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This paper presents an algorithm for in-surveillance and out-of-surveillance mobile ground target tracking. In this respect, a nonlinear Bayesian estimation filter is presented. Then, an adaptive algorithm is derived to reduce remarkably the computational burden of this filter, while not degrading the accuracy of the state estimates. Additionally, an algorithm employing the concepts of hospitability and synthetic inclination maps is introduced and is coupled with the nonlinear Bayesian filter to track the mobile ground target once it goes out-of-surveillance. Loosely speaking, the hospitability map can be viewed as a terrain-based map defining a likelihood or a "weight" for each point on the earth's surface proportional to the ability of the target to move and maneuver at that location. On the other hand, the synthetic inclination map describes how the target favors certain regions within the search area, hence being "synthetically" inclined to move toward them.