A nonlinear second-order filtering strategy for state estimation of uncertain systems

In this paper, a new strategy referred to as the nonlinear second-order (NSO) filter is presented and used for estimation of linear and nonlinear systems in the presence of uncertainties. Similar to the popular Kalman filter estimation strategy, the proposed strategy is model-based and formulated as a predictor-corrector. The NSO filter is based on variable structure theory that utilizes a switching term and gain that ensures some level of estimation stability. It offers improvements in terms of robustness to modeling uncertainties and errors. The proof of stability is derived based on Lyapunov that demonstrates convergence of estimates towards the true state values. The proposed filtering strategy is based on a second-order Markov process that utilizes information from the current and past two time steps. An experimental system was setup and characterized in order to demonstrate the proposed filtering strategy's performance. The strategy was compared with the popular Kalman filter (and its nonlinear form) and the smooth variable structure filter (SVSF). Experimental results demonstrate that the proposed nonlinear second-order filter provides improvements in terms of state estimation accuracy and robustness to modeling uncertainties and external disturbances.