Information Fusion using the Kalman Filter based on Karhunen-Loève Decomposition

Properties of porous media, such as hydraulic conductivity and porosity, are intrinsically deterministic. However, due to the high cost associated with direct measurements, these properties are usually measured only at a limited number of locations. The number of direct measurements is definitely not enough to infer the true parameter fields. This problem is further complicated by the fact that medium properties exhibit a high degree of spatial heterogeneity. This combination of significant spatial heterogeneity and a relatively small number of direct observations leads to uncertainty in characterizing medium properties, which in turn results in uncertainty in estimating or predicting the corresponding system responses (such as hydraulic head). Fortunately, it is relatively easy to measure the system responses, which can be used to infer medium properties. With newly developed measurement techniques such as remote sensing and in-situ permanent sensors, more observations on system responses become available.