Geometric-Polar Tracking From Bearings-Only and Doppler-Bearing Measurements

Bearings-only tracking (BOT) and Doppler-bearing tracking (DBT) perform target motion analysis from measurements of bearings, Doppler and bearings, respectively. The state equations are simple for both the target and observer in the rectangular coordinates. Hence, BOT and DBT mostly work in that coordinate. By developing the trigonometric relations between target and observer postions over time, this paper first derives the pseudolinear equations for direct range and bearing estimation. It then provides a generalized total least squares (GTLS), and a maximum likelihood solution. Polar tracking has two advantages over rectangular. First, for applications that require range and bearing, polar output avoids a coordinate conversion at every output instant. Second, polar equations often have a smaller bias than rectangular. Consequently, polar estimates can give a closer (to the optimum) initialization for iterative algorithms. Simulation results have validated the theoretical development, confirming the near optimality of the GTLS and maximum likelihood solutions.