We present a fully automated multi-sperm tracking algorithm. It has the demonstrated capability to detect and track simultaneously hundreds of sperm cells in recorded videos while accurately measuring motility parameters over time and with minimal operator intervention. Algorithms of this kind may help in associating dynamic swimming parameters of human sperm cells with fertility and fertilization rates. Specifically, we offer an image processing method, based on radar tracking algorithms, that detects and tracks automatically the swimming paths of human sperm cells in timelapse microscopy image sequences of the kind that is analyzed by fertility clinics. Adapting the well-known joint probabilistic data association filter (JPDAF), we automatically tracked hundreds of human sperm simultaneously and measured their dynamic swimming parameters over time. Unlike existing CASA instruments, our algorithm has the capability to track sperm swimming in close proximity to each other and during apparent cell-to-cell collisions. Collecting continuously parameters for each sperm tracked without sample dilution (currently impossible using standard CASA systems) provides an opportunity to compare such data with standard fertility rates. The use of our algorithm thus has the potential to free the clinician from having to rely on elaborate motility measurements obtained manually by technicians, speed up semen processing, and provide medical practitioners and researchers with more useful data than are currently available.