Convergence conditions for an optimal solution in adaptive recursive filters

In this paper, a One Step Adaptive Recursive Prediction Filter (OSARPF) is described. OSARPF is an adaptive filter for recursive systems and is suitable for parameter estimation problems. By representing the recursion in matrix notation, blocks of input data are used for adaptation. Using the past reference input for recursion, the adaptive filter can be shown to converge to an optimal solution. Adaptation equations are then developed for updating the coefficients of the adaptive filter and the adaptation process can be shown to converge to the optimal solution.