# Towards Explainable Artificial Intelligence for GNSS Multipath LSTM Training Models
## 2 Background
### Deep Learning for Time Series Analysis  
Our choice of RNNs with LSTM cells for this study is driven by several key considerations, particularly the balance between model capability and explainability. While more recent architectures such as Gated Recurrent Units (GRU), Minimal Gated Units (MGU), and Transformers have demonstrated superior performance in various sequence modeling tasks [6], LSTM cells offer distinct advantages for our specific investigation into explainable AI for GNSS applications. First, LSTM cells are particularly well suited for capturing the temporal dependencies inherent in GNSS multipath effects. The cell's memory mechanism can maintain relevant information over extended sequences, which is crucial for tracking gradual changes in multipath patterns. While Transformer architectures excel at modeling long-range dependencies through self-attention mechanisms, their complexity poses additional challenges for interpretation and real-time implementation in GNSS systems. Second, the established theoretical framework for Layer-wise Relevance Propagation (LRP) with LSTM cells provides a solid foundation for our explainability investigation. The well-understood gating mechanisms in LSTM cells allow for the clearer interpretation of how the model processes temporal information, making it easier to attribute relevance scores to specific features and time steps. More recent architectures, while potentially offering better performance, lack the same level of theoretical development in terms of explainability techniques. Third, practical considerations for GNSS applications influenced our choice. LSTM cells offer a good balance between computational efficiency and model capability, making them suitable for potential real-time implementation in GNSS receivers. Additionally, their simpler architecture compared to Transformers facilitates easier deployment on embedded systems with limited computational resources. Alternative architectures such as Convolutional Neural Networks (CNNs) were also considered, as they could potentially capture spatial patterns in GNSS signals. However, our focus on temporal dependencies and the sequential nature of multipath effects made RNNs with LSTM cells a more appropriate choice. Future work could explore hybrid architectures combining CNNs for spatial feature extraction with recurrent cells for temporal pattern recognition. It is worth noting that while architectures like GRU might offer similar capabilities with fewer parameters, and Transformers might provide better performance on certain tasks, our primary goal was to investigate model explainability rather than maximizing prediction accuracy. The LSTM cell's well-understood architecture and established explainability techniques made it an ideal candidate for developing and demonstrating interpretable AI methods for GNSS applications. LSTM-based RNN, first introduced by [PERSON] (1997) in 1997, represents a specialized form of recurrent neural networks designed to address the vanishing gradient problem in traditional RNNs. In 2024, [PERSON] et al. [PERSON] et al. (2024) provided a state-of-the-art review of the LSTM and its future trend. The LSTM architecture incorporates sophisticated gating mechanisms that allow it to learn long-term dependencies in sequential data effectively. The standard architecture of an LSTM memory cell is illustrated in Figure 1, showing the key components including the memory cell state, forget gate, input gate, and output gate. This architecture enables the network to effectively learn and maintain relevant information over time. Each gate serves a specific purpose in controlling information flow through the network. The key equations governing LSTM cell operation are:  
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