Mean Square Projection Error Gradient-based Variable Forgetting Factor FAPI Algorithm

Abstract

This paper proposes a fast subspace tracking methods, which is called GVFF FAPI, based on FAPI (Fast Approximated Power Iteration) method and GVFF RLS (Gradient-based Variable Forgetting Factor Recursive Lease Squares). Since the conventional FAPI uses a constant forgetting factor for estimating covariance matrix of source signals, it has difficulty in applying to non-stationary environments such as continuously changing DOAs of source signals. To overcome the drawback of conventioanl FAPI method, the GVFF FAPI uses the gradient-based variable forgetting factor derived from an improved means square error (MSE) analysis of RLS. In order to achieve the decreased subspace error in non-stationary environments, the GVFF-FAPI algorithm used an improved forgetting factor updating equation that can produce a fast decreasing forgetting factor when the gradient is positive and a slowly increasing forgetting factor when the gradient is negative. Our numerical simulations show that GVFF-FAPI algorithm offers lower subspace error and RMSE (Root Mean Square Error) of tracked DOAs of source signals than conventional FAPI based MUSIC (MUltiple SIgnal Classification