非高斯/非线性滤波理论及其在GNSS动态定位中的应用

For the non-Gaussian and non-linear problem of stochastic system both in GNSS and INS navigation and kinematic positioning, in view of concrete problem and condition in practical GNSS application, modern time series analysis, modern statistic learning theory, colored noise filtering and adaptive estimation are synthetically used in real-time modeling and parameter estimating of the function model, which is non-linear, and stochastic model, which is non-Gaussian. A practicable method for measuring the non-linearity intensity of kinematic non-linear filtering model is introduced and an evaluation criteria based on three capabilities of non-linear filtering, accuracy, conformance and confidence, is established. The methods for measuring distribution character and detecting correlation of noise are studied. Considering the more complicated problem of non-Gaussian colored noise, a new adaptive filtering algorithm using time series and kernel semi-parametric model compensation is proposed. Gaussian mixture ARMA filtering for system with serious non-linearity and non-Gaussian noise is devised. For the pivotal issue of parameter estimation in Gaussian mixture model, a practicable efficient adaptive Gaussian mixture EKF algorithm is researched and employed in data processing of non-linear system with non-Gaussian colored noise. Thus, the comprehensive methodology including both filtering theories and algorithms for non-Gaussian and non-linear system of GNSS kinematic positioning, able to simultaneously control model error such as outlier, colored noise and linearization error, is set up to enhance accuracy, reliability, integrity and availability of navigation, providing rigorous scientific theories and feasible technical approaches for application in navigation, kinematic positioning and correlative fields. This research is of great theoretic and applicable value for data processing in airborne and astronautic gravimetry, maritime real-time navigation, target tracking, precise spacecraft orbit determination and so on.

针对GNSS动态导航定位和组合导航解算中非高斯、非线性随机系统问题，将现代时间序列分析法和现代统计学习理论、以及现有的有色噪声估计理论、自适应估计理论综合应用于非高斯/非线性的函数模型和随机模型的实时构模与参数估计，提出实用的动态非线性滤波模型非线性强度的度量方法，建立评价非线性滤波性能的实用准则，研究噪声的分布和相关性度量与探测的有效方法，提出基于时间序列模型补偿和核半参数模型补偿的自适应滤波新算法，设计适用于强非线性、非高斯噪声系统模型的高斯混合ARMA模型滤波器，建立一套能同时控制异常和有色噪声及线性化模型误差的影响、适合于GNSS动态导航定位的非高斯/非线性随机系统的滤波理论和实用算法，为动态导航定位及相关领域的应用提供严密的科学理论和行之有效的技术手段。本研究对航空航天重力测量、海洋动态载体的实时导航定位、目标跟踪定位、航天器精密定轨等领域的数据处理具有重要的理论意义和实用价值。

动态载体导航定位涉及非线性模型误差、有色噪声及异常误差影响。针对GNSS动态导航定位和GNSS/INS组合导航解算实际，在GNSS和GNSS/INS组合导航定位中的模型误差分析与处理，GNSS数据的周跳探测与修复方法，GNSS精密定位随机模型估计，非高斯滤波算法，GNSS/INS定姿关键技术等方面做了较深入研究，取得一些重要成果。针对惯性元件误差中有色噪声影响远大于白噪声的情况，提出基于经验模分解的惯性导航误差阈值消噪方法，提高了惯性导航的精度；提出改正伪距多路径误差的北斗三频周跳探测与修复方法，提高了周跳修复成功率；提出惯性辅助GNSS实时动态单频周跳探测新算法；针对北斗系统不同轨道卫星高度差异和卫星信号质量差异较大的特点，应用Bancroft算法提出一种新的BDS观测值定权公式；提出利用时频分析法精化GNSS/INS组合导航的先验滤波模型；提出基于现代时间序列分析法处理有色噪声的滤波算法；针对动态环境下导航定位异常和非高斯噪声影响问题，提出基于高斯混合分布的抗差Bayes滤波算法和基于高斯混合模型的自适应UKF新算法，有效抑制异常误差的影响，提高了导航的可靠性；提出附加基线约束和附加方向余弦矩阵约束的整周模糊度快速求解算法，提高了模糊度固定成功率和效率；提出基于拉格朗日乘子的正交化矩阵Kalman滤波新算法；提出基于自适应抗差Kalman滤波的瞬时测姿方法，提高了姿态确定速度和可靠性，满足载体定姿的实时性需求。. 项目组公开发表学术论文40多篇，其中SCI、EI收录论文14篇，获河南省自然科学优秀学术论文6篇，中国卫星导航学术年会年会优秀论文1篇；完成研究生学位论文8篇，获全军优秀硕士学位论文1篇，河南省优秀学位论文2篇，信息工程大学优秀学位论文3篇；1项成果获军队科技进步二等奖。研究成果丰富和发展了现代测量测量数据处理理论和方法，具有重要的科学意义和军事应用价值，将为动态导航定位及其相关领域的应用提供基础理论和技术支持。