System Identification, Estimation, and Forecasting of Water Quality - Part I: Theory

Beck, M.B. (1979). System Identification, Estimation, and Forecasting of Water Quality - Part I: Theory. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-79-031

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Abstract

This paper presents some background theory for algorithms of system identification, estimation, and forecasting. Special attention is given to the application of these algorithms in the field of water quality modeling.

The paper starts with some qualitative definitions of the problems to be addressed, for example, problems of model structure identification, parameter estimation, state estimation, state reconstruction, and combined state-parameter estimation. The central theme of the paper, however, is the idea of an on-line, or recursive estimation algorithm. In particular a derivation of the linear Kalman filter is given; this is achieved by extending the principle of linear least squares regression analysis. Having derived the filtering algorithms, which refer to the problem of state estimation, the paper turns to the subject of recursive parameter estimation algorithms in the context of conventional time-series analysis. Finally, the algorithms of an extended Kalman filter are developed in order to treat the problem of combined state-parameter estimation.

The primary objective of the paper is to present the methods of system identification, estimation, and forecasting in a fashion which will be understandable for those more familiar with the subject of water quality modeling.

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