New Normalized LMS Algorithms Based on the Kalman Filter

While the LMS algorithm and its normalized version (NLMS), have been thoroughly used and studied. Connections between the Kalman filter and the RLS algorithm have been established however, the connection between the Kalman filter and the LMS algorithm has not received much attention. By linking these two algorithms, a new normalized Kalman based LMS (KLMS) algorithm can be derived that has some advantages to the classical one. Their stability is guaranteed since they are a special case of the Kalman filter. More, they suggests a new way to control the step size, that results in good convergence properties for a large range of input signal powers, that occur in many applications. They prevent high measurement noise sensitivity that may occur in the NLMS algorithm for low order filters, like the ones used in OFDM equalization systems. In these paper, different algorithms based on the correlation form, information form and simplified versions of these are presented. The simplified form maintain the good convergence properties of the KLMS with slightly lower computational complexity.