Abstract
The problem of estimating the location of a mobile robot in an unstructured environment is discussed. This work extends earlier results in two important ways. First, the bias and variance of the estimation are analytically derived as functions of the angular error and distance between frames. Second, the uncertainty covariance matrix is derived and is compared to the first-order approximation previously used to estimate the result of compounding uncertain transformations to provide a framework in which the appropriateness of the first-order estimate can be formally studied. A simulation study, showing how the biases and expected distance between the estimate and true position of the robot vary as a function of measurement errors and different path plannings, is presented. Some possible improvements of the estimation method and future research topics are also given.
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