Bayesian Sigmoid-Type Time Series Forecasting with Missing Data for Greenhouse Crops

Abstract

This paper follows an integrated approach of Internet of Things based sensing and machine learning for crop growth prediction in agriculture. A Dynamic Bayesian Network (DBN) relates crop growth associated measurement data to environmental control data via hidden states. The measurement data, having (non-linear) sigmoid-type dynamics, are instances of the two classes observed and missing, respectively. Considering that the time series of the logistic sigmoid function is the solution to a reciprocal linear dynamic model, the exact expectation-maximization algorithm can be applied to infer the hidden states and to learn the parameters of the model. At iterative convergence, the parameter estimates are then used to derive a predictor of the measurement data several days ahead. To evaluate the performance of the proposed DBN, we followed three cultivation cycles of micro-tomatoes (MicroTom) in a mini-greenhouse. The environmental parameters were temperature, converted into Growing Degree Days (GDD), and the solar irradiance, both at a daily granularity. The measurement data were Leaf Area Index (LAI) and Evapotranspiration (ET). Although measurement data were only available scarcely, it turned out that high quality measurement data predictions were possible up to three weeks ahead.