J D Stigter and M B Beck
Warnell School of Forest Resources, University of Georgia, Athens, Georgia 30602-2152, USA
Abstract
Most models of environmental systems are based on sets of differential equations. The paper investigates the problem of identifying the number and form of appropriately parameterized terms in such continuous-time state-space models, a problem referred to as model structure identification. Filtering theory (recursive estimation) is used as an approach to the solution of this problem. Central to this approach is the notion that the patterns of the (posterior) trajectories of the model's parameters, when contrasted with the prior assumptions about their expected variability, will yield insights into the adequacy, or otherwise, of a candidate model's structure. The particular algorithm employed herein is based upon an analysis of Ljung (1979), who proposed a significant modification of the conventional extended Kalman filter wherein the elements of the Kalman gain matrix may be estimated directly as unknown parameters of an innovations process representation of the system's behaviour. Whereas Ljung's filter was designed for an entirely discrete-time system, the present version of the filter has been derived for a system with continuous-time dynamics and discrete-time observations. Using time series data from the River Cam, the paper presents a case study in identifying a sequence of three candidate model structures for describing the assimilation and generation of easily degradable organic matter. The trajectories of recursive estimates for the elements of the gain matrix provide informative insights into, and better defined evidence of, the failure of an inadequate model structure.
Environmetrics, 5, pp. 315-333 (1994).