State Estimation with Probability Constraints

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 e...

Full description

Saved in:
Bibliographic Details
Published inProceedings of the 44th IEEE Conference on Decision and Control pp. 380 - 385
Main Authors Rotea, M., Lana, C.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2005
Subjects
Error analysis
Linear systems
Mean square error methods
Minimax techniques
Noise generators
Noise measurement
Probability
Random processes
State estimation
Statistics
Online AccessGet full text

Cover

More Information
Summary: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.
ISBN:9780780395671
0780395670
ISSN:0191-2216
DOI:10.1109/CDC.2005.1582185