A Novel and Computationally Efficient Joint Unscented Kalman Filtering Scheme for Parameter Estimation of a Class of Nonlinear Systems

Unscented Kalman filter (UKF) is one type of the sigma point Kalman filters and it is based on unscented transformation. UKF is used for parameter estimation of various dynamic systems and for such purpose either joint UKF (JUKF) or dual UKF (DUKF) schemes are considered. JUKF is based on estimating states and parameters together by using only one filter. For DUKF, states and parameters are decoupled and two separate filters are considered. In this paper, a modification to standard JUKF is proposed for parameter estimation which is based on decoupling parameter vector and updating parameter estimates by considering the error transformation between measurements and transformed sigma points during measurement update into the parameter errors. A linear transformation is proposed for such a purpose. Thus, the computational complexity of the standard JUKF is reduced significantly since parameters are decoupled from the state vector while the convergence of parameter estimate(s) is guaranteed. The new modified JUKF scheme is promising to be used for the parameter estimation of dynamic systems for which a linear transformation between measurement and parameter errors can be obtained. The effectiveness of this new scheme is proven by applying it to two nonlinear dynamic systems.