Risk sensitive Kalman filter with non-scalar risk-sensitive factor

A risk-sensitive estimator/filter optimizes (minimizes) an exponential cost criterion in order to obtain increased robustness compared to risk-neutral filters. Risk sensitive estimation depends on the choice of a parameter known as risk sensitive factor which provides a weight on the previous (and current) estimation errors. In existing literature, the RSF is formulated with a scalar risk sensitive factor, limiting its potential use as a flexible tuning parameter. In this paper, we extend the RSF formulation by proposing the use of risk sensitive matrix (RSM) instead of a scalar factor. It is argued that the use of the risk sensitive matrix provides enhanced flexibility when used as a filter tuning artefact. Using a two dimensional linear problem, it has been demonstrated that the RSM provides more robust estimates in the presence of modelling uncertainties. It is conjectured that this theory may be further extended to nonlinear risk sensitive estimators like extended risk sensitive filter (ERSF), central difference risk sensitive filter (CDRSF), risk sensitive unscented Kalman filter (RSUKF), adaptive grid risk sensitive filter (AGRSF) and risk sensitive particle filter (RSPF).