  Mission planners for aircraft that operate in radar detection environments
are often concerned the probability of detection. The probability of detection
is a nonlinear function of the aircraft pose and radar position. Current path
planning techniques for this application assume that the aircraft pose is
deterministic. In practice, however, the aircraft pose is estimated using a
navigation filter and therefore contains uncertainty. The uncertainty in the
aircraft pose induces uncertainty in the probability of detection, but this
phenomenon is generally not considered when path planning. This paper provides
a method for combining aircraft pose uncertainty with single-pulse radar
detection models to aid mission planning efforts. The method linearizes the
expression for the probability of detection and three radar cross section
models. The linearized models are then used to determine the variability of the
probability of detection induced by uncertainty in the aircraft pose. The
results of this paper validate the linearization using Monte Carlo analysis and
explore the sensitivity of the probability of detection to aircraft pose
uncertainty.
