Conjugate gradient algorithm design with RLS normal equation

In this paper, the conjugate gradient (CG) algorithm is modified using the RLS normal equation and new data windowing scheme. It is known that CG algorithm has fast convergence rate and numerical stability. However, the existing CG algorithms still suffer from either slow convergence or high misadjustment compared with the RLS algorithm. In this paper, the parameter beta for CG algorithm is redesigned from the RLS normal equation and a general data windowing scheme reusing the data inputs is presented to solve these problems. The optimal property of parameter alpha is also analyzed using the control Lyapunov function (CLF) of the square deviation of weight error vector. The superior performance of the proposed algorithms over the RLS algorithm and the other existing CG algorithms is demonstrated by computer simulations.