Robust Recursive Estimation for Uncertain Systems With Delayed Measurements and Noises

In this article, the problem of robust recursive estimation is studied for a class of uncertain systems with delayed measurements and delayed noises. The system model is subject to stochastic uncertainties which can be described by multiplicative noises. The phenomenon of delayed measurements occurs in a random way and the delay rate is characterised by a binary switch sequence with known probability distribution. The process noise and the measurement noise are both deterministic delay. By combining the noise at present time and the delayed noise into a whole one, the original system is transformed into an auxiliary stochastic uncertain system with discrete autocorrelated noises across time. Then, based on the orthogonal projection theorem and an innovation analysis approach, the desired robust recursive estimators including robust recursive filter, robust recursive predictor and robust recursive smoother are derived. A numerical simulation example is exploited to show the effectiveness of the proposed approaches.