改进容积卡尔曼滤波及其导航应用研究

发布时间：2018-04-04 02:29

本文选题：容积卡尔曼滤波　切入点：扩维容积卡尔曼滤波　出处：《哈尔滨工程大学》2015年博士论文

【摘要】：本文主要研究容积卡尔曼滤波(Cubature Kalman filter,CKF)及其改进滤波,并应用到导航系统。CKF是一种基于球面径向容积准则对状态向量进行采样,获得相同权值的容积点,经过非线性函数传递来逼近非线性高斯系统的状态估计。该滤波算法实现简单、估计精度高,应用前景广阔。论文主要研究工作如下:首先,研究容积卡尔曼滤波(CKF)。根据最小方差估计准则推导非线性滤波递推公式,详尽介绍CKF推导过程。把推导过程相似的无迹卡尔曼滤波(Unscented Kalman filter,UKF)和CKF进行比较研究,二者在函数泰勒展开式高阶项及数值稳定性方面存在差异。CKF能够精确保留一阶矩和二阶矩信息,在三维及三维以上非线性系统CKF的滤波精度优于UKF。其次,研究扩维容积卡尔曼滤波(Augmented cubature Kalman filter,ACKF)。ACKF是一种在非线性滤波过程中获得函数均值、方差和奇阶矩等统计信息,并对非线性函数均值进行泰勒展开的滤波。通过研究发现:在一维系统,ACKF获得的均值和方差更接近真实值、还能额外获得部分奇阶矩信息,使其精度比CKF更高;而二维及以上系统,ACKF传播的统计信息反而误差更大,使其精度比CKF更差。该研究所得结论为不同维数非线性系统滤波方法的选取提供参考依据。再次,研究强跟踪容积卡尔曼滤波(Strong tracking cubature Kalman filter,STCKF)。通常情况下,惯性器件常值漂移会被视为状态变量的一部分而采用滤波进行估计,但是其易受运行环境中不确定因素的影响而发生突变。CKF会因系统模型不确定的影响导致滤波稳定性下降,而不再具有克服模型不确定的鲁棒性。针对这种情况,研究在状态预测协方差阵中引入渐消因子的STCKF算法。仿真结果表明:STCKF对突变的惯性器件常值漂移具有很强的跟踪能力,具有克服非线性系统模型不确定的鲁棒性。第四,研究自适应容积卡尔曼滤波(Adaptive cubature Kalman filter,ADCKF)。在噪声先验统计未知情况下,CKF滤波精度下降甚至发散。根据极大后验估计原理,针对惯性器件随机噪声统计在恶劣工作环境下出现时变性的情况,研究了一种带噪声统计估计器的ADCKF算法。仿真结果表明:ADCKF在滤波前不需要精确已知惯性器件随机噪声的先验统计,具有应对惯性器件随机噪声统计变化的自适应能力。最后,研究容积卡尔曼滤波及其改进滤波应用于导航系统。建立以速度及姿态等误差为基础的惯性导航系统非线性误差模型,将CKF及其改进滤波算法应用到惯导非线性系统。仿真结果表明:改进滤波算法中的STCKF和ADCKF能够解决量测方程无法精确获知情况下的滤波估计问题,可靠性高、实用性强,比CKF更有优越性,具有更好的导航精度。
[Abstract]:In this paper, cubital Kalman filter and its improved filtering are studied, and applied to navigation system. CKF is a kind of volume point based on spherical radial volume criterion to sample the state vector and get the same weight.The state estimation of nonlinear Gao Si system is approximated by nonlinear function transfer.The filter algorithm is simple to realize, high estimation precision and wide application prospect.The main work of this paper is as follows: firstly, the volume Kalman filter CKF is studied.According to the minimum variance estimation criterion, the nonlinear filtering recursive formula is derived, and the derivation process of CKF is introduced in detail.The unscented Kalman filter UKF, which is similar in derivation process, is compared with CKF. There are differences between them in terms of higher order terms and numerical stability of the function Taylor expansions. CKF can accurately retain the information of first and second moments.The filtering accuracy of CKF is better than that of CKF in 3D and above.Secondly, it is studied that augmented cubature Kalman filter ACKFN. ACKF is a kind of statistical information, such as function mean value, variance and odd order moment, which is obtained in nonlinear filtering process, and the nonlinear function mean value is filtered by Taylor expansion.It is found that the mean value and variance obtained by ACKF in one-dimensional system are closer to the real value, and some odd moment information can be obtained, which makes the accuracy higher than that of CKF, but the error of statistical information propagated by ACKF in two dimensional and above systems is even greater.Make its accuracy worse than CKF.The conclusion provides a reference for the selection of filtering methods for nonlinear systems with different dimensions.Thirdly, strong tracking cubature Kalman filter with strong tracking volume is studied.In general, the constant drift of the inertial device is regarded as part of the state variable and the filter is used to estimate the drift.However, it is vulnerable to the influence of uncertain factors in the operating environment, and the sudden change of CKF will lead to the degradation of filter stability due to the uncertainty of the system model, and it will no longer have the robustness to overcome the uncertainty of the model.In order to solve this problem, the STCKF algorithm which introduces fading factor into the state prediction covariance matrix is studied.The simulation results show that: STCKF has a strong tracking ability to the constant drift of the abrupt inertial device and is robust to overcome the uncertainty of the nonlinear system model.Fourthly, adaptive cubature Kalman filter (ADCKF) is studied.In the case of noise prior statistics, the accuracy of CKF filter decreases or even diverges.According to the principle of maximum posteriori estimation, a ADCKF algorithm with noise statistics estimator is studied in this paper.The simulation results show that the prior statistics of random noise of inertial devices are not required accurately before filtering, and they have adaptive ability to deal with the statistical changes of random noise of inertial devices.Finally, the volume Kalman filter and its improved filtering are studied in the navigation system.The nonlinear error model of inertial navigation system based on the error of velocity and attitude is established. The CKF and its improved filtering algorithm are applied to the nonlinear inertial navigation system.The simulation results show that the STCKF and ADCKF in the improved filtering algorithm can solve the filtering estimation problem when the measurement equation can not be accurately known. It has higher reliability, better practicability and better navigation accuracy than CKF.
【学位授予单位】：哈尔滨工程大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TN713;TN96

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