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Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter

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Title Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter
 
Creator BAVDEKAR, VA
DESHPANDE, AP
PATWARDHAN, SC
 
Subject LEAST-SQUARES METHOD
STATISTICS
TUTORIAL
SYSTEMS
MODEL
Nonlinear state estimation
Extended Kalman filter
Covariance estimation
Maximum likelihood estimates
Expectation maximisation algorithm
 
Description The performance of Bayesian state estimators, such as the extended Kalman filter (EKE), is dependent on the accurate characterisation of the uncertainties in the state dynamics and in the measurements. The parameters of the noise densities associated with these uncertainties are, however, often treated as 'tuning parameters' and adjusted in an ad hoc manner while carrying out state and parameter estimation. In this work, two approaches are developed for constructing the maximum likelihood estimates (MLE) of the state and measurement noise covariance matrices from operating input-output data when the states and/or parameters are estimated using the EKF. The unmeasured disturbances affecting the process are either modelled as unstructured noise affecting all the states or as structured noise entering the process predominantly through known, but unmeasured inputs. The first approach is based on direct optimisation of the ML objective function constructed by using the innovation sequence generated from the EKF. The second approach - the extended EM algorithm - is a derivative-free method, that uses the joint likelihood function of the complete data, i.e. states and measurements, to compute the next iterate of the decision variables for the optimisation problem. The efficacy of the proposed approaches is demonstrated on a benchmark continuous fermenter system. The simulation results reveal that both the proposed approaches generate fairly accurate estimates of the noise covariances. Experimental studies on a benchmark laboratory scale heater-mixer setup demonstrate a marked improvement in the predictions of the EKE that uses the covariance estimates obtained from the proposed approaches. (C) 2011 Elsevier Ltd. All rights reserved.
 
Publisher ELSEVIER SCI LTD
 
Date 2012-06-26T07:30:37Z
2012-06-26T07:30:37Z
2011
 
Type Article
 
Identifier JOURNAL OF PROCESS CONTROL,21(4)585-601
0959-1524
http://dx.doi.org/10.1016/j.jprocont.2011.01.001
http://dspace.library.iitb.ac.in/jspui/handle/100/14140
 
Language English