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, , China

2 Outline  Introduction of WUST and College of ISE  Motivation and related works  Problem statements  State estimator design  Simulation  Conclusion

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 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

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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 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 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 Motivation and related works  Static decentralized estimation problem Xiao and Luo (2005, 2006) and Riberiro and Giannakis (2006)

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 Problem statements  Dynamic decentralized estimation Fusion Center

14 Problem statements  In the figure

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

16 Problem statements  Power spectral density where  Power norm of the error is defined as

17 State estimator design  The augment system G e

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 State estimator design  To design the state estimator such that is minimized.

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 Numerical example  Consider the following LTI system Let

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  Basic multirate elements in digital signal processing  M-fold decimator  M M yD[n]yD[n] x[n]x[n] n 01n x[n]x[n] yD[n]yD[n] M=2 Multirate signal processing

24  L-fold expander n x[n]x[n] n 012 yE[n]yE[n] Vaidyanathan 93 Multirate signal processing

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 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 , 2004.

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 Thank you!