We address the issue of MIMO channel estimation with the aid of a priori temporal correlation statistics of the channel as well as the spatial correlation. The temporal correlations are incorporated to the estimation scheme by assuming the Gauss-Markov channel model. Under the MMSE criteria, the Kalman filter performs an iterative optimal estimation. To take advantage of the enhanced estimation capability, we focus on the problem of channel estimation from a partial channel measurement in the MIMO antenna selection system. We discuss the optimal training sequence design, and also the optimal antenna subset selection for channel measurement based on the statistics. In a highly correlated channel, the estimation works even when the measurements from some antenna elements are omitted at each fading block.