TY - JOUR

T1 - An iteratively reweighted least-squares approach to adaptive robust adjustment of parameters in linear regression models with autoregressive and t-distributed deviations

AU - Kargoll, Boris

AU - Omidalizarandi, Mohammad

AU - Loth, Ina

AU - Paffenholz, Jens-André

AU - Alkhatib, Hamza

N1 - Funding information: We thank the editors and the reviewers for their constructive comments and valuable suggestions, which helped to improve this paper. The presented application of the PCB Piezotronics accelerometer within the vibration analysis experiment was performed as a part of the collaborative project “Spatio-temporal monitoring of bridge structures using low cost sensors” with ALLSAT GmbH, which is funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) and the Central Innovation Programme for SMEs (ZIM Kooperationsprojekt, ZF4081803DB6). In addition, the authors would like to acknowledge the Institute of Concrete Construction (Leibniz Universität Hannover) for providing the shaker table and the reference accelerometer used within this experiment.

PY - 2017/9/9

Y1 - 2017/9/9

N2 - In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student’s) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.

AB - In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student’s) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.

KW - Adaptive robust estimation

KW - Autoregressive process

KW - Expectation maximization (EM) algorithm

KW - Iteratively reweighted least squares

KW - Linear regression model

KW - Scaled t-distribution

UR - http://www.scopus.com/inward/record.url?scp=85028975280&partnerID=8YFLogxK

U2 - 10.1007/s00190-017-1062-6

DO - 10.1007/s00190-017-1062-6

M3 - Article

VL - 92

SP - 271

EP - 297

JO - Journal of geodesy

JF - Journal of geodesy

SN - 0949-7714

IS - 3

ER -