Quantized innovations Kalman filter: stability and modification with scaling quantization  

作　　者：Jian XU Jian-xun LI Sheng XU 

机构地区：[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

出　　处：《Journal of Zhejiang University-Science C(Computers and Electronics)》2012年第2期118-130,共13页浙江大学学报C辑（计算机与电子（英文版）

基　　金：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);the Aeronautical Science Foundation of China (No. 20105557007)

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.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.

关 键 词：Kalman filtering Quantized innovation STABILITY Scaling quantization Wireless sensor network 

分 类 号：TP274.2[自动化与计算机技术—检测技术与自动化装置] TN713[自动化与计算机技术—控制科学与工程]