Source positioning in a large-scale tiny-sensor network of arbitrary topology

Abstract

To effectively localise a source node in a dense wireless tiny-sensor network with an arbitrary 2D/3D node distribution, a novel approach suitable to describe the hop progress of source-to-sink path in such a system is proposed. In this approach, the network topology is described as a regular lattice and relates the statistical parameters of the hop count in the source-to-sink propagation path to the fractal properties of a percolating cluster. Based on this approach, a mathematical model is developed to estimate the probability P(r, t) of successful reception of the message by a sink node spaced at distance r from a source in a given time t. The accuracy analysis of the positioning method demonstrates its high performance for the very broad spectrum of values of the occupation probability p occ .

Distributed piecewise filtering design for large-scale networked nonlinear systems

“…where (2) , ikj (3) , ikj (4) are given by (18). By using Schur complement lemma on (17), it is easy to see from (26) that the inequality (17) implies E { V (t)} < 0 when w i (t) ≡ 0.…”

“…Due to the fact that P is > 0, we have G ij (2) + G T ij (2) > 0, which means that the matrix variable G ij (2) are nonsingular. Thus, the filtering gains A Fij , B Fij , B Fikj , C Fij can be obtained by (32) and completing this proof.…”

“…It is easy to see that the matrix variable G ij (2) , j ∈ J i is absorbed by the filter gain variables A Fij , B Fij , B Fikj , j ∈ J i when introducinḡ…”

“…Without loss of generalit, we can specify G ij(4) = G ij (2) . Thus, we can directly specify the multipliers G i as…”

“…In practical application, some complex systems, such as transportation systems, power systems, communication networks, and industrial processes, are referred to as large-scale systems [1,2]. Due to strong interconnection and high dimensionality, large-scale systems lead to severe difficulties for their analysis and control synthesis.…”