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Good find, the AMCL software package doesn't have this right. I made an issue to track this: https://github.com/ros-planning/navigation/issues/20

As for the distributions, summing the variance is absolutely required, as seen here: http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/50250.html

The rest of the algorithm is explained in the 3rd edition in section 5.4.3. d_trans must be in units of meters since it is the translation component of the odometry update. The lines you quote are the ones described as "To model the motion error, we assume that the "true" values of the rotation and translation are obtained from the measured ones by subtracting independent noise (SAMPLE) with zero mean and variance b^2). So the formula from edition 1 cannot be correct since d_trans and d_trans_hat are in meters, not meters^2 (see equation 5.38 and 5.40).

Finally, it may help to remember that this is sampling the noise for a particle filter where the overall distribution is tracked by the particles, not a closed-form estimate. Each particle in the filter experiences these updates, so the 'A' compoment of AMCL allows an adaptive (KLD sampling) approach that increases and decreases the number of particles in order to keep the particles from diverging and to ensure there are enough to track the important high-probability areas of distribution.

Good find, the AMCL software package doesn't have this right. I made an issue to track this: https://github.com/ros-planning/navigation/issues/20

As for the distributions, summing the variance is absolutely required, as seen here: http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/50250.html

The rest of the algorithm is explained in the 3rd edition in section 5.4.3. d_trans must be in units of meters since it is the translation component of the odometry update. The lines you quote are the ones described as "To model the motion error, we assume that the "true" values of the rotation and translation are obtained from the measured ones by subtracting independent noise (SAMPLE) with zero mean and variance b^2). So the formula from edition 1 cannot be correct since d_trans and d_trans_hat are in meters, not meters^2 (see equation 5.38 and 5.40).

Finally, it may help to remember that this is sampling the noise for a particle filter where the overall distribution is tracked by the particles, not a closed-form estimate. Each particle in the filter experiences these updates, so the 'A' compoment of AMCL allows an adaptive (KLD sampling) approach that increases and decreases the number of particles in order to keep the particles from diverging and to ensure there are enough to track the important high-probability areas of distribution.


Edit to show units of alpha, along with the units of the other values:

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