  This paper develops an accurate, efficient filter (called the `TT filter')
for tracking multiple targets using a spatially-distributed network of
amplitude sensors that estimate distance but not direction. Several innovations
are included in the algorithm that increase accuracy and reduce complexity. For
initial target acquisition once tracking begins, a constrained Hessian search
is used to find the maximum likelihood (ML) target vector, based on the
measurement model and a Gaussian approximation of the prior. The Hessian at the
ML vector is used to give an initial approximation of the negative log
likelihood for the target vector distribution: corrections are applied if the
Hessian is not positive definite due to the near-far problem. Further
corrections are made by applying a transformation that matches the known
nonlinearity introduced by distance-only sensors. A set of integration points
is constructed using this information, which are used to estimate the mean and
moments of the target vector distribution. Results show that the TT filter
gives superior accuracy and lower complexity than previous alternatives such as
Kalman-based or particle filters.
