Geometric factors in target positioning and tracking

In target positioning and tracking, most sensors provide measurements either as range or bearing or both. The measurements are used to update an a priori estimate either via a linearized least squares method or an extended Kalman filter. In either case, the resulting solution has two components, one is related to the measurement prediction errors and the other is an observation matrix obtained from linearizing the nonlinear measurement equations around the a priori estimate. This paper studies the geometric factors explicitly and relates the observation matrix to the line of sight (LOS) vector for a ranging sensor and the direction perpendicular to the LOS vector of a bearing-only sensor. As a result, the updating of estimation error covariance with range and bearing measurements can be intuitively assessed via the shaping of estimation error ellipse along LOS directions. It provides a valuable means for target positioning and tracking performance modeling and prediction and can thus be used in active management of distributed sensor resources and sensor path planning.