
Wherein, "
" represent the point processing in Matlab.
(II) VB iteration initialization, order
, provide iterations
value, iterative loop starts
(12)
(III) calculate the
tthe measurement noise variance matrix of inferior iteration
(13)
Wherein, "
diag" represent vector to be converted into diagonal matrix.
(IV) calculate the
tthe root mean square of inferior iteration newly ceases covariance matrix
(14)
(V) calculate the
tthe gain battle array of inferior iteration
(15)
(VI) calculate the
tthe optimal estimation of inferior iteration
and error covariance
(16)
(VII) upgrade iterative estimate parameter
(17)
Wherein,
.
If
, order
, then return to (3.3.5); Otherwise execution step (VIII).
(VIII) calculate in moving window the
inferior VB-UKF filtering estimated result
(18)
(2.4) if
, order
, then return
step 2; Otherwise VB-UKF calculates in end moving window, carry out
step 3.
step 3utilize fuzzy logic method dynamically to adjust
, specifically comprise:
(3.1) calculate the actual value of the residual error variance battle array of current time
.
(3.2) calculate the estimated value of the residual error variance battle array of current time
(19)
Wherein
the starting point that represents moving window.
(3.3) calculate matching degree index
(20)
(3.4) adopt fuzzy logic method adjustment to measure noise variance
With
for the input parameter of fuzzy inference system (FIS), the adjustment amount of computation and measurement noise variance matrix
, and the measurement noise variance of VB method being estimated with this
adjust.To variance battle array
adjustment can adopt main diagonal element
the mode of revising is one by one carried out.Therefore, for scalar, input
, via the adjustment amount of the exportable scalar of FIS
.Specifically comprise following steps:
(3.4.1) fuzzy division
Input quantity
be divided into three class fuzzy sets:
nbe expressed as negative,
zEbe expressed as zero,
pjust be expressed as.Output quantity
be divided into three class fuzzy sets:
irepresenting increases,
mexpression remains unchanged,
dexpression reduces.
with
relation as shown in Figure 2.
(3.4.2) fuzzy rule base
According to the fuzzy division in (3.4.2), formulate following fuzzy rule base:
(I) if
, so
;
(II) if
, so
;
(III) if
, so
.
(3.4.3) adjust and measure noise variance
(21)
step 4after whole for readjustment
,
kconstantly carry out standard UKF algorithm (i.e. employing formula (2)-Shi (10), formula (14)-Shi (16) calculates), the estimation of acquisition dbjective state
and error covariance
.
Claims (1)
1. a fuzzy self-adaption variation Bayes Unscented kalman filtering method, is characterized in that:
Step 1 arranges filtering starting condition, specifically comprises:
(1.1) original state and covariance matrix thereof
;
(1.2) size of the moving window in fuzzy logic method W;
(1.3) VB iterations N, initiation parameter
,
,
;
The variation Bayes Unscented kalman filtering (VB-UKF) that step 2 is carried out in moving window calculates, and specifically comprises:
(2.1) loop control variable is set
initial value, order
, iterative loop starts;
(2.2) time upgrades, and estimates one-step prediction dbjective state
and covariance matrix
, wherein,
represent to use
target information constantly estimates the
target information constantly;
(2.3) measure and upgrade, specifically comprise:
(2.3.1) the prediction estimated value of computation and measurement value
;
(2.3.2) Cross-covariance of computing mode and measured value
;
(2.3.3) adopt variational Bayesian method iterative computation to measure noise variance matrix
, root mean square newly ceases covariance matrix
, gain battle array
, optimal estimation
and error covariance
, iterative process is as follows:
(I) loop control variable is set
tinitial value, order
t=1, according to the value of iterations N, iterative loop starts;
(II) computation and measurement noise variance matrix
, subscript wherein
trepresent the
tvalue during inferior iteration;
(III) calculate root mean square and newly cease covariance matrix
with gain battle array
;
(IV) calculate the optimal estimation of the t time iteration
and error covariance
;
(V) if
, order
t=
t+1, then return to (II), otherwise carry out (VI);
(VI) finish VB iterative process, try to achieve in moving window the
inferior VB-UKF filtering estimated result:
,
,
;
(2.4) if
, order
, then return to step 2, otherwise finish VB-UKF in moving window, calculate execution step 3;
Step 3 utilizes fuzzy logic method dynamically to adjust
, detailed process comprises:
(3.1) calculate the actual value of the residual error variance battle array of current time
, estimated value
and matching degree index
;
(3.2) with
for the input parameter of fuzzy inference system (FIS), the adjustment amount of computation and measurement noise variance matrix
, and the measurement noise variance of VB method being estimated with this
adjust, obtain current time and measure noise variance
;
Measurement noise variance after step 4 generation readjustment is whole
, at current time, carry out a UKF algorithm, obtain the estimation of dbjective state
and error covariance
.
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| CN104794101A (en) * | 2015-04-08 | 2015-07-22 | 河海大学 | Fractional order nonlinear system state estimating method |
| CN104820788A (en) * | 2015-05-15 | 2015-08-05 | 河海大学 | Fractional order extended Kalman filtering method considering Levy noise |
| CN105699903A (en) * | 2016-01-15 | 2016-06-22 | 宁波飞拓电器有限公司 | Emergency lamp cell SOC estimation method based on variational Bayesian CKF |
| CN106487297A (en) * | 2016-11-24 | 2017-03-08 | 北京邮电大学 | A kind of PMSM parameter identification method based on covariance matching Unscented kalman filtering algorithm |
| CN107229060A (en) * | 2017-06-26 | 2017-10-03 | 北京工商大学 | A kind of gps measurement data processing method based on adaptive-filtering |
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Application publication date: 20141022 |