Can robot_localization package be used on a full NED system?

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Actually, robot_localization expects all IMU data to be in the ENU format, as stated on this documentation page under the heading "Coordinate Frames and Transforming Sensor Data".

To answer your question: No, you could technically have every frame on your robot in NED orientation, but the orientation vector is not going to be reported in the same way as if your robot used the ENU convention.

Orientation, especially concerning IMUs, is something you can get wrong VERY easily. And it is a huge pain to sort out when it does go wrong. Trust me on that. So I highly recommend you stick to the ROS conventions as closely as possible. If your IMU reports orientation in the NED format, you will need to write a small rosnode to dynamically convert and republish the data in the ENU format. Plus, if something does happen and you need to ask the ROS community here for help, it will become much harder for people to help you if you are using a custom orientation system.