**3. Results and discussion**

#### **3.1 Analysis of results of ANFIS-based GPS-IMU data correction models**

Different combinations of ANFIS optimization algorithms and several epochs are applied to train and test the data to select the best ANFIS model for GPS latitude and longitude correction. The 2521 input and output data rows were divided into training, validation, and test data. About 55% is used as training data, 25% for validation, and 20% for testing. The input data used are collected actual data, specifically the GPS latitude and longitude coordinates, 3-axis coordinates of the accelerometer, and 3-axis coordinates of the magnetometer, while the output data used is the extracted reference GPS latitude and longitude from Google Maps. The simulated models are further quantified numerically using training RMSE, validation RMSE, and testing RMSE. Presented in **Table 3** is the summary of simulated ANFIS models with different hyperparameters for latitude correction. Model 1 corresponds to the ANFIS latitude correction model, which resulted in four models known as models 1A, 1B, 1C, and 1D. In model 1A, hybrid optimization is applied, and after 100 epochs, the model training has stopped attaining training RMSE of 0.009121, validation RMSE of 0.008567, and testing RMSE of 0.012093. On the other hand, model 1C with the backpropagation algorithm applied was trained for 100 epochs, achieving training RMSE of 1.101670, validation MSE of 1.136290, and testing RMSE of 4.383700. Similarly, model 1D with the backpropagation algorithm at 300 epochs obtained a low training RMSE of 1.090430, validation RMSE of 1.114220, and testing RMSE of 4.473100. However, model 1B with a hybrid optimization algorithm achieved the lowest training RMSE of 0.008770, 0.008300 validation RMSE, and 0.011814 testing RMSE at 300 training epochs. It is evident that model 1B significantly exhibited the best training and test results out of the other models for GPS latitude correction using the simulated ANFIS tool.


**Table 3.**

*Summary of simulated ANFIS models with different hyperparameters for latitude correction.*


**Table 4.**

*Summary of simulated ANFIS models with different hyperparameters for longitude correction.*

Moreover, the summary of simulated ANFIS models for different combinations of hyperparameters for GPS longitude correction is presented in **Table 4**. In contrast to model 1, model 2 represents the ANFIS longitude correction model, which resulted in models 2A, 2B, 2C, and 2D models. Model 2C with the backpropagation algorithm applied was trained for 100 epochs, achieving a high training RMSE of 0.766548, validation MSE of 0.773640, and testing RMSE of 3.360600. But model 2D with a backpropagation algorithm at 300 epochs obtained the highest training RMSE of 0.915090, validation RMSE of 0.905851, and testing RMSE of 2.565400. With a hybrid optimization algorithm applied, model 1A and model 2B resulted in the lowest and same values of training RMSE, validation RMSE, and testing RMSE of 0.007361, 0.007100, and 0.015321, respectively. However, based on the training results, model 2B seems to overfit the training data and has a more complex model with higher computational resources required for training because of the higher training epoch value. Thus, the superior performance of model 2A in correcting GPS longitude is apparent as it has shown significantly better training and test results than the other models.
