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

Abstract

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. INDEX TERMS Kalman filter, unscented Kalman filter, joint unscented Kalman filter, parameter estimation, dynamic systems.

Non-Contact Respiratory Rate Estimation in Real-Time With Modified Joint Unscented Kalman Filter

“…It is reported in [57], [68], [69] that there are two main types of parameter estimation approaches using family of KFs, these are dual and joint filtering. In joint filtering, the parameters are concatenated to state vector and they are estimated by just one filter, whereas in dual filtering, two filters are separately used for the state and parameter estimation.…”

“…The selection of T and ξ are the important points of the proposed modification for RR estimation. For the further details of the modification and the selection of T and ξ please refer to [57]. As indicated previously, parameter update rule is changed and a hyperbolic tangent function is considered in this study to include non-linearity between measurements and parameters.…”

“…MLE) [41], and MAP estimation is a regularization of MLE in case of prior statistics. This analysis includes a similar one given in [57], [68] for JUKF and a similar modified JUKF. Conditions, which make the parameter estimate in ModJUKF a MAP estimate, are discussed hereby in comparison with standard JUKF case.…”

“…This expression is called as posterior log-likelihood function [57], [68], and map parameter estimate is given aŝ θ…”

“…In Kalman filtering framework general assumption is that all noise densities are Gaussian. Probability densities in posterior log-likelihood function [57], [68] can be given as L, Lm, L θ Size of state,measurement and parameter vector, respectively 3:…”