This paper proposes a novel joint probabilistic data association (JPDA) filter for joint target tracking and track maintenance under unknown detection probability and clutter rate. The proposed algorithm consists of two main parts: (1) the standard JPDA filter with a Poisson point process birth model for multi-object state estimation; and (2) a multi-Bernoulli filter for detection probability and clutter rate estimation. The performance of the proposed JPDA filter is evaluated through empirical tests. The results of the empirical tests show that the proposed JPDA filter has comparable performance with ideal JPDA that is assumed to have perfect knowledge of detection probability and clutter rate. Therefore, the algorithm developed is practical and could be implemented in a wide range of applications.