System Identification Using Known Input-Output Data with Fading Memory Augmented Least Squares Algorithm

In this documentation, we utilize known input-output data and implement a fading memory augmented least squares identification software to determine the order of a known system and estimate its parameters. The software's correctness is demonstrated through comprehensive validation procedures. To achieve this objective, we must consider various scenarios and conditions, such as input and output precision, system stability, and data reliability. The algorithm implementation involves key components including a recursive parameter update mechanism that applies weighting factors to prioritize recent data (fading memory feature), and an augmented approach that handles both system parameters and noise characteristics simultaneously. Through in-depth analysis and discussion of these factors, we can further refine and optimize our software to ensure its accuracy and reliability. The implementation typically includes functions for data preprocessing, covariance matrix initialization, and recursive parameter estimation with forgetting factor adjustment. Therefore, this process requires continuous experimentation and testing to improve and optimize our algorithms and techniques, including validation against known system models and sensitivity analysis under different noise conditions.