Unscented statistical linearization and robustified Kalman filter for nonlinear systems with parameter uncertainties

Kalman filter (KF) design is well established for perfectly known linear system and observation models. Real-world phenomena, however, have significant associated uncertainties, and the tuning of the KF is not so straightforward for tackling them. In this paper, we present a method of designing a robust filter for nonlinear systems with model parameter uncertainties. The uncertainties are imposed on the temporal changes in system parameters, which corresponds to the conditions that most real-world problems exhibit. Our proposed filter is based on a robustified KF, which assumes Gaussian distributed states and is designed to be robust to significant changes in the system parameters. The uncertain nonlinear systems are handled by using the linearized approximation models to guarantee the Gaussianity of states. This is achieved by using a statistical linearization in conjunction with unscented transformations and we thus call the linearization technique unscented statistical linearization (USL). The USL is employed for the prediction step of nonlinearly transformed state and the subsequent filtering is executed by using the robustified KF to make the filter robust to upcoming observations. We call our proposed filter for the uncertain nonlinear systems a robustified nonlinear KF (robustified NKF) and confirm the effectiveness by experiments using artificially generated data.