Kalman filtering for state delay systems with multiplicative noises and random one-step sensor delay

The Kalman filtering problem is studied for a class of discrete state delay stochastic systems with multiplicative noises and random one-step sensor delay. A Bernoulli distributed random variable with known conditional probability is employed to characterize the phenomena of random one-step sensor delay. Based on the innovative analysis approach and recursive projection formula, a new linear optimal filter is designed such that, for the state delay, multiplicative noises and random one-step sensor delay, the estimation error is minimized. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed filtering scheme.