This contribution extends the theory of integer equivariant estimation (Teunissen in J Geodesy 77:402–410, 2003) by developing the principle of best integer equivariant (BIE) estimation for the class of elliptically contoured distributions. The presented theory provides new minimum mean squared error solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Next to the BIE estimator for the multivariate normal distribution, special attention is given to the BIE estimators for the contaminated normal and the multivariate t-distribution, both of which have heavier tails than the normal. Their computational formulae are presented and discussed in relation to that of the normal distribution.

中文翻译：

---

椭圆轮廓分布的最佳整数等变估计

这一贡献扩展了整数等变估计的理论（Teunissen in J Geodesy 77:402–410, 2003）通过开发椭圆轮廓分布类的最佳整数等变 (BIE) 估计原理。所提出的理论为解决各种分布的 GNSS 载波相位模糊度问题提供了新的最小均方误差解决方案。相关联的 BIE 估计量是普遍最优的，因为它们的精度永远不会低于任何整数估计量和任何线性无偏估计量的精度。除了多元正态分布的 BIE 估计量之外，还要特别注意污染正态和多元 t 分布的 BIE 估计量，它们的尾部都比正态重。