The best integer equivariant (BIE) estimator for the multivariate t-distribution was introduced in Teunissen (J Geod, 2020. https://doi.org/10.1007/s00190-020-01407-2), where it was shown that the BIE-weights will be different from that of the normal distribution. In this contribution, we analyze these BIE estimators while making use of multi global navigation satellite system (GNSS) data. The BIE-estimators are also compared to their least-squares (LS) and integer least-squares (ILS) contenders. Monte Carlo simulations are conducted so as to realize controlled performance comparisons of the different estimators for the purpose of multi-GNSS (GPS, Galileo, BDS and QZSS) single-frequency real-time kinematic positioning. The analyses are done in a qualitative sense by means of positioning scatter plots, and in a quantitative sense by means of numerical mean-squared-error (MSE) curves for the different estimators under different model strengths (receiver-satellite geometries and varying degrees of freedom). Particular attention is given to the difference in impact the multivariate t-distribution has when either only its cofactor matrix is in common with the normal distribution or its complete variance-covariance matrix. It will be shown that the BIE-estimators give better MSEs to both the LS- and ILS-estimator when the ILS success rate is different from zero and one, respectively. We also demonstrate that using the same BIE-estimator on different data distributions can give users an unrealistic sense of their solution quality, while the usage of two different BIE-estimators on the same data can have a marginal impact.

Teunissen (J Geod, 2020. https://doi.org/10.1007/s00190-020-01407-2) 中引入了多元 t 分布的最佳整数等变 (BIE) 估计量，其中表明 BIE -权重将不同于正态分布的权重。在此贡献中，我们在利用多全球导航卫星系统 (GNSS) 数据的同时分析了这些 BIE 估计量。还将 BIE 估计量与其最小二乘法 (LS) 和整数最小二乘法 (ILS) 竞争者进行比较。为了实现多 GNSS（GPS、Galileo、BDS 和 QZSS）单频实时运动定位的目的，进行蒙特卡罗模拟以实现不同估计器的受控性能比较。分析是通过定位散点图在定性意义上完成的，并在定量意义上通过不同模型强度（接收机卫星几何形状和不同自由度）下不同估计器的数值均方误差 (MSE) 曲线。特别注意多元 t 分布在仅其辅因子矩阵与正态分布或其完整方差-协方差矩阵相同时的影响差异。将表明当 ILS 成功率分别不同于 0 和 1 时，BIE 估计器为 LS 和 ILS 估计器提供更好的 MSE。我们还证明，在不同的数据分布上使用相同的 BIE 估计器会给用户带来不切实际的解决方案质量的感觉，而在同一数据上使用两个不同的 BIE 估计器可能会产生边际影响。