# Towards Explainable Artificial Intelligence for GNSS Multipath LSTM Training Models
## 1 Introduction
Meaningful Perturbation [27; 28] and Activation Maximum [29] represent further developments in this direction, though their optimization requirements increase computational complexity. The third major approach involves a propagation-based explanation, with LRP emerging as a leading technique. [PERSON] et al. [14] and [PERSON] et al. [16] introduced LRP, which integrates explanation processes with model structure and has demonstrated effectiveness across various architectures, including deep neural networks, LSTMs [30], and Fisher vector classifiers [31]. Recent work has extended LRP's application to anomaly detection through neuralization [32; 33; 34]. LRP has evolved to include several variants. The Basic Rule (LRP-0) provides proportional relevance distribution based on neuron weights. The Epsilon Rule (LRP-\(\epsilon\)) introduces numerical stability for handling small or contradictory contributions. The Gamma Rule (LRP-\(\gamma\)) offers enhanced control over positive and negative contributions, with parallels to other techniques like DeepLIFT [35] and Top-down neural attention [36]. Recent research has particularly focused on applying these explainability techniques to regression problems, an area that has received less attention compared to classification tasks [12]. This evolution in explainable AI research reflects a growing recognition of the importance of understanding AI decision-making processes, particularly in critical applications where transparency and accountability are essential. The literature reveals a clear trend toward integrating explainability directly into model architectures rather than treating it as a post-hoc analysis. This integration allows for more robust and reliable interpretations while potentially improving model performance through better understanding of internal decision mechanisms. Recent advances have specifically addressed time-series regression problems. [PERSON] et al. [37] demonstrated the application of Layer-wise Relevance Propagation to LSTM-based regression models in predictive maintenance, showing how relevance scores can be meaningfully interpreted for continuous predictions. Building on this work, [PERSON] et al. [32] developed techniques for explaining anomalies in regression outputs, particularly relevant for our investigation of GNSS signal anomalies. In the context of GNSS security and reliability, [PERSON] et al. [38] in the study of pattern detection, demonstrate how explainable AI can enhance the robustness of deep learning models in critical applications. As the reliance on AI-driven systems increases in critical applications such as autonomous navigation and precision timing, there is a growing need for explainable artificial intelligence (XAI) in the field of GNSS. XAI aims to make the decisions and predictions of AI models more transparent and interpretable to humans, which is crucial for ensuring the reliability, safety, and trustworthiness of these systems. This study focuses on developing explainable AI techniques for LSTM-based GNSS multipath models. By incorporating LRP and other interpretability methods, we aim to provide insights into how these models process GNSS data and make predictions about multipath effects. This research not only contributes to the advancement of GNSS technology but also addresses the broader challenge of making complex AI systems more understandable and accountable. The objectives of this study are to:  
1. Implement an LSTM-based model for GNSS multipath prediction. 2. Apply LRP and other XAI techniques to interpret the model's decision-making process. 3. Analyze the relevance of different input features in multipath prediction. 4. Evaluate the model's behavior under normal and anomalous conditions. 5. Discuss the implications of explainable AI for improving GNSS reliability and integrity. By achieving these objectives, this research aims to bridge the gap between the high performance of deep learning models and the need for transparency in critical GNSS applications.