Precise kinematic GPS positioning with Kalman filtering and smoothing
Sammanfattning: The Global Positioning System (GPS) has proven to be auseful tool for the determination of positions of a widevariety of moving platforms to accuracies in the order of a fewcentimetres. One of the critical aspects of precise kinematicGPS positioning at the centimetre level is the determination ofinteger carrier phase cycle ambiguities. The carrier phaseobservable is the most precise measurement available, but onlythe fractional part of the phase can be measured. In thisthesis, a newly developed method at KTH for resolving theunknown integer ambiguities has been implemented and tested onreal data. The results show that the method is very efficientand fast on kinematic GPS data at short baselines. In allcases, the new method was able to resolve the ambiguitieswithin five epochs after that both L1 and L2 observables areavailable from at least five satellites.For a land mobile user, however, the satellite signal isoften subject to shadowing by trees, bridges, buildings, orhills. This situation will for the precise user, working withresolved ambiguities, severely degrade the accuracy of theestimated positions until enough of satellites,i.e.at least four, are available again. With respect tothe necessary effort, it should be carefully investigatedwhether the realtime capacity is in fact needed for a giventask. If it is found appropriate for the surveying task topost-process the data, a very cost-effective way to bridge theintervals with data deficiency is to use mathematical means asoptimal smoothing algorithms. In this thesis, three differentsmoothing algorithms have been reviewed, discussed and testedon kinematic GPS data: The Fraser-Mayne smoother, theRauch-Tung-Striebel smoother, and the Bryson-Frazier smoother.During shorter intervals of data deficiency (some tenths ofseconds), it is found that the smoothing algorithms will helpsustainingthe precision and estimates that are close to thetrue ones. In fact, their performances at these occasions arefound to be remarkably good.At short baselines, it is common practice only to usestandard models for describing the influence from theatmosphere on the observables. Additionally, multipath is noteasily described in the model and is another disturbing factorinfluencing the measurements that is left unmodelled.Consequently, it is not a wild guess that time correlationsbetween measurements, in some cases, may exist. Aiming ataccuracies at the level of some few centimetres, it is foundthat kinematic GPS measurement sequences should be carefullyinvestigated in terms of existing time correlations.In this thesis, a general recursive statistical testingscheme for measurement model errors are reviewed and discussedfor Kalman filter design and error analysis. The adoptedapproximate adaption algorithms were found to be viablealternatives to their more rigorous counterparts. The resultsshow that in practice it is possible to revert the filter tooperate under the null hypothesis after adaption of up to threeslips, which is in contrast to what Teunissen and Salzmann(1989) and Salzmann (1995) found out. However, in this case,the obtained results may be sub-optimal.Key words:GPS, Kalman filter, smoothing
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