# Towards Explainable Artificial Intelligence for GNSS Multipath LSTM Training Models
## 4 Experimental Results
The upper path shows the forward propagation process through the LSTM network layers, while the lower path demonstrates the backward propagation of relevance scores using LRP technique. demonstrate good accuracy across all measured parameters. The model shows small prediction errors, with deviations between predicted and actual values being nearly indistinguishable in most cases. For multipath, the errors are usually well within 1 m, and, for CNR, the errors are with \(1\,\mathrm{dB/Hz}\). Figure 5: LSTM prediction results for GNSS observables. (**a**) First frequency multipath error variation (MP1), (**b**) second frequency multipath error variation (MP2), (**c**) first frequency carrier-to-noise ratio (CNR1), (**d**) second frequency carrier-to-noise ratio (CNR2), and (**e**) satellite elevation angle (EL). The blue lines represent actual measurements while red lines show the LSTM predictions. All parameters except EL demonstrate significant temporal variations, with the model achieving high prediction accuracy across different signal characteristics. In Figure 5a, the MP1 (first frequency multipath error variation) prediction results show strong agreement between the predicted and actual values. The model successfully captures both the general trend and local fluctuations in the multipath error, indicating its effectiveness in modeling first-frequency multipath patterns. Similarly, Figure 5b displays the MP2 (second frequency multipath error variation) predictions, which also demonstrate high accuracy in tracking the actual measurements, though with slightly different patterns from MP1 due to the frequency-dependent nature of multipath effects. The carrier-to-noise ratio predictions shown in Figure 5c (CNR1) and Figure 5d exhibit particularly robust performance. The model accurately predicts the signal strength variations, which are crucial indicators of signal quality and potential multipath interference. The close alignment between predicted and actual values suggests that the LSTM-based RNN has effectively learned the underlying patterns in signal strength fluctuations. While Figure 5e shows that the elevation angle (EL) remains relatively stable during the experiment period, its inclusion in the model proves to be valuable for a different reason. Although EL does not show significant temporal variation, subsequent analysis reveals its importance in explaining abnormal signal behaviors. The elevation angle serves as a crucial reference parameter that helps interpret multipath effects and signal anomalies, as demonstrated in the following sections of our analysis. This highlights that the significance of a parameter cannot be judged solely by its temporal variability but must also consider its role in the overall signal interpretation framework. The minimal prediction errors across all parameters validate the effectiveness of our LSTM architecture and training approach, while also providing a reliable foundation for the subsequent LRP analysis. To analyze the model's decision-making process, we examined the distribution of LRP relevance scores across the network's neurons. Figure 6 presents these distributions for different GNSS features under normal conditions, providing insights into how different neurons contribute to the model's predictions for each input feature. Here we use the LRP-\(\gamma\) method and \(\gamma\) is set to 2.5 in our experiment. While the analysis reveals varying levels of neuron activation and contribution patterns for different features, the interpretability of these results remains limited. The relevance scores show complex distributions across neurons, but they do not provide clear insights into how specific neurons or groups of neurons contribute to the model's decision-making process. Looking at individual features, the MP1 and MP2 relevance distributions (Figure 6a,b) show some neurons with notably higher relevance scores, suggesting their potential importance in multipath detection.