Riccati Observers for Position Estimation Using (Pseudo) Range and Biased Velocity Information

摘要

This paper addresses the problems of estimating the position of an object moving in n( ≥ 2) -dimensional Euclidean space using possibly biased velocity measurements and possibly biased range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global uniform exponential stability of zero estimation errors. These results are obtained under persistent excitation (p.e.) conditions whose satisfaction i) depends on the number and relative positioning of source points and on the object motion properties, and ii) ensures uniform observability and good conditioning of the CRE solutions. In particular, these conditions can be satisfied in the case of a single source point and a moving object. Simulation results illustrate the performance of the proposed observers in this latter case.