Introduction Automatic guidance of agricultural tractors requires accurate estimation of both position and heading, which can be achieved through the integration of multiple sensors. Combining data from an inertial measurement unit (IMU) with satellite-based positioning systems (GPS) using a Kalman filter significantly improves the performance of inertial navigation systems (INS). The GPS module provides global position information, while the IMU measures linear acceleration and angular velocity. By processing IMU outputs, the vehicle’s local position and orientation can also be estimated. Finally, fusing GPS and IMU data through a Kalman filter enables precise determination of the tractor’s position and heading. The aim of this research was to develop an INS for determining the position and heading of agricultural tractors by integrating GPS, IMU, and digital compass data using an Extended Kalman filter algorithm. The resulting outputs can be applied in automatic tractor guidance systems.

Materials and Methods In this study, a NEO-6M GPS module, an MPU6050 IMU module, and a CMPS03 digital compass were used to develop the INS. Data acquisition from the sensors, data fusion, as well as result display and storage, were managed using an Arduino MEGA2560 microcontroller. The implementation of the data fusion algorithm and system programming was carried out in the Arduino IDE environment. In general, IMU outputs contain noise and offset errors. First, the noise was reduced using a median filter, and the offset values were determined by recording the sensor outputs over 200 repetitions, calculating their average, and subtracting the resulting offset from the data. By integrating the gyroscope data, the system rotation angles about the three body axes, namely roll, pitch, and yaw, were obtained. Using the yaw angle derived from the gyroscope data, a rotation matrix was constructed to transform the accelerometer outputs from the body coordinate system to the global coordinate system, thereby obtaining the acceleration components in the global frame. Assuming that the experimental ground surface was flat and level, the gravitational acceleration component was removed only from the vertical acceleration data. The acceleration components in the global coordinate system were then integrated once over time to estimate velocity and integrated a second time to determine the tractor position in three directions. In addition, the tractor pitch and roll angles relative to the global coordinate system were calculated from the acceleration components in the global frame. Finally, the pitch and roll angles obtained from the accelerometer data were fused with the angular velocity measurements around the y- and x-axes, respectively, using an extended Kalman filter to achieve more accurate orientation estimates. Similarly, the digital compass output was combined with the angular velocity around the z-axis to improve the yaw angle estimation. Furthermore, the position estimates obtained from the GPS module were fused with those derived from the accelerometer data to provide a more accurate estimation of the tractor position. After preparation of the hardware and software components and completion of laboratory testing, the developed system was installed on a MF 285 tractor, and its performance in determining tractor position and heading was evaluated. The position and heading values recorded by the system were compared with the actual tractor values, and the corresponding errors were determined. Root mean square error (RMSE) and maximum error (Emax) were used to evaluate system accuracy.

Results and Discussion Laboratory evaluation results showed that gyroscope-derived angle measurements were initially free from noise and offset; however, they gradually deviated over time due to integration drift. In contrast, pitch and roll angles derived from accelerometer data exhibited both noise and offset. Application of the Kalman filter effectively reduced noise and compensated for drift in pitch and roll estimates. Furthermore, fusion of digital compass data with gyroscope-based yaw angles using the Kalman filter successfully eliminated yaw drift. Integration of GPS and IMU data through the Kalman filter also improved positional accuracy. During road tests, the system achieved an RMSE of In the X direction equal to 61.4 m, in the Y direction equal to 50.3 m and in total 4.09 m in estimating tractor position. The maximum error (Emax) in determining position was 11.15 m in the X direction and 11.05 m in the Y direction, resulting in a total maximum positional error of 11.15 m. These errors were mainly caused by interruptions in GPS signal reception at certain points along the test path, which disrupted system performance and resulted in inaccurate position estimation and Kalman filter outputs. Variance analysis of Emax values indicated that tractor forward speed had no significant effect on position determination in the X and Y directions or on total positional accuracy at the 5% probability level. Therefore, the developed system is capable of determining tractor position under different forward speed conditions.

Conclusion The developed INS demonstrated strong potential for application in the automatic guidance of agricultural tractors. To further improve system performance, the use of more accurate GPS and IMU modules is recommended. In addition, alternative noise reduction techniques and advanced versions of the Kalman filter, as well as other data fusion algorithms, should be investigated and evaluated.