Recursive Least Squares Algorithm Implementation

In this project, I implemented the Recursive Least Squares (RLS) algorithm using MATLAB programming language. The RLS algorithm is an efficient method for handling linear regression problems, which continuously updates parameter estimates through iterative computations to find optimal solutions. The implementation includes key mathematical components: initialization of the covariance matrix P, calculation of the gain vector K, parameter update using weight vector θ, and covariance matrix recursion. The algorithm efficiently processes streaming data by updating estimates with each new observation without requiring batch processing of the entire dataset.

The project incorporates an Excel dataset in XLS format for runtime execution. This dataset contains diverse data types including numerical values, text entries, and date information, all of which undergo proper data cleaning and transformation processes. The MATLAB implementation uses xlsread() function for data import, followed by data preprocessing steps such as handling missing values, normalizing numerical data, and converting categorical variables. These preprocessing steps ensure program correctness and computational accuracy.

The core algorithm implementation utilizes MATLAB's matrix operations for efficient computation, featuring functions like inv() for matrix inversion and element-wise operations for real-time parameter updates. Through this implementation, I gained deeper understanding of the RLS algorithm's theoretical foundations, including convergence properties and computational efficiency. The practical application demonstrated improved results in adaptive filtering and system identification scenarios, showcasing the algorithm's capability to handle time-varying systems and non-stationary environments effectively.