The recursive form of error bounds for RFS state and observation with Pd < 1

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. This performance limit is derived based on the meaningful distance error between two random sets, the target state set and its estimation. The estimation set is a function of the time-sequence of measurement sets. These measurement sets can be either empty or the Bernoulli random finite sets. Hence this bound can be applied when the probability of detection is less than unity. The state set model is a Markov process. The state set can be empty or not, which accounts for appearance and disappearance of the targets. Moreover, as a bound for discrete-time multidimensional filtering problems, it appears in recursive form. An application is presented to confirm the theory and reveal this bound is more general than previous bounds in the framework of random vector statistics.