Sensor Selection with Correlated Noise

We consider the problem of selecting k sensors out of m available (linear) sensors, so that the error in estimating some parameters is minimized. When the sensor noises are uncorrelated, the sensor selection problem can be (approximately) solved by a method recently suggested by Joshi and Boyd, which relies on a convex relaxation of the underlying combinatorial optimization problem. This thesis describes a non-trivial extension of the relaxation method to the case when the measurement noises are correlated, as occurs, for example, in a sensor scheduling problem in a dynamic system. We develop several new semidenite programming (SDP) relaxations for the problem, which give provable bounds on the attainable performance, as well as suboptimal sensor selections. Numerical experiments for sensor scheduling suggest that the methods work well