Tracking of uncertain time-varying systems by state-space recursive least-squares with adaptive memory

State-space recursive least-squares (SSRLS) allows the designer to choose an appropriate model, resulting in superior tracking performance over the standard recursive least-squares (RLS) and least mean square (LMS). However, the tracking capability of this algorithm is dependent on the forgetting factor in presence of factors like model uncertainties and time-varying nature of observation noise etc. We address such problems In this work by developing time-varying SSRLS with adaptive memory. The tuning of the forgetting factor is done by stochastic gradient method. The ability to handle time-varying linear systems is a major enhancement of our previous work. The new filter is therefore, much more flexible and powerful. Based on this theory, we design a tracking algorithm that efficiently tracks time-varying systems.