Title: The KFIoU Loss for Rotated Object Detection. Abstract: As a fundamental building block for visual analysis across aerial images, scene text etc., rotated object detection has established itself an emerging area, which is more general than classic horizontal object detection. Differing from the horizontal detection case whereby the alignment between final detection performance and regression loss is well kept thanks to the differentiable IoU loss, rotation detection involves the so-called SkewIoU that is undifferentiable. In this paper, we design a novel approximate SkewIoU loss based on Kalman filter, namely KFIoU loss. To avoid the standing and well-known boundary discontinuity and square-like problems, we convert the rotating bounding box into a Gaussian distribution, in line with recent Gaussian-based rotation detection works. Then we use the center loss to narrow the distance between the center of the two Gaussian distributions, followed by calculating the overlap area under the new position through Kalman filter. We qualitatively show the value consistency between KFIoU loss and the SkewIoU loss for rotation detection in different cases. We further extend our technique to the 3-D case which also suffers from the same issues as 2-D object detection. Extensive experimental results on various public datasets (2-D/3-D, aerial/text images) with different base detectors show the effectiveness of our approach. The source code will be made public available.