Observation-parameterised risk-sensitive state estimation with correlated noise processes

In this article we consider risk sensitive filtering and smoothing for a nonlinear scalar-valued dynamical system with correlated state and observer noise processes. The model we consider is an Ito diffusion state process observed through a Wiener process. Using gauge transformation techniques, we compute an observation-parameterised risk sensitive filter for the system just described. An important feature of the filters we compute is that no stochastic integrations are involved. An observation-parameterised smoother is also computed.