A second-order recursive algorithm with applications to adaptive filtering and subspace tracking

A second-order recursive algorithm for adaptive signal processing is proposed, and a similar algorithm is derived for signal subspace tracking. 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 some extra memory storage is required. The associated ordinary differential equation (ODE) for the autoregressive exogenous (ARX) case algorithm is proven to be globally exponentially stable. Furthermore, 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 well those situations where there is a simultaneous system change and a decrease of signal power.