This paper deals with the challenging problem of mutual synchronization of discrete-time chaotic systems. This particular type of synchronization allows to model successfully the complex dynamics of diverse systems, such as ecological, economical, physical, chemical etc. Unlike the usual master-slave synchronization, here we consider bidirectionaly connected sub-systems with identical priority. Switched Luenberger observers are designed to carry out the mutual synchronization, and their performances are compared in the cases with, and without gaussian noise.