Growing window recursive quadratic optimization with variable regularization

We present a growing-window variable-regularization recursive least squares (GW-VR-RLS) algorithm. Standard recursive least squares (RLS) uses a time-invariant regularization. More specifically, the inverse of the initial covariance matrix in classical RLS can be viewed as a regularization term, which weights the difference between the next state estimate and the initial state estimate. The present paper allows for time-varying in the weighting as well as what is being weighted. This extension can be used to modulate the speed of convergence of the estimates versus the magnitude of transient estimation errors. Furthermore, the regularization term can weight the difference between the next state estimate and a time-varying vector of parameters rather than the initial state estimate as is required in standard RLS.