Abstract
This paper discusses an approach of constructing a state estimator for a class of linear stochastic systems with randomly delayed observation data. State variables of the system is assumed to be observed over a communication network which causes the random delay. In our study, the random delay is assumed to consist of a sum of an average delay and a randomness. The observation data with the random delay can be represented by an observation model with state-dependent additive noise by using the Taylor series expansion around the time behind the average delay. This observation system becomes a stochastic bilinear system. The Kalman filter is constructed as the state estimator for the linear stochastic system based on the bilinear observation system. The effectiveness of the proposed Kalman filter is demonstrated for the several types of input signals such as a sinusoidal wave, a step function, a square wave and so on by numerical simulations.
