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We consider the problem of randomly choosing the sensors of a lineartime-invariant dynamical system subject to process and measurement noise. Wesample the sensors independently and from the same distribution. We measure theperformance of a Kalman filter by its estimation error covariance. Using toolsfrom random matrix theory, we derive probabilistic bounds on the estimationerror covariance in the semi-definite sense. We indirectly improve theperformance of our Kalman filter for the maximum eigenvalue metric and showthat under certain conditions the optimal sampling distribution that minimizesthe maximum eigenvalue of the upper bound is the solution to an appropriatelydefined convex optimization problem. Our numerical results show the efficacy ofthe optimal sampling scheme in improving Kalman filter performance relative tothe trivial uniform sampling distribution and a greedy sampling $\textit{withreplacement}$ algorithm.

Probabilistic Performance Bounds for Randomized Sensor Selection in Kalman Filtering