Optimal filtering and smoothing for discrete-time stochastic singular systems

A stochastic singular system with correlated noises at the same time is transferred to the equivalent nonsingular system with correlated noises at the same and neighboring time. Applying time-domain innovation analysis method, the recursive full-order predictor, filter and smoother are presented for this nonsingular system. Further, the full-order filter and smoother are given for original stochastic singular linear systems with correlated noises. Recursive and nonrecursive computational formulas for estimation error covariance matrices are given. Furthermore, the steady-state filter and smoother are also investigated. The asymptotic stability is proved. All results generalize the standard Kalman filtering. A simulation example shows the effectiveness.