This paper examines techniques for measuring the stability of both the state-space dynamics and uncertainty propagation of space objects within a multi-object, multi-sensor satellite tracking problem. These measurements of stability are quantified through the calculation of various Lyapunov exponents, and applied as (or within) a utility metric to create sensor schedules dictating when a particular sensor should observe a particular object. It is the goal of these schedules to reduce the total uncertainty of all objects tracked, a process that is inherently coupled with the object's state-uncertainty estimation, handled through the application of a nonlinear filter. These methods of scheduling (also known as sensor tasking) and nonlinear filtering are applied to a simulation which attempts to represent a simplified tracking component of the Space Situational Awareness problem. As a primary objective, results from simulations utilizing these stability measures are compared to a more traditional information-theoretic based tasking approach utilizing Shannon information gain. As a secondary objective two nonlinear filters, an extended Kalman filter and unscented Kalman filter, are studied to see the effect of estimator selection on sensor scheduling based on these various tasking methods.