Recursive Least Squares (RLS) and Related Algorithms Implementation

In my research work, I have developed MATLAB implementations of three fundamental recursive parameter estimation algorithms: RLS (Recursive Least Squares), extended RLS with recursive augmentation, and RIV (Recursive Instrumental Variable) method. All implementations are initially configured for 2nd-order systems but can be easily adapted to different orders through parameter modification. The RLS algorithm implementation features a recursive covariance matrix update with forgetting factor for tracking time-varying parameters. The extended RLS version incorporates augmented data vectors for handling correlated noise conditions. The RIV algorithm employs instrumental variables to achieve consistent estimates under noisy measurement scenarios. These MATLAB programs effectively process research data and provide reliable parameter estimation results. During development, significant effort was devoted to ensuring algorithmic accuracy and computational efficiency through proper initialization of covariance matrices and optimal forgetting factor selection. The code structure includes modular functions for parameter update, covariance matrix recursion, and residual calculation. Collaborative discussions with colleagues ensured these implementations adhere to industry standards and maintain compatibility across various application scenarios. These algorithms constitute a crucial component of my research framework, and continuous improvements are being made to enhance their robustness and applicability for advanced system identification tasks.