State-space RLS

Abstract

Kalman filter is linear optimal estimator for random signals. We develop state-space RLS that is counterpart of Kalman filter for deterministic signals i.e. there is no process noise but only observation noise. State-space RLS inherits its optimality properties from the standard least squares. It gives excellent tracking performance as compared to existing forms of RLS. A large class of signals can be modeled as outputs of neutrally stable unforced linear systems. State-space RLS is particularly well suited to estimate such signals. The paper commences with batch processing the observations, which is later extended to recursive algorithms. Comparison and equivalence of Kalman filter and state-space RLS become evident during the development of the theory. State-space RLS is expected to become an important tool in estimation theory and adaptive filtering.