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 -