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从理论上推导全球导航卫星系统(GNSS)中基于双星故障的接收机自主完好性监测(RAIM)中的两个基本定理,为基于双星故障的RAIM技术提供了理论支撑。第一个定理给出了RAIM中奇偶矢量与导航误差的关系,指出了两者的统计独立性,它表明只能通过多次测量的累积以统计方法得到导航定位精度;第二个定理指出可通过偏差修正方式得到正确的导航解。这两个结论与单星故障假设条件下得到的结论是相同的,这就表明,基于单星故障假设的RAIM方法,其基本原理是可以通用于双星以至于多星故障情形的,只需在具体操作上进行适应性改进。另外,推导方法本身也提供了一种进行GNSS分析的有力工具。
Theoretically deducing two basic theorems in receiver autonomous integrity monitoring (RAIM) based on binary failure in GNSS provides theoretical support for RAIM technology based on binary star failure. The first theorem gives the relationship between the parity vectors and navigation errors in RAIM and points out the statistical independence of the two. It shows that the accuracy of navigation and positioning can only be obtained by statistical methods through the accumulation of multiple measurements. The second theorem states that The correct navigation solution is obtained by means of deviation correction. These two conclusions are the same as those obtained under the single-star failure assumption, which shows that the basic principle of the RAIM method based on the assumption of single-star failure is that it can be used universally in double-star and even multi-star failure scenarios, Specific operations on the adaptive improvement. In addition, the derivation method itself also provides a powerful tool for GNSS analysis.