  This paper delves into the predictive sensor tasking algorithm for the
multi-observer, multi-target sensor setting, leveraging the Extended
Information Filter (EIF). Conventional predictive formulations suffer from the
curse of dimensionality due to the dependence of the performance metric on the
target-observer assignment history. This paper exploits the EIF's additive
structure of measurement information to break the dependence and devises an
efficient linear integer programming formulation. We further investigate the
resulting formulation to study how the cislunar dynamics expands and shrinks
the measurement information, and discuss when the information gain is maximized
in relation to the observation space and the uncertainty deformation caused by
the dynamics. We numerically demonstrate that the predictive sensor tasking
algorithm outperforms the myopic algorithm in two different metrics, depending
on the formulation.
