Stepped sine system identification, errors-in-variables and the quotient singular value decomposition

Abstract

We develop a parameter estimation algorithm for the stepped sine identification of the transfer function of a linear system when all measurements are corrupted by noise. It consists of three steps: (1) An overdetermined set of linear equations containing stepped-sine measurements is solved in a linear least squares sense. (2) The resulting error covariance matrix is used to construct the noise covariance matrix for a second set of linear equations. (3) This second set of equations, in which all data are noisy, is solved using the quotient singular value decomposition, which is a generalisation of the singular value decomposition. Simulation results show that this new method remains accurate even at extremely bad signal-to-noise ratios. It is also possible to take into account offset and drift of the measurement sensors. Finally, all algorithmic steps involved led themselves to recursive updating.