Gauss, Kalman and advances in recursive parameter estimation

Abstract

The paper considers how the Kalman filter has influenced the development of recursive parameter estimation since the publication of Rudolf Kalman's seminal article in 1960. It will present a partial review of developments over the past half century and provide a tutorial introduction to the refined instrumental variable approach to the optimal recursive estimation of parameters in both discrete and continuous-time transfer function models. The paper concludes with a case study that shows how recursive parameter estimation and the Kalman filter can be combined in the design and development of a real-time adaptive forecasting and data assimilation system for flow in river systems.