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Analysis of quantization noise and state estimation with quantized measurements

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Abstract

The approximate correction of the additive white noise model in quantized Kalman filter is investigated under certain conditions. The probability density function of the error of quantized measurements is analyzed theoretically and experimentally. The analysis is based on the probability theory and nonparametric density estimation technique, respectively. The approximator of probability density function of quantized measurement noise is given. The numerical results of nonparametric density estimation algorithm demonstrate that the theoretical conclusion is reasonable. Based on the analysis of quantization noise, a novel algorithm for state estimation with quantized measurements also is proposed. The algorithm is based on the least-squares estimator and unscented transform. By least-squares estimator, the effective information is extracted from the quantized measurements. Also, using the information to update the estimated state can give a better estimation under the influence of quantization. The root mean square error (RMSE) of the proposed algorithm is compared with the RMSE of the existing methods for a typical tracking scenario in wireless sensor networks systems. Simulations provide a strong evidence that this tracking algorithm could indeed give us a more precise estimated result.

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jian Xu & Jianxun Li

  2. College of Mechanical Engineering, Chongqing University, Chongqing, 400030, China

    Sheng Xu

Authors
  1. Jian Xu
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  2. Jianxun Li
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  3. Sheng Xu
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Corresponding author

Correspondence to Jian Xu.

Additional information

This work was supported by National Natural Science Foundation (No. 60935001, 60874104), 973 Project (No. 2009CB824900, 2010CB734103), and the Shanghai Key Basic Research Foundation (No. 08JC1411800).

Jian XU received his B.S. degree in Pure Mathematics, in 2001, and M.S. degree in Probability Theory and Mathematical Statistics, in 2007, from the Department of Mathematics, Xuzhou Normal University, Xuzhou, China. He is currently a Ph.D. candidate with the School of Electronics and Information Technology, Shanghai Jiao Tong University, Shanghai, China. His main research interests are information fusion for stochastic recursive algorithms, and signal and data processing.

Jianxun LI received his Ph.D. degree in Control Theory and Engineering with highest honors from Northwestern Polytechnical University, Xi’an, China, in 1996. He is currently a professor with the School of Electronics and Information Technology, Shanghai Jiao Tong University, Shanghai, China. From 1997 to 1999, he joined the Key Laboratory of Radar Signal Processing of Xidian University, Xi’an, China, as a postdoctoral fellow. He was a visiting professor at the Imperial College London, London, U.K., from 2006 to 2007. His main research interests include information fusion, and infrared image processing and parameter estimation

Sheng XU is currently a bachelor candidate with the College of Mechanical Engineering, Chongqing University, Chongqing, China. He is going to be a Ph.D. candidate with the School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China. His research interests include robotics, control engineering, and manufacturing automation.

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Xu, J., Li, J. & Xu, S. Analysis of quantization noise and state estimation with quantized measurements. J. Control Theory Appl. 9, 66–75 (2011). https://doi.org/10.1007/s11768-011-0239-4

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  • DOI: https://doi.org/10.1007/s11768-011-0239-4

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