Parameter Identification Using Recursive Least Squares with Forgetting Factor

In dynamically changing systems, traditional parameter identification methods often fail to track parameter variations promptly. The recursive least squares (RLS) method with forgetting factor introduces enhanced flexibility to adapt to time-varying system characteristics by gradually reducing the influence of historical data.

The forgetting factor mechanism systematically diminishes the impact of older data on current parameter estimates, enabling the algorithm to respond more rapidly to recent system changes. The core RLS algorithm provides online parameter updating by continuously incorporating new observation data to refine estimates, while the forgetting factor further optimizes this process. In code implementation, this typically involves modifying the covariance matrix update equation: P(k) = (P(k-1) - K(k)*phi(k)'*P(k-1))/lambda, where lambda represents the forgetting factor ranging between 0 and 1.

Selection of the forgetting factor is critical in practical applications: excessively large values may cause oversensitivity to measurement noise, while too small values can result in sluggish parameter adaptation. An optimal forgetting factor achieves balanced performance between tracking capability and noise immunity. Algorithm implementation often requires tuning this parameter through simulation studies or experimental validation.

This method proves particularly valuable in real-time monitoring and control scenarios such as adaptive filtering, system identification, and dynamic process control. The implementation typically involves initializing parameter vectors and covariance matrices, then recursively updating them with new data samples while applying the forgetting factor to maintain system responsiveness. This approach significantly enhances parameter identification accuracy and adaptability in evolving systems.