Filter initialization and batch estimation for tracking with angular-only measurements

The task of tracking objects with angular-only measurements imposes an interesting estimation problem due to the fact that range information is not obtainable when the sensor is mounted on a non-maneuvering platform and the tracked object itself is moving as well. Here, the use of log-spherical state variables within an extended Kalman filter is a well-established approach to tackle the problem. This paper focusses on the initialization of such a filter. A suitable (approximate) prior for the non-observed quantities is derived aiming for an initialization with a single measurement pair of bearing and elevation. Alternatively, filter initialization can be performed by applying a batch estimator using several such measurement pairs. One possible estimator of this kind is also presented. Simulation results using both schemes are provided.