Introduction to Geodetic Time Series Analysis

TL;DR

This chapter introduces methods for fitting trajectory models to geodetic time series, emphasizing Bayesian algorithms and noise modeling to extract accurate geophysical information with realistic error estimates.

Contribution

It provides an accessible overview of parameter estimation techniques for geodetic time series, focusing on Bayesian methods and noise modeling, for both beginners and experienced researchers.

Findings

Discussion of Bayesian algorithms for parameter estimation

Emphasis on noise modeling in geodetic time series

Numerical aspects of trajectory model fitting

Abstract

This contribution is the chapter 2 of the book "geodetic time series analysis" (10.1007/978-3-030-21718-1). The book is dedicated to the art of fitting a trajectory model to those geodetic time series in order to extract accurate geophysical information with realistic error bars in geodymanics and environmental geodesy related studies. In the vast amount of the literature published on this topic in the past 25 years, we are specifically interested in parametric algorithms which are estimating both functional and stochastic models using various Bayesian statistical tools (maximum likelihood, Monte Carlo Markov chain, Kalman filter, least squares variance component estimation, information criteria). This chapter will focus on how the parameters of the trajectory model can be estimated. It is meant to give researchers new to this topic an easy introduction to the theory with references to key books and articles where more details can be found. In addition, we hope that it refreshes some of the details for the more experienced readers. We pay special attention to the modelling of the noise which has received much attention in the literature in the last years and highlight some of the numerical aspects.