Adaptive Kalman filtered compressed sensing for streaming signals

In this paper, we propose an adaptive Kalman filter based on compressed sensing for the reconstruction of streaming signals. The Analog Information Converter (AIC) structure is implemented for streaming compressive sampling while the signal is observed from a sliding window of finite length. Then we use the correlations between the signals of two continuous windows to model the process in the state-space form so that the Kalman Filter can be implemented to obtain the MMSE estimation of the streaming signals. A simple algorithm with low complexity is proposed to estimate the support at the beginning of every recursion and the estimation that will be refined during the whole operation. As such, the proposed method doesn’t need an accurate initial estimation which always demands more observations and higher complexity. The simulation results show that the proposed adaptive Kalman filter can greatly reduce the observation dimensions based on compressed sensing and converge to the ideal Kalman filter with low complexity.