Adaptive grid risk-sensitive filter for non-linear problems

A novel adaptive grid-based method has been proposed for risk-sensitive state estimation in non-linear non-Gaussian problems. The algorithm, which is based on point-mass approximation, is called the adaptive grid risk-sensitive filter (AGRSF). Although risk-sensitive estimators have been known to be robust compared to their risk-neutral counterparts, the implementation of risk-sensitive filters (RSFs) is almost impossible except for very trivial systems like linear Gaussian systems. The existing extended risk-sensitive filter (ERSF) fails to take care of non-Gaussian problems or severe non-linearities. Recently, other variants of RSFs have been proposed for extending the range of applications of risk-sensitive techniques. The AGRSF has been formulated to act as a benchmark and aid in the validation of other RSFs. The algorithm uses a modified form of information state-based recursive relation and provides guidelines for the adaptive choice of grid points to improve the numerical efficiency. The developed filter has been applied to a single-dimensional non-linear poorly observable system and a non-linear two-dimensional bearing only tracking problem. The convergence of the algorithm has been shown by simulation. The estimation efficiency and computational load of AGRSF has been compared with other RSFs.