In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization. Range and trajectory smoothness constraints are constructed in a position graph, then the robot trajectory over a sliding window is estimated by a graph based optimization algorithm. Moreover, convergence analysis of the algorithm is provided, and the effects of the number of iterations and window size in the optimization on the localization accuracy are analyzed. Extensive experiments on quadcopter under a variety of scenarios verify the effectiveness of the proposed algorithm and demonstrate a much higher localization accuracy than the existing range-based localization methods, especially in the altitude direction.
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