To regulate the energy flow in orchard ecosystems and maintain the environment, weeding has become a necessary measure for fruit farmers, and the use of automated mowers can help reduce labor costs and improve the economic efficiency of orchards. However, due to the complexity of the geographic and spatial environment of the orchard, in particular, the loose and undulating road surface, the interference of satellite signals by large trees, etc., which decreases the positioning accuracy and stability of the positioning system of the mower, and the high cost of the sensor also affect the popularization of intelligent mowers for these applications. To address the above problems, this paper constructs a positioning system through a low-cost global navigation satellite system (GNSS), inertial measurement unit (IMU), and odometry, and utilizes the Kalman filter algorithm based on the error state for a combined GNSS/IMU positioning so that the inertial navigation system can maintain a more accurate positioning when the GNSS signals are poor. Considering the side-slip and error accumulation problems of the odometry of the traction mower, the combined GNSS/IMU positioning information is used to optimize the odometry model and improve the navigation and positioning accuracy. To reduce the measurement error of the IMU and the problem of error accumulation, this paper utilizes the nonholonomic constraint (NHC) of a lawn mower to suppress the dispersion of IMU measurement errors and constructs periodic and nonperiodic zero-velocity updating (ZUPT) strategies in combination with the travel paths of lawn mower navigation operations in the region to update the IMU data to improve the positioning accuracy and stability of the positioning system. The experiments show that the average error of the constructed positioning system is controlled within 0.15 m, the maximum error is maintained at approximately 0.3 m, and the positioning system constructed by using low-cost sensors can achieve a positioning accuracy similar to that of the differential global navigation satellite system (DGNSS), which is beneficial for the promotion and application of intelligent mowers in orchards.