Kalman filtering for general discrete-time linear systems

Information Filtering and Array Algorithms for Descriptor Systems Subject to Parameter Uncertainties

“…The filtered estimate recursion that solves the problem 1) is given by [12], [20] (9) (10) Remark 2.1: As it was demonstrated in [12], for the existence of a recursive solution of (9), it is required that has full column rank for all . It is easy to observe that for the usual state-space systems, this condition is always satisfied.…”

“…Lemma 2.1: Consider the problem of solving (19) where is the data matrix, is the measurement vector which is assumed to be known, is the unknown vector, , and are given weighting matrices, are perturbations modeled by (20) The solution of the optimization problem (19) is given by (21) where the modified weighting matrices are defined by…”

“…Recently, filtering and control of descriptor systems have received great attention in the literature [3]- [7], [20], [21], [25]- [28]. This interest is motivated by the fact that many systems can be modeled naturally in descriptor formulation.…”

Applications of Robust Descriptor Kalman Filter in Robotics

“…The answer is given by the elegant recursive algorithm of the Kalman filter which can be obtained considering recursively the one-step deterministic optimum data fitting problem (12) The resulting descriptor Kalman filter in filtered form is given by the following theorem (cf. [6], [24], [23], [12]). …”

Optimal unbiased reduced order filtering for discrete-time descriptor systems via LMI

“…As in the standard systems, the knowledge of the state is required for the control or for the failure detection. Full order state estimation for discrete-time descriptor systems has been studied in [4,5,6,7]. Recent attention has been concentrated on the H ∞ filtering since, in contrast to the standard Kalman filtering, it does not need any knowledge of the statistical properties of the noise.…”