Adaptive Kalman Filtered Compressive Sensing for Streaming Signals

In this paper, we investigate the problem of utilizing the Kalman Filter to reconstruct signals with sparse frequency content under a streaming CS framework. We develop a Gaussian Markov model of the sparse streaming signal under the Analog-to-Information Converter (AIC) hardware structure and propose an adaptive Kalman Filter for the reconstruction. Different from existing CS schemes for streaming signals, we exploit the correlations between the signals of two consecutive observation windows to model the process in the state transition form so that the Kalman Filter can be incorporated to obtain the convergent estimation of the input streaming signal. Simulation experiments show the feasibility of the proposed model and demonstrate the superior performance of the proposed algorithms.