# GNSS/INS Integration Based on Machine Learning LightGBM Model for Vehicle Navigation
## 4 Results and Discussion  
### Performance of the PUA-LightGBM Model  
Table 2 presents the performance comparison of the PUA-LightGBM model to the PUA-RandomForest model. Both the PUA-LightGBM model and the PUA-RandomForest model are position prediction models for vehicles in the event of a GNSS outage. PUA-RandomForest is an INS/GPS integrated method for position prediction based on PUA  
using a random forest regression model. PUA-RandomForest reduces position errors compared to PUA-ANN, which has been proven to work better than the Kalman filter [19]. Because LightGBM only supports a single output, training the PUA-LightGBM model requires sequential training of the PUA-LightGBM (\(\delta E\)) for longitude difference prediction and PUA-LightGBM (\(\delta N\)) for latitude difference prediction, resulting in a total training time of 3.076 s. The performance metrics (root mean square error and coefficient of determination) of the PUA-LightGBM model for longitude and latitude change prediction are evidently similar to those of the PUA-RandomForest model. However, the training time of the PUA-LightGBM model for longitude and latitude variation prediction is only 3.7% of the training time of the PUA-RandomForest model. This demonstrates the ability of the PUA-LightGBM model to have a short training time while maintaining accuracy. This is attributed to the existence of algorithms and strategies for efficiency optimization in LightGBM, such as the histogram-based decision tree algorithm, leaf-wise leaf growth strategy with max depth limitation, gradient-based one-side sampling (GOSS) algorithm, exclusive feature bundling (EFB), etc. This is in line with the findings of [PERSON] et al. [22] and [PERSON] et al. [23]. The former used LightGBM to efficiently predict protein interactions, while the latter combined convolutional neural networks and LightGBM to improve the accuracy and efficiency of ultra-short-term wind power prediction models. The existing algorithms for vehicle position prediction can give more accurate and reliable navigation solutions than traditional machine learning algorithms. However, these algorithms have disadvantages such as long design time and high computational burdens [15], complex and insufficiently streamlined structures [12], and complex modelling processes [16]. PUA-LightGBM model has a high-efficiency working process while maintaining a high level of accuracy. An efficient training process is critical in application scenarios of vehicle position prediction during a GNSS outage. Firstly, the shorter training time allows the model dataset to be expanded, and an updated model is retrained while the vehicle is moving. Meanwhile, the GNSS outage vehicle position prediction model can be updated at a low cost, enabling the prediction of position changes in the presence of more dynamic changes in the vehicle. However, this may necessitate an analysis of data characteristics and the removal of similar training data to avoid wasting resources due to data redundancy. Secondly, the models can be applied to various land vehicles and do not require data to be collected and modeled in advance for the type of vehicle or driving characteristics. Data are simply collected while the vehicle is moving, and the model is quickly trained when the dataset reaches a certain volume. This allows for the prediction of vehicle position changes in the event of a GNSS outage. A major requirement for safe travel is fast and accurate navigation assistance [1]. From the transport provider's point of view, using the PUA-LightGBM model provides accurate vehicle positioning at a low hardware cost. Even if the vehicle encounters GNSS outages (e.g., obstruction of GNSS signals by tall buildings, forests, and tunnels), the vehicle's position information is still provided. Furthermore, based on the high adaptability of PUA-LightGBM, positioning products using PUA-LightGBM are easily scalable. To the best of our knowledge, the LightGBM algorithm has not been used to predict vehicle position in the event of a GNSS failure.