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The geometry of optimal experiment design for vector-valued Ornstein-Uhlenbeck processes.

Presented by: 
Mohamed-Ali Belabbas University of Illinois at Urbana-Champaign, University of Illinois at Urbana-Champaign
Thursday 24th November 2016 - 14:00 to 15:00
INI Seminar Room 2
Ornstein-Uhlenbeck processes are commonly used as models in engineering, biology and finance. Consider the estimation of the state of such processes from linear, noisy measurements; the Kalman filter is known to be the minimum mean square error estimator when the measurement noise is Gaussian. We address here how to design the measurements that minimize the error afforded by the Kalman filter. This problem of optimal experiment design, which is almost as old as the Kalman filter itself,  is however not convex. As a consequence, many ad hoc methods have been used over the years to solve it. We show in this talk how a geometric approach allows us to characterize and obtain the optimal designs exactly. This optimal design yields the lowest possible estimation error from linear measurements with a fixed signal to noise ratio. 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons