Vortrag von Prof. Ali Belabbas

Linear systems with process and observation noises are widely used in engineering and physics to model systems as varied as the stock market and epidemics. Consider the estimation of the state of such systems  from the noisy measurements; the Kalman filter is known to be the minimum mean square error estimator when the noises are Gaussian. We address here how to design the sensors that minimize the error afforded by the Kalman filter. This problem of optimal sensor 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.  The approach can be used to solve the dual problem of optimal actuator design to minimize control energy.