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In this paper we derive computationally-tractable approximations of the Probability Hypothesis Density (PHD) and Cardinalized Probability Hypothesis Density (CPHD) filters for superpositional sensors with Gaussian noise. We present implementations of the filters based on auxiliary particle filter approximations. As an example, we present simulation experiments that involve tracking multiple targets using acoustic amplitude sensors and a radio-frequency tomography sensor system. Our simulation study indicates that the CPHD filter provides promising tracking accuracy with reasonable computational requirements.