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This paper presents recursive performance bounds for dynamic estimation and tracking problems in both single and multiple target cases within the framework of finite set statistics. Because the targets can appear and disappear when the detection probability of a sensor is less than unity (P_d < 1), we must determine the existence or nonexistence of the state as well as its value. Following the possible detection/miss sequences within the framework of a random vector, possible observation sets sequences are first defined. Based on these sequences, the performance bounds can be represented by a multivariate function of some time-based auxiliary elements. Recursive relations for all the auxiliary elements are derived rigorously. For the multitarget case, this recursive estimated bound can be applied without data association. Applications are analyzed through simulations to verify our theoretical results and show that our bounds are tighter than all other bounds for the case where detection probability P_d < 1. [ABSTRACT FROM PUBLISHER]