Particle filtering has been successfully used in complex target tracking applications such as multiple target tracking. The particle filter can be used to incorporate constraints on target motion to improve tracking performance; this can be achieved using likelihood functions and sampling distributions. In this paper, we propose the constraint likelihood function independent partitions (CLIP) algorithm that uses constraints on target motion. This is achieved by incorporating a constraint likelihood function with the particle weights. As demonstrated by our simulations, a higher increase in tracking performance is obtained with our proposed constrained motion proposal (COMP) algorithm that incorporates target kinematic constraint information directly into the proposal density of the particle filter.