Recursive least squares estimation with rank two updates

New recursive least squares algorithms with rank two updates (RLSR2) that include both exponential and instantaneous forgetting (implemented via a proper choice of the forgetting factor and the window size) are introduced and systematically associated in this report with well-known RLS algorithms with rank one updates. Moreover, new properties (which can be used for further performance improvement) of the recursive algorithms associated with the convergence of the inverse of information matrix and parameter vector are established in this report. The performance of new algorithms is examined in the problem of estimation of the grid events in the presence of significant harmonic emissions.