In the target tracking and its engineering applications, recursive state
estimation of the target is of fundamental importance. This paper presents a
recursive performance bound for dynamic estimation and filtering problem, in
the framework of the finite set statistics for the first time. The number of
tracking algorithms with set-valued observations and state of targets is
increased sharply recently. Nevertheless, the bound for these algorithms has
not been fully discussed. Treating the measurement as set, this bound can be
applied when the probability of detection is less than unity.