Novel LLM Algorithms for Time Series Signal Processing

Large language models (LLM) have recently demonstrated remarkable capabilities in sequence modeling tasks, particularly in human speech and text. This research investigates whether similar principles can be applied to the domain of time series signal processing, especially under nonlinear and non-Gaussian conditions. A novel signal estimation framework has been developed based on a Transformer architecture, in which multi-dimensional time series inputs are treated as structured sequential data, enabling the modeling of both temporal dependencies and inter-channel correlations through self-attention mechanisms. Unlike traditional filtering approaches that rely on system equations or linear assumptions, the proposed model operates without explicit knowledge of the underlying dynamics. The estimation process is formulated as a denoising task, where the model learns to recover clean signals from noisy observations through a combination of attention-based encoding and confidence-weighted fusion. Each time step is predicted multiple times via a sliding window mechanism, and these overlapping predictions are aggregated using learned confidence scores, allowing the model to assign lower weight to unreliable outputs near signal boundaries or under high noise. To evaluate the framework, experiments have been conducted using synthetically generated three dimensional time series signals governed by nonlinear dynamics and subject to heavy-tailed, non-Gaussian noise distributions. The proposed method has been compared against a classical extended Kalman filter (EKF), which assumes local linearity and Gaussian noise. The LLM-based model is evaluated by multiple quantitative metrics which includes mean squared error (MSE), mean absolute error (MAE), signal-to-noise ratio (SNR), and frequency-domain error, and the results represent the novel model consistently outperforms the EKF by a wide margin. Visual analysis of residual distributions and reconstructed signals further confirms the model’s ability to preserve signal structure while suppressing irregular noise components. This study demonstrates that language-inspired modeling techniques can be effectively transferred to the domain of physical signal estimation. By treating time series as structured sequences and leveraging Transformer architectures, it becomes possible to handle highly nonlinear and noisy systems without relying on handcrafted models or tuning procedures. The framework introduced here lays the groundwork for future research in interpretable, modular, and multimodal time series modeling.