线性滤波估计算法研究及在惯性导航系统中的应用

发布时间：2018-04-10 21:30

本文选题：惯性导航系统 + 卡尔曼滤波　；参考：《北京理工大学》2014年博士论文

【摘要】：在惯性导航系统中，由于载体运动无法预知、惯性器件测量精度变化等因素的影响，引起导航系统误差模型存在结构不确定，同时由于随机噪声的统计特性难以精确获知等问题，使得标准的卡尔曼滤波算法无法解决这类系统的状态估计问题。采用自适应卡尔曼滤波算法可以解决未知噪声统计特性参数的在线估计问题，但其稳定性分析十分困难，理论上尚未完全解决。论文针对惯性导航系统中线性模型存在结构不确定性、噪声统计特性未知条件下的滤波估计问题开展研究，主要创新点如下： (1)针对模型存在结构不确定的滤波估计问题，引入有限模型自适应控制思想，建立了有限模型卡尔曼滤波算法框架。提出了一种基于极小化矢量距离准则的有限模型卡尔曼滤波算法，通过二阶多项式函数拟合系统量测信息在特定时间窗内的动态过程，构建了系统模型切换目标函数，提高了算法的鲁棒性。 (2)针对导航系统中模型存在过程(或观测)噪声统计特性未知时的状态估计问题，提出了利用量测序列来进行未知参数在线辨识的方法，构建了存在未知过程(或观测)噪声协方差矩阵的卡尔曼滤波算法。以数理统计理论和代数黎卡提方程为分析工具，证明了所提出算法的噪声协方差矩阵估计收敛于真值，且状态估计与标准的卡尔曼滤波算法的收敛性一致。 (3)提出采用二阶随机游走模型描述未知系统动态过程，针对该模型中存在噪声统计特性未知时的滤波估计问题，提出噪声协方差矩阵未知的卡尔曼滤波算法。证明了所提出算法的噪声协方差矩阵估计收敛于真实值，且状态估计与标准卡尔曼滤波算法的收敛性一致。 (4)利用提出的有限模型卡尔曼滤波算法和噪声协方差矩阵未知的卡尔曼滤波算法，解决了惯性导航系统实际应用中由于环境扰动导致惯性器件漂移变大等问题，有效抑制了随机误差对测量精度的影响，提高了输出信号的平稳性和可靠性。利用提出的观测噪声协方差矩阵未知的卡尔曼滤波算法，，解决了惯导系统初始对准过程中观测噪声协方差矩阵未知时的误差状态估计问题，降低了滤波算法对观测信息随机误差统计特性的要求，提高了算法的鲁棒性和实用性。
[Abstract]:In the inertial navigation system, the structure of the navigation system error model is uncertain because of the unpredictable motion of the carrier and the change of the measuring accuracy of the inertial device.At the same time, it is difficult to accurately know the statistical characteristics of random noise, so the standard Kalman filtering algorithm can not solve the state estimation problem of this kind of system.Adaptive Kalman filter algorithm can be used to solve the problem of on-line estimation of unknown noise statistical characteristic parameters, but its stability analysis is very difficult and has not been completely solved theoretically.In this paper, the filtering estimation problem of linear model in inertial navigation system under the condition of uncertain structure and unknown noise statistical characteristics is studied. The main innovations are as follows:1) aiming at the problem of filter estimation with uncertain structure, a framework of finite model Kalman filter algorithm is established by introducing the idea of finite model adaptive control.A finite model Kalman filter algorithm based on minimization vector distance criterion is proposed. The system model switching objective function is constructed by fitting the dynamic process of system measurement information in a specific time window by second order polynomial function.The robustness of the algorithm is improved.In order to solve the problem of state estimation when the statistical characteristics of process (or observation) noise are unknown in navigation system, a method of on-line identification of unknown parameters using measurement sequence is proposed.A Kalman filter algorithm with unknown process (or observation) noise covariance matrix is constructed.Using mathematical statistics theory and algebraic Riccati equation as analytical tools, it is proved that the estimation of noise covariance matrix of the proposed algorithm converges to the true value, and the convergence of the state estimation is consistent with that of the standard Kalman filtering algorithm.(3) A second-order random walk model is proposed to describe the dynamic process of unknown systems. A Kalman filtering algorithm with unknown noise covariance matrix is proposed for the filtering estimation of unknown noise statistical characteristics in the model.It is proved that the estimation of the noise covariance matrix of the proposed algorithm converges to the real value, and the convergence of the state estimation is consistent with that of the standard Kalman filtering algorithm.4) using the proposed finite model Kalman filter algorithm and the Kalman filter algorithm with unknown noise covariance matrix, the problem of inertial device drift in inertial navigation system caused by environmental disturbance is solved.The influence of random error on measurement accuracy is effectively restrained, and the stability and reliability of output signal are improved.Using the proposed Kalman filtering algorithm with unknown observation noise covariance matrix, the problem of error state estimation in the initial alignment of inertial navigation system is solved when the observation noise covariance matrix is unknown.The requirements of the filtering algorithm for the statistical characteristics of random error of observation information are reduced, and the robustness and practicability of the algorithm are improved.
【学位授予单位】：北京理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN966;TN713

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