Bernoulli–Gaussian Model with Model Parameter Estimation
Publication: Journal of Surveying Engineering
Volume 150, Issue 4
Abstract
First, this paper introduces a statistical model of gross errors, namely the Bernoulli–Gaussian (BG) model, which characterizes the gross error as a product of a Bernoulli variable and a Gaussian variable. The BG model offers a framework to interpret various causes of outliers through the perspective of gross errors. In addition, it unifies commonly used observation models for outliers by adjusting the range of BG model parameters. Second, this paper proposes an estimation method for BG model parameters based on the expectation maximization (EM) algorithm. This approach attributes different gross error parameters for distinct types of observations, facilitating parameter estimation in both single-source and multisource observation systems. Additionally, by organizing equations in the form of individual observations, its applicability can be broadened to both static and dynamic scenarios. Finally, a normal sample example and a Global Navigation Satellite System (GNSS) positioning example verified the effectiveness of the proposed method for estimating the BG model parameters.
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Data Availability Statement
All data, models, or code generated or used during the study are available in a repository online in accordance with funder data retention policies. This includes the GNSS observation data, which can be downloaded from the IGS website (https://igs.org/).
Acknowledgments
This work is sponsored by the National Natural Science Foundation of China (42274030 and 42192532) and the Fundamental Research Funds for the Central Universities (22120210522).
Author contributions: Y. Yu proposed the idea and wrote the manuscript. L. Yang and Y. Shen revised the manuscript and supervised the study.
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Published In
Journal of Surveying Engineering
Volume 150 • Issue 4 • November 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Dec 19, 2023
Accepted: Jun 7, 2024
Published online: Aug 24, 2024
Published in print: Nov 1, 2024
Discussion open until: Jan 24, 2025
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