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

this, the activation values will be identified by the fuzzy rules and sent to the output MF before being transferred to the output node [35].

Through ANFIS, a fuzzy system may correct several inputs at the same time, and these multiple inputs employed in the ANFIS model are GPS latitude, GPS longitude, 3-axis point coordinates of the accelerometer, and 3-axis point coordinates of the magnetometer. Two fuzzy systems are developed in this case, one for correcting the latitude and the other for longitude correction. The combined GPS and IMU sensors provided the same data to both fuzzy systems. The data used for training and testing are collected data through the GPS-RTK with an integrated IMU sensor. In particular, the subclustering method was utilized for FIS generation in the two models-latitude and longitude, as it demonstrated the best performance during algorithm pre-evaluation. This method generates a Sugeno-type FIS structure that is utilized to initialize the membership function parameters (**Figures 7** and **8**) [38]. This method involves dividing the input space into several subsets, known as clusters, and identifying the optimal number of clusters required to represent the input space accurately [39]. Once the clusters are identified, the corresponding membership function parameters are initialized based on the cluster centers and widths. This initialization allows for faster and more accurate training of the ANFIS network using two different optimization methods.

#### **Figure 7.**

*Sugeno-type FIS for training the latitude ANFIS model.*

#### **Figure 8.**

*Sugeno-type FIS for training the longitude ANFIS model.*

In the ANFIS tool, the range of influence was configured to 0.25 to allow the model to create smaller data clusters and produce more fuzzy rules. The squash factor is 0.6 to also create more and smaller data clusters. The acceptance ratio value is 0.25, which is greater than the rejection ratio value of 0.15. For each of the two models, four models are generated by changing the number of epochs of either 100 or 300 and altering the optimization methods used-hybrid, which is the combination of backpropagation and least mean squared error method and backpropagation. The best model will be selected based on which has the lowest error in training and testing.

For the latitude correction ANFIS model (**Figure 9**), the resulting ANFIS structure has eight inputs and one output node with 21 input MF for each input, generating 21 fuzzy rules and 389 nodes. The eight inputs represent the collected GPS latitude and longitude data points, the 3-axis coordinates of the accelerometer, the 3-axis coordinates of the magnetometer, and the reference latitude as the targeted output. The rest of the other latitude models followed the same structure and configuration of the network.

### **Figure 9.**

*ANFIS subclustering network structure for corrected latitude prediction.*

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

Moreover, **Figure 10** shows the resulting ANFIS structure of the longitude correction ANFIS model that has eight inputs-the collected GPS latitude and longitude datapoints, 3-axis coordinates of the accelerometer, and 3-axis coordinates of the magnetometer, and reference longitude as the target output with 32 input MF for each input allowing to producing of 32 fuzzy rules and 439 nodes. All the simulated longitude models followed the same structure and configuration of the network.
