In this brief, we present a nontraditional approach for estimating and tracking signal direction-of-arrival (DOA) using an array of sensors. The proposed method consists of two stages: in the first stage, the sources modeled by autoregressive (AR) processes are estimated by the celebrated Kalman filter, and in the second stage, the efficient QR-decomposition-based recursive least square (QRD-RLS) technique is employed to estimate the DOAs and AR coefficients in each observed time interval. The AR-modeled sources can provide useful temporal information to handle cases such as the number of sources being larger than the number of antennas. In addition, the symmetric array enables one to transfer a complex-valued nonlinear problem to a real-valued linear one, which can reduce the computational complexity. Simulation results demonstrate the superior performance of the algorithm for estimating and tracking DOA under different scenarios.