Sparse Sensing for Estimation with Correlated Observations

Abstract—We focus on discrete sparse sensing for non-linear parameter estimation with colored Gaussian observations. In particular, we design offline sparse samplers to reduce the sensing cost as well as to reduce the storage and communications requirements, yet achieving a desired estimation accuracy. We optimize scalar functions of the Cramér-Rao boundmatrix, which we use as the inference performance metric to design the sparse samplers of interest via a convex program. The sampler design does not require the actual measurements, however it needs the model parameters to be perfectly known. The proposed approach is illustrated with a sensor placement example. Index Terms—Sparse sensing, sensor selection, sensor place-ment, dependent observations, non-linear least squares. I