Research ArticleStochastic stability of sigma-point Unscented Predictive Filter

- The UPF is derived based on unscented transformation (UT), which extends the study of traditional predictive filter.
- The algorithm flow of UPF is proposed and demonstrated that the estimation accuracy of UPF is higher than that of the conventional PF.
- The error behavior of UPF for general nonlinear systems is analyzed.
- The estimation error remains bounded if the system satisfies the initial estimation error, the disturbing noise terms as well as the model error are small enough.

In this paper, the Unscented Predictive Filter (UPF) is derived based on unscented transformation for nonlinear estimation, which breaks the confine of conventional sigma-point filters by employing Kalman filter as subject investigated merely. In order to facilitate the new method, the algorithm flow of UPF is given firstly. Then, the theoretical analyses demonstrate that the estimate accuracy of the model error and system for the UPF is higher than that of the conventional PF. Moreover, the authors analyze the stochastic boundedness and the error behavior of Unscented Predictive Filter (UPF) for general nonlinear systems in a stochastic framework. In particular, the theoretical results present that the estimation error remains bounded and the covariance keeps stable if the system׳s initial estimation error, disturbing noise terms as well as the model error are small enough, which is the core part of the UPF theory. All of the results have been demonstrated by numerical simulations for a nonlinear example system.