Design of Confidence Sets for Estimation with Approximate Piecewise Linear Constraint

Constrained state estimation has been studied in the literature usually from the point estimation perspective. That is, a random vector is designed and its covariance matrix is searched based on contextual information available in addition to the measured data. This paper deals with interval/ set estimation. A random set covering the unknown state with a predefined probability is constructed for a Gaussian estimate and an approximate piecewise linear constraint. The proposed approach combines constrained estimation with hypothesis testing and its discussion is provided.