In this paper, we propose a new sparse signal recovery algorithm, referred to as sparse Kalman tree search (sKTS), that provides a robust reconstruction of the sparse vector when the sequence of correlated observation vectors are available. The proposed sKTS algorithm builds on expectation-maximization (EM) algorithm and consists of two main operations: 1) Kalman smoothing to obtain the a posteriori statistics of the source signal vectors and 2) greedy tree search to estimate the support of the signal vectors. Through numerical experiments, we demonstrate that the proposed sKTS algorithm is effective in recovering the sparse signals and performs close to the Oracle (genie-based) Kalman estimator.