A fast estimation algorithm for stochastic descriptor systems with delayed measurements

The problem of state estimation for discrete-time stochastic descriptor systems with delayed measurements is addressed. Using the method of measurements reorganisation, the recursive state estimation and corresponding filtering error covariance are derived. The calculation of the estimator includes two steps. One is for the steady estimator and the other is the 'non-steady-state' estimator. The former is obtained by the autoregressive moving average (ARMA) innovation model and projection formula. The latter is derived by utilising the singular value decomposition and standard Kalman filtering. The authors' concept is the measurements reorganisation which converts the time-delay system into a delay-free but with- different-measurement system, and leads to the computation saving of the estimator. A numerical example is presented to illustrate the given algorithm.