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Having worked with the NDT localization package of the Autoware.AI for quite a while with various car sized applications and I can say that fitness score is not a reliable source of matched-ness. And it couldn't reliably report its health state.

It could be very low or high in various parts of the point cloud and it could tell it's doing fine when it is floating all around the map.

I wouldn't attempt to directly calculate the covariance with the current state of the algorithm.

I suggest you use a combination of some wheel odometry, imu, vehicle model and decide that the localization is broken when the pose coming from NDT Matching algorithm disagrees with these sources more than some threshold.

Having worked with the NDT localization package of the Autoware.AI for quite a while with various car sized applications and I can say that fitness score is not a reliable source of matched-ness. And it couldn't reliably report its health state.

It could be very low or high in various parts of the point cloud map and it could tell it's doing fine when it is floating all around the map.

I wouldn't attempt to directly calculate the covariance with the current state of the algorithm.

I suggest you use a combination of some wheel odometry, imu, vehicle model and decide that the localization is broken when the pose coming from NDT Matching algorithm disagrees with these sources more than some threshold.