<p>This paper introduces a cost-effective methodology to optimally extract the required subspace from the measured covariance matrix (CM) for angle-of-arrival (AOA) estimation. The suggested approach, a low cost subspace extraction technique (LCSET), leverages a limited number of the most independent columns from the CM to formulate the so-called projection matrix (PM) which can be considered as the best approximation of noise subspace (NSS). To improve the column selection, the diagonal elements of the CM (i.e., signal variances) are set to zero before the selection process. This is because these entries of the CM do not represent any information about the dependency between the signals collected from different array elements. By adopting the suggested procedure, we can significantly speed up the subspace computation without sacrificing estimation performance. Therefore, we are able to tackle the trade-off between accuracy and complexity in classical subspace-based algorithms. Subsequently, the introduced technique is employed to develop a reliable AOA estimation which is then applied for target tracking in frequency modulated continuous wave (FMCW) radar system. To validate the theoretical claims and highlight the benefit of the LCSET, a computational complexity analysis is presented followed by comprehensive Monte Carlo simulations where the performance of the proposed algorithm is systematically compared to several AOA estimators, including the Cramer-Rao lower bound (CRLB). Relying on the achieved results, the performance of the suggested technique aligns with that for super-resolution multiple signal classification (MUSIC) algorithm and surpasses other well-known subspace methods with drastically reduced computational complexity.</p>