Sequential Sensing with Model Mismatch

TL;DR

This paper analyzes the performance of sequential sensing methods under model mismatch, providing bounds on information loss and power requirements, and explores strategies for initializing sensing with estimated covariance matrices.

Contribution

It offers novel theoretical bounds on Info-Greedy Sensing performance under model mismatch and proposes methods for effective initialization using sample covariance or sketching.

Findings

Performance bounds relate to posterior entropy gap.

Additional power needed under model mismatch.

Effective initialization strategies improve sensing accuracy.

Abstract

We characterize the performance of sequential information guided sensing, Info-Greedy Sensing, when there is a mismatch between the true signal model and the assumed model, which may be a sample estimate. In particular, we consider a setup where the signal is low-rank Gaussian and the measurements are taken in the directions of eigenvectors of the covariance matrix in a decreasing order of eigenvalues. We establish a set of performance bounds when a mismatched covariance matrix is used, in terms of the gap of signal posterior entropy, as well as the additional amount of power required to achieve the same signal recovery precision. Based on this, we further study how to choose an initialization for Info-Greedy Sensing using the sample covariance matrix, or using an efficient covariance sketching scheme.