Default Sensor Network Setup based on the Anisotropic Criterion

Abstract

The paper considers the problem of setting up a communication scheme associated with the adjacency matrix between separate non-ideal sensors and known probability of their failsafe operation. As the evaluation object, a linear discrete non-stationary model in the state space was chosen, which was affected by external perturbations with the inaccurately specified stochastic characteristics. For external perturbations, upper limit of the anisotropy of the extended vector consisting of all the perturbing sequence elements was determined. Sensors were combined into a common network, where each separate node was able to use not only the own measurements to build an estimate of the desired output, but also the measurements received from the adjacent sensors. The model took into account the failure of specific sensors, where failures had the Bernoulli distribution. A failure should be understood as the random readings of a measurement device containing no useful information. The criterion is anisotropic norm of the system in the estimation errors from the perturbing action to the estimated output error. The problem was in selecting such adjacency matrix coefficients, where the anisotropic norm value in the estimation errors was not exceeding a certain threshold value. Solution to the problem was reduced to a numerical procedure of solving a special system of matrix inequalities ensuring boundedness of the system anisotropic norm in the estimation errors