Knowledge of the system parameters is necessary for optimum performance of the system, A new class of parameter estimation and adaptive control algorithms was shown in [6], which was applied to the robotic system. These algorithms require relaxed conditions of persistent excitation for parameter convergence, Here we propose an enhancement of these algorithms via improved initialization resulting from sliding surface in parameter error space, As a result we achieve faster convergence of parameters with proper initialization, Examples giving quantitative results from the robotics systems are provided, comparing the results with the original algorithms and a classical approach of a gradient-type algorithm.