Simultaneous approximation of measurement values and derivative data using discrete orthogonal polynomials

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Abstract

This paper presents a new method for polynomial approximation using the fusion of value and derivative information emanating from different sources, i.e., sensors. Therefore, the least-squares error in both domains is simultaneously minimized. A covariance weighting is used to introduce a metric between the value and derivative domain, to handle different noise behaviour. Based on a recurrence relation with full re-orthogonalization, a weighted polynomial basis function set is generated. This basis is numerically more stable compared to other algorithms, making it suitable for the approximation of data with high degree polynomials. With the new method, the fitting problem can be solved using inner products instead of matrix-inverses, yielding a computational more efficient method, e.g., for realtime approximation.A Monte Carlo simulation is performed on synthetic data, demonstrating the validity of the method. Additionally, various tests on the basis function set are presented, showing the improvement on the numerical stability.

Details

OriginalspracheEnglisch
TitelProceedings - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019
Herausgeber (Verlag)Institute of Electrical and Electronics Engineers Inc.
Seiten282-289
Seitenumfang8
ISBN (elektronisch)9781538685006
DOIs
StatusVeröffentlicht - 1 Mai 2019
Veranstaltung2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019 - Taipei, Taiwan
Dauer: 6 Mai 20199 Mai 2019

Publikationsreihe

NameProceedings - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019

Konferenz

Konferenz2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019
LandTaiwan
OrtTaipei
Zeitraum6/05/199/05/19