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Integrity monitoring for carrier phase ambiguities
Jofre, Martí; Ramos Bosch, Pedro; Feng, S.; Ochieng, W.; Samson, J; Tossaint, M; Hernández Pajares, Manuel; Juan Zornoza, José Miguel; Sanz Subirana, Jaume; Aragón Ángel, María Ángeles
Universitat Politècnica de Catalunya. Departament de Física Aplicada; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
The determination of the correct integer number of carrier cycles (integer ambiguity) isthe key to high accuracy positioning with carrier phase measurements from GlobalNavigation Satellite Systems (GNSS). There are a number of current methods for resolvingambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA)method, which is a combination of least-squares and a transformation to reduce the searchspace. The current techniques to determine the level of confidence (integrity) of the resolvedambiguities (i.e. ambiguity validation), usually involve the construction of test statistics,characterisation of their distribution and definition of thresholds. Example tests appliedinclude ratio, F-distribution, t-distribution and Chi-square distribution. However, theassumptions that underpin these tests have weaknesses. These include the application of afixed threshold for all scenarios, and therefore, not always able to provide an acceptableintegrity level in the computed ambiguities. A relatively recent technique referred to as IntegerAperture (IA) based on the ratio test with a large number of simulated samples of floatambiguities requires significant computational resources. This precludes the application of IAin real time.This paper proposes and demonstrates the power of an integrity monitoring technique thatis applied at the ambiguity resolution and positioning stages. The technique has the importantbenefit of facilitating early detection of any potential threat to the position solution, originatingin the ambiguity space, while at the same time giving overall protection in the positiondomain based on the required navigation performance. The proposed method uses theconventional test statistic for ratio testing together with a doubly non-central F distribution tocompute the level of confidence (integrity) of the ambiguities. Specifically, this is determinedas a function of geometry and the ambiguity residuals from least squares based ambiguityresolution algorithms including LAMBDA. A numerical method is implemented to computethe level of confidence in real time.The results for Precise Point Positioning (PPP) with simulated and real data demonstratethe power and efficiency of the proposed method in monitoring both the integrityof the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolutionalgorithms, it is easily transferable to conventional Real Time Kinematic (RTK)positioning.
Àrees temàtiques de la UPC::Enginyeria electrònica i telecomunicacions::Radiocomunicació i exploració electromagnètica::Satèl·lits i ràdioenllaços
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
Geometry, Algebraic
Satèl·lits artificials
Geometria computacional
14Q Computational aspects in algebraic geometry
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