The effect of correlation on uncertainty estimates – with GPS examples

Abstract

This article deals with the effect of correlation on the estimates of measurement uncertainty, with some focus on Global Positioning Satellite (GPS) time series analysis. Analytical derivations and Monte Carlo simulations form the theoretical basis, which shows that uncompensated correlation produces unrealistic uncertainty estimates. Tools for handling correlation in connection with estimation of uncertainty, construction of confidence intervals, hypothesis testing, design of measurement strategies, and development of tolerances are outlined and demonstrated. The GPS observation time series used in the article has a short to medium range correlation, and can therefore be handled with the presented tools - based on a simple Location-model and stationary stochastic processes.

Keywords

• correlation
• least squares estimation
• measurement uncertainty
• monte carlo simulation
• time series analysis