**4. Conclusion**

The CR method utilizes GPS to create accurate maps quickly and with less equipment and labor than traditional surveying. However, errors can occur due to GPS sensor accuracy, digital map quality, and map-matching errors. To improve accuracy, an IMU-GPS sensor fusion method can be used. Environmental factors can still cause GPS sensors to fail, so reducing errors in GPS receiver accuracy is crucial for correct underground utility location and map matching. The study proposes using fuzzy logic with ANFIS to correct the latitude and longitude of the CR vehicle's position by integrating RTK-GPS sensor data with IMU linear acceleration and magnetometer data. The ANFIS tool trains two fuzzy systems, one for latitude and one for longitude correction. The developed combined GPS-IMU circuit was tested by conducting field testing from Lumban to De La Salle University Manila Campus to collect actual GPS latitude and longitude, triaxial accelerometer, and triaxial magnetometer data. The study evaluated different ANFIS models with varying hyperparameters, and the selected model for latitude correction is model 1B with a hybrid optimization algorithm at 300 training epochs. This model achieved the lowest training RMSE of 0.008770, validation RMSE of 0.008300, and testing RMSE of 0.011814 at 300 training epochs. Model 1B showed the lowest MSE of 0.000069, highest R2 of 0.995479, and lowest MAE of

*Adaptive Neuro-Fuzzy Inference System-Based GPS-IMU Data Correction for Capacitive… DOI: http://dx.doi.org/10.5772/intechopen.112921*

0.000375 compared to other models, proving superior results. For ANFIS longitude correction, model 2B was selected, and a hybrid optimization algorithm was applied at 100 epochs, which resulted in the lowest training RMSE of 0.007361, 0.007100 validation RMSE, and 0.01532 testing RMSE. Among the four prediction models of model 2, model 2A achieved the lowest MSE of 0.000050, the highest R2 of 0.997675, and the lowest MAE of 0.000042 for longitude correction, demonstrating the best results.

The selected best ANFIS models' performances were then validated by comparing them to simulated LSTM and ELM models; however, the ANFIS models still outperformed the two other models. The ANFIS models were also tested on the collected actual dataset for verification of results. The visualized map obtained from this simulation test revealed that the uncorrected GPS data points were significantly distant from the target GPS reference values compared to the ANFIS corrected output. This indicates that the ANFIS models proved to combine the benefits of neural networks with fuzzy logic in a single structure for predicting corrected latitude and longitude with greater accuracy. The comparison of findings also demonstrated that ANFIS is a potential solution for vehicle localization and tracking using GPS and IMU data, making it suitable to be integrated into capacitive resistivity underground imaging system and can be extremely useful in mapping the precise location of the investigated subterranean utility objects.

To further validate the ANFIS models' performance, additional GPS latitude and longitude datasets must be collected and tested against the simulated ANFIS models. This is considered the study's lacking strategy that can be done for future research. Furthermore, it suggests retraining and adjusting the hyperparameters when tested on newly obtained actual data to maximize the ANFIS model performance. Lastly, the study's results can be further examined by comparing them to other ways of sensor fusion, such as the employment of other machine learning models, which will be the paper's next goal.
