In this paper we present a novel compressed sensing (CS) algorithm for the recovery of compressible, possibly time-varying, signal from a sequence of noisy observations. The newly derived scheme is based on the acclaimed unscented Kalman filter (UKF), and is essentially self reliant in the sense that no peripheral optimization or CS algorithm is required for identifying the underlying signal support. Relying exclusively on the UKF formulation, our method facilitates sequential processing of measurements by employing the familiar Kalman filter predictor corrector form. As distinct from other CS methods, and by virtue of its pseudo-measurement mechanism, the CS-UKF, as we termed it, is non iterative, thereby maintaining a computational overhead which is nearly equal to that of the conventional UKF.