This paper presents a method for modeling and simulation of Global Navigation Satellite System (GNSS) constellations by the use of Chebyshev polynomials fit to publicly available precision data. The Global Positioning System (GPS) is used to demonstrate the method, but the method applies to all GNSS with precise ephemeris data including Galileo and GLONASS. The method facilitates highly accurate satellite orbit and clock modeling, including relativistic effects, with mean fit differences of the order ${10}^{-4}\mathrm{m}$ in position, ${10}^{-8}\mathrm{m}/\mathrm{s}$ in velocity, and ${10}^{-4}$ microseconds in clock offset. The method also improves simulation run time by using a fast technique for evaluating the Chebyshev polynomials. Runtime comparisons demonstrate the polynomial method reduces runtime by up to 72% of more traditional methods. The speed of the method makes it well suited for practical, accurate Monte Carlo simulation techniques. The method can be used in simulations for the verification and validation of GNSS receivers embedded in autonomous aerospace navigation systems, for uncertainty analysis, and for other purposes. Details for validating the precision data are given. Pseudocode algorithms are provided for fitting and evaluating Chebyshev polynomials. Also provided are high-level concepts of one approach for integrating the method into larger, multisystem aerospace simulations, including the effects of signal propagation delay and Earth blockage.

本文介绍了一种通过使用切比雪夫多项式拟合公开可用的精确数据对全球导航卫星系统 (GNSS) 星座进行建模和仿真的方法。全球定位系统 (GPS) 用于演示该方法，但该方法适用于所有具有精确星历数据的 GNSS，包括 Galileo 和 GLONASS。该方法有助于高度准确的卫星轨道和时钟建模，包括相对论效应，平均拟合差异为${10}^{-4}\mathrm{米}$ 在位， ${10}^{-8}\mathrm{米}/\mathrm{秒}$ 在速度上，和 ${10}^{-4}$时钟偏移中的微秒。该方法还通过使用评估 Chebyshev 多项式的快速技术来缩短仿真运行时间。运行时比较表明多项式方法的运行时间比更传统的方法减少了 72%。该方法的速度使其非常适合实用、准确的蒙特卡罗模拟技术。该方法可用于验证和验证嵌入在自主航空航天导航系统中的 GNSS 接收器、不确定性分析和其他目的的模拟。给出了验证精度数据的详细信息。提供了用于拟合和评估切比雪夫多项式的伪代码算法。还提供了将方法集成到更大的多系统航空航天模拟中的一种方法的高级概念，