In this paper, we investigate a problem of estimating time-varying sparse channel impulse response for wireless communications. We are primarily interested in the scenario where the support of channels (i.e., the location of nonzero elements in channel impulse response) rarely changes within a local period of time. The proposed channel estimator estimates both support and amplitudes of the channel impulse response in an iterative fashion using the expectation and maximization algorithm. In order to exploit the (temporal) joint sparsity as well as temporal correlation of the channel gains, the proposed channel estimator performs two steps 1) E-step: Kalman smoothing of channel gains under the sparsity constraint and 2) M-step: semidefinite relaxation (SDR) technique for estimating the common support of channel impulse responses. Numerical evaluation shows that the proposed method performs close to the Oracle-based Kalman smoother and outperforms the existing sparse channel estimators.