Research on the inital phase ambiguity in evaluating GPS observables

ABSTRACTThis research work proposes a new method or improves the well-known methods forambiguity resolution at relative positioning with GPS (Global Positioning System), whileeffective factors on it are examined. For this reason, one of most known methods beingLAMBDA (Least AMBiguity Decorelation Adjustment), which demonstrate general characterof ambiguity estimation, is stood on. When the effective factors on ambiguity resolution areexamined, the method is used and is also argued with its success of ambiguity estimation atdifferent conditions. The factors on ambiguity estimation are studied on simulated GPSobservation files at RINEX (Receiver INdependent EXchange) format. Moreover, reliabilityof proposed test procedures for ambiguity validation also inspects on the simulatedobservation files.There are two main positioning methods in GPS and the other methods are derived fromthem. These are point positioning and relative positioning. Generally, while the first use fornavigation or improve approximated point coordinates before relative positioning because ofmeter accuracy, the second used to precise positioning.Relative position with centimeter or sub centimeter precision is up to some restrictions whichare observation type/types, mathematical model, atmospheric models and ambiguityestimation. The restrictions are altered according to baseline length. If the length of thebaseline is sufficiently short (<10km), atmospheric effects are ignored at DD phaseobservation model. Then unknowns of baseline components and integer DD ambiguities areonly remained in the model. Most likely integer ambiguities are generally determined byLeast Squares (LS or ℓ2_Norm estimation). But the ambiguities after the LS are floatnumbers. Since it is known that the ambiguities are to be integer numbers, the most likelyinteger ambiguities are computed from the ordinary LS solution via a discrete search process.There are a lot of methods for that process. One of them is LAMBDA method. LAMBDAmethod is very efficient to find correct integer DD ambiguities for especially shortobservation time span. In spite of this, this method and the other methods need some epochobservations to estimate correct DD ambiguities under some restrictionsEnd point for DD integer ambiguity estimation is instantaneous estimation. If this is possible,one epoch data is enough to centimeter or sub centimeter precision of positioning. Studiesabout DD integer ambiguity estimation will continue to the stage. To reach the end point DDambiguity estimation, one has to study on two main topics or improved them.• To improve the mathematical model.• To use robust estimation methods.If observations are normally distributed and the model is complete, then the LS gives mostoptimum results for relative positioning, too. But, LS is very sensitive to outliers in theobservations. Short multipath, one of important random errors sources, is like outlier and itseffect has to be reduced on parameters. In this study, it is proposed ℓ1_Norm estimation thatis more insensitive to outliers then LS for the second topic. End of this study, It is convincedthat ℓ1_Norm estimation is not suitable for the relative positioning due to its solution type andcondition problem in geometry of the relative position with GPS.Keywords: Relative Positioning with GPS, ℓ2_Norm and ℓ1_Norm Estimations, AmbiguityResolution and Validation.viii