Convergence of continuous time stochastic ELS parameter estimation

This paper presents continuous-time adaptive estimation schemes associated with a class of finite dimensional, time invariant, linear stochastic signal models. A global convergence theory is given for such schemes under a coloured noise/prefiller positive real condition, which may be side-stepped for moving average models. Attention is first focused on extended least squares (ELS) identification of stable signal models driven by bounded inputs. A particular feature is that weighting is introduced into the ELS scheme according to a stability measure. This weighting selection ensures that there is almost surely no finite escape time, and also there is improved transient performance in the presence of ill-conditioning. Next, some convergence results for least squares (LS) estimation of unstable signal models are extracted from the earlier theory. The ELS and LS theory suggests construction of identification schemes based on both ELS and LS. Analysis results for such are studied. The results apply within the indirect adaptive control context under reasonable controller design constraints, although details are not included in this paper.