This paper presents methods for the estimation of the time-varying directions of arrival (DOAs) of signals emitted by moving sources. Following the sparse Bayesian learning (SBL) framework, prior information of unknown source amplitudes is modeled as a multi-variate Gaussian distribution with zero-mean and time-varying variance parameters. For sequential estimation of the unknown variance, we present two sequential SBL-based methods that propagate statistical information across time to improve DOA estimation performance. The first method heuristically calculates the parameters of an inverse-gamma hyperprior based on the source signal estimate from the previous time step. In addition, a second sequential SBL method is proposed, which performs a prediction step to calculate the prior distribution of the current variance parameter from the variance parameter estimated at the previous time step. The SBL-based sequential processing provides high-resolution DOA tracking capabilities. Performance improvements are demonstrated by using simulated data as well as real data from the SWellEx-96 experiment.