A Blind channel estimation of Multiple-Input Multiple-Output-Orthogonal Space Time Block Code (MIMO-OSTBC), using Higher Order Statistics with Kalman Filter (HOS-KF), is proposed. It offers better performance, improvement in spectral efficiency and moderate computational complexity. This paper focuses on channel estimation without CSI information for fast time varying MIMO systems. It adds advantages of HOS as well as of KF. Minimization of cost function obtained by higher order kurtosis is done by Kalman filter. KF estimates the value after each iteration and then update it. Matlab simulation used to evaluate the channel estimation. Performance parameters, Bit Error Rate (BER) and Mean Square Error (MES) versus Signal to Noise Ratio (SNR) are plotted. Simulation results with different modulation schemes like M-QAM and M-PSK depict that proposed method outperforms as compare to traditional Independent Component analysis (ICA) and KF method in terms of BER, MES. Spectral efficiency also improves as no Channel State Information (CSI) is needed for proposed estimation, as it is needed in KF. This all good results we got at the cost of moderate computational complexity. This is the first research of HOS and KF based channel impulse response estimation, for the time varying velocity of the receiver in an OSTBC-MIMO system. All the performance criteria BER, MES & spectral efficiency are improved in proposed HOS-KF method.