1. www.wust.edu.cn Distributed State-Estimation Using Quantized Measurement Data from Wireless Sensor Networks Li Chai with Bocheng Hu Professor College of Information Science and Engineering Wuhan University of Science and Technology Wuhan, 430081, China Email: eechai@gmail.com

2. www.info.wust.edu.cn 2 Outline  Introduction of WUST and College of ISE  Motivation and related works  Problem statements  State estimator design  Simulation  Conclusion

3. www.info.wust.edu.cn 3 Introduction of WUST and College of ISE  Location Wuhan, besides the Yangtze river and very near to Three Gorges Dam  20 colleges, about 1,500s academic staff  Feature: tight link with metallurgical company (Wuhan Iron & Steel Co., Ltd, Panzhihua Iron & Steel Co., Ltd, Handan Iron & Steel Co., Ltd, Baoshan Iron & Steel Co., Ltd)

4. www.info.wust.edu.cn 4 Introduction of WUST and College of ISE  College of Information Science and Engineering  75 Academic staff including 16 professors, 15 AP and 8 professional engineer  Two Departments: Dept. of Automatic Control, Dept. of Electrical Engineering  About 200 PG students and 1,200 UG  Feature: metallurgical automation Engineering Research Center for Metallurgical Automation and Measurement Technology, Ministry of Education, China

5. www.info.wust.edu.cn 5

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8. 8 Motivation and related works  A typical sensor network consists of a large number of nodes deployed in an environment being sensed and/or controlled.  The sensors collaborate to perform certain high level task: detection, estimation …  The sensors’ dynamic range, resolution, power and wireless communication capability can be severely limited.  Local data quantization/compression is not only a necessity, but also an integral part of the design of sensor networks.

9. www.info.wust.edu.cn 9 Motivation and related works  Sensor network applications –Environmental monitoring –Habitat monitoring –Acoustic detection –Seismic Detection –Military surveillance –Inventory tracking –Medical monitoring –Smart spaces –Process Monitoring

10. www.info.wust.edu.cn 10 Motivation and related works  The highly decentralized network architecture and severely limited communication constraints presents significant challenges in the design of signal processing algorithms.  In this talk, we will focus on a general state estimation problem  Will not consider  Details of communication protocol / network topology  Channel fading and uncertainty  Location and routing issues

11. www.info.wust.edu.cn 11 Motivation and related works  Static decentralized estimation problem Xiao and Luo (2005, 2006) and Riberiro and Giannakis (2006)

12. www.info.wust.edu.cn 12 Motivation and related works  Static decentralized estimation problem  Methods to design local message functions and final fusion function  Methods of estimation if one-bit sensor is assumed.  Analysis of the MSE.  Tradeoff between network size K and MSE under bandwidth constraint.

13. www.info.wust.edu.cn 13 Problem statements  Dynamic decentralized estimation Fusion Center

14. www.info.wust.edu.cn 14 Problem statements  In the figure

15. www.info.wust.edu.cn 15 Problem statements  To design the state estimator such that is “close” to x ( k ).  Here, “close” means is small, where

16. www.info.wust.edu.cn 16 Problem statements  Power spectral density where  Power norm of the error is defined as

17. www.info.wust.edu.cn 17 State estimator design  The augment system G e

18. www.info.wust.edu.cn 18 State estimator design  The power norm of error  An upper bound  The above bound is tight in the sense that it can be achieved if is arbitrary.

19. www.info.wust.edu.cn 19 State estimator design  To design the state estimator such that is minimized.

20. www.info.wust.edu.cn 20 State estimator design  Step 1, find g, and upper bound of  Step 2, find such that is minimized.  Remark: Step 2 is a typical mixed optimization filtering problem, for which various efficient algorithms exist.

21. www.info.wust.edu.cn 21 Numerical example  Consider the following LTI system Let

22. www.info.wust.edu.cn 22 Conclusion  Distributed state estimator is designed.  The power norm of the error is minimal in worst- case.  The idea applies to other cases, such as different types of sensors are used.

23. www.info.wust.edu.cn 23  Basic multirate elements in digital signal processing  M-fold decimator  M M yD[n]yD[n] x[n]x[n] -2 0123n 01n x[n]x[n] yD[n]yD[n] M=2 Multirate signal processing

24. www.info.wust.edu.cn 24  L-fold expander n 401238657 x[n]x[n] n 012 yE[n]yE[n] 3 4 5 6 7 8 Vaidyanathan 93 Multirate signal processing

25. www.info.wust.edu.cn 25 Multirate Signal Processing in WSNs (a) Direct high sampling rate measurement x(n) (b) Low sampling rate measurements v i (n) (c) Relation between x(n) and v i (n)

26. www.info.wust.edu.cn 26 Multirate Signal Processing in WSNs To estimate the power spectral density of x(n) using statistics of the low-rate observable signals v i (n). O. S. Jahromi, B. A. Francis, and R. H. Kwong, Relative information of multi-rate sensors, Information Fusion, 5, pp. 119-129, 2004.

27. www.info.wust.edu.cn 27 Multirate Signal Processing in WSNs Our research:  Is it possible to achieve other goals using low-rate sampling data? If yes, how to design suitable algorithms and how to evaluate those algorithms?  How to deal with quantization and channel uncertainty?  Does the dual-rate assumption make sense? For arbitrary sampling-rate data, what shall we do?  Key Distributed (multirate) signal processing

28. www.info.wust.edu.cn 28 Thank you!