Development and numerical investigation of new non-linear Kalman filter variants

This study deals with recursive state estimation for non-linear systems. A new set of σ-points for the unscented Kalman filter is proposed as well as a way to substitute a non-linear output with a linear one. The importance of the function of the state which must be estimated is also illustrated and also the need for taking it into account when designing the state estimator. Mode-based estimators are proposed. All the suggested methods are compared with standard extended Kalman filter, unscented Kalman filter and particle filter with sampling importance resampling using simulations. The results show that the modifications proposed in some cases lead to considerable reduction in the estimation error.