Simultaneous input & state estimation, singular filtering and stability

A Deterministic Least Squares Approach for Simultaneous Input and State Estimation

“…z = ẑ = C x + D ŵ. The third term is zero with x = x from (29). We therefore conclude that w = ŵ, x(0) = x(0) achieve a minimum of the performance index with the minimum given by (35).…”

“…In [27] there is no direct feedthrough of the process noise to the measurements and there is an assumption that the first Markov parameter has full column rank. In [29] there is further analysis with reference to stability, convergence and system inversion. In [28] the case where there is a direct feedthrough matrix of full column rank is treated.…”

“…In [28] the case where there is a direct feedthrough matrix of full column rank is treated. We mention that [27], [28] and [29] contrast with the present work in considering discrete time stochastic systems, whereas here we deal with the continuous time case and present a first principles approach which is purely deterministic.…”