  This paper is concerned with finding an optimal path for an observer, or
sensor, moving at a constant speed, which is to estimate the position of a
stationary target, using only bearing angle measurements. The generated path is
optimal in the sense that, along the path, information, and thus the efficiency
of a potential estimator employed, is maximized. In other words, an observer
path is deemed optimal if it maximizes information so that the location of the
target is estimated with smallest uncertainty, in some sense. We formulate this
problem as an optimal control problem maximizing the determinant of the Fisher
information matrix, which is one of the possible measures of information. We
derive analytical results for optimality using the Maximum Principle. We carry
out numerical experiments and discuss the multiple (locally) optimal solutions
obtained. We check graphically that the necessary conditions of optimality are
verified by the numerical solutions. Finally we provide a comprehensive list of
possible extensions for future work.
