Lambda1 teunissen - Journal of Geodesy(1997 71 589602 The least-squares ambiguity decorrelation adjustment its performance on short GPS baselines

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The least-squares ambiguity decorrelation adjustment: its performance on short GPS baselines and short observation spans P. J. G. Teunissen, P. J. de Jonge, C. C. J. M. Tiberius Delft Geodetic Computing Centre (LGR), Faculty of Geodetic Engineering, Delft University of Technology, Thijsseweg 11, 2629 JA Delft, The Netherlands Fax: +31 15 2783711; e-mail: [email protected] Received: 31 October 1995 /Accepted: 21 March 1997 Abstract. The least-squares ambiguity decorrelation adjustment is a method for fast GPS double-di±erence (DD) integer ambiguity estimation. The performance of the method will be discussed, and although it is stressed that the method is generally applicable, attention is restricted to short-baseline applications in the present contribution. With reference to the size and shape of the ambiguity search space, the volume of the search space will be introduced as a measure for the number of candidate grid points, and the signature of the spectrum of conditional variances will be used to identify the di²culty one has in computing the integer DD ambigu- ities. It is shown that the search for the integer least- squares ambiguities performs poorly when it takes place in the space of original DD ambiguities. This poor performance is explained by means of the discontinuity in the spectrum of conditional variances. It is shown that through a decorrelation of the ambiguities, trans- formed ambiguities are obtained which generally have a flat and lower spectrum, thereby enabling a fast and e²cient search. It is also shown how the high precision and low correlation of the transformed ambiguities can be used to scale the search space so as to avoid an abundance of unnecessary candidate grid points. Nu- merical results are presented on the spectra of condi- tional variances and on the statistics of both the original and transformed ambiguities. Apart from presenting numerical results which can typically be achieved, the contribution also emphasizes and explains the impact on the method’s performance of di±erent measurement scenarios, such as satellite redundancy, single vs dual- frequency data, the inclusion of code data and the length of the observation time span. Key words. GPS Æ Ambiguity resolution Æ Ambiguity decorrelation 1 Introduction The GPS double-di±erence (DD) carrier-phase mea- surements are ambiguous by an unknown integer number of cycles. The a priori knowledge of the integer nature of the ambiguities can be used to strengthen the baseline solution. This is of particular relevance to applications where use is made of short observation time spans. No deterministic method exists for the computa- tion of the most likely integer ambiguity estimates. In the literature, many important contributions have already been made in the area of GPS integer ambiguity estimation. Examples of proposed methods, together with suggested refinements, can be found in e.g. Blewitt (1989), Dong and Bock (1989), Frei and Beutler (1990), Hatch (1991), Frei (1991), Wu ¨ bbena (1991) and Euler and Landau (1992).
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This note was uploaded on 06/02/2011 for the course GEO INFORM 014852 taught by Professor Giladeventzur during the Spring '11 term at Technion.

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Lambda1 teunissen - Journal of Geodesy(1997 71 589602 The least-squares ambiguity decorrelation adjustment its performance on short GPS baselines

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