Theory for the ambiguity function method: probability model and global solution

doi:10.1007/s00190-025-01945-7

Theory for the ambiguity function method: probability model and global solution

2025-04-01

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DOI：10.1007/s00190-025-01945-7

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In this contribution, we introduce some new theory for the classical GNSS ambiguity function (AF) method. We provide the probability model by means of which the AF-estimator becomes a maximum likelihood estimator, and we provide a globally convergent algorithm for computing the AF-estimate. The algorithm is constructed from combining the branch-and-bound principle, with a special convex relaxation of the multimodal ambiguity function, to which the projected-gradient-descent method is applied to obtain the required bounds. We also provide a systematic comparison between the AF-principle and that of integer least-squares (ILS). From this comparison, the conclusion is reached that the two principles are fundamentally different, although there are identified circumstances under which one can expect AF- and ILS-solutions to behave similarly.

Keywords:

GNSS

Ambiguity function (AF) method

Maximum likelihood

Integer least-squares (ILS)

Branch-and-bound (BB)

Convex relaxation

Projected-gradient-descent (PGD)

Theory for the ambiguity function method: probability model and global solution

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