Stability of Distributed 3-D Systems Implemented on Grid Sensor Networks

Using the Givone-Roesser and the Fornasini-Marchesini state space models for m-D systems, a method for distributed information processing in rectangular grid based wireless sensor networks is presented. It can be used for distributed implementation of any general linear system on a grid sensor network. Nonlinearities caused by finite precision number representation schemes used for in node computations and inter node communication are modeled. Stability of the system is analyzed with special consideration given to the influence of inter-node communication on system dynamics. A necessary and sufficient condition for global asymptotic stability under finite precision arithmetic is established. Simulation results are presented to illustrate the theoretical results.

[1]  Zhihua Wang,et al.  Fast spatial combinative lifting algorithm of wavelet transform using the 9/7 filter for image block compression , 2000 .

[2]  S. Sitharama Iyengar,et al.  Computing reliability and message delay for Cooperative wireless distributed sensor networks subject to random failures , 2005, IEEE Transactions on Reliability.

[3]  Peter H. Bauer.  Absolute response error bounds for floating point digital filters in state space representation , 1993, 1993 IEEE International Symposium on Circuits and Systems.

[4]  J. Mendel,et al.  Modeling and recursive state estimation for two-dimensional noncausal filters with applications in image restoration , 1987 .

[5]  Yiannis Andreopoulos,et al.  Software Designs of Image Processing Tasks With Incremental Refinement of Computation , 2010, IEEE Transactions on Image Processing.

[6]  Peter Schelkens,et al.  Scalable wavelet video-coding with in-band prediction - implementation and experimental results , 2002, Proceedings. International Conference on Image Processing.

[7]  S. Mitra,et al.  Realizations of two-dimensional recursive digital filters , 1975 .

[8]  Peter H. Bauer,et al.  Asymptotic behavior of block floating-point digital filters , 1999 .

[9]  Zhiping Lin,et al.  A Constructive Procedure for Three-Dimensional Realization , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[10]  M. Vetterli,et al.  Lattice sensor networks: capacity limits, optimal routing and robustness to failures , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[11]  Donald D. Givone,et al.  Multidimensional Linear Iterative Circuits - General Properties , 1972, IEEE Trans. Computers.

[12]  Peter H. Bauer,et al.  New criteria for asymptotic stability of one- and multidimensional state-space digital filters in fixed-point arithmetic , 1994, IEEE Trans. Signal Process..

[13]  Ramachandran Vaidyanathan,et al.  Reconfigurable Implementation of Wavelet Integer Lifting Transforms for Image Compression , 2006, 2006 IEEE International Conference on Reconfigurable Computing and FPGA's (ReConFig 2006).

[14]  Lorenzo Ntogramatzidis,et al.  On the Partial Realization of Noncausal 2-D Linear Systems , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  I. Daubechies,et al.  Factoring wavelet transforms into lifting steps , 1998 .

[16]  Qun Li,et al.  Global Clock Synchronization in Sensor Networks , 2006, IEEE Trans. Computers.

[17]  Zhiping Lin,et al.  On Realization of 2D Discrete Systems by Fornasini-Marchesini Model , 2005 .

[18]  R. Srikant,et al.  Unreliable sensor grids: coverage, connectivity and diameter , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[19]  Mauro Leoncini,et al.  Analysis of a wireless sensor dropping problem in wide-area environmental monitoring , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[20]  Kamal Premaratne,et al.  An exhaustive search algorithm for checking limit cycle behavior of digital filters , 1995, Proceedings of ISCAS'95 - International Symposium on Circuits and Systems.

[21]  D. Barr,et al.  Absolute response error bounds for floating point digital filters in state space representation , 1995 .

[22]  Peter H. Bauer.  A set of necessary stability conditions form-D nonlinear digital filters , 1995 .

[23]  Hossam S. Hassanein,et al.  On the robustness of grid-based deployment in wireless sensor networks , 2006, IWCMC '06.

[24]  G. Marchesini,et al.  Dynamic regulation of 2D systems: A state-space approach , 1989 .

[25]  Ki-Hyung Kim,et al.  Node-link-failure resilient routing architecture for sensor grids , 2006, 2006 8th International Conference Advanced Communication Technology.

[26]  Liang-Gee Chen,et al.  Efficient VLSI architectures of lifting-based discrete wavelet transform by systematic design method , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[27]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[28]  V. Singh,et al.  Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities , 2001, IEEE Trans. Signal Process..

[29]  Zhiping Lin,et al.  A direct-construction approach to multidimensional realization and LFR uncertainty modeling , 2008, Multidimens. Syst. Signal Process..

[30]  Maria E. Angelopoulou,et al.  Implementation and Comparison of the 5/3 Lifting 2D Discrete Wavelet Transform Computation Schedules on FPGAs , 2008, J. Signal Process. Syst..

[31]  S. Hamid Nawab,et al.  Incremental refinement of DFT and STFT approximations , 1995, IEEE Signal Processing Letters.

[32]  Buddika Sumanasena,et al.  A Roesser model based multidimensional systems approach for grid sensor networks , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[33]  Zhiping Lin,et al.  A New Constructive Procedure for 2-D Coprime Realization in Fornasini–Marchesini Model , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[34]  P. H. Bauer,et al.  Limit cycle bounds for floating point implementations of second-order recursive digital filters , 1993 .

[35]  Hossam S. Hassanein,et al.  A flow-based reliability measure for wireless sensor networks , 2007, Int. J. Sens. Networks.

[36]  Sanjay Jha,et al.  A Communication Paradigm for Hybrid Sensor/Actuator Networks* , 2004, 2004 IEEE 15th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE Cat. No.04TH8754).

[37]  Peter H. Bauer,et al.  A novel approach to grid sensor networks , 2008, 2008 15th IEEE International Conference on Electronics, Circuits and Systems.

[38]  Peter H. Bauer,et al.  Stability of distributed 3-D systems implemented on grid sensor networks using floating point arithmetic , 2010, IEEE Conference on Decision and Control and European Control Conference.

[39]  John D. Villasenor,et al.  Visibility of wavelet quantization noise , 1997, IEEE Transactions on Image Processing.

[40]  Leonard T. Bruton,et al.  Practical-BIBO stability of n-dimensional discrete systems , 1983 .

[41]  Po-chih Tseng,et al.  Advances in Hardware Architectures for Image and Video Coding - A Survey , 2005, Proceedings of the IEEE.

[42]  G. Antoniou,et al.  2-D lattice discrete filters: minimal delay and state space realization , 2001, IEEE Signal Processing Letters.

[43]  G. E. Antoniou,et al.  Minimal state space realisation of 3-D systems , 1988 .

[44]  P. Paraskevopoulos,et al.  On the canonical state-space realisation of 3-D discrete systems , 1989 .