Recursive Nonlinear Set–Theoretic Estimation Based on Pseudo Ellipsoids

In this paper, the problem of estimating a vector x of unknown quantities based on a set of measurements depending nonlinearly on x is considered. The measurements are assumed to be taken sequentially and are corrupted by unknown but bounded uncertainties. For this uncertainty model, a systematic design approach is introduced, which yields closed–form expressions for the desired nonlinear estimates. The estimates are recursively calculated and provide solution sets X containing the feasible sets, i.e., the sets of all x consistent with all the measurements available and their associated bounds. The sets X are tight upper bounds for the exact feasible sets and are in general not convex and not connected. The proposed design approach is versatile and the resulting nonlinear filter algorithms are both easy to implement and efficient.