State and parameter estimation using extended Kitanidis Kalman filter

State estimation in presence of unknown parameter variations has received considerable attention in literature. The conventional approach is to model the unknown drifting parameters as random walk model and estimate them simultaneously with states by augmenting them with the states of the system. However, the estimates critically depend on the tuning of the random walk model. Kitanidis Kalman Filter (KKF) [1] is an unbiased minimum variance estimator for only the states in presence of unknown inputs for linear systems. KKF allows optimal estimates of states to be obtained in presence of unknown inputs by appropriately choosing the gain matrix during the state update step. In this work, we investigate the problem of state and parameter estimation for nonlinear systems using extended Kitanidis Kalman Filter (EKKF). EKKF enables state and parameter estimation separately. In particular, we extend the work of Ganesh et al. [2] by providing a maximum likelihood based moving window framework for parameter estimation based on the innovations generated by EKKF. Towards this end, we characterise the innovations generated by KKF and show that unlike Kalman filter where the innovations are white, the innovations generated in KKF are a coloured Gaussian stochastic process. We also present a recursive approach for computing the covariance kernel of the innovations. The proposed method is applied to a simulation and an experimental case study to demonstrate its utility. The results indicate that the proposed method can be a useful tool for state and parameter estimation of nonlinear systems. (C) 2019 Elsevier Ltd. All rights reserved.