  Observability is a fundamental concept in system inference and estimation.
This paper is focused on structural observability analysis of Cartesian product
networks. Cartesian product networks emerge in variety of applications
including in parallel and distributed systems. We provide a structural approach
to extend the structural observability of the constituent networks (referred as
the factor networks) to that of the Cartesian product network. The structural
approach is based on graph theory and is generic. We introduce certain
structures which are tightly related to structural observability of networks,
namely parent Strongly-Connected-Component (parent SCC), parent node, and
contractions. The results show that for particular type of networks (e.g. the
networks containing contractions) the structural observability of the factor
network can be recovered via Cartesian product. In other words, if one of the
factor networks is structurally rank-deficient, using the other factor network
containing a spanning cycle family, then the Cartesian product of the two
nwtworks is structurally full-rank. We define certain network structures for
structural observability recovery. On the other hand, we derive the number of
observer nodes--the node whose state is measured by an output-- in the
Cartesian product network based on the number of observer nodes in the factor
networks. An example illustrates the graph-theoretic analysis in the paper.
