Abstract: In the practical mobile communication systems, the number of multipaths, the corresponding path gains and path delays vary along with the mobile stations, and CCS methods fail to work in this dynamic scenario. A timevarying sparse channel estimate algorithm is proposed for MIMO OFDM systems, which is straightforwardly implemented in a standalone manner based on the wellknown Kalman Filter (KF) formulation. Exact reconstruction is provided by converting the Reweighed minimum 1 norm (RW1) problem into a KF with nonlinear equality constraints problem. In particularly, a PseudoMeasurement (PM) equation is formulated for the linearization of the RW1 constrained equation. Thereafter, KF is employed twice to recover the timevarying sparse channel. Simulation results are presented to demonstrate that Mean Square Error (MSE) of the proposed algorithm is superior to the conventional algorithms, e.g. Basic Persuit (BP), in the dynamic sparse scenario.