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Precise scene understanding is key for most robot monitoring and intervention tasks in agriculture. In this work we present PAg-NeRF which is a novel NeRF-based system that enables 3D panoptic scene understanding. Our representation is trained using an image sequence with noisy robot odometry poses and automatic panoptic predictions with inconsistent IDs between frames. Despite this noisy input, our system is able to output scene geometry, photo-realistic renders and 3D consistent panoptic representations with consistent instance IDs. We evaluate this novel system in a very challenging horticultural scenario and in doing so demonstrate an end-to-end trainable system that can make use of noisy robot poses rather than precise poses that have to be pre-calculated. Compared to a baseline approach the peak signal to noise ratio is improved from 21.34dB to 23.37dB while the panoptic quality improves from 56.65% to 70.08%. Furthermore, our approach is faster and can be tuned to improve inference time by more than a factor of 2 while being memory efficient with approximately 12 times fewer parameters.