Within the random finite set framework, the error bound for joint detection and estimation(JDE) of multiple targets is proposed based on the optimal sub-pattern assignment distance in the presence of clutter and missed detection. The JDE here refers to estimating the number of the targets and their existing states. Example 1 shows the variation of the bound with the probability of detection and clutter density. Example 2 verifies the effectiveness of the bound by using the multiple hypothesis tracking, probability hypothesis density(PHD), and cardinalized PHD filters.