A comparative analysis of various least-squares identification algorithms

The purpose of this paper is to clarify the relations and to provide some selection guides among several time-series identification algorithms that appear in the literature under different names but which are essentially least-squares identification algorithms where only the numerical solution of the least-squares estimation problem is different. Such algorithms are, apart from the batch and the sequential forms of direct least-squares, the PARCOR (partial correlation) algorithm, (which may be in the Durbin, the Levinson or the autocorrelation form), the lattice or the ladder algorithm, also known as the Markel-Gray algorithm, the square-root algorithm, the equation-error algorithm, and related algorithms.Further to the above, we shall discuss why certain such algorithms differ in performance from the direct least-squares forms, in terms of convergence, convergence-rate, computational effort (speed) per iteration, and in terms of robustness to computational errors, such as arise when using short word-length computers.