Since the data matrix of the forward-backward linear prediction (FBLP) in spatial domain is not a Toeplitz-Hankel structure, the well-developed fast FBLP in temporal domain cannot be straightforwardly applied to the directions-of-arrival (DOAs) estimation of radiating sources via an array of sensors. Moreover, the slow convergence of the least mean square (LMS)-based FBLP presented by Lee et al. (1990) limits its practical application in the DOAs estimation by a short data record. Therefore, this correspondence proposes a Kalman-based forward-backward linear predictor in spatial domain for DOAs estimation with rapid convergence rate. The convergence rate of the mean-square prediction error and the convergent behavior of the estimated weight vector in mean square are analyzed to show that the Kalman-based FBLP is superior to the Kalman-based one-directional prediction (forward or backward prediction) algorithms for a finite data record. Simulation results are provided to substantiate the analysis. >