Applying an Improved Square Root Unscented Kalman Filtering in Tomographic Projections of Agricultural Soil Samples

Abstract

Agricultural soil tomography aims at investigating soil proprieties as water and solute transport, soil porosity, soil contents, root growing and humidity. For a better analysis about these proprieties, an image quality is required. The enhancement of tomographic images can be reached by the use of filters in their projections (signals) with the objective to reach a better signal/noise relation. Previous works focused on image filtering or in the use of filters specialized in Gaussian process estimation. These techniques not presented significant improvement in signal to noise relation and additionally have showed losses in image details. These projections have different types of noises affecting the image quality directly and omitting important details that can be recognized as if they were noise or fake details caused by noises. This paper presents formulations for the use of unscented Kalman filter with neural networks in a dual estimation filtering: a filter for state estimation and a filter for weight estimation with the objective of obtaining better quality in the signal / noise relation of tomographic projections. Besides the filter uses nonlinear functions, the square root technique also improves the performance and numerical stability compared with the basic unscented Kalman Filter. The use of neural network applied to the square-root unscented Kalman filter showed significant results, as high ISNR values together with an image where details are kept.