  One of the most complex tasks of decision making and planning is to gather
information. This task becomes even more complex when the state is
high-dimensional and its belief cannot be expressed with a parametric
distribution. Although the state is high-dimensional, in many problems only a
small fraction of it might be involved in transitioning the state and
generating observations. We exploit this fact to calculate an
information-theoretic expected reward, mutual information (MI), over a much
lower-dimensional subset of the state, to improve efficiency and without
sacrificing accuracy. A similar approach was used in previous works, yet
specifically for Gaussian distributions, and we here extend it for general
distributions. Moreover, we apply the dimensionality reduction for cases in
which the new states are augmented to the previous, yet again without
sacrificing accuracy. We then continue by developing an estimator for the MI
which works in a Sequential Monte Carlo (SMC) manner, and avoids the
reconstruction of future belief's surfaces. Finally, we show how this work is
applied to the informative planning optimization problem. This work is then
evaluated in a simulation of an active SLAM problem, where the improvement in
both accuracy and timing is demonstrated.
