# Towards Explainable Artificial Intelligence for GNSS Multipath LSTM Training Models
## 2 Background
### Architecture Selection and Implementation  
The LSTM architecture used in this study was designed to balance model complexity with computational efficiency while maintaining robust performance for GNSS multipath detection. The network configuration was determined through a systematic evaluation process, considering both empirical testing and insights from the related literature in GNSS applications. The primary architecture consists of a single LSTM layer with 256 hidden units, followed by a dense output layer. This configuration was chosen after testing various architectures with hidden units ranging from 64 to 512. While deeper architectures with multiple LSTM layers were evaluated, the single-layer configuration with 256 units provided optimal performance without excessive computational overhead. The number of hidden units (256) proved sufficient to capture the temporal dependencies in GNSS signals while avoiding overfitting, as validated through our cross-validation experiments. The model processes sequences of length 60 (window size), chosen based on the temporal correlation characteristics of GNSS multipath effects. This window size represents approximately one minute of data at our sampling rate, providing sufficient context for the  
Figure 1: Standard architecture for an LSTM memory cell. model to learn relevant patterns while maintaining computational efficiency. The batch size of 32 was selected as a compromise between training stability and memory usage, following common practice in deep learning applications. The learning rate of 0.000025 was determined through a grid search over the range [\(1\times 10^{-6}\), \(1\times 10^{-2}\)]. This relatively small learning rate ensures stable convergence given the sensitivity of GNSS measurements. We employed the Adam optimizer with default beta parameters (\(\beta_{1}\) = 0.9, \(\beta_{2}\) = 0.999), as it demonstrated superior convergence characteristics compared to standard SGD in our preliminary experiments. The number of training epochs (500) was established through convergence analysis. Figure 2 shows the learning curves for both training and validation loss, indicating that the model typically converges around 400 epochs, with the additional 100 epochs ensuring stable optimization. The selected architecture was validated against several alternatives (Table 1). While larger models (512 units) showed marginally better validation MSE (\(2.83\times 10^{-3}\) vs. \(2.87\times 10^{-3}\)), they required significantly more computational resources and training time. The dual-layer configuration (256 units per layer) performed similarly to our chosen architecture but with increased complexity and training time. A dropout rate of 0.2 was implemented based on validation performance, providing regularization without significantly impacting model capacity. This value was selected after testing rates between 0.1 and 0.5, with 0.2 offering the best trade-off between regularization and model performance. The selected architecture requires approximately 312 MB of GPU memory during training, making it feasible to deploy on most modern hardware. The model contains 329,728 trainable parameters, which is relatively modest for deep learning applications while sufficient for our task. During inference, the model processes a single time step in approximately 2.3 ms on standard GPU hardware, making it suitable for real-time applications. This architecture represents a practical compromise between model complexity and performance, prioritizing robust performance and interpretability over marginal improvements in accuracy that might come from more complex configurations. The relatively simple architecture also facilitates the application of Layer-wise Relevance Propagation, as fewer layers reduce the complexity of relevance propagation paths. Figure 2: Training and validation loss curves over 500 epochs for the LSTM model.