Tracking and Data Association

The mathematical theory of tracking had an early and distinguished start. In 1801, Carl Friedrich Gauss, on the basis of meager observations, computed the orbit of the newly discovered asteroid Ceres. When, a year later, Ceres was rediscovered precisely where Gauss predicted it would be, his fame as a mathematician was secured. In his calculations Gauss employed a procedure he had invented in 1795 at the age of 18: that was the method of least squares for determining the most probable value of a quantity from a set of inaccurate measurements. Thus were the foundations laid for the subject of tracking a target, meaning any kinematical object of interest, using a sequence of noisy measurements. In their new monograph, Tracking and Data Association, Y. Bar-Shalom and T. Fortmann expound the modern formulation of tracking rooted in Kalman recursive leastsquares estimation. However, as the title indicates, there is another more recent aspect to the target tracking problem. Present day tracking applications, as well as being concerned with target state estimation and prediction, are typically beset with uncertainty regarding the source of each measurement. The techniques for handling the measurement association problem, that is, for partitioning observations from the same source, date from the 1970s and include important contributions by Bar-Shalom and Fortmann.