On the numerical minimisation of the objective function applied to spherical harmonics fitting
More details
Hide details
University of Warmia and Mazury in Olsztyn Poland
University of Warmia and Mazuty in Olsztyn Poland
Submission date: 2023-08-17
Final revision date: 2023-09-05
Acceptance date: 2023-09-05
Online publication date: 2023-09-18
Publication date: 2023-09-18
Corresponding author
Jacek Rapinski   

University of Warmia and Mazuty in Olsztyn Poland
Diagnostyka 2023;24(3):2023313
The paper presents some considerations on the performance of various objective function minimization methods in the process of GNSS antenna PCV determination. It is particulary important in the case of structural health monitoring and diagnostics. PCV are used as an additional feature to improve the GNSS positioning accuracy. The process of PCV derivation is complex and involves fitting spherical harmonics into a set of observables. The paper compares computing performance and accuracy of few methods used in the fitting process.
Dennis JE, Schnabel RB. Numerical methods for unconstrained optimization and nonlinear equations vol. 16; Classics in Applied Mathematics. SIAM 1996.
Guo F, Zhang X, Li X. Impact of sampling rate of IGS satellite clock on precise point positioning. Geo spatial information science 2010; 13 (2): 150-156 https://doi.org/10.1007/s11806....
Hestenes M. R, Stiefel E. Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau Standards 1952; 49: 409-436.
Khoh WH, Pang YH, Ooi SY, Wang LYK, Poh QW. Predictive churn modeling for sustainable business in the telecommunication industry: optimized weighted machine learning. Sustainability 2023; 15(11): 8631. https://doi.org/10.3390/su1511....
Maciuk K. Aging of ground global nvigation satellite system oscillators. Eksploatacja i Niezawodność – Maintenance and Reliability 2022; 24(2): 371-376. https://doi.org/10.17531/ein.2....
Margques JPPG, Cuhna DC, Harada LMF, Silva LN, Silva ID. A cost-effective trilateration-based radio localization algorithm using machine learning and sequential least-square programming optimization. Computer Communications 2021; 177: 1-9. https://doi.org/10.1016/j.comc....
Nash SG. A survey of truncated-Newton methods. Journal of Computational and Applied Mathematics 2000; 124(1-2): 45-59. https://doi.org/10.1016/S0377-....
Nash SG, Sofer A. Assessing a search direction within a truncated-newton method. Operations Research Letters 1990; 9 (4): 219-221. https://doi.org/10.1016/0167-6....
Powell MJD. A view of algorithms for optimization without derivatives. Cambridge University Technical Report DAMTP 2007.
Royer CW, O’Neill M, Wright SJ. A Newton-CG algorithm with complexity guarantees for smooth unconstrained optimization. Mathematical Programming 2019; 180: 451-488. https://doi.org/10.1007/s10107....
Sahin FE. Open-source optimization algorithms for optical design. Optik 2019; 1781016-1022. http://dx.doi.org/10.1016/j.ij....
Schmidt M, Dettmering D, Mößmer M, Wang Y, Zhang J. Comparison of spherical harmonic and B spline models for the vertical total electron content. Radio Science 2011; 46(6): 1-8. https://doi.org/10.1029/2010RS....
Stuetzle W. The conjugate gradient method. Statistical Computing 2001.
Zhu C, Byrd RH, Lu P, Nocedal J. Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Transactions on Mathematical Software 1997; 23(4): 550-560. https://doi.org/10.1145/279232....
Journals System - logo
Scroll to top