This paper presents a continuous-time radar-inertial and lidar-inertial odometry system using a Gaussian process motion prior. The system aims to improve computational complexity during preintegration and interpolation by employing a sparse prior. The authors use a white-noise-on-acceleration motion prior and treat the gyroscope as a direct measurement of the state, while preintegrating accelerometer measurements to form relative velocity factors. The odometry is implemented using sliding-window batch trajectory estimation, achieving real-time performance. The system demonstrates significant improvements in performance, particularly when incorporating an IMU, with a 43% improvement in radar-inertial odometry. The approach is efficient and robust, handling challenging conditions such as aggressive motion and adverse weather. The paper provides experimental results on three datasets: KITTI-raw, Boreas, and the Newer College Dataset, showcasing the system's effectiveness in various scenarios.This paper presents a continuous-time radar-inertial and lidar-inertial odometry system using a Gaussian process motion prior. The system aims to improve computational complexity during preintegration and interpolation by employing a sparse prior. The authors use a white-noise-on-acceleration motion prior and treat the gyroscope as a direct measurement of the state, while preintegrating accelerometer measurements to form relative velocity factors. The odometry is implemented using sliding-window batch trajectory estimation, achieving real-time performance. The system demonstrates significant improvements in performance, particularly when incorporating an IMU, with a 43% improvement in radar-inertial odometry. The approach is efficient and robust, handling challenging conditions such as aggressive motion and adverse weather. The paper provides experimental results on three datasets: KITTI-raw, Boreas, and the Newer College Dataset, showcasing the system's effectiveness in various scenarios.