# Towards Explainable Artificial Intelligence for GNSS Multipath LSTM Training Models
## 4 Experimental Results  
The experimental design and setup for analyzing GNSS multipath effects using LRP-interpreted LSTM-based RNNs was conducted using a Trimble BD970 dual-frequency GNSS receiver. The experimental setup focused on data collection from specific satellites, with particular attention to those at low elevation angles. Figure 3 shows the skylplot of satellite distribution at 9:00 a.m. on 17 February 2023, where the G03 satellite was selected for analysis due to its low elevation angle, making it more susceptible to multipath effects in urban environments. The receiver collected one second of vibration signal data every 10 min, with each snapshot containing 20,480 data points. The LSTM model was designed to process five key features: L1 frequency multipath error variation (MP1), L2 frequency multipath error variation (MP2), L1 frequency carrier-to-noise ratio (CNR1), L2 frequency carrier-to-noise ratio (CNR2), and satellite elevation angle (EL). The network architecture was configured with 256 hidden units, using a learning rateof 0.000025 over 500 training epochs. The model processed data in batches of 32 samples, with a window size of 60 time steps. To prevent overfitting, a dropout rate of 0.2 was implemented, and 15% of the dataset was reserved for validation. The model was trained using Mean Square Error as the loss function. Configuration parameters of the LSTM are summarized in Table 2.  
The flow chart of the experiment is shown in Figure 4. The experimental flow began with initial model training and validation using normal, non-anomalous data. After establishing baseline performance, the LRP algorithm was applied to analyze the trained model, generating relevance scores for each neuron corresponding to different features. Subsequently, three sets of experiments were conducted with varying periods of anomaly injection: from sample 1700 to 2000, 1400 to 2000, and 1100 to 2000. This progressive expansion of the anomaly period allowed for comprehensive analysis of the model's response to different anomaly durations. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Long Short-Term Memory Neural Network Parameter and Info.**} \\ \hline Input Feature & 5 & Batch Size & 32 \\ Output Feature & 5 & Window Size & 60 \\ Learning Rate & 0.000025 & Loss Function & MSE \\ Epoch & 500 & Validation Rate & 0.15 \\ Neuron Number & 256 & Dropout & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Configuration parameters of the LSTM neural network model. The architecture consists of five input and output features with 256 hidden neurons. Training parameters include a learning rate of 0.000025, batch size of 32, and window size of 60, optimized through empirical testing to achieve stable convergence while maintaining model performance. Figure 3: Skyplot showing satellite distribution at 9:00 a.m. on 17 February 2023. The G03 satellite (marked in the plot) was selected for analysis due to its low elevation angle, which makes it more susceptible to multipath effects in urban environments. The evaluation process included both quantitative and qualitative analyses. Model performance was assessed through MSE calculations, while the effectiveness of LRP interpretation was evaluated through relevance score growth rates and distribution patterns. Visual analysis tools, including heat maps and distribution plots, were employed to examine the relationship between anomalies and relevance score changes. This comprehensive experimental approach enabled thorough evaluation of both the LSTM model's predictive capabilities and the effectiveness of LRP in providing interpretable results for GNSS multipath detection. The prediction results from the LSTM model for different GNSS parameters are illustrated in Figure 5, demonstrating the model's ability to predict both normal and anomalous conditions. The prediction results from the LSTM model for different GNSS parameters  
Figure 4: Experimental workflow diagram illustrating the sequence of data processing, model training, and analysis stages.