Statistical Characterisation of GNSS Data for a Stationary Receiver using Non-Gaussian Distributions

Model	Parameters						CI^*	ℒ	AIC	BIC	RMSE
	μ^*	σ	ν	α	λ	β
	×10⁻⁵	×10⁻⁵	×10³					×10⁶	×10⁶	×10⁶
Laplace	864	20	–	–	–	–	[805; 924]	1.16	−2.33	−2.33	3.5 · 10⁻⁴
Skew-normal	857	21	–	0.50	–	–	[825; 904]	1.13	−2.27	−2.27	2.5 · 10⁻⁴
GH	845	0.06	–	0.05	1.39	0.43	[841; 917]	1.20	−2.40	−2.40	2.8 · 10⁻⁴
Skew-t	861	14	5.0	–	–	–	[825; 897]	1.16	−2.32	−2.32	2.6 · 10⁻⁴

* Note: The values marked with an asterisk (μ and CI) are expressed as least significant digits relative to a base latitude of 50.28000° N and scaled by 10⁻⁵.

Probability density function (a) and cumulative distribution function (b) for latitude data with fitted distributions using weighted MLE.

Residual analysis of the selected distributions using P–P plot.

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DOI: https://doi.org/10.2478/msr-2025-0037 | Journal eISSN: 1335-8871

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Language: English

Page range: 338 - 346

Submitted on: Jun 26, 2025

Accepted on: Oct 29, 2025

Published on: Dec 23, 2025

Published by: Slovak Academy of Sciences, Institute of Measurement Science

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

non-Gaussian,

weighted maximum likelihood estimation,

generalised hyperbolic distribution,

goodness-of-fit test,

uncertainty quantification,

confidence interval

Related subjects:

Engineering,

Electrical engineering,

Control engineering, metrology and testing

© 2025 Abu Bantu, Józef Wiora, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 25 (2025): Issue 6 (December 2025)

Statistical Characterisation of GNSS Data for a Stationary Receiver using Non-Gaussian Distributions

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