The error bound is a typical measure of the limiting performance of all filters for the given sensor measurement setting. This is of practical importance in guiding the design and management of sensors to improve target tracking performance. Within the random finite set (RFS) framework, an error bound for joint detection and estimation (JDE) of multiple targets using a single sensor with clutter and missed detection is developed by using multi-Bernoulli or Poisson approximation to multi-target Bayes recursion. Here, JDE refers to jointly estimating the number and states of targets from a sequence of sensor measurements. In order to obtain the results of this paper, all detectors and estimators are restricted to maximum a posteriori (MAP) detectors and unbiased estimators, and the second-order optimal sub-pattern assignment (OSPA) distance is used to measure the error metric between the true and estimated state sets. The simulation results show that clutter density and detection probability have significant impact on the error bound, and the effectiveness of the proposed bound is verified by indicating the performance limitations of the single-sensor probability hypothesis density (PHD) and cardinalized PHD (CPHD) filters for various clutter densities and detection probabilities.