GPS Carrier Phase Ambiguity Fixing Concepts

DOI: 10.1007/BFb0117685 In book: GPS for Geodesy, pp.263-335

ABSTRACT High precision relative GPS positioning is based on the very precise career phase measurements. A prerequisite for obtaining high precision relative positioning results, is that the double-differenced carrier phase ambiguities become sufficiently separable from the baseline coordinates. Different approaches are in use and have been proposed to ensure a sufficient separability between these two groups of parameters. In particular, the approaches that explicitly aim at resolving the integer-values of the double-differenced ambiguities have been very successful. Once the integer ambiguities are successfully fixed, the carrier phase measurements will start to act as if they were high-precision pseudorange measurements, thus allowing for a baseline solution with a comparable high precision. The fixing of the ambiguities on integer values is however a non-trivial problem, in particular if one aims at numerical efficiency. This topic has therefore been a rich source of GPS-research over the last decade or so. Starting from rather simple but timeconsuming integer rounding schemes, the methods have evolved into complex and effective algorithms. Among the different approaches that have been proposed for cartier phase ambiguity fixing are those documented in Counselman and Gourevitch [1981], Remondi [1984;1986;1991], Hatch [1986; 1989; 1991], Hofmann-WeUenhof and Remondi [1988], Seeber and Wtibbena [1989], Blewitt [1989], Abott et al. [1989], Frei and Beutler [1990], Euler and Goad [1990], Kleusberg [1990], Frei [1991], Wiibbena [1991], Euler and Landau [1992], Erickson [1992], Goad [1992], Teunissen [1993a; 1994a, b], Hatch and Euler [1994], Mervart et al. [1994], De Jonge and Tiberius [1994], Goad and Yang [1994]. The purpose of the present lecture notes is to present the theoretical concepts of the GPS ambiguity fixing problem, to formulate procedures of solving it and to outline some of the intricacies involved. Several examples are included in the

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    • "In many applications, it is advantageous if the basis vectors are short and close to be orthogonal [1]. For more than a century, lattice reduction have been investigated by many people and several types of reductions have been proposed, including the KZ reduction [2], the Minkowski reduction [3], the LLL reduction [4] and Seysen's reduction [5] etc. Lattice reduction plays an important role in many research areas, such as, cryptography (see, e.g., [6]), communications (see, e.g., [1], [7]) and GPS (see, e.g., [8]), where the closest vector problem (CVP) and/or the shortest vector problem (SVP) need to be solved: "
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    • "The two key elements of the ambiguity discrimination test are the test statistic and the corresponding critical value (CV). Although well-documented acceptance test procedures are available for ambiguity validation testing, a rigorous discrimination testing procedure is still lacking (Teunissen 1996). "
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    Surveys in Geophysics 03/2012; 34(2). DOI:10.1007/s10712-012-9211-1 · 5.11 Impact Factor
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    • "This ILS procedure is efficiently mechanized in the LAMBDA method, see e.g. (Teunissen, 1998a). Note that the success rate of integer least-squares estimation is independent of the parameterization of the float ambiguities. "
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