动态定位有色噪声自适应抗差滤波理论的拓展与应用研究
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摘要
本文对动态定位有色噪声自适应抗差滤波理论与算法进行了较深入的研究。主要内容和创新点如下：
1.对现有的多种有色噪声自适应滤波算法进行了总结和分类，简要介绍了各种滤波算法的理论和模型，分析了它们在有色噪声处理中的优缺点，并对多种有色噪声自适应滤波算法进行了比较分析。计算结果表明，各种滤波算法在控制有色噪声影响的侧重点是不相同的，实际应用时需根据有色噪声的特性和用户需求选择适当的自适应滤波算法来控制有色噪声对动态滤波结果的影响。
2.在假设观测噪声和动力学模型噪声主要是具有一阶自相关特性的有色噪声的基础上，提出了一种基于移动窗口的有色噪声函数模型和随机模型的自适应拟合法。给出了计算有色噪声估值和噪声协方差矩阵的表达式，并利用实测数据验证了模型和算法的可行性和实用性。计算结果表明该算法能有效地抵制有色噪声对导航滤波结果的影响。
3.在自适应抗差滤波和双因子相关观测抗差估计原理的基础上，提出了分类因子自适应抗差Kalman滤波算法。该算法基于常用的常速度模型，将状态参数分为位置和速度两类，并分别构造相应的自适应因子的思想。导出了分类因子自适应抗差滤波计算表达式，给出了相应的位置和速度自适应因子计算式。计算结果表明，分类因子自适应抗差滤波不仅能有效地控制观测异常和动态扰动异常的影响，而且利用分类因子合理地平衡了位置预报信息和速度预报信息对状态参数估值的贡献，其精度要优于基于位置不符值和速度不符值的单因子自适应抗差滤波。
4.基于双因子相关观测抗差估计和自适应Kalman滤波原理，提出了多因子自适应抗差滤波的思想。基于状态不符值构造了状态各分量自适应因子，推导了多因子自适应抗差滤波解算表达式。将多因子自适应滤波与单因子自适应滤波进行了比较，分析了多因子自适应滤波可能存在的问题。
5.在GPS/INS组合导航中，观测信息并不足以解算相应的状态参数，此时将无法构造基于状态不符值的自适应因子来控制动力学模型误差对组合导航解的影响。针对此，提出了利用部分状态不符值来构造相应的自适应因子，并成功地用于GPS/INS组合导航中。
6.在移动测量系统中，常常直接使用GPS/INS进行导航定位解算。在GPS失效时直接使用INS获得定位解，此时误差积累太快，定位精度难以保证。基于此，提出了使用可量测影像序列信息的定位算法，并将其与GPS/INS相组合，推导了相应的自适应组合定位解。该算法可以充分利用CCD传感器提供的可量测影像序列，进一步提高移动测量系统的整体性能。
7.介绍了GPS广播星历参数拟合算法，给出了其在低轨卫星轨道拟合和预报中的一些注意事项。分析了常用的几何法定轨的优缺点。基于GPS广播星历的预报特性和自适应抗差滤波原理，提出了一种基于GPS广播星历算法的自适应抗差滤波综合定轨方法，有效地解决了几何法定轨存在的一些问题和缺陷。计算结果表明，新提出的自适应抗差滤波综合定轨方法不仅充分利用了几何观测信息，而且通过自适应因子合理地调节了几何观测信息和星历预报信息对滤波解的贡献，有效地保证了定轨的精度和可靠性。
8.在卫星导航系统广播星历参数拟合中，由于GEO卫星轨道面倾角接近于零，容易出现星历参数估值超限的情况。基于此，提出了参数加权的Givens变换算法，并将其用于控制超限的GEO卫星星历参数估值的的变化范围。计算表明，该算法具有较高的数值稳定性和计算效率，而且参数先验权可以通过逐渐增大的方式获得，很方便地解决了导航卫星广播星历参数估值超限的问题。
9.在基于GEO、IGSO和MEO三类卫星的北斗二代导航定位系统中，GEO卫星的广播星历参数拟合是迫切需要解决的难点之一。基于广播星历参数的最小二乘解法，推导出了轨道面旋转角对广播星历参数的影响表达式，分析了轨道面旋转角的大小对广播星历参数拟合稳定性的影响。计算结果表明，通过增加轨道面旋转角不仅很好地解决了GEO卫星广播星历参数超限的问题，而且确保了广播星历参数拟合算法的精度和可靠性。
This paper mainly focuses on the theories and algorithms of adaptive robust filtering forControlling Influence of Colored Noise in kinematic positioning. The main works andcontributions are summarized as follows:
1. A variety of adaptive filter algorithms for controlling the influence of the colorednoises are summarized and classified. Based on the theories and models of filters, theadvantages and disadvantages of each filter are analyzed. Comparison and analysis ofadaptive filter algorithms for controlling influence of colored noise is performanced. Thecalculation results show that the emphases of each filter in controlling the influence of thecolored noises are different. In actual application, the appropriate adaptive filter algorithmwill be chosed to control the influence of the colored noises on the kinematic filter resultaccording to the characters of the colored noises and user demand.
2. Adaptive fitting of both colored noise and covariance matrices by using movingwindows are presented based on the assumption that the observation and dynamic modelnoises mainly include the colored noises with the first order self-correlation character. Theexpressions to calculate the colored noise estimators and covariance matrices of the modifiedobservations and predicted states are obtained. The feasibility and practicability of the modeland algorithm are tested by an example. It is shown that the Kalman filtering, based on theadaptive fittings of the colored noises and covariance matrices, can be effective in resistingthe influence of the colored noises on the navigation results.
3. An adaptively robust filtering with classified adaptive factors was proposed, based onthe principles of the adaptively robust filtering and bi-factor robust estimation for correlatedobservations. According to the constant velocity model of Kalman filtering, the stateparameter vector was divided into two groups, namely position and velocity. The estimator ofthe adaptively robust filtering with classified adaptive factors was derived, and the calculationexpressions of the classified adaptive factors were presented. Test results show that theadaptively robust filtering with classified adaptive factors is not only robust in controlling themeasurement outliers and the kinematic state disturbing but also reasonable in balancing the contributions of the predicted position and velocity, respectively, and its filtering accuracy issuperior to the adaptively robust filter with single adaptive factor based on the discrepancy ofthe predicted position or the predicted velocity.
4. An adaptively robust filter with multi adaptive factors is proposed, based on theprinciples of adaptive Kalman filter and bi-factor robust estimation for correlated observations.The estimator of the adaptive filter with multi adaptive factors is derived. An adaptive factorfor the component of the state vector is set up based on the discrepancy of the predicted statefrom the kinematic model and estimated state from the measurements. The adaptively robustfilter with multi adaptive factors is compared with the adaptively robust filter with unifiedadaptive factor. The existing problems of the adaptive filter with multi adaptive factors areanalyzed.
5. In the GPS/INS integrated navigation, the adaptive factor based on the statediscrepancy cannot be applied to control the influence of the dynamic model errors on theintegrated navigation results when the number of measurements at some epochs is smallerthan the number of the state parameters. In order to solve this problem, a new adaptive factorbased on partial state discrepancy was developed and successfully applied in GPS/INSintegated navigation.
6. An adaptive integrated positioning filter algorithm based on the DMI sequences, GPSand IMU is presented. The integrated estimator of position vector is derived based on theadaptively robust filter. By analyzing this algorithm, it is shown that the algorithm makes fulluse of the measurements of all the sensors installed in the MMS (Mobile Mapping System),and improves the performance of the system.
7. Some notices of the GPS ephemeris algorithm in the application of the fitting orpredicting of low satellite orbit are given. And the advantages and disadvantages of geometricorbit determination are analyzed. A new adaptively robust synthetic orbit determinationalgorithm is developed based on the predicting characteristic of GPS broadcast ephemeris andthe adaptively robust filtering principle, which can effectively solve some problems orshortages of geometric orbit determination. The results show that the adaptively robustsynthetic orbit determination algorithm can not only make good use of the geometricobservation information but also reasonably adjust the contributions of the geometric observations and ephemeris predicted information to the filtering solution, and the precisionand reliability of orbit determination are insured.
8. The formula of Givens transformation with weighted parameter is deduced, which isused to control the estimator range of the navigation satellite ephemeris parameters. Theresults show that Givens transformation with weighted parameter not only is steady innumerical computation and efficient in calculation but also can easily give the prior weight ofthe ephemeris parameters and expediently make the abnormal navigation satellite parametersback in the prescriptive range.
9. The influence formula of the orbital plane rotation angle on the broadcast ephemerisparameters is deduced and the main factors determining the calculation value of the influencefunction are analyzed based on the least square fitting solution of the broadcast ephemerisparameters. And the effect of the orbital plane rotation angle on the ephemeris fittingalgorithm stability is analyzed. The calculation results show that not only the over limitproblem of the GEO satellite broadcast ephemeris parameters can be solved but also theprecision and reliability of the broadcast ephemeris parameter fitting algorithm can be insuredby increasing the orbital plane rotation angle.
1.对现有的多种有色噪声自适应滤波算法进行了总结和分类，简要介绍了各种滤波算法的理论和模型，分析了它们在有色噪声处理中的优缺点，并对多种有色噪声自适应滤波算法进行了比较分析。计算结果表明，各种滤波算法在控制有色噪声影响的侧重点是不相同的，实际应用时需根据有色噪声的特性和用户需求选择适当的自适应滤波算法来控制有色噪声对动态滤波结果的影响。
2.在假设观测噪声和动力学模型噪声主要是具有一阶自相关特性的有色噪声的基础上，提出了一种基于移动窗口的有色噪声函数模型和随机模型的自适应拟合法。给出了计算有色噪声估值和噪声协方差矩阵的表达式，并利用实测数据验证了模型和算法的可行性和实用性。计算结果表明该算法能有效地抵制有色噪声对导航滤波结果的影响。
3.在自适应抗差滤波和双因子相关观测抗差估计原理的基础上，提出了分类因子自适应抗差Kalman滤波算法。该算法基于常用的常速度模型，将状态参数分为位置和速度两类，并分别构造相应的自适应因子的思想。导出了分类因子自适应抗差滤波计算表达式，给出了相应的位置和速度自适应因子计算式。计算结果表明，分类因子自适应抗差滤波不仅能有效地控制观测异常和动态扰动异常的影响，而且利用分类因子合理地平衡了位置预报信息和速度预报信息对状态参数估值的贡献，其精度要优于基于位置不符值和速度不符值的单因子自适应抗差滤波。
4.基于双因子相关观测抗差估计和自适应Kalman滤波原理，提出了多因子自适应抗差滤波的思想。基于状态不符值构造了状态各分量自适应因子，推导了多因子自适应抗差滤波解算表达式。将多因子自适应滤波与单因子自适应滤波进行了比较，分析了多因子自适应滤波可能存在的问题。
5.在GPS/INS组合导航中，观测信息并不足以解算相应的状态参数，此时将无法构造基于状态不符值的自适应因子来控制动力学模型误差对组合导航解的影响。针对此，提出了利用部分状态不符值来构造相应的自适应因子，并成功地用于GPS/INS组合导航中。
6.在移动测量系统中，常常直接使用GPS/INS进行导航定位解算。在GPS失效时直接使用INS获得定位解，此时误差积累太快，定位精度难以保证。基于此，提出了使用可量测影像序列信息的定位算法，并将其与GPS/INS相组合，推导了相应的自适应组合定位解。该算法可以充分利用CCD传感器提供的可量测影像序列，进一步提高移动测量系统的整体性能。
7.介绍了GPS广播星历参数拟合算法，给出了其在低轨卫星轨道拟合和预报中的一些注意事项。分析了常用的几何法定轨的优缺点。基于GPS广播星历的预报特性和自适应抗差滤波原理，提出了一种基于GPS广播星历算法的自适应抗差滤波综合定轨方法，有效地解决了几何法定轨存在的一些问题和缺陷。计算结果表明，新提出的自适应抗差滤波综合定轨方法不仅充分利用了几何观测信息，而且通过自适应因子合理地调节了几何观测信息和星历预报信息对滤波解的贡献，有效地保证了定轨的精度和可靠性。
8.在卫星导航系统广播星历参数拟合中，由于GEO卫星轨道面倾角接近于零，容易出现星历参数估值超限的情况。基于此，提出了参数加权的Givens变换算法，并将其用于控制超限的GEO卫星星历参数估值的的变化范围。计算表明，该算法具有较高的数值稳定性和计算效率，而且参数先验权可以通过逐渐增大的方式获得，很方便地解决了导航卫星广播星历参数估值超限的问题。
9.在基于GEO、IGSO和MEO三类卫星的北斗二代导航定位系统中，GEO卫星的广播星历参数拟合是迫切需要解决的难点之一。基于广播星历参数的最小二乘解法，推导出了轨道面旋转角对广播星历参数的影响表达式，分析了轨道面旋转角的大小对广播星历参数拟合稳定性的影响。计算结果表明，通过增加轨道面旋转角不仅很好地解决了GEO卫星广播星历参数超限的问题，而且确保了广播星历参数拟合算法的精度和可靠性。
This paper mainly focuses on the theories and algorithms of adaptive robust filtering forControlling Influence of Colored Noise in kinematic positioning. The main works andcontributions are summarized as follows:
1. A variety of adaptive filter algorithms for controlling the influence of the colorednoises are summarized and classified. Based on the theories and models of filters, theadvantages and disadvantages of each filter are analyzed. Comparison and analysis ofadaptive filter algorithms for controlling influence of colored noise is performanced. Thecalculation results show that the emphases of each filter in controlling the influence of thecolored noises are different. In actual application, the appropriate adaptive filter algorithmwill be chosed to control the influence of the colored noises on the kinematic filter resultaccording to the characters of the colored noises and user demand.
2. Adaptive fitting of both colored noise and covariance matrices by using movingwindows are presented based on the assumption that the observation and dynamic modelnoises mainly include the colored noises with the first order self-correlation character. Theexpressions to calculate the colored noise estimators and covariance matrices of the modifiedobservations and predicted states are obtained. The feasibility and practicability of the modeland algorithm are tested by an example. It is shown that the Kalman filtering, based on theadaptive fittings of the colored noises and covariance matrices, can be effective in resistingthe influence of the colored noises on the navigation results.
3. An adaptively robust filtering with classified adaptive factors was proposed, based onthe principles of the adaptively robust filtering and bi-factor robust estimation for correlatedobservations. According to the constant velocity model of Kalman filtering, the stateparameter vector was divided into two groups, namely position and velocity. The estimator ofthe adaptively robust filtering with classified adaptive factors was derived, and the calculationexpressions of the classified adaptive factors were presented. Test results show that theadaptively robust filtering with classified adaptive factors is not only robust in controlling themeasurement outliers and the kinematic state disturbing but also reasonable in balancing the contributions of the predicted position and velocity, respectively, and its filtering accuracy issuperior to the adaptively robust filter with single adaptive factor based on the discrepancy ofthe predicted position or the predicted velocity.
4. An adaptively robust filter with multi adaptive factors is proposed, based on theprinciples of adaptive Kalman filter and bi-factor robust estimation for correlated observations.The estimator of the adaptive filter with multi adaptive factors is derived. An adaptive factorfor the component of the state vector is set up based on the discrepancy of the predicted statefrom the kinematic model and estimated state from the measurements. The adaptively robustfilter with multi adaptive factors is compared with the adaptively robust filter with unifiedadaptive factor. The existing problems of the adaptive filter with multi adaptive factors areanalyzed.
5. In the GPS/INS integrated navigation, the adaptive factor based on the statediscrepancy cannot be applied to control the influence of the dynamic model errors on theintegrated navigation results when the number of measurements at some epochs is smallerthan the number of the state parameters. In order to solve this problem, a new adaptive factorbased on partial state discrepancy was developed and successfully applied in GPS/INSintegated navigation.
6. An adaptive integrated positioning filter algorithm based on the DMI sequences, GPSand IMU is presented. The integrated estimator of position vector is derived based on theadaptively robust filter. By analyzing this algorithm, it is shown that the algorithm makes fulluse of the measurements of all the sensors installed in the MMS (Mobile Mapping System),and improves the performance of the system.
7. Some notices of the GPS ephemeris algorithm in the application of the fitting orpredicting of low satellite orbit are given. And the advantages and disadvantages of geometricorbit determination are analyzed. A new adaptively robust synthetic orbit determinationalgorithm is developed based on the predicting characteristic of GPS broadcast ephemeris andthe adaptively robust filtering principle, which can effectively solve some problems orshortages of geometric orbit determination. The results show that the adaptively robustsynthetic orbit determination algorithm can not only make good use of the geometricobservation information but also reasonably adjust the contributions of the geometric observations and ephemeris predicted information to the filtering solution, and the precisionand reliability of orbit determination are insured.
8. The formula of Givens transformation with weighted parameter is deduced, which isused to control the estimator range of the navigation satellite ephemeris parameters. Theresults show that Givens transformation with weighted parameter not only is steady innumerical computation and efficient in calculation but also can easily give the prior weight ofthe ephemeris parameters and expediently make the abnormal navigation satellite parametersback in the prescriptive range.
9. The influence formula of the orbital plane rotation angle on the broadcast ephemerisparameters is deduced and the main factors determining the calculation value of the influencefunction are analyzed based on the least square fitting solution of the broadcast ephemerisparameters. And the effect of the orbital plane rotation angle on the ephemeris fittingalgorithm stability is analyzed. The calculation results show that not only the over limitproblem of the GEO satellite broadcast ephemeris parameters can be solved but also theprecision and reliability of the broadcast ephemeris parameter fitting algorithm can be insuredby increasing the orbital plane rotation angle.
引文
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