  We consider the problem of selecting an optimal set of sensor precisions to
estimate the states of a non-linear dynamical system using an Ensemble Kalman
filter and an Unscented Kalman filter, which uses random and deterministic
ensembles respectively. Specifically, the goal is to choose at run-time, a
sparse set of sensor precisions for active-sensing that satisfies certain
constraints on the estimated state covariance. In this paper, we show that this
sensor precision selection problem is a semidefinite programming problem when
we use l1 norm over precision vector as the surrogate measure to induce
sparsity. We formulate a sensor selection scheme over multiple time steps, for
certain constraints on the terminal estimated state covariance.
