Performance of extended and unscented Kalman filters for state and parameter estimation of a greenhouse climate model

Abstract

In dynamic modeling of the greenhouse climate, prediction errors are a significant issue due to uncertainties in initial state values, input variables, model parameters and model structure, all propagating in time in a nonlinear way. We investigated a data assimilation approach using two non-linear Kalman filters in light of prediction uncertainty. An extended (EKF) and an unscented (UKF) Kalman filters were designed to estimate climate states, and also both the states and model parameters. The states to be estimated were air temperature, absolute humidity and carbon dioxide concentration inside a greenhouse. Year round measurements from a Dutch greenhouse with a rose crop were used. The dynamic model was first calibrated manually by estimating ten of its parameters. Uncertainties of the measurements needed for designing EKF and UKF were specified via literature sources whereas the uncertainties related to the process were tuned. Both filters increased the model predictive power several orders of magnitude with respect to mean squared error (MSE) statistics and one order of magnitude with respect to mean absolute error (MAE) analyzed during autumn-winter and spring-summer seasons when only the model states were estimated. However, no improvement on the one step ahead state predictions were achieved when both states and model parameters were estimated by both nonlinear filters. Results showed that data assimilation based on nonlinear Kalman filters is advantageous over data assimilation that uses only model calibration. Therefore, improved model of the greenhouse climate by data assimilation can be used in controlling and optimizing more efficiently the greenhouse system.