Tracking multiple road users is playing a significant role in autonomous vehicles and advanced driver assistance systems. Different from Multiple Target Tracking (MTT) in aerospace, the motion of the ground vehicles is likely constrained by their operational environment such as road and terrain. This information could be taken as additional domain knowledge and exploited in the development of tracking algorithms so as to enhance tracking quality and continuity.This paper proposes a new MTT strategy, Multiple Hypothesis Tracking using Moving Horizon Estimation approach (MHE-MHT), for tracking ground vehicles aided by road width constraints. In this strategy, tracking association ambiguity is handled by MHT algorithms which are proved as a preferred data association method for solving the data association problem arising in MTT. Unlike most of the MTT strategies, which solve target state estimation using Kalman filter (and its derivations), we propose a new solution using the moving horizon estimation (MHE) concept. By applying optimization based MHE, not only nonlinear dynamic systems but additional state constraints in target tracking problems such as road width can be naturally handled. The proposed MHE-MHT algorithm is demonstrated by a ground vehicle tracking scenario with an unknown and time varying number of targets observed in clutter environments. Using the optimal subpattern assignment metric, numerical results are presented to show the advantages of the constrained MHE-MHT structure by comparing it with the Kalman filter based MHT.