State Estimation with Probability Constraints

• Published in: Proceedings of the 44th IEEE Conference on Decision and Control pp. 380 - 385
• Main Authors: Rotea, M., Lana, C.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Error analysis; Linear systems; Mean square error methods; Minimax techniques; Noise generators; Noise measurement; Probability; Random processes; State estimation; Statistics
• ISBN: 9780780395671; 0780395670
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2005.1582185

This paper considers a state estimation problem for a discrete-time linear system driven by a Gaussian random process. The second order statistics of the input process and state initial condition are uncertain. However, the probability that the state and input satisfy linear constraints during the estimation interval is known. A minimax estimation problem is formulated to determine an estimator that minimizes the worst-case mean square error criterion, over the uncertain second order statistics, subject to the probability constraints. It is shown that a solution to this constrained state estimation problem is given by a Kalman filter for appropriately chosen input and initial condition models. These models are obtained from a finite dimensional convex optimization problem. The application of this estimator to an aircraft tracking problem quantifies the improvement in estimation accuracy obtained from the inclusion of probability constraints in the minimax formulation.