  We study a scenario where an aircraft has multiple heterogeneous sensors
collecting measurements to track a target vehicle of unknown location. The
measurements are sampled along the flight path and our goals to optimize sensor
placement to minimize estimation error. We select as a metric the Fisher
Information Matrix (FIM), as "minimizing" the inverse of the FIM is required to
achieve small estimation error. We propose to generate the optimal path from
the Hamilton-Jacobi (HJ) partial differential equation (PDE) as it is the
necessary and sufficient condition for optimality. A traditional method of
lines (MOL) approach, based on a spatial grid, lends itself well to the highly
non-linear and non-convex structure of the problem induced by the FIM matrix.
However, the sensor placement problem results in a state space dimension that
renders a naive MOL approach intractable. We present a new hybrid approach,
whereby we decompose the state space into two parts: a smaller subspace that
still uses a grid and takes advantage of the robustness to non-linearities and
non-convexities, and the remaining state space that can by found efficiently
from a system of ODEs, avoiding formation of a spatial grid.
