Enhanced Integer Bootstrapping for Single Frequency GPS Attitude Determination

James Pinchin

Abstract:	Attitude determination using GNSS often finds application on platforms where the navigation payload weight, cost and size are most limited. Typically these platforms require a robust real time navigation solution which uses a minimum of processing power. Cost requirements often also limit the GNSS receivers used to a single frequency. To obtain a precise attitude solution carrier phase measurements are used. To exploit these measurements fully, the ambiguous number of wavelengths between antenna and satellite must be resolved to an integer. This paper concerns itself with integer ambiguity resolution over a single baseline of known length. Using a version of the popular LAMBDA method, modified to incorporate the known baseline length, the success rate of integer ambiguity resolution has been shown to reach 100 %. The LAMBDA approach requires that a set of candidate integer ambiguity vectors be searched to find the candidate which minimises the objective function. When singe frequency, low cost receivers are used the set of set of candidate vectors may be very large placing big computational demands on the system. This paper uses another integer ambiguity estimator, the bootstrapped estimator. Integer bootstrapping utilises covariance information from the float ambiguity covariance matrix to sequentially round the float ambiguities. Although the bootstrapped estimator itself cannot be modified to incorporate a baseline length constraint, it may be applied to constrained float ambiguity vectors. Applying the baseline constraint to the float ambiguity vectors may be expected to improve their precision. It has been shown that if the precision of the float ambiguity vector is sufficiently high, the success rate of the bootstrapped estimator will approach that of the more optimal LAMDA method. This work measures the effect of using a constrained float solution as an input to the integer bootstrapping estimator using three metrics. First the theoretical and empirical success rates are examined. It is shown that the increased precision of the constrained float solution means that the theoretical success rate of the bootstrapped estimator is often very close to 100 %. In data collected using a GPS hardware simulator and in real world trials the empirical success rate is seen to be as good as 97 %. The third metric used is the size of the LAMBDA search space. The bootstrapped estimator is often used to set the size of this search space so the use of a constrained float ambiguity estimate may be expected to have an effect. The data collected in this work show that the use of a constrained float ambiguity estimate has often has the effect of enlarging the search space. Finally a novel statistical approach is taken to the use of the known baseline length in ambiguity validation. This approach allows the user to select the acceptable test failure rate depending on the application.
Published in:	Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008) September 16 - 19, 2008 Savannah International Convention Center Savannah, GA
Pages:	1290 - 1298
Cite this article:	Pinchin, James, "Enhanced Integer Bootstrapping for Single Frequency GPS Attitude Determination," Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008), Savannah, GA, September 2008, pp. 1290-1298.
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