A Bayesian approach to beamforming is used to derive a sequential adaptive beamformer for estimating Gauss-Markov signals when the source direction-of-arrival (DOA) is uncertain. The DOA is assumed to be randomly selected from a discrete set of candidate directions, with a known probability mass function (PMF). Through a development similar to that of Bell, et al.[l], for i.i.d. sources, the resulting estimator becomes a weighted-combination of Kalman estimators for the source, where the observations for each estimator are retrieved using an MVDR beamformer for each of the candidate DOA's and where the relative weighting is proportional to the likelihood of the DOA given the observed data so far. Aspects of the proposed beamformer, such as robustness to DOA and asymptotic estimation performance are compared with conventional MVDR-based approaches.