GNSS中基于双星故障的RAIM中的数学关系

Mathematical Aspects of GNSS RAIM Based on Dual-satellite Fault

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。

Two basic theorems of receiver autonomous integrity monitoring(RAIM) are obtained by theory deduction based on dual-satellite fault in global navigation satellite system(GNSS).These theorems provide theory support for the RAIM technology facing the dual-satellite fault.The first theorem demonstrates the relationship between the navigation error and the parity vector of RAIM,and it points out the independence of the navigation error and parity vector,which means that the navigation precision can be estimated only by accumulating many sets of measurements.The second theorem shows that the correct navigation solution can be obtained by error correcting.The two theorems based on dual-satellite fault are same as the condition of single satellite fault,which means that the fundament of RAIM methods based on single satellite fault can be used in the case of dual-satellite fault or even multi-satellite fault,just with the proper improvement of the detailed operation.In addition the method of deduction is in itself of great interest and a powerful tool for GNSS analysis.