SIFt-RLS: Subspace of Information Forgetting Recursive Least Squares

This paper presents subspace of information forgetting recursive least squares (SIFt-RLS), a directional forgetting algorithm which, at each step, forgets only in row space of the regressor matrix, or the \textit{information subspace}. As a result, SIFt-RLS tracks parameters that are in excited directions while not changing parameter estimation in unexcited directions. It is shown that SIFt-RLS guarantees an upper and lower bound of the covariance matrix, without assumptions of persistent excitation, and explicit bounds are given. Furthermore, sufficient conditions are given for the uniform Lyapunov stability and global uniform exponential stability of parameter estimation error in SIFt-RLS when estimating fixed parameters without noise. SIFt-RLS is compared to other RLS algorithms from the literature in a numerical example without persistently exciting data.