One-step optimal measurement selection for linear gaussian estimation problems

This paper considers the problem of choosing the optimal linear measurement for the estimation of a state vector X in a Bayesian context where the prior distribution for X is multivariate Gaussian. The motivation for this comes from waveform-agile active sensing systems that have the capability of choosing transmit or illumination waveforms in real time. The measurement is characterized by a measurement matrix B with an energy constraint along each row. Qualitatively, the optimal solution applies the available transmit energy to each of the eigenmodes of the prior covariance of X, such that more energy is applied to modes with higher prior variance, in an attempt to bring the posterior variances down to a small common value. The allocation of the energy along the various eigenmodes requires the solution of a straightforward waterfilling problem.