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The problem of state estimatio for discrete-time stochastic descriptor systems ith delayed measurements is addressed. Using the method of measurements reorganisation, the recursive state estimatio and corresponding filtering error covariance are derived. The calculatio of the estimator includes t o 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) innovatio model and projectio formula. The latter is derived by utilising the singular value decompositio and standard Kalma filtering. The authors' concept is the measurements reorganisatio hich converts the time-delay system into a delay-free but ith-different-measurement system, and leads to the computatio saving of the estimator. A numerical example is presented to illustrate the give algorithm.