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Quantized innovations Kalman filter: stability and modification with scaling quantization

ISSN号：1869-1951
期刊名称：Journal of Zhejiang University-Science C(Computers
时间：2012.2
页码：118-130
分类：TP274.2[自动化与计算机技术—控制科学与工程;自动化与计算机技术—检测技术与自动化装置] TN713[电子电信—电路与系统]
作者机构：[1]Science and Technology on Avionics Integration Laboratory, Shanghai Jiao Tong University, Shanghai 200240, [2]MOE Key Laboratory of System Control and Information Processing, Shanghai Jiao Tong University, Shanghai 200240, China, [3]School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
相关基金：Project supported by the National Natural Science Foundation of China （Nos. 61175008, 60935001, and 60874104）, the National Basic Research Program （973） of China （Nos. 2009CB824900 and 2010CB734103）, the Space Foundation of Supporting-Technology （No. 2011-HT-SHJD002）, and the Aeronautical Science Founda- tion of China （No. 20105557007） The authors would like to thank Prof. Min-yue FU, Prof. Li-hua XIE, and Dr. Ke-you YOU for their helpful advice.
相关项目：空间可变软形态学理论及在红外图像处理中的应用

关键词：卡尔曼滤波器, 量化误差, 稳定性, 创新, 缩放, 协方差矩阵, 修改, 估计误差, Kalman filtering, Quantized innovation, Stability, Scaling quantization, Wireless sensor network

中文摘要：

过滤的使量子化的革新 Kalman (QIKF ) 的稳定性被分析。在分析，在量子化错误和测量噪音之间的关联被考虑。由在观察系统作为随机的不安拿量子化错误，为原来的系统的 QIKF 等价于为相等的州观察的系统过滤的象 Kalman 一样。因此， QIKF 的估计错误协变性矩阵能更确切被分析。QIKF 的估计错误协变性矩阵的固定在一些弱条件下面被获得。使量子化的层次的数字的设计被讨论保证 QIKF 的稳定性。为了克服 QIKF 的不稳定性和分叉，当量子化层次的数字是小的时，我们用放大使量子化的革新建议一个 Kalman 过滤器。数字模拟显示出定理和算法的有效性。

英文摘要：

The stability of quantized innovations Kalman filtering （QIKF） is analyzed. In the analysis, the correlation between quantization errors and measurement noises is considered. By taking the quantization errors as a random perturbation in the observation system, the QIKF for the original system is equivalent to a Kalman-like filtering for the equivalent state-observation system. Thus, the estimate error covariance matrix of QIKF can be more exactly analyzed. The boundedness of the estimate error covariance matrix of QIKF is obtained under some weak conditions. The design of the number of quantized levels is discussed to guarantee the stability of QIKF. To overcome the instability and divergence of QIKF when the number of quantization levels is small, we propose a Kalman filter using scaling quantized innovations. Numerical simulations show the validity of the theorems and algorithms.