In this paper, an estimation problem for the sensor networks is studied in the frameworks of anisotropy-based theory. The considered system is described by linear discrete time-varying model with several sensors on finite horizon. Each sensor operates its own measurements and measurements given from some others. Any sensor could fail in random time instant. The external disturbance is assumed to be coloured sequence with given level of anisotropy. Dynamics of combined error and extended state system is governed by multiplicative noise system. Anisotropic norm boundedness for error system is guaranteed by applying of anisotropy-based bounded real lemma for multiplicative noise system. The solution of considered problem is reduced to convex optimisation problem.