On sensor configurations in a lettuce greenhouse via observability analysis using the empirical gramian

Estimating crop states accurately through combining measurements and a dynamical model in a data assimilation algorithm is a promising alternative for high tech crop sensing investments. In order to successfully do this, the employed model and chosen sensor configuration need to be observable. This paper demonstrates, in a lettuce greenhouse model, the applicability of an observability analysis that shows a large potential for soft sensing in a greenhouse where only a small subset of states is monitored. The analysis is done using the empirical gramian, which only requires simulation data. It is shown that measuring the indoor CO2 and humidity is in theory sufficient to estimate the lettuce’s biomass and the indoor carbon dioxide, temperature, and humidity through data assimilation assuming knowledge on the outdoor weather and control signal. The demonstrated method can be applied to any simulator that models a different application and can be used to find an optimal sensor configuration.