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The cardinalized probability hypothesis density (CPHD) filter is a recursive Bayesian algorithm for estimating multiple target states with varying target number in clutter. In the present work, it is shown that a missed detection in one part of the field of view has a significant effect on the probability hypothesis density (PHD) arbitrarily far apart from the missed detection. In the case of zero false alarm rate, this effect is particularly pronounced and can be calculated by solving the CPHD filter equations analytically. While the CPHD filter update of the total cardinality distribution is exact, the local target number estimate close to the missed detection is artificially strongly reduced. A first ad-hoc approach towards a "locally" CPHD filter for reducing this deficiency is presented and discussed.