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Some sequential Monte Carlo techniques for Data Assimilation in a plant growth model
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International audience. Data assimilation techniques have received considerable attention due to their capability to improve prediction and the most important applications concern weather forecasting and hydrology. Among many competing data assimilation approaches, those based on sequential Monte Carlo (SMC) methods, known as "particle filters", have gained their popularity because they are adaptive to nonlinearity and non-Gaussianity. In this study we test the performance of three SMC methods to predict biomass production and allocation in a dynamically evolving plant-growth model that can be formalized as a nonlinear state space model. The first method concerns a post-regularized particle filter which uses a mixture of Gaussian kernels (or more generally a kernel based method) to avoid sample impoverishment in the resampling step, the second and the third method involves the unscented Kalman filter (UKF) and the ensemble Kalman filter (EnKF) which are the extensions of classic Kalman filter invented for nonlinear systems. All the three approximate Bayesian estimation techniques deal simultaneously in their state vector fixed model parameters and state variables. We show that these methods perform well in realistic scenarios with sparse observations and discuss their limitations. Outside the context of data assimilation, we also present a maximum likelihood approach based on a stochastic version of an EM (Expectation-Maximization) algorithm, where the E-step can be approximated by the aforementioned SMC methods and discuss the pros and cons of the resulting algorithm. The performance of our methods is illustrated on data from the sugar-beet.
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