  This paper explores the problem of selecting sensor nodes for a general class
of nonlinear dynamical networks. In particular, we study the problem by
utilizing altered definitions of observability and open-loop lifted observers.
The approach is performed by discretizing the system's dynamics using the
implicit Runge-Kutta method and by introducing a state-averaged observability
measure. The observability measure is computed for a number of perturbed
initial states in the vicinity of the system's true initial state. The sensor
node selection problem is revealed to retain the submodular and modular
properties of the original problem. This allows the problem to be solved
efficiently using a greedy algorithm with a guaranteed performance bound while
showing an augmented robustness to unknown or uncertain initial conditions. The
validity of this approach is numerically demonstrated on a $H_{2}/O_{2}$
combustion reaction network.
