To address the urgent demand for high-precision positioning in power industry operations within sparse reference station areas, this paper proposes a real-time kinematic positioning method integrating BeiDou multi-antenna Precise Point Positioning-Real-Time Kinematic (PPP-RTK) with inertial measurement unit (IMU) assistance. By combining the strengths of Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) technologies, we establish a multi-antenna observation model based on State Space Representation (SSR), incorporating satellite-based augmentation signals and atmospheric correction information from sparse reference station networks. Lie group theory is employed to enhance the Extended Kalman Filter (EKF) for simultaneous estimation of position, attitude, and ambiguity parameters. The integration of IMU measurements significantly improves robustness against environmental interference in dynamic scenarios. Experimental results demonstrate average positioning errors of 3.12 cm, 3.71 cm, and 6.23 cm in the East, North, and Up (ENU) directions, respectively, with an average convergence time of 1.62 min. Compared with non-IMU-augmented single-antenna PPP-RTK solutions, the proposed method achieves accuracy improvements up to 59.6% while maintaining stability in signal-occluded environments. This approach provides centimeter-level real-time positioning support for critical power grid operations in remote areas such as desert and Gobi regions, including infrastructure inspection and precise tower assembly, thereby significantly improving the efficiency of intelligent grid operation and maintenance.