In this paper, we demonstrate that the uncertainty of the dual-satellite ephemeris must be included in order for the geolocation covariance to be accurate. Without the inclusion of this additional error source, the covariance is no longer consistent with the true uncertainty and can convey misleading results. The larger the uncertainty associated with the dual-satellite ephemeris the larger the geolocation covariance becomes. Therefore, we first demonstrate a technique for improving the dual-satellite ephemeris knowledge by using calibrator transmitters for orbit determination. Second, we derive a consider batch filter, which computes the best estimate of position of the unknown radio frequency source while taking into account the dual-satellite ephemeris uncertainty. An algorithm is also proposed for adding a probabilistic altitude constraint, which significantly reduces the solution error. Finally, we briefly touch upon a technique that allows for the dual-satellite ephemeris and source position to be estimated simultaneously thereby maintaining the correlations and optimality. All algorithms introduced have since been applied to real-world data and conveys actual capabilities rather than a theoretical approach alone.

中文翻译：

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具有星历校正和不确定性映射的双卫星地理定位

在本文中，我们证明了双星星历的不确定性必须包括在内，以便地理定位协方差是准确的。如果不包括这个额外的误差源，协方差就不再与真正的不确定性一致，并且可能会传达误导性的结果。与双卫星星历相关的不确定性越大，地理定位协方差就越大。因此，我们首先展示了一种通过使用校准器发射机进行轨道确定来提高双卫星星历知识的技术。其次，我们推导出一个考虑批量滤波器，它计算未知射频源位置的最佳估计，同时考虑到双卫星星历的不确定性。还提出了一种添加概率高度约束的算法，这大大减少了解决方案的错误。最后，我们简要介绍一种允许同时估计双卫星星历和源位置从而保持相关性和最优性的技术。此后引入的所有算法都已应用于现实世界的数据，并传达实际能力，而不仅仅是理论方法。