Risk Sensitive Fir Filters for Stochastic Discrete-time State Space Models

In this paper, the finite impulse response (FIR) filter based on an exponential quadratic cost function is proposed for a stochastic discrete-time state space model. The joint probability density function of the current state and the external noises on the recent finite horizon is introduced and the corresponding expected value of the exponential quadratic cost function is minimized with respect to the current state. According to the sign of the scalar real parameter in the cost function, we have a risk averse or seeking criterion, from which the optimal FIR filter, called a risk sensitive FIR filter (RSFF), is derived. Being risk averse means that large weights are put on large estimation errors which are suppressed as much as possible. Being risk seeking means that large weights are put on moderate estimation errors. It is also shown via simulation that the proposed FIR filter has better performance than the conventional infinite impulse response (IIR) robust Kalman filter.