In signal processing, the lattice algorithms have been widely applied to spectral analysis. Their best known example in geophysics is Burg's filtering. In fact, lattice structures can be used to construct algorithms solving any kind of prediction problems. In this paper, I derive two of these algorithms. They generalize two classical adaptive algorithms used in spectral analysis: the least-squares lattice (LSL) algorithm, and Burg's adaptive algorithm. I will apply these algorithms to the problem of multiples removal with non-stationary data; these applications will show the superiority of Burg's algorithm.