Estimating uncertain spatial relationships in robotics
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Cites methods from "Estimating uncertain spatial relati..."
...The � operator applies the increment �xi to xi by using the standard motion composition operator � (see [ 25 ]) after converting the increment to the same representation as the state variable:...
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Cites methods from "Estimating uncertain spatial relati..."
...The idea of probabilistic state estimation goes back to Kalman filters (Gelb 1974; Smith, Self, & Cheeseman 1990 ), which use multivariate Gaussians to represent the robot’s belief....
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"Estimating uncertain spatial relati..." refers background or methods in this paper
...Given the sensor model, the conditional estimates of the sensor values and their uncertainties, and an actual sensor measurement, we can update the state estimate using the Kalman Filter equations [Gelb, 1984] given below, and described in the next section:...
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...The error in the estimation due to the non-linearities in h can be greatly reduced by iteration, using the Iterated Extended Kalman Filter equations [Gelb, 1984]:...
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...A continuous dynamics model can be developed given a particular robot, and the above equations can be reformulated as functions of time (see [Gelb, 1984])....
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...If the functions f in (17) and h in (15) are linear in the state vector variables, then the partial derivative matrices F and H are simply constants, and the update formulae (16) with (17), (15), and (18), represent the Kalman Filter [Gelb, 1984]....
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