This paper considers the problem of estimating the 3D states of a salvo of thrusting/ballistic endo-atmospheric objects using 2D Cartesian measurements from the focal plane array (FPA) of a single fixed optical sensor. Since the initial separations in the FPA are smaller than the resolution of the sensor, this results in merged measurements in the FPA, compounding the usual false-alarm and missed-detection uncertainty. We present a two-step methodology. First, we assume a Wiener process acceleration (WPA) model for the motion of the images of the projectiles in the optical sensor’s FPA. We model the merged measurements with increased variance, and thence employ a multi-Bernoulli (MB) filter using the 2D 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 estimate can be obtained via numerical search and can be used for impact point prediction. Simulation results illustrate the performance of the proposed method.
Qin Lu, Yaakov Bar-Shalom, Peter Willett, Karl Granström, R. Ben-Dov, and B. Milgrom, "Tracking initially unresolved thrusting objects in 3D using a single stationary optical sensor," Proc. SPIE 10200, Signal Processing, Sensor/Information Fusion, and Target Recognition XXVI, 1020002 (Presented at SPIE Defense + Security: April 10, 2017; Published: 2 May 2017); https://doi.org/10.1117/12.2262832.
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