Parameter Estimation: A Second Order Recursive Least Squares Algorithm

Abstract A second order recursive least squares algorithm is derived. It is shown that the algorithm encompasses both the RLS and the LMS algorithms as special cases. The computational complexity is the same as for the RLS algorithm, but requires some extra memory storage. The associated Ordinary Differential Equation (ODE) for the algorithm is proven to be globally exponentially stable. Further, it is demonstrated that the proposed algorithm has a higher ability to track time-varying signals than has the RLS-algorithm. The proposed algorithm especially handles those situations well where there is a simultaneous system change and decrease of signal power.