有限模型卡尔曼滤波的框架及一个实例：MVDP-FMKF算法

冯波; 马宏宾; 付梦印; 汪顺亭

doi:10.3724/SP.J.1004.2013.01246

有限模型卡尔曼滤波的框架及一个实例：MVDP-FMKF算法

doi: 10.3724/SP.J.1004.2013.01246

冯波^1,,
马宏宾^1,2,
付梦印^1,2,
汪顺亭^1,2

1.
北京理工大学自动化学院北京 100081;
2.
北京理工大学复杂系统的智能控制与决策的重点实验室北京 100081

基金项目:

Supported by National Natural Science Foundation of China (61004059, 61004139, 60904086, 61211130359), Program for New Century Excellent Talents in University (NCET-09-0045), and Graduate Teaching Group Funding of Beijing Institution of Technology

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出版历程
- 收稿日期: 2012-05-08
- 修回日期: 2013-01-09
- 刊出日期: 2013-08-20

A Framework of Finite-model Kalman Filter with Case Study：MVDP-FMKF Algorithm

1.
School of Automation, Beijing Institution of Technology, Beijing 100081, China;
2.
Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institution of Technology, Beijing 100081, China

Funds:

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Corresponding author: FENG Bo

摘要

摘要: 卡尔曼滤波技术在很多领域已得到广泛的应用, 标准卡尔曼滤波算法是基于线性高斯系统模型假设, 需要已知精确的系统模型. 当系统模型存在较大不确定性时, 运用基于不精确系统模型设计的卡尔曼滤波算法时, 滤波效果通常不能满足系统需求甚至发散. 在很多实际应用中, 往往需要大量工作才能得到较为精确的系统模型或者基本不可能给出精确的系统模型. 为解决这一具有工程实践意义的问题, 受有限模型自适应控制思想的启发, 本文介绍了一个有限模型卡尔曼滤波算法的框架. 在该框架中, 假设系统模型的不确定性可由有限个已知模型的集合(模型个数不限)来刻划或近似, 从而先验未知的系统模型可以通过充分挖掘系统运行的动态后验数据中的信息, 利用已知模型集在线自适应估计以逼近真实系统的模型, 最终实现模型有较大不确定性时仍能有效滤波. 在此框架下, 基于最小化距离向量的准则, 我们引入一种模型自适应切换的算法(MVDP-FMKF), 给出其数学描述, 并通过仿真研究及MEMS陀螺漂移测试验证了算法的有效性. 本工作展现了有限模型卡尔曼滤波的机制在导航系统等应用中具有有效性、实用性.
- 有限模型卡尔曼滤波 /
- 最小矢量距离准则 /
- 自适应切换 /
- MEMS陀螺降噪
Abstract: Kalman filtering techniques have been widely used in many applications, however, standard Kalman filters for linear Gaussian systems usually cannot work well or even diverge in the presence of large model uncertainty. In practical applications, it is expensive to have large number of high-cost experiments or even impossible to obtain an exact system model. Motivated by our previous pioneering work on finite-model adaptive control, a framework of finite-model Kalman filtering is introduced in this paper. This framework presumes that large model uncertainty may be restricted by a finite set of known models which can be very different from each other. Moreover, the number of known models in the set can be flexibly chosen so that the uncertain model may always be approximated by one of the known models, in other words, the large model uncertainty is "covered" by the "convex hull" of the known models. Within the presented framework according to the idea of adaptive switching via the minimizing vector distance principle, a simple finite-model Kalman filter, MVDP-FMKF, is mathematically formulated and illustrated by extensive simulations. An experiment of MEMS gyroscope drift has verified the effectiveness of the proposed algorithm, indicating that the mechanism of finite-model Kalman filter is useful and e±cient in practical applications of Kalman filters, especially in inertial navigation systems.
- Finite-model Kalman filter /
- minimizing vector distance principle /
- adaptive switching /
- MEMS gyroscope de-noising

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