Parameter estimation with scarce measurements

Coupled Least Squares Identification Algorithms for Multivariate Output-Error Systems

“…Collect the observation data {Φ s (t), y(t)} and form the information matrixΦ x (t) by (22). (19), and P i (t) by (20), and update the parameter estimation vectorθ i (t) by (18). 5.…”

“…The RLS algorithm has been applied to the identification of various systems [17,18]. For example, on the basis of the work in [19], Jin et al proposed an auxiliary model based recursive least squares algorithm for autoregressive output-error autoregressive systems [20]; and Wang and Tang presented an auxiliary model based recursive least squares algorithm for a class of linear-in-parameter output-error moving average systems [21].…”

Performance analysis of the recursive parameter estimation algorithms for multivariable Box–Jenkins systems

“…Assume that the non-negative sequences fTðtÞg, fηðtÞg and fζðtÞg satisfy the inequality [38] TðtÞr Tðt À 1Þ þ ηðtÞÀζðtÞ and ∑ 1 t ¼ 1 ηðtÞo1, then we have ∑ 1 t ¼ 1 ζðtÞo1 and fTðtÞg converges to a finite random variable T 0 as t goes to infinity, i.e., TðtÞ-T 0 .…”

Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle

“…The performance of the proposed algorithm is analyzed and it is proved that the parameter estimation errors converge to zero in the mean-square sense under persistent excitation conditions, by using the martingale convergence theorem [32,33].…”