In this work we propose an approach for the direction of arrival (DOA) estimation problem which increases the performance of subspace algorithms. The approach is based on the extrapolation of the data matrix using an autoregressive model. In the proposed method, the AR coefficients are calculated using least square lattice (LSL) structure. In low signal to noise levels the coefficients steming from the LSL structure enable a more efficient modeling of subspaces. Via simulations, it is shown that the estimation performance of subspace algorithms is enhanced compared to non-extrapolated data based estimation and other extrapolated data based estimation methods mentioned in the literature.