A multidimensional systems approach to grid sensor networks

A method for distributed information processing in rectangular grid based wireless sensor networks is presented, employing the Givone-Roesser and the Fornasini-Marchesini state space models for m-D systems. It can be used for distributed implementation of any general linear system on a grid sensor network. The method is highly scalable and requires only communication between immediate neighbors.;Usage of finite precision schemes for the representation of numbers and computations introduce nonlinearities to the otherwise linear m-D system models. Nonlinearities caused by fixed point and floating point 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. Necessary and sufficient conditions for the global asymptotic stability under both fixed point and floating point arithmetic is derived. It has been shown that the global asymptotic stability of the sensor networks is equivalent to that of a 1-D system for both the cases of fixed point and floating number representation.;Issues posed by communication time delay, in real-time implementation of the proposed method, are discussed. It is shown that, in order to implement a real-time sensor network, system matrices of the state space models have to satisfy certain conditions. A necessary and sufficient condition for a transfer function to be realizable in the constrained state space models is established. Realization algorithms to derive state space models of the desired form given an admissible transfer function are also presented. Node and link failure introduce complications not encountered in centralized implementation of m-D systems. Givone-Roesser and the Fornasini-Marchesini state space models are extended to include node and link failure. Necessary and sufficient conditions for mean square stability are then derived with the help of these two state space models. Input output stability of the distributed systems under node and link failure is also discussed.;The utility of the proposed method is demonstrated by examples. In particular a distributed Kalman filter is proposed for grid sensor networks. Implementation of the proposed Kalman filter on grid sensor networks is discussed in some detail. A method for contaminant detection and its implementation using the proposed method is also presented.