Track initiation and termination is an important function in multi-target tracking (MTT), it is a decision part for establishing the records of the new targets and terminating the unwanted records of the inexistent targets when they leave the surveillance region. But in the heavy cluttered environment, there exists so called "incomplete data problem", due to the unknown state of the target and the sequence of measurements which originate from the target. Because the EM algorithm is an efficient means to solve the "incomplete data problem", a fast track initiation and termination approach applicable to engineering is presented, which combines the sequential probabilistic ratio test (SPRT) with recursive expectation maximization (EM). Here, track initiation and termination is modeled as a hypothesis testing problem. And aiming at the computational difficulty of the likelihood function due to the unknown target state and the sequence of measurements which originate from the target, the recursive EM-based formula of likelihood function is introduced. It gives an efficient solution to track initiation and termination by processing the measurement data sequentially, and its recursive form can meet the real-time demand. The simulation results indicate that the proposed method performs well for track initiation and termination, especially in heavy cluttered environment.