Adaptive beamforming methods, when applied to practical problems, are known to suffer severe performance degradation if a mismatch occurs between the presumed and actual steering vectors. Such mismatch results in the suppression of the desired signal component, i.e., signal self-nulling phenomenon. Hence, robust approaches to adaptive beamforming and efficient steering vector estimation techniques are required. In this paper, a non-blind steering vector estimation technique is developed as a solution to the signal mismatch problem. The proposed technique extends the least mean square (LMS) and recursive least square (RLS) algorithms to estimate the array steering vector from the desired signal and array weights for robustness against possible mismatch. The resulting array vector is tested using the Kalman filter-based minimum variance distortionless response algorithm (KMVDR) by constraining the desired look direction, i.e., estimated steering vector, in the presence of additive white Gaussian noise. Moreover, a fast converging adaptive algorithm is proposed based on cascaded stages and error feedback. Experimental results have shown satisfactory convergence given the estimated steering vector, hence validating the proposed approach.