非线性滤波方法在导航系统中的应用研究
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摘要
目前，扩展卡尔曼滤波是研究初始对准和惯性／GPS组合导航问题的一个主要手段。但初始对准和惯性／GPS组合导航问题本质上是非线性的，对模型进行线性化的扩展卡尔曼滤波在一定程度上影响了系统的性能。近年来，直接使用非线性模型的UKF(Unscented Kalman Filtering，UKF)和粒子滤波，正在逐渐成为研究非线性估计问题的热点和有效方法。
本文研究了UKF和粒子滤波两种非线性滤波方法，并将其应用于非线性静基座对准和惯性／GPS组合导航，系统地研究了初始对准和惯性／GPS组合导航中各种非线性项对系统性能的影响。
在非线性滤波方法上，本文主要在以下几个方面做了深入研究：
1) 从多元分布代表点的角度，分析并扩展了UKF方法。
2) 研究了两类混合系统的UKF滤波问题，提出了针对混合系统的简化UKF方法。
3) 将多元分布的代表点理论应用于粒子滤波，设计了使用代表点代替随机粒子的确定性粒子滤波方法，进一步提高了粒子滤波的性能。
同时，利用研究得到的结论，将非线性滤波方法应用于静基座对准和惯性／GPS组合导航问题，并在以下几个方面做了主要工作：
1) 考察了惯性导航系统的非线性误差模型，完善了误差模型间的关系并对其做了统一的描述。
2) 将UKF方法应用于静基座对准，研究了非线性静基座对准问题。仿真及转台试验均表明：非线性静基座对准不仅具有很好的对准精度，而且大大放宽了对方位失准角的约束(10°以内即可)。
3) 将UKF和粒子滤波方法应用于惯性／GPS组合导航，通过仿真、转台试验及车载试验，研究了模型中的非线性项对组合导航性能的影响。结果表明：非线性系统方程可以进一步提高系统对方位角的估计性能：非线性伪距观测方程对组合系统的精度没有明显提高。
Currently, extended Kalman filtering (EKF) has been one of the main methods for studying the two problems of initial alignment and INS/GPS integrated navigation that have nonlinear characteristics. Because EKF necessitate the linearization of the original nonlinear models, the performances achieved through using EKF are limited to some extent. In recent years, unscented Kalman filtering (UKF) and particle filtering (PF) are becoming the focus of nonlinear estimation.The dissertation investigates the two nonlinear filtering methods, namely UKF and PF, and then applies them to the two problems of initial alignment and INS/GPS integrated navigation, concentrating on the impacts of various nonlinear characteristics. The researches on nonlinear filtering are organized as following:1. UKF is analyzed and extended from the aspect of representative points of random distribution;2. UKF for two classes of hybrid system are investigated and a specific simplified UKF (SUKF) is raised.3. The representative points of random distribution are applied to PF, resulting in a deterministic PF using the representative points rather than random samples which has better performance than the original PF.Consequently, the above results are applied to the two problems of initial alignment and INS/GPS integrated navigation. The main work consists of the following aspects:1. The nonlinear models of SINS are investigated. The relationship among them is completed and a unified description is presented.2. UKF is applied to nonlinear initial alignment of SINS on the stationary base. Simulation and experiment results on the three-axis table show that the nonlinear initial alignment not only release the constraint on the azimuth error (within 10 degree), but result in a good estimate.3. UKF and PF are applied to INS/GPS integrated navigation. The influences of nonlinear parts on the performance are investigated by means of simulation, rotating table, and filed tests. The results show that using nonlinear process equation can further improve the performance, but using nonlinear pseudo-range equation has no significant improvement compared to the linearized pseudo-range equation.
本文研究了UKF和粒子滤波两种非线性滤波方法，并将其应用于非线性静基座对准和惯性／GPS组合导航，系统地研究了初始对准和惯性／GPS组合导航中各种非线性项对系统性能的影响。
在非线性滤波方法上，本文主要在以下几个方面做了深入研究：
1) 从多元分布代表点的角度，分析并扩展了UKF方法。
2) 研究了两类混合系统的UKF滤波问题，提出了针对混合系统的简化UKF方法。
3) 将多元分布的代表点理论应用于粒子滤波，设计了使用代表点代替随机粒子的确定性粒子滤波方法，进一步提高了粒子滤波的性能。
同时，利用研究得到的结论，将非线性滤波方法应用于静基座对准和惯性／GPS组合导航问题，并在以下几个方面做了主要工作：
1) 考察了惯性导航系统的非线性误差模型，完善了误差模型间的关系并对其做了统一的描述。
2) 将UKF方法应用于静基座对准，研究了非线性静基座对准问题。仿真及转台试验均表明：非线性静基座对准不仅具有很好的对准精度，而且大大放宽了对方位失准角的约束(10°以内即可)。
3) 将UKF和粒子滤波方法应用于惯性／GPS组合导航，通过仿真、转台试验及车载试验，研究了模型中的非线性项对组合导航性能的影响。结果表明：非线性系统方程可以进一步提高系统对方位角的估计性能：非线性伪距观测方程对组合系统的精度没有明显提高。
Currently, extended Kalman filtering (EKF) has been one of the main methods for studying the two problems of initial alignment and INS/GPS integrated navigation that have nonlinear characteristics. Because EKF necessitate the linearization of the original nonlinear models, the performances achieved through using EKF are limited to some extent. In recent years, unscented Kalman filtering (UKF) and particle filtering (PF) are becoming the focus of nonlinear estimation.The dissertation investigates the two nonlinear filtering methods, namely UKF and PF, and then applies them to the two problems of initial alignment and INS/GPS integrated navigation, concentrating on the impacts of various nonlinear characteristics. The researches on nonlinear filtering are organized as following:1. UKF is analyzed and extended from the aspect of representative points of random distribution;2. UKF for two classes of hybrid system are investigated and a specific simplified UKF (SUKF) is raised.3. The representative points of random distribution are applied to PF, resulting in a deterministic PF using the representative points rather than random samples which has better performance than the original PF.Consequently, the above results are applied to the two problems of initial alignment and INS/GPS integrated navigation. The main work consists of the following aspects:1. The nonlinear models of SINS are investigated. The relationship among them is completed and a unified description is presented.2. UKF is applied to nonlinear initial alignment of SINS on the stationary base. Simulation and experiment results on the three-axis table show that the nonlinear initial alignment not only release the constraint on the azimuth error (within 10 degree), but result in a good estimate.3. UKF and PF are applied to INS/GPS integrated navigation. The influences of nonlinear parts on the performance are investigated by means of simulation, rotating table, and filed tests. The results show that using nonlinear process equation can further improve the performance, but using nonlinear pseudo-range equation has no significant improvement compared to the linearized pseudo-range equation.
引文
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