Keenan, Cristopher Ryan; (2001) Stochastic modelling for high-fidelity differential GPS quality measures. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The offshore energy industries use differential Global Positioning System (DGPS) methods extensively to provide positioning for activities such as seismic exploration and pipeline inspection surveys. It has long been a criticism of DGPS that the quality measures delivered by most processing algorithms do not truly reflect the real quality of the derived positions and underestimate the likely sizes of the errors. In practice, this problem is often resolved by quoting extremely conservative upper error bounds so that users can be sure that real positioning errors are always within these. Significant improvements have been seen in both solutions and quality measures for post-processed applications with the use of reverse-engineered stochastic models. A common goal for researchers involved with single-frequency DGPS positioning is to identify a general case stochastic algorithm that can be relied upon completely to describe correctly, in real-time, the quality of position solutions. Many groups have found that the use of an elevation-weighting function is preferable over a model that incorrectly assumes all code pseudoranges are of equal precision and uncorrelated. However, such functions cannot accurately represent the high-frequency variations within DGPS measurements. This research has investigated the improvement in the fidelity of DGPS quality measures when developing and applying stochastic functions that represent the errors in the basic DGPS measurements, i.e. undifferenced phase-filtered C/A-code pseudoranges. These analytical functions take into account the impact of distance-independent errors such as residual multipath and Selective Availability, and the distance-dependent errors within satellite orbits, the ionosphere and the troposphere. A number of processing strategies, incorporating various combinations of the candidate functions, have been afforded to the least squares stochastic model for testing on single epoch DGPS solutions. A data collection campaign was organised that provided high-rate GPS data for seven static sites around the North Sea. With the benefit of truth positions from this campaign, the performance of each processing strategy has been investigated and assessed in terms of accuracy and precision estimates. By computing the fidelity of these quality measures, it was possible to quantify the percentage of position estimates whose quality measures had been wrongly assigned relative to the truth positions. The results of a large number of post-processing tests on real GPS data have shown that it is extremely difficult to design an a-priori stochastic algorithm containing functions that can correctly reflect all variations in the quality of phase-filtered C/A-code pseudoranges. The candidate functions have been unable to reduce the impact of unmodelled systematic errors on the final position solutions and quality measures. This has led to their failure in significantly, and consistently, improving the fidelity of quality measures associated with differential code positioning. In general, the research has shown that the use of an elevation-weighting function can provide, for single-baseline datasets, consistent time series with minimal step functions even over periods of constellation change. For multiple-baseline datasets, a full variance-covariance matrix containing an adaptive multipath variance estimation routine generally afforded more robust time series of true and formal errors than other candidate model types. The acknowledgement of mutual spatial correlations between the observations at each receiver was seen to improve the quality measure fidelities for single-baseline datasets only, and not for networks. It has been shown that the effective omission of a stochastic model, i.e. the use of a unit weight matrix, can sometimes yield higher fidelity quality measures than an incorrectly assigned full stochastic model with spatial correlation terms. Clearly the nature of the relationships between the variances and covariances of phase-filtered differentially corrected pseudoranges are more complex than any of the models tested here. In some cases however, significant improvements on current practice have been achieved.

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