Enhanced quaternion recursive least squares: adaptive prediction in stationary and non-stationary environments

Quaternion adaptive filters provide an effective framework for multidimensional signal processing by effectively modeling four-dimensional signals with improved convergence and robustness, making them suitable for multidimensional applications like 3D motion tracking and wind dynamics. This paper proposes an Enhanced Quaternion Recursive Least Squares (Enhanced QRLS) algorithm to further improve performance in both stationary and non-stationary environments. The method incorporates adaptive forgetting factors, dynamic learning rates, enhanced numerical stability, and momentum-based weight updates with smoothing. Experiments with real-world datasets show that Enhanced QRLS achieves lower Mean Squared Error (MSE) and Mean Squared Deviation (MSD) compared to traditional QRLS and QLMS, excelling in predicting wind speed, direction, and chaotic time series. The algorithm demonstrates faster convergence, reduced oscillations, and superior adaptability, demonstrating its effectiveness for quaternion-based adaptive filtering tasks.