  The concept of identifying codes was introduced by Karpovsky, Chakrabarty and
Levitin in 1998. The identifying codes can be applied, for example, to sensor
networks. In this paper, we consider as sensors the set Z^2 where one sensor
can check its neighbours within Euclidean distance r. We construct tolerant
identifying codes in this network that are robust against some changes in the
neighbourhood monitored by each sensor. We give bounds for the smallest density
of a tolerant identifying code for general values of r and Delta. We also
provide infinite families of values (r,Delta) with optimal such codes and study
the case of small values of r.
