Risk-sensitive filtering for discrete-time systems with time-varying delay

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