Risk-sensitive estimation for systems with time-varying observation delay

In this paper the risk-sensitive filtering problem with time-varying delay is investigated. The problem is first transformed into an equivalent optimization problem in Krein space. Then the observations with time-varying delays are restructured as ones with multiple constant delays by defining a binary variable to model the arrival process of the observations, which contain the same state information as the original observations. Finally, based on the reorganized innovation analysis approach in Krein space, the solution to the proposed risk-sensitive filtering is given in terms of the solutions to Riccati and matrix difference equations.