无迹卡尔曼滤波及其在SINS初始对准中的应用

发布时间：2018-09-05 10:37

【摘要】：初始对准是捷联惯导(Strapdown Inertial Navigation System,SINS)的一项关键技术。滤波(即状态估计)在初始对准中发挥了至关重要的作用。当误差模型为线性时,经典的卡尔曼滤波具有十分出色的估计效果。当误差模型为非线性时,采用不同的非线性滤波方法估计效果是不同的。无迹卡尔曼滤波(Unscented Kalman Filter, UKF)是一种性能十分出色的非线性滤波方法。从产生之日起,便在工程上得到了广泛的应用。自由调节参数κ的取值对于UKF的滤波精度和稳定性是至关重要的。一直以来,传统取值认为在满足n + κ = 3 (n为状态变量的维数),滤波精度是最优的。但是,随着容积卡尔曼滤波(Cubature Kalman Filter,CKF)的产生,自由调节参数的传统取值面临了巨大的问题。因为从滤波方法上看,CKF滤波是UKF滤波在自由调节参数κ=0时的一种特例。在不同的维数下,两种滤波方法的精度是不同的。因此,本文以自由调节参数为核心,主要研究了κ对于UKF滤波精度的影响。同时,针对滤波模型中会存在线性方程的情况,分别给出了两种模型化的UKF算法。文章首先介绍了重力场的分布特性、地球形状的两种定义方式以及经、纬度的有关定义。对坐标系及坐标变换进行了详细的介绍,在此基础上推导了捷联惯导系统的误差方程。本文中给出了扩展与非扩展UT变换的过程,同时也给出了扩展与非扩展UKF滤波算法。对于两种方式滤波算法的精度比较,推导了基于泰勒展开式的扩展与非扩展UKF的表达形式,分析了在不同维数、不同调节参数取值下两种滤波的精度。同时,也基于均值、方差与奇次矩的形式比较了两种滤波的精度。从而指出了在两种调节参数取值下,如何选择扩展或非扩展UKF会更佳的结论。同时,推导了 UKF的均值近似误差的表达形式,并证明了 κ的取值与系统模型具有相关性。进而提出了 κ的在线调整算法,即自调整UKF算法。整个算法第一步先根据模型初步选取κ的值,使得估计的误差在几个事先设定的κ下能够达到最小。然后在每一时刻滤波时根据量测量的一步预测信息在第一步的κ取值附近进行在线调整,使得滤波估计达到最优。在线调整算法相比固定参数的UKF,虽然计算量有所增加,但是估计精度会得到提高。若状态方程或量测方程有一个是线性时,那么UKF算法就会得到简化,从而推导了两种模型化的UKF。本文对两种模型化UKF算法的计算量进行了定量的分析。相比传统UKF算法,两种模型化的算法在保证精度不会降低的同时,算法的计算量都会得到减小。最后,本文根据SINS误差模型的特点,将自调整UKF和模型化UKF应用到初始对准中,分别解决传统UKF估计精度低和计算量大的问题。仿真结果表明了两种非线性滤波算法的有效性,为实际工程应用提供了有力的理论保证。
[Abstract]:Initial alignment is a key technology of sins (Strapdown Inertial Navigation System,SINS. Filtering (state estimation) plays an important role in initial alignment. When the error model is linear, the classical Kalman filter has a very good estimation effect. When the error model is nonlinear, the estimation effect of different nonlinear filtering methods is different. Unscented Kalman filter (Unscented Kalman Filter, UKF) is an excellent nonlinear filtering method. Since its birth, it has been widely used in engineering. It is very important for the filtering accuracy and stability of UKF to adjust the parameter 魏 freely. Traditionally, it is considered that the filtering accuracy is optimal when n 魏 = 3 (n is the dimension of the state variable). However, with the production of volumetric Kalman filter (Cubature Kalman Filter,CKF), the traditional value of freely adjusted parameters is faced with great problems. Because from the view of filtering method, CKF filter is a special case of UKF filter when the parameter 魏 = 0. Under different dimensions, the accuracy of the two filtering methods is different. Therefore, the effect of 魏 on the accuracy of UKF filtering is mainly studied with the freely adjusted parameters as the core. At the same time, two modelled UKF algorithms are given to solve the problem of linear equations in the filter model. In this paper, the distribution characteristics of gravity field, two definitions of earth shape, and the definitions of longitude and latitude are introduced. The coordinate system and coordinate transformation are introduced in detail, and the error equation of strapdown inertial navigation system is derived. In this paper, the process of extended and non-extended UT transform is given, and the extended and non-extended UKF filtering algorithms are also given. For the comparison of the accuracy of the two filtering algorithms, the expressions of extended and non-extended UKF based on Taylor expansion are derived, and the accuracy of the two filtering methods under different dimensions and different adjusting parameters are analyzed. At the same time, the accuracy of the two filtering methods is compared based on the mean, variance and odd moment. It is pointed out that it is better to choose extended or non-extended UKF under two adjusting parameters. At the same time, the expression of the mean approximation error of UKF is deduced, and the correlation between the value of 魏 and the system model is proved. Furthermore, an online adjustment algorithm of 魏, self-tuning UKF algorithm, is proposed. The first step of the whole algorithm is to select the value of 魏 according to the model, so that the error of estimation can be minimized under several pre-set 魏. Then the filter is adjusted online according to the one-step prediction information of the measurement at every time, which makes the filter estimate to be optimal. Compared with the UKF, with fixed parameters, the estimation accuracy of the online adjustment algorithm will be improved. If one of the equations of state or measurement is linear, the UKF algorithm is simplified and two modelled UKF. are derived. In this paper, the computational complexity of two modeling UKF algorithms is analyzed quantitatively. Compared with the traditional UKF algorithm, the computational complexity of the two modeling algorithms will be reduced at the same time as the accuracy will not be reduced. Finally, according to the characteristics of SINS error model, self-adjusting UKF and modelled UKF are applied to initial alignment to solve the problems of low accuracy and large computational complexity of traditional UKF estimation, respectively. The simulation results show the effectiveness of the two nonlinear filtering algorithms and provide a strong theoretical guarantee for practical engineering applications.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN713;TN96

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