Some alternatives in recursive estimation†

Abstract

Abstract A summary is presented of several different ways of computing recursive linear least-squares estimates for discrete-time stochastic processes. First focussing on processes with known finite-dimensional models—state-space, ARM A and lumped covariance. Several different algorithms are described—Riccati, square root, Chandrasekhar, fast square root—and also results on convergence and steady-state behaviour. Smoothed estimates and the use of scattering theory to describe their inter-play with filtered estimates are briefly mentioned. Secondly results available for general stationary and non-stationary processes are noted.