# Towards Explainable Artificial Intelligence for GNSS Multipath LSTM Training Models
## 1 Introduction
[7] demonstrated the effectiveness of deep learning-based approaches for interference detection using time frequency analysis. Recent work by [PERSON] et al. [8] has established comprehensive frameworks for network-based GNSS interference monitoring, while [PERSON] et al. [9] have shown how transfer learning can enable real-time interference classification. In [10], [PERSON] and [PERSON] proposed a CNN-based method for GNSS jamming detection and classification. These developments in interference detection share common challenges with multipath mitigation, particularly in terms of real-time processing requirements and the need for reliable detection methods. Furthermore, [PERSON] et al. [11] highlighted the importance of feature extraction and interpretation in interference detection systems, emphasizing the growing need for explainable AI approaches in GNSS signal quality monitoring. Parallel to these developments in GNSS applications, the field of explainable artificial intelligence has gained increasing attention. While much of the early work in explainable AI focused on classification tasks, a distinct research field has emerged addressing the unique challenges of explaining regression models. In 2022, [PERSON] et al. [12] published a ground-breaking paper in the IEEE Signal Processing Journal, proposing methods to apply XAI principles to regression models, opening new possibilities for GNSS applications. In [13], the authors also provided a comprehensive overview of the XAI technique. Unlike classification problems where feature importance can be directly linked to discrete class decisions, regression problems require different approaches to interpret continuous output predictions. This distinction is particularly relevant for GNSS applications, where the primary task involves predicting continuous values for signal parameters and error estimates. The evolution of deep learning interpretability has seen various approaches. Layer-wise Relevance Propagation (LRP), introduced by [PERSON] et al. [14] in 2015, has emerged as a powerful technique for explaining neural network decisions. Recent work by [PERSON] et al. [15] has extended LRP to recurrent neural networks, including LSTM architectures, making it particularly relevant for time-series analysis in GNSS applications. In 2019, [PERSON] et al. [16] provided a detailed review of the LRP method. As deep learning and artificial intelligence systems become increasingly prevalent, concerns about their transparency and interpretability have grown significantly. These concerns include potential threats like negative side effects, reward hacking, scaling oversight, safe exploration, and robustness to distribution shifts [17]. The field of XAI for regression has developed several specialized approaches. Local Interpretable Model-agnostic Explanations (LIME) for regression, introduced by [PERSON] et al. [18], provides local approximations of complex models using interpretable linear models. However, these approximations often struggle with temporal dependencies, making them less suitable for time-series applications like GNSS signal processing. The second approach focuses on local perturbation analysis. This category includes gradient-based methods [19], which have a long history in deep learning interpretation. Sensitivity Analysis (SA) represents a prominent example of this approach [20; 21; 22], though it faces challenges such as gradient shattering and explanation discontinuities. Recent advancements by [PERSON] et al. [23] and [PERSON] et al. [24] have addressed these limitations through techniques like regional average gradients and specific path integration methods. Perturbation-based and optimization-based methods form another subset of this approach. [PERSON] and [PERSON] [25] demonstrated the effectiveness of masking input regions to test feature importance. Prediction Difference Analysis (PDA) [26] advanced this concept by employing conditional sampling within feature regions.