In this thesis, four methods specifically designed for sparse systems estimation are originally developed and presented, which were called here: Relaxations method, Successive Expansions method, l1-norm Minimization method and Automatic Adjustment of the Regularization Factor method. The four proposed methods are based on the Least Squares (LS) Estimation method and incorporate techniques related to convex optimization and to the theory of compressive sensing. The simulation results show that the proposed methods herein present superior performance than the ordinary LS estimation method and the Recursive Least Squares (RLS) with convex regularization method (l1-RLS), in many cases achieving the same optimal performance presented by the LS Oracle method. Furthermore, the proposed methods demand lower computational cost than the l1-RLS method.