Some Results on Linear Unbiased Filtering with Polar Measurements

The problem of tracking objects moving in Cartesian space with sensors delivering polar measurements has been under investigation of several researchers for quite some time now. Different proposals for using measurement conversion techniques in combination with a linear Kalman filter have been made. As one possible alternative approach, an (approximate) best linear unbiased estimator (BLUE) has been proposed. In this paper, some of these approaches are reinvestigated by means of a common representation form for all covered techniques (that is, including the BLUE filter) that helps analyzing and understanding the general behavior of these estimators. Some noteworthy results are presented. It will be argued that the BLUE filter in its original form may be prone to yielding indefinite estimation error variance matrices and that later variants of this filter do not exhibit this behavior. A new initialization method for these filters will be derived