Optimisation of GNSS networks – considering baseline correlations

Abstract

By considering global navigation satellite system (GNSS) observations, one can perform optimisation according to some pre-defined criteria and come up with the best location of receivers and optimum number of baselines. In practice, it is quite common to neglect the effect of correlations between baselines, and instead assume single-baseline-adjusted data in the optimisation procedure. However, in each session of observation, usually more than two receivers are simultaneously taking data from a number of common GNSS satellites, implying that the single- or double-difference observations are correlated. Our study designs an optimal observation plan for a GPS network in Skåne in southern Sweden, with the aim of determining possible displacements. Assuming three receivers in each session of observations leads to correlation between the GPS baselines, and consequently a fully populated weight matrix for each session of observation. A bi-objective optimisation model of precision and reliability is chosen to optimise the variance factor of each session, and eventually, design an observation plan. It is shown in this study that observing six out of ten possible sessions is sufficient to enable the network to detect a 5 mm displacement at each station. Assuming that the double-difference phase observations are uncorrelated changes the observation plan by retaining two more sessions. However, defining the weight matrix based on the double-difference observations requires the correlations to be taken into account, and neglecting them leads to incorrect results.