  Fertilization is commonly used to increase harvests. The lack of knowledge of
soil properties and the excessive use of fertilizers can result in
overfertilization. Current sensor technology is able to measure the
concentrations of some of the involved substances only at selected locations
and depths. Point measurements of adjacent sensors in coarse sensor networks
can be used to infer upon the state of nitrate concentrations in the sensor
surroundings. For this purpose, a high gain observer is proposed. Models of the
nitrification process as well as the measurement dynamics for the observer
design are derived and discretized on a grid to obtain a system of ordinary
differential equations. It is shown that the nonlinearities of the model can be
bounded and how the observer gain can be computed via linear matrix
inequalities. Furthermore, a model reduction is proposed, which allows the
consideration of more grid points. A simulation study demonstrates the proposed
approach.
