  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.
