Optimal filtering for systems with finite-step autocorrelated process noises, random one-step sensor delay and missing measurements

• We study the optimal filtering problem for time-varying systems with correlated noises and uncertain observations.
• We design an optimal Kalman filtering algorithm in the sense of minimum mean square error (MMSE).
• We propose a new Kalman filtering algorithm which is suitable for online applications.

The optimal filtering problem is investigated for a class of discrete stochastic systems with finite-step autocorrelated process noises, random one-step sensor delay and missing measurements. The random disturbances existing in the system are characterized by the multiplicative noises and the phenomena of sensor delay and missing measurements occur in a random way. The random sensor delay and missing measurements are described by two Bernoulli distributed random variables with known conditional probabilities. By using the state augmentation approach, the original system is converted into a new discrete system where the random one-step sensor delay and missing measurements exist in the sensor output. The new process noises and observation noises consist of the original stochastic terms, and the process noises are still autocorrelated. Then, based on the minimum mean square error (MMSE) principle, a new linear optimal filter is designed such that, for the finite-step autocorrelated process noises, random one-step sensor delay and missing measurements, the estimation error is minimized. By solving the recursive matrix equation, the filter gain is designed. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed filtering scheme.