Analysis of the parameter estimate error when algebraic differentiators are used in the presence of disturbances

Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification

“…derived in Mboup et al (2009) and analysed in Kiltz (2017). A detailed analysis of the estimation errors is carried out in Othmane, Rudolph, and Mounier (2020). This model is then used to design signals, called residuals, sensitive only to faults.…”

“…In the absence of faults, r contains only measurement noise and errors stemming from the parameter estimation. These errors are analysed in detail in Othmane et al (2020). In the presence of a fault f , the function r satisfies r ≈ q 4 g f (4) + q 2 g f = q 4 g (4) f + q 2 g f.…”

Differentiator for Noisy Sampled Signals With Best Worst-Case Accuracy

“…. This is so because the rows of the matrices A k , M k and the vector b k are grouped into 3 blocks, of k, k and k + 1 rows, where the first block corresponds to (8), the second to (7), and the third to (9).…”

“…Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works." time [8], [10], and they converge exactly for different classes of noise-free signals [9], [11]. With measurement noise, the accuracy, i.e., the achievable worst-case differentiation error, is limited for all differentiators.…”

“…Popular existing methods for differentiation include linear high-gain observers [7], linear algebraic differentiators [8], [9], and sliding mode differentiators [10], [11]. These differ in terms of their convergence properties; while high-gain differentiators converge exponentially [7], algebraic and slidingmode differentiators exhibit convergence in finite or fixed *Work supported by FONCYT, Argentina, under grant PICT 2018-1385, and by Christian Doppler Research Association, Austrian Federal Ministry for Digital and Economic Affairs, and National Foundation for Research, Technology and Development.…”