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.