TY - GEN

T1 - Adjustment of Gauss-Helmert Models with Autoregressive and Student Errors

AU - Kargoll, Boris

AU - Omidalizarandi, Mohammad

AU - Alkhatib, Hamza

N1 - Funding information: Funded by the Deutsche Forschungsgemein-schaft (DFG, German Research Foundation) – 386369985.

PY - 2020/6/26

Y1 - 2020/6/26

N2 - In this contribution, we extend the Gauss-Helmert model (GHM) with t-distributed errors (previously established by K.R. Koch) by including autoregressive (AR) random deviations. This model allows us to take into account unknown forms of colored noise as well as heavy-tailed white noise components within observed time series. We show that this GHM can be adjusted in principle through constrained maximum likelihood (ML) estimation, and also conveniently via an expectation maximization (EM) algorithm. The resulting estimator is self-tuning in the sense that the tuning constant, which occurs here as the degree of freedom of the underlying scaled t-distribution and which controls the thickness of the tails of that distribution’s probability distribution function, is adapted optimally to the actual data characteristics. We use this model and algorithm to adjust 2D measurements of a circle within a closed-loop Monte Carlo simulation and subsequently within an application involving GNSS measurements.

AB - In this contribution, we extend the Gauss-Helmert model (GHM) with t-distributed errors (previously established by K.R. Koch) by including autoregressive (AR) random deviations. This model allows us to take into account unknown forms of colored noise as well as heavy-tailed white noise components within observed time series. We show that this GHM can be adjusted in principle through constrained maximum likelihood (ML) estimation, and also conveniently via an expectation maximization (EM) algorithm. The resulting estimator is self-tuning in the sense that the tuning constant, which occurs here as the degree of freedom of the underlying scaled t-distribution and which controls the thickness of the tails of that distribution’s probability distribution function, is adapted optimally to the actual data characteristics. We use this model and algorithm to adjust 2D measurements of a circle within a closed-loop Monte Carlo simulation and subsequently within an application involving GNSS measurements.

KW - Autoregressive process

KW - Circle fitting

KW - Constrained maximum likelihood estimation

KW - Expectation maximization algorithm

KW - Gauss-Helmert model

KW - Scaled t-distribution

KW - Self-tuning robust estimator

UR - http://www.scopus.com/inward/record.url?scp=85092202519&partnerID=8YFLogxK

U2 - 10.1007/1345_2019_82

DO - 10.1007/1345_2019_82

M3 - Conference contribution

SN - 978-3-030-54266-5

T3 - International Association of Geodesy Symposia

SP - 79

EP - 87

BT - 9th Hotine-Marussi Symposium on Mathematical Geodesy

A2 - Novák, Pavel

A2 - Crespi, Mattia

A2 - Sneeuw, Nico

A2 - Sansò, Fernando

CY - Cham

ER -