Simultaneous approximation of measurement values and derivative data using discrete orthogonal polynomials
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
Authors
Organisational units
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
Original language | English |
---|---|
Title of host publication | Proceedings - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019 |
Publisher | Institute of Electrical and Electronics Engineers |
Pages | 282-289 |
Number of pages | 8 |
ISBN (electronic) | 9781538685006 |
DOIs | |
Publication status | Published - 1 May 2019 |
Event | 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019 - Taipei, Taiwan, Province of China Duration: 6 May 2019 → 9 May 2019 |
Publication series
Name | Proceedings - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019 |
---|
Conference
Conference | 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019 |
---|---|
Country/Territory | Taiwan, Province of China |
City | Taipei |
Period | 6/05/19 → 9/05/19 |