GPS局域增强系统的完善性监测技术研究
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摘要
为了能够将GPS作为主要的导航手段应用到民用航空的精密进场与着陆阶段,需要进一步提高系统的定位精度、连续性、完善性和可用性等性能。20世纪90年代提出的局域增强系统,它采用载波平滑的差分定位技术,极大地提高了GPS系统的定位精度,因此引起了相关领域学者和民用航空机构的广泛关注。实践已经证明,LAAS很容易满足Ⅰ类精密进场的性能要求,但是对于Ⅱ类和Ⅲ精密进场阶段,则还需进一步完善系统的结构和功能。
在飞机精密进场阶段所需的各种性能指标中,最难满足的是完善性方面的性能需求。完善性监测的主要目的是保证系统工作在正常状态,提高导航数据的可信度。常用的完善性监测手段包括LAAS地面站设备的完善性监测和接收机自主完善性检测。本文主要针对GPS局域增强系统的完善性技术进行研究,通过一些监测手段和算法的改进,以有效降低完善性监测存在的风险。论文主要研究工作如下:
1.对LGF广播修正误差在非零均值高斯分布和非高斯分布下膨胀系数的确定方法进行了深入研究。对于非零均值的高斯分布模型,通过向量范数的不等式转化关系,得到了标准差膨胀和均值膨胀两种确定方法;对于修正误差的非高斯分布模型,通过高斯混合模型拟合修正误差的概率密度分布,进而将非高斯分布下确定标准差的膨胀系数转化为高斯混合模型下确定标准差的膨胀系数,采用EM算法估计高斯混合模型的参数,通过BIC准则和SEM算法对模型的结构进行选择和优化,通过仿真试验证明在这种处理方法下得到的修正误差的高斯混合模型满足确定膨胀系数的要求,并给出相应的膨胀系数计算公式。
2.结合修正误差的有限采样点限制和不同分布模型的影响,给出了LGF广播标准差的总膨胀系数,在伪卫星增强、采用相对精确的标准差模型以及采用膨胀的标准差等情况下,计算垂直保护水平,并得到如下结论:如果修正误差的标准差不进行膨胀,则无论是否使用伪卫星增强,GPS局域增强系统能够满足各阶段精密进场的性能要求,但这种计算结果很难保证定位误差小于保护水平,从而产生完善性风险;如果采用膨胀的标准差计算VPL,无论是否使用伪卫星增强,系统只满足CATⅠ的可用性要求,但是伪卫星增强后,系统可用性明显提高,而且性能更加稳定;如果使用相对精确的标准差模型计算VPL,在伪卫星增强后,系统可以满足CATⅡ的可用性要求,但是这只能用于理论分析。
3.对广播修正误差的标准差和均值监测进行了深入的研究,针对CUSUM算法不能一步检测较大的标准差和均值偏移的缺陷,提出了应用Shewhart-CUSUM组合算法监测均值和标准差异常。以平均运行长度为指标,对CUSUM、Shewhart和Shewhart-CUSUM这三种算法的特性进行了详细地分析,结果表明,组合算法的检测门限只需比CUSUM算法稍大,便可以获得与CUSUM算法相近的失控状态平均运行长度。最后通过仿真试验验证了组合算法在标准差和均值监测中的性能,结果表明:组合算法可以一步检测较大的异常,在检测累积型异常时与CUSUM算法性能相同,并且失控状态下的平均运行长度与理论计算的相等。
4.针对“快照”的奇偶空间的RAIM算法受到测量方程的数学模型限制,当测量误差是非零均值高斯分布或带有不确定的扰动输入时,故障检测的误警率和漏警率增大。改进测量方程的数学模型,在其中加入不确定输入项增加了算法的鲁棒性和抗干扰能力,通过估计方法将这种不确定性输入转化为确定性的输入,并利用双重最优解耦,将奇偶向量和故障向量分离。最后通过仿真证明了这种改进的RAIM算法的确可以有效降低卫星故障检测的漏警率和误警率。
5.提出了一种多维累积RAIM算法—MCRAIM,它通过多维累积和处理奇偶残差,解决了“快照”的奇偶空间RAIM算法不能检测累积型故障的缺陷。针对GPS系统的特殊应用情况,将算法分为检测系统的累积型故障和检测卫星的累积型故障。通过仿真试验证明了算法在检测这两种累积型异常时的独特优势和性能,又对MCRAIM算法做进一步改进,形成了RAIM-MCRAIM组合算法,它既有“快照”RAIM一步检测较大故障的能力,又具有MCRAIM检测中等累积型故障的能力,并通过仿真试验对组合算法的这种性能进行了证明。
In order to make GPS support aircraft precision approach and landing of civil aviation as the main means,the system needed a further improvement in positioning accuracy,continuity,integrity and availability.In the nineties of twentieth century,the local area augmentation system which using carrier smooth and difference positioning technology was put forward,It was so greatly enhanced the accuracy of GPS that addressing the related fields scholars and civil aviation bodies extensive attention.Practice had proved that LAAS could easily meet the performance requirements of category I precision approach,but it needed a further improvement on the system structure and function for CATⅡ/Ⅲ.
All of the performance indicators required in precision approach,the most difficult to meet was the integrity.The main purpose of integrity monitoring was to guarantee the system operating at the normal state and improve the credibility of navigation data.The means of integrity monitoring included LAAS ground facility integrity monitoring and receiver autonomous integrity monitoring.The research purpose of this paper was about the integrity problem of GPS local area augmentation system,and the main researches were as follows:
1.This thesis researched on the detailed methods of standard deviation inflation factor determination when the true distribution of LGF Broadcasting correction error was non-zero mean Gaussian or non-Gaussian.Under the non-zero mean Gaussian distribution,inflation factor of standard deviation and mean were given by vector norm inequality.Under the non-Gaussian distribution, Gaussian mixture model was used to fit the probability density of LGF correction error,which would be determining the inflation factor under non-Gaussian model into Gaussian mixture model.Then EM algorithm estimated Gaussian mixture model parameters,BIC and SEM algorithm modelled the structure of selection and optimization.Simulation result was proved that inflator coefficient determinated in this way could meet requirement,and estabilished the calculation formula of Sigma inflation factor.
2.The total inflation factor of LGF broadcasting standard deviation was determinating with the limited sampling restriction.Vertical protection level was calculated with pseudolites augmentation,the relative accurate model of standard deviation and standard deviation inflation,and got the following conclusions:If standard deviation was not inflated,regardless of with the augmentation of pseudolites,GPS could meet the performance requirements of CATⅠ/Ⅱ/Ⅲ,but it was difficult to guarantee that positioning error was less than protection level.If standard deviation was inflated,regardless of with the augmentation of pseudolites,GPS only met the performance requirements of CAT I,but the availability was significantly improved with pseudolites.If VPL was calculated with the standard deviation relative accurate model and the augmentation of pseudolites,the system can meet the availability requirements of CATⅡ,but it could only be used for theoretical analysis.
3.Standard deviation and mean monitoring method was carried out detailed research.Because CUSUM scheme could not detect a larger standard deviation and mean displacement within a step,Combined Shewhart-CUSUM scheme was put forward to solve those defects.The detailed performance of CUSUM, Shewhart and Shewhart-CUSUM was analysed as the indicator of the average run length,Result was shown that the detection threshold of combination scheme was only slightly larger than that of CUSUM,we could get the same performance for checking cumulative anomaly.Finally,the performance of standard deviation and mean monitoring was anslysed by simulation test,which showed that the combinated scheme could detect the larger anomaly within a step,and had the same performance with CUSUM for detecting cumulative anomaly.
4.The "snapshot" RAIM algorithm of parity space was restricted by the mathematical model of measurement equation,when the measurement error was non-zero mean Gaussian distribution or had an unknown disturbance input,the false alarm rate and misleading alarm rate of fault detection were increased.The measurement equation was improved by inputing the uncertainty model,which added the robustness and anti-jamming capability of the parity space algorithm. The uncertainty input was estimated to turn into certainty input,and the double optimal Decoupling method was used to separate between uncertainty input and fault vector.Finally,simulation was proved that the improved RAIM algorithm could reduce false alarm rate and misleading alarm rate of satellite fault detection.
5.The multivariable cumulative RAIM(MCRAIM) was presented in this paper,the multivariable cumulative sum algorithm was adopted to handle parity residual error,which solved the defect of "snapshot" RAIM not detecting cumulative fault within a step.In allusion to the special application case of GPS, it respectively detected cumulative anomaly of system and cumulative anomaly of satellite.Simulation result was shown that MCRAIM algorithm had a unique advantages and performance for GPS fault detection.A further improvement for MCRAIM algorithm formed combined RAIM-MCRAIM algorithm,it not only had capability of "snapshot" RAIM detecting larger fault within one step,but also could detect cumulative fault.Finally the characteristics of combined algorithm were proved by the way of simulation.
在飞机精密进场阶段所需的各种性能指标中,最难满足的是完善性方面的性能需求。完善性监测的主要目的是保证系统工作在正常状态,提高导航数据的可信度。常用的完善性监测手段包括LAAS地面站设备的完善性监测和接收机自主完善性检测。本文主要针对GPS局域增强系统的完善性技术进行研究,通过一些监测手段和算法的改进,以有效降低完善性监测存在的风险。论文主要研究工作如下:
1.对LGF广播修正误差在非零均值高斯分布和非高斯分布下膨胀系数的确定方法进行了深入研究。对于非零均值的高斯分布模型,通过向量范数的不等式转化关系,得到了标准差膨胀和均值膨胀两种确定方法;对于修正误差的非高斯分布模型,通过高斯混合模型拟合修正误差的概率密度分布,进而将非高斯分布下确定标准差的膨胀系数转化为高斯混合模型下确定标准差的膨胀系数,采用EM算法估计高斯混合模型的参数,通过BIC准则和SEM算法对模型的结构进行选择和优化,通过仿真试验证明在这种处理方法下得到的修正误差的高斯混合模型满足确定膨胀系数的要求,并给出相应的膨胀系数计算公式。
2.结合修正误差的有限采样点限制和不同分布模型的影响,给出了LGF广播标准差的总膨胀系数,在伪卫星增强、采用相对精确的标准差模型以及采用膨胀的标准差等情况下,计算垂直保护水平,并得到如下结论:如果修正误差的标准差不进行膨胀,则无论是否使用伪卫星增强,GPS局域增强系统能够满足各阶段精密进场的性能要求,但这种计算结果很难保证定位误差小于保护水平,从而产生完善性风险;如果采用膨胀的标准差计算VPL,无论是否使用伪卫星增强,系统只满足CATⅠ的可用性要求,但是伪卫星增强后,系统可用性明显提高,而且性能更加稳定;如果使用相对精确的标准差模型计算VPL,在伪卫星增强后,系统可以满足CATⅡ的可用性要求,但是这只能用于理论分析。
3.对广播修正误差的标准差和均值监测进行了深入的研究,针对CUSUM算法不能一步检测较大的标准差和均值偏移的缺陷,提出了应用Shewhart-CUSUM组合算法监测均值和标准差异常。以平均运行长度为指标,对CUSUM、Shewhart和Shewhart-CUSUM这三种算法的特性进行了详细地分析,结果表明,组合算法的检测门限只需比CUSUM算法稍大,便可以获得与CUSUM算法相近的失控状态平均运行长度。最后通过仿真试验验证了组合算法在标准差和均值监测中的性能,结果表明:组合算法可以一步检测较大的异常,在检测累积型异常时与CUSUM算法性能相同,并且失控状态下的平均运行长度与理论计算的相等。
4.针对“快照”的奇偶空间的RAIM算法受到测量方程的数学模型限制,当测量误差是非零均值高斯分布或带有不确定的扰动输入时,故障检测的误警率和漏警率增大。改进测量方程的数学模型,在其中加入不确定输入项增加了算法的鲁棒性和抗干扰能力,通过估计方法将这种不确定性输入转化为确定性的输入,并利用双重最优解耦,将奇偶向量和故障向量分离。最后通过仿真证明了这种改进的RAIM算法的确可以有效降低卫星故障检测的漏警率和误警率。
5.提出了一种多维累积RAIM算法—MCRAIM,它通过多维累积和处理奇偶残差,解决了“快照”的奇偶空间RAIM算法不能检测累积型故障的缺陷。针对GPS系统的特殊应用情况,将算法分为检测系统的累积型故障和检测卫星的累积型故障。通过仿真试验证明了算法在检测这两种累积型异常时的独特优势和性能,又对MCRAIM算法做进一步改进,形成了RAIM-MCRAIM组合算法,它既有“快照”RAIM一步检测较大故障的能力,又具有MCRAIM检测中等累积型故障的能力,并通过仿真试验对组合算法的这种性能进行了证明。
In order to make GPS support aircraft precision approach and landing of civil aviation as the main means,the system needed a further improvement in positioning accuracy,continuity,integrity and availability.In the nineties of twentieth century,the local area augmentation system which using carrier smooth and difference positioning technology was put forward,It was so greatly enhanced the accuracy of GPS that addressing the related fields scholars and civil aviation bodies extensive attention.Practice had proved that LAAS could easily meet the performance requirements of category I precision approach,but it needed a further improvement on the system structure and function for CATⅡ/Ⅲ.
All of the performance indicators required in precision approach,the most difficult to meet was the integrity.The main purpose of integrity monitoring was to guarantee the system operating at the normal state and improve the credibility of navigation data.The means of integrity monitoring included LAAS ground facility integrity monitoring and receiver autonomous integrity monitoring.The research purpose of this paper was about the integrity problem of GPS local area augmentation system,and the main researches were as follows:
1.This thesis researched on the detailed methods of standard deviation inflation factor determination when the true distribution of LGF Broadcasting correction error was non-zero mean Gaussian or non-Gaussian.Under the non-zero mean Gaussian distribution,inflation factor of standard deviation and mean were given by vector norm inequality.Under the non-Gaussian distribution, Gaussian mixture model was used to fit the probability density of LGF correction error,which would be determining the inflation factor under non-Gaussian model into Gaussian mixture model.Then EM algorithm estimated Gaussian mixture model parameters,BIC and SEM algorithm modelled the structure of selection and optimization.Simulation result was proved that inflator coefficient determinated in this way could meet requirement,and estabilished the calculation formula of Sigma inflation factor.
2.The total inflation factor of LGF broadcasting standard deviation was determinating with the limited sampling restriction.Vertical protection level was calculated with pseudolites augmentation,the relative accurate model of standard deviation and standard deviation inflation,and got the following conclusions:If standard deviation was not inflated,regardless of with the augmentation of pseudolites,GPS could meet the performance requirements of CATⅠ/Ⅱ/Ⅲ,but it was difficult to guarantee that positioning error was less than protection level.If standard deviation was inflated,regardless of with the augmentation of pseudolites,GPS only met the performance requirements of CAT I,but the availability was significantly improved with pseudolites.If VPL was calculated with the standard deviation relative accurate model and the augmentation of pseudolites,the system can meet the availability requirements of CATⅡ,but it could only be used for theoretical analysis.
3.Standard deviation and mean monitoring method was carried out detailed research.Because CUSUM scheme could not detect a larger standard deviation and mean displacement within a step,Combined Shewhart-CUSUM scheme was put forward to solve those defects.The detailed performance of CUSUM, Shewhart and Shewhart-CUSUM was analysed as the indicator of the average run length,Result was shown that the detection threshold of combination scheme was only slightly larger than that of CUSUM,we could get the same performance for checking cumulative anomaly.Finally,the performance of standard deviation and mean monitoring was anslysed by simulation test,which showed that the combinated scheme could detect the larger anomaly within a step,and had the same performance with CUSUM for detecting cumulative anomaly.
4.The "snapshot" RAIM algorithm of parity space was restricted by the mathematical model of measurement equation,when the measurement error was non-zero mean Gaussian distribution or had an unknown disturbance input,the false alarm rate and misleading alarm rate of fault detection were increased.The measurement equation was improved by inputing the uncertainty model,which added the robustness and anti-jamming capability of the parity space algorithm. The uncertainty input was estimated to turn into certainty input,and the double optimal Decoupling method was used to separate between uncertainty input and fault vector.Finally,simulation was proved that the improved RAIM algorithm could reduce false alarm rate and misleading alarm rate of satellite fault detection.
5.The multivariable cumulative RAIM(MCRAIM) was presented in this paper,the multivariable cumulative sum algorithm was adopted to handle parity residual error,which solved the defect of "snapshot" RAIM not detecting cumulative fault within a step.In allusion to the special application case of GPS, it respectively detected cumulative anomaly of system and cumulative anomaly of satellite.Simulation result was shown that MCRAIM algorithm had a unique advantages and performance for GPS fault detection.A further improvement for MCRAIM algorithm formed combined RAIM-MCRAIM algorithm,it not only had capability of "snapshot" RAIM detecting larger fault within one step,but also could detect cumulative fault.Finally the characteristics of combined algorithm were proved by the way of simulation.
引文
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