惯性元件长相关随机漂移多重分数阶建模及滤波研究

项目名称： 惯性元件长相关随机漂移多重分数阶建模及滤波研究

项目编号： No.61203186

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 沈晓蓉

作者单位： 北京航空航天大学

项目金额： 23万元

中文摘要： 惯性元件长相关随机漂移产生因素众多，难以从机理角度进行建模及滤波分析，是目前制约惯性导航系统高精度应用的主要误差源。前期研究表明，惯性元件长相关随机漂移具有非线性、非平稳性以及多分形维特性，其自相关函数呈近似幂函数缓慢下降，不适于整数阶时间序列建模和卡尔曼滤波。 因此，本课题提出多重分数阶建模及分数阶卡尔曼滤波方法，采用分数阶随机微积分数学作为分析工具，开展惯性元件长相关随机漂移建模及滤波处理研究，探索多分形维对象体多重分数阶连续时间域、离散时间域建模及评价方法，设计分数阶卡尔曼滤波器并证明其估计的优化性能。本课题研究为惯性技术高精度应用奠定基础的同时，也为图像处理、水文、经济等多个领域提供长相关随机漂移解决思路，具有广泛的基础理论研究价值。

中文关键词： 激光陀螺仪；随机噪声；非高斯特性；Alpha是稳定分布；自适应滤波

英文摘要： The sources that cause long dependence random drifts of inertial elements are too complex to be analized from mechanism points for modeling and filtering.Long range drifts have been the main error sources limit the inertial navigation precision. The researches before shows that the long dependence random drifts of inertial elements are nonlinear,nonstationary. Especialy they have slow decreasing auto-correlated function that is similar to power function. The traditional time series model and the Kalman Filter cannot deal with such long depence random drifts. Therefore, this project puts forward multi-fractional model and fractional Kalman Filter methods. How to model and filter the long dependence random drifts of inertial elements are researched with the fractional random calculus as analysis tool.Besides constructing the continuous and the descrete multi fractional models and evaluation methods, fractional Kalman filter is designed and its optimal estimation property is proven. The results of this project provids basis for high precision application of inertial technology. Furthermore, it also can be applied to several fields, such as image processing, hydrology and economics,which has generalized basic research value.

英文关键词： Ring Laser Gyroscope；random noise；Non-Gaussian characteristic；Alpha stable distribution;；adaptive filter