Target tracking has tremendous applications in both military and civilian surveillance systems. Typical applications are satellite surveillance systems, air-traffic control, undersea surveillance, sophisticated weapon delivery systems, global positioning systems, etc. The rapid developments in hardware and software technology have increased the signal processing capabilities of these surveillance systems. Advances in sensing resources have made possible to collect the enormous and complex amount of observation data from the targets. This has generated a continuing need for further development in information processing capabilities of these systems. Besides that, target tracking is as such a very complex problem. Complexity of the overall tracking problem increases substantially with the presence of maneuvering target, multiple targets, multiple distributed sensors, and background noise or clutter. In this book we develop a set of new suboptimal filtering and smoothing algorithms for maneuvering target tracking application. The proposed algorithms provide better performance in terms of estimation accuracy over the existing algorithms.