This study investigates the ability of recursive least squares (RLS) and
least mean square (LMS) adaptive filtering algorithms to predict and quickly
track unknown systems. Tracking unknown system behavior is important if
there are other parallel systems that must follow exactly the same behavior
at the same time. The adaptive algorithm can correct the filter coefficients
according to changes in unknown system parameters to minimize errors between
the filter output and the system output for the same input signal. The RLS
and LMS algorithms were designed and then examined separately, giving them a
similar input signal that was given to the unknown system. The difference
between the system output signal and the adaptive filter output signal
showed the performance of each filter when identifying an unknown system.
The two adaptive filters were able to track the behavior of the system, but
each showed certain advantages over the other. The RLS algorithm had the
advantage of faster convergence and fewer steady-state errors than the LMS
algorithm, but the LMS algorithm had the advantage of less computational
complexity.