Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman教材.pdf

Journal of Process Control 21 (2011) 585–601
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Journal of Process Control
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Identification of process and measurement noise covariance for state and
parameter estimation using extended Kalman filter
Vinay A. Bavdekar a, Anjali P. Deshpande b, Sachin C. Patwardhan a,∗
a Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076, India
b Systems and Control Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
article info abstract
Article history: The performance of Bayesian state estimators, such as the extended Kalman filter (EKF), is dependent
Received 12 August 2010 on the accurate characterisation of the uncertainties in the state dynamics and in the measurements.
Received in revised form The parameters of the noise densities associated with these uncertainties are, however, often treated as
24 December 2010
‘tuning parameters’ and adjusted in an ad hoc manner while carrying out state and parameter estima-
Accepted 3 January 2011
tion. In this work, two approaches are developed for constructing the maximum likelihood estimates
Available online 4 March 2011
(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
Keywords:
Nonlinear state estimation process are either modelled as unstructured noise affecting all the states or as structured noise entering
Extended Kalman filter the process predominantly through known, but unmeasured inputs. The first approach is based on direct
Covariance estimation optimisation of the ML objective function constructed by using the innovation sequence generated from
Maximum likelihood estimates the EKF. The second approach – the extended EM algorithm – is a derivative-free method, that uses the
Expectation maximisation alg