The probability hypothesis density (PHD) and cardinalized PHD (CPHD) filters were introduced in 2000 and 2006, respectively, as approximations of the full multitarget Bayes detection and tracking filter. Both filters are based on the ldquostandardrdquo multitarget measurement model that underlies most multitarget tracking theory. This paper is one of a series of theoretical studies that address PHD and CPHD filters for nonstandard multitarget measurement models. In this paper I derive the measurement-update equations for a PHD filter that presumes a Poisson model for extended targets due to Gilholm, Godsill, Maskell, and Salmond.