Estimation of fluctuating power spectral density across a sensor array

In this paper, we address the challenge of estimating the power spectral density of noise tied to a single source measured at an array of sensors. The purpose is to identify windows of opportunity when the noise possesses sufficiently low power to potentially observe weaker signals in the environment. The scenario is formulated via basis expansion models, which then define the time-varying ground truth power spectral densities. We compare this to a number of estimation methods based on data. This includes an averaged periodogram — the Welch method — as a baseline. We also apply a space-time covariance matrix estimation approach, where the matrix is perturbed since the estimate is based on finite data; a first advantage of this method is achieved by optimally limiting the lag support based on a recently proposed method; a second advantage is gained by performing a rank one approximation via an analytic eigenvalue decomposition. We discuss some of the relevant theoretical background, and demonstrate in examples and simulations how the number of sensors and some of the parameters of the basis expansion model influence the results.