Steady-state mean squared error and tracking performance analysis of the quasi-OBE algorithm

Abstract

The quasi-OBE (QOBE) algorithm is a set-membership adaptive filtering algorithm based on the principles of optimal bounding ellipsoid (OBE) processing. This algorithm can provide enhanced convergence and tracking performance as well as reduced average computational complexity in comparison with the more traditional adaptive filtering algorithms such as the recursive least squares (RLS) algorithm. In this paper, we analyze the steady-state mean squared error (MSE) and tracking performance of the QOBE algorithm. For this purpose, we derive energy conservation relation of the QOBE algorithm. The analysis leads to a nonlinear equation whose solution gives the steady-state MSE of the QOBE algorithm in both stationary and nonstationary environments. We prove that there is always a unique solution for this equation. The results predicted by the analysis show good agreement with the simulation experiments.