Long-run on-line identification with hybrid regularized exponential forgetting method

The paper compares three on-line identification methods with forgetting of unnecessary data: regularized exponential forgetting (REF), regularized exponential forgetting with alternative covariance matrix (REFACM) and the newly created hybrid regularized exponential forgetting with alternative covariance matrix (HREFACM), which is composed of the first two and uses their benefits. Their quality and ability to track time varying parameters of dynamic systems in terms of long-run operation is analyzed by the comparison of integral sum of the Euclidean norm of the deviation of the parameters or outputs (IS), and integral sum of prediction error count (PE). In previous tests of long-run operation of time variant dynamic systems the REF algorithm showed his advantages during short simulations and REFACM proved its quality in long simulations. All three algorithms are tested by benchmark simulations in the Matlab - Simulink software environment, where the resulting IS and PE values are monitored and then compared to each other.