Bearings-only tracking in the plane

It is known that the conditional probability density function for the general filtering problem can be represented as a path integral. This representation is the basis of a new finite dimensional recursive filter which is applied to bearings only tracking. The filter computes an approximation to the density for the target position conditional on the measurements. The approximation is accurate provided only the most recent measurements are used. Two different models for the target motion are considered. In the first the model is a known motion subject to a perturbation by an Ornstein-Uhlenbeck process. In the second the acceleration of the target is a Brownian motion. Numerical experiments show that for the first model the bearing angle measurements add little or no range information, but for the second model they do add significant range information, especially if the noise level in the model is high.