The single sensor probability hypothesis density (PHD) and cardinalized probability hypothesis density (CPHD) filters have been developed in the literature using the random finite set framework. The existing multisensor extensions of these filters have limitations such as sensor order dependence, numerical instability or high computational requirements. In this paper we derive update equations for the multisensor CPHD filter. The multisensor PHD filter is derived as a special case. Exact implementation of the multisensor CPHD involves sums over all partitions of the measurements from different sensors and is thus intractable. We propose a computationally tractable approximation which combines a greedy measurement partitioning algorithm with the Gaussian mixture representation of the PHD. Our greedy approximation method allows the user to control the tradeoff between computational overhead and approximation accuracy.Index Terms-Random finite sets, multisensor CPHD filter, multisensor PHD filter, multisensor multitarget tracking.

Cryogenic air separation plants that produce argon in addition to oxygen and nitrogen use two heat-integrated distillation columns and a side rectifier. The dynamics of the side rectifier are very slow because of three factors:  the large number of separation stages, the small amount of argon in the air feed, and the high product purity. Currently, when the plant shuts down, the liquid inventory in the argon column drains into the upper (low-pressure) column. A normal start-up takes about 10 h to achieve argon product purity. The start-up time can be reduced significantly by using storage vessels to collect the liquid that drains from the argon column upon shutdown and reintroducing the liquid during the subsequent start-up. Compared to a 10 h start-up time with no collection points, the time required to achieve argon product purity is reduced to 3.35 h by using 2 collection points and is reduced to 2.23 h by using 6 collection points.

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