LS-Type Estimation for Time-Varying Parameters

Estimating the time-varying parameter ¿k^o, of linear model yk = ¿k^r¿k^o + vk is attracting many experts attension in the field of system identification and adaptive control. Guo[1990] established the convergence and stability properties of Kalman filter based parameter estimator for the model. Chen [1990] proved the consistency of LMS-type algorithm for estimating the parameter ¿k^o. However, there is still no result on the properties of LS- type estimator for the model. In this paper, we propose the concept of generalized consistency of algorithms for estimating time-varying parameter, thus construct a kind of least-square(LS) algorithm which has the property of generalized consistency under the condition of "conditional richness".