Inertial Measurement Units (IMU) are successfully utilized to compensate localization errors in sensor fused inertial navigation systems. An IMU generally produces high frequency signals ranging from hundreds to thousands of Hz, and preintegration methods are applied to effectively process these high frequency signals for inertial navigation systems. The main problem with an existing preintegration method is that the inertial propagation models in the method are only generated at the IMU's coordinate system. Hence, the models have to be converted to the coordinate system of the other sensor in order to apply its constraint. So the iterative optimization framework using the conventional method takes large amount of time. In addition, since a general rigid body transformation can not transfer a velocity propagation model to the other coordinate system, the concept of relative motion analysis needs to be considered. To solve the problems above, in this paper, we propose a novel relative preintegration method that can generate inertial propagation models at any sensor's coordinate system in a rigid body. This permits accurate and fast IMU processing in sensor fused inertial navigation systems. We applied new non-linear optimization frameworks to solve initialization and extrinsic calibration problems for the IMU-IMU, IMU-Camera, and IMU-LiDAR pair based on the proposed relative preintegration method in an on-line manner, and the superior results of the mentioned processes are presented as well.