Enhanced Kalman gain in RLS algorithm for identification accuracy with low excitation and heavy noise

Abstract : Within the context of linear system identification, when harsh conditions might be involved such as low system excitation and high power noise on measured data, the conventional recursive least squares (RLS) algorithm encounters difficulties to converge properly at steady-state. We show with numerical experiments that an adequate adaptive magnification of the Kalman gain vector enables a better accuracy by reducing the estimation bias and divided by a factor of 1.5 at least the steady-state mean squared error on the estimated parameters compared to conventional RLS and to other techniques involving modifications on the Kalman gain. From a theoretical point of view the proposed approach enhances a previously existing technique while adding reasonable computational complexity making our approach still valuable for a real-time implementation. In addition we found formally a condition to apply on the Kalman gain magnifying factor so as to guarantee the inverse covariance matrix to always remain positive definite.