Orthogonality defect and reduced search-space size for solving integer least-squares problems

Wang, Jun & Feng, Yanming (2013) Orthogonality defect and reduced search-space size for solving integer least-squares problems. GPS Solutions, 17(2), pp. 261-274.

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In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

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1 citations in Web of Science®

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ID Code: 54202
Item Type: Journal Article
Refereed: Yes
Keywords: GNSS, Ambiguity resolution, Multiple constellations, Ambiguity search space
DOI: 10.1007/s10291-012-0276-6
ISSN: 1080-5370
Subjects: Australian and New Zealand Standard Research Classification > EARTH SCIENCES (040000) > OTHER EARTH SCIENCES (049900)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Deposited On: 05 Dec 2012 01:31
Last Modified: 12 Jun 2013 15:14

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