Simultaneous approximation of measurement values and derivative data using discrete orthogonal polynomials
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Proceedings - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019. Institute of Electrical and Electronics Engineers, 2019. p. 282-289 8780356 (Proceedings - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
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TY - GEN
T1 - Simultaneous approximation of measurement values and derivative data using discrete orthogonal polynomials
AU - Ritt, Roland
AU - Harker, Matthew
AU - O'Leary, Paul
PY - 2019/5/1
Y1 - 2019/5/1
N2 - 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.
AB - 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.
KW - basis functions
KW - discrete orthogonal polynomials
KW - Hermite approximation
KW - multisensor fusion
KW - optimization
UR - http://www.scopus.com/inward/record.url?scp=85070862466&partnerID=8YFLogxK
U2 - 10.1109/ICPHYS.2019.8780356
DO - 10.1109/ICPHYS.2019.8780356
M3 - Conference contribution
T3 - Proceedings - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019
SP - 282
EP - 289
BT - Proceedings - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019
PB - Institute of Electrical and Electronics Engineers
T2 - 2019 IEEE International Conference on Industrial Cyber Physical Systems, ICPS 2019
Y2 - 6 May 2019 through 9 May 2019
ER -
