Principal component pursuit (PCP) is a state-of-the-art approach to background estimation problems. Due to their higher computational cost, PCP algorithms, such as robust principal component analysis (RPCA) and its variants, are not feasible in processing high definition videos. To avoid the curse of dimensionality in those algorithms, several methods have been proposed to solve the background estimation problem incrementally. We build a batch-incremental background estimation model by using a special weighted low-rank approximation of matrices. Through experiments with real and synthetic video sequences, we demonstrate that our model is superior to the existing state-of-the-art background estimation algorithms such as GRASTA, ReProCS, incPCP, and GFL.