Extended, Unscented Kalman, and Sigma Point Multiple Distribution Estimation Filters for Nonlinear Discrete State-Space Models

The extended and unscented Kalman multiple distribution estimation filters (EKMDEF/UKMDEF) were recently proposed for nonlinear continuous-discrete state-space models and their superior filtering accuracy was shown in the simulation of satellite reentry. The EKMDEF/UKMDEF is based on the multiple distribution estimation (MDE) for the filtered state probability density function (PDF) and this letter provides its alternate derivation with a comparison of the Gaussian sum filter (GSF). This result sheds light on the relationship between the EKMDEF/UKMDEF and the GSF and a new filter that is more stable than the EKMDEF/UKMDEF can be designed. The performance of the proposed filter is examined for nonlinear discrete state-space models using benchmark simulation problems and is compared with those of the representative filters including particle filters (PFs).