Generalized integer least-squares success-rate bounds under heavy-tailed distributions

Integer least-squares (ILS) ambiguity resolution has become a cornerstone of high-precision GNSS positioning due to the availability of a rigorous probabilistic theory under the Gaussian assumption. In realistic operating environments, however, GNSS observations are frequently affected by non-Gaussian disturbances arising from multipath propagation, atmospheric interference, receiver anomalies, and intermittent signal blockage. Such effects may induce heavy-tailed behavior, thereby increasing the probability of incorrect integer estimation beyond what is predicted by classical Gaussian success-rate theory. This contribution generalizes the ILS success-rate bounds of Teunissen (1998a, b) to a broad class of elliptically contoured distributions, including the multivariate Student- t and contaminated normal distribution. The resulting success-rate bounds retain the simplicity and sharpness of their Gaussian counterparts, with heavy-tailed effects entering only through a one-dimensional expectation over the scale distribution. It is demonstrated how the theory can be used to characterize the robustness of integer ambiguity resolution under heavy-tailed disturbances, thus substantially extending the applicability of classical success-rate analysis to realistic non-Gaussian GNSS environments while maintaining computational tractability.