Tracking Initially Unresolved Thrusting Objects Using an Optical Sensor

This paper considers the problem of estimating the three-dimensional states of a salvo of thrusting/ballistic endo-atmospheric objects using two-dimensional (2-D) Cartesian measurements from the focal plane array (FPA) of a single fixed optical sensor. Since the initial separations in the FP are smaller than the resolution of the sensor, there are merged FP measurements, compounding the usual false-alarm and missed-detection uncertainty. We present a two-step methodology. First, we assume a Wiener process acceleration model for the motion of the images of the objects in the optical sensor's FPA. We model the merged measurements with increased variance, and thence employ a multi-Bernoulli (MB) filter using the 2-D measurements in the FPA. Second, using the set of associated measurements for each confirmed MB track, we formulate a parameter estimation problem, whose maximum likelihood solution can be obtained via numerical search and can be used for impact point prediction. Simulation results illustrate the performance of the proposed method.