Self-stabilizing Numerical Iterative Computation

Abstract: Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a linear system of equations. Several recent works propose different distributed algorithms for solving these problems, usually by using linear iterative numerical methods. The main problem with previous approaches is that once the problem inputs change during the process of computation, the computation may output unexpected results. In real life settings, sensor measurements are subject to varying environmental conditions and to measurement noise. We present a simple iterative scheme called SS-Iterative for solving systems of linear equations, and examine its properties in the self-stabilizing perspective. We analyze the behavior of the proposed scheme under changing input sequences using two different assumptions on the input: a box bound, and a probabilistic distribution. As a case study, we discuss the sensor calibration problem and provide simulation results to support the applicability of our approach.