The problem of state/parameter estimation represents a key issue in crop models, which are nonlinear, non-Gaussian, and include a large number of parameters. The prediction errors are often important due to uncertainties in the equations, the input variables, and the parameters. The measurements needed to run the model and to perform calibration and validation are sometimes not numerous or known with some uncertainty. In these cases, estimating the state variables and/or parameters from easily obtained measurements can be extremely useful. In this chapter, the authors address the problem of modeling and prediction of time-varying Leaf area index and Soil Moisture (LSM) to better handle nonlinear and non-Gaussian processes without a priori state information. The performances of various conventional and state-of-the-art estimation techniques are compared when they are utilized to achieve this objective. These techniques include the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF), and the more recently developed technique Variational Bayesian Filter (VF). The original data was issued from experiments carried out on silty soil in Belgium with a wheat crop during two consecutive years, the seasons 2008-09 and 2009-10.
Unscented Kalman filter for time varying spectral analysis of earthquake ground motions
