Risk Sensitive Estimators for Inaccurately Modelled Systems

Robustness of risk sensitive (RSE) estimators/filters for inaccurately modelled plant are elucidated and exemplified. A theorem which allows alternative pathway for deriving RSE filter relation and derivation of different closed form relations for RS filters in linear Gaussian cases is provided. Consequently, errors in expressions in earlier publications have been detected and rectified. Properties of RS filters are briefly reviewed and the interpretation of robustness of RS filters elaborated. Using Monte Carlo simulation, it is shown that RS filters perform significantly better compared to risk-neutral filters when (i) process noise covariance is in error (ii) the true system (truth model) contains unmodelled bias (iii) the state transition matrix is inaccurately known. Design pragmatics for the choice of the risk sensitive parameter is indicated.