TSEP positioning accuracy evaluation approach applied in 4D guidance
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摘要: 随着人类深空探测活动的增加及空间导航装备鉴定的需求,传统的概率指标和评估方法已不能满足系统鉴定使用要求.推导归纳了3种球概率误差(SEP,Sphere Error Probability)的计算方法:三重积分方程法、卡方(χ2)分布近似法和极大似然估计(MLE,Maximum Likelihood Estimate)法.研究了2种统计试验方案,提出了TSEP(Time SEP)精度评估方法.仿真及试验验证表明:TSEP方法能对空间装备的定位精度给出相对全面的评价,方案可行,兼容传统指标的计算方法且可充分利用单次试验数据,试验验证简单.3种算法计算的SEP值,其最大相对误差均不超过7%;χ2分布近似值稍偏保守,推荐工程使用;而MLE计算值可作为积分运算的初值,以减少积分运算次数,快速获取真值.Abstract: As humans exploration activities increase in deep space and identification needs of space navigation equipment, traditional probability indicators and evaluation approach cannot meet the system requirements. Three sphere error probabilitiy (SEP) calculation methods were deduced and induced: triple integral equation algorithm, χ2 distribution approximation algorithm, and maximum likelihood estimation (MLE) optimization algorithm. Combined with the two statistical test schemes, time SEP (TSEP) accuracy evaluation method was raised. Simulation and test verification shows that: TSEP method of positioning accuracy of space equipment gives a relative comprehensive evaluation, the scheme is viable, compatible with traditional method of calculating indicators and takes full advantage of single test data, test simple. Three SEP algorithms can all compute SEP, maximum relative error of no more than 7%; slightly conservative the χ2 distribution approximation is recommended; MLE calculation values can be used as initial values of the integral operator in order to reduce the number of integral operation, in quickly gets the true value.
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