A New Type of Normalized LMS Algorithm Based on the Kalman Filter

While the LMS algorithm and its normalized version (NLMS), have been thoroughly used and studied, and connections between the Kalman filter and the RLS algorithm have bean established, the connection between the Kalman filter and the LMS algorithm has not received much attention. By linking these two algorithms, a new normalized LMS algorithm can be derived that has some advantages to the classical one. Firstly, its stability is guaranteed since it is a special case of the Kalman filter. Secondly, it suggests a new way to control the step size that results in optimum convergence for a large range of input signal powers, that occur in many applications. Finally, it prevents measurement noise amplification that occurs in the NLMS algorithm for low order filters, like the ones used in OFDM equalization systems.