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Random mobility models (RMMs) capture the statistical movement characteristics of mobile agents and play an important role in the evaluation and design of mobile wireless networks. Particularly, RMMs are used to model the movement of unmanned aerial vehicles (UAVs) as the platforms for airborne communication networks. In many RMMs, the movement characteristics are captured as stochastic processes constructed using two types of independent random variables. The first type describes the movement characteristics for each maneuver and the second type describes how often the maneuvers are switched. We develop a generic method to estimate RMMs that are composed of these two types of random variables. Specifically, we formulate the dynamics of movement characteristics generated by the two types of random variables as a special Jump Markov System and develop an estimation method based on the Expectation–Maximization principle. Both off-line and on-line variants of the method are developed. We apply the estimation method to the Smooth–Turn RMM developed for fixed-wing UAVs. The simulation study validates the performance of the proposed estimation method. We further conduct a UAV experimental study and apply the estimation methods to real UAV trajectories.