A Search-Free Approach to Ambiguity Resolution

J.G.G. Svendsen

Abstract:	As with the most recent contributions to ambiguity resolution, the approach presented in this article puts emphasis on ambiguity resolution in the ambiguity space. The method presented is based on lattice basis reduction. Given a diagonal covariance matrix, the integer optimization problem can be solved by simply rounding the float estimates of the ambiguities to the nearest integer, i.e. the correct solution are the integers giving the minimum Euclidean distance from the float estimate. Consider the integer optimization problem of finding the closest vector to a lattice point. As all bases generating lattices arise from transformation of the unknowns through unimodular matrices (i.e. having integer elements and being volume preserving), it seems reasonable to classify an admissible integer ambiguity transformation matrix to hold the following properties: • The transformation matrix must be unimodular. • The new basis must in some sense be reduced. The first property implies the mapping from the original space to the reduced integer lattice to be one-to-one and onto from the integer lattice into itself, while the second reduces the variance of the integer ambiguity estimates. However, there exist many transformations that fulfill the two conditions given above, and in this approach we would like to choose a basis that is "shortest" in the sense of minimizing the product of the norm of each basis vector. It is possible to guarantee the rounded float estimate of the ambiguities to be the correct solution if the distance from the lattice integer is shorter than half the norm of the shortest basis vector in the lattice. Note that when this condition is satisfied, there will be no need to perform a search for the correct integer ambiguity, as one can adopt the rounded candidate as the correct solution. The performance of the search-free ambiguity resolution approach is demonstrated through various scenarios at the double difference level, and its performance is compared with state of the art methods as e.g. the LAMBDA method.
Published in:	Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003) September 9 - 12, 2003 Oregon Convention Center Portland, OR
Pages:	769 - 774
Cite this article:	Svendsen, J.G.G., "A Search-Free Approach to Ambiguity Resolution," Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003), Portland, OR, September 2003, pp. 769-774.
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