Sensor Selection via Randomized Sampling

Given a linear dynamical system, we consider the problem of selecting a subset of sensors out of the total set in order to optimize two commonly used metrics of observability, namely the maximum eigenvalue and the trace of the observability Gramian. We apply a variant of a well-known randomized sampling algorithm and derive novel lower bounds on the two metrics relative to the total value with high probability. The computational complexity of the algorithm is linear in the total number of sensors while the lower bounds are independent of the total number of sensors. The empirical performance of the proposed approach on synthetically generated datasets shows a remarkable improvement over the theoretical bounds, especially in the regime of low number of sensors selected.