Kalman filtered compressive sensing with intermittent observations

• Published in: Signal processing Vol. 163; pp. 49 - 58
• Main Authors: Karimi, Hazhar Sufi, Natarajan, Balasubramaniam
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2019
• Subjects: Compressive sensing; Dynamic compressive sensing; Kalman filtered CS; Missing measurements; Packet losses; Dynamic compressive sensing; Missing measurements; Compressive sensing; Packet losses; Kalman filtered CS
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2019.05.004

•Kalman filter compressive sensing approach to deal with lossy measurements.•Quantify Error in Kalman Filter compressive sensing approach for the first time.•Uncover relationship between estimation error, sparsity and measurement loss.•Upper bound for the expected covariance of the estimation error is derived. Dynamic recursive recovery of a spatially sparse signal from compressed measurements has received a lot of attention recently. For example, Kalman filtered compressed sensing (KF-CS) has been proposed as a technique to estimate a sparse signal and its support set. However, these techniques can also suffer from performance degradation due to measurement loss. In this paper, we quantify the error dynamics in both sparse signal estimation and support set estimation for a KF-CS based strategy in the presence of measurement losses. Using input-to-state stability analysis, we provide an upper bound for the expected covariance of the estimation error for a given rate of information loss. This upper bound in turn allows us to evaluate the critical value for loss in measurements that ensures convergence of error in the KF-CS based algorithm. Simulations are presented to both validate theoretical results and highlight the efficiency of the recursive estimation of a sparse system with lossy measurements.