Abstract-We propose a generalization of the matched subspace filters for the detection of unknown signals in a background of non-Gaussian and non-independent noise. The generalization is based on a modification of the Rao test by including a linear transformation derived from Independent Component Analysis (ICA). Receiver Operating Characteristic (ROC) curves computed for simulated examples illustrate the significant improvement achieved with the generalized solution.Index Terms-Rao test, matched subspace filter, non-Gaussian noise, ICA.
Parameter identification is an essential step in constructing a groundwater model. The process of recognizing model parameter values by conditioning on observed data of the state variable is referred to as the inverse problem. A series of inverse methods has been proposed to solve the inverse problem, ranging from trialand-error manual calibration to the current complex automatic data assimilation algorithms. This paper does not attempt to be another overview paper on inverse models, but rather to analyze and track the evolution of the inverse methods over the last decades, mostly within the realm of hydrogeology, revealing their transformation, motivation and recent trends. Issues confronted by the inverse problem, such as dealing with multiGaussianity and whether or not to preserve the prior statistics are discussed.
Real-time data from on-line sensors offer the possibility to update environmental simulation models in realtime. Information from on-line sensors concerning contaminant concentrations in groundwater allow for the real-time characterization and control of a contaminant plume. In this paper it is proposed to use the CPU-efficient Ensemble Kalman Filter (EnKF) method, a data assimilation algorithm, for jointly updating the flow and transport parameters (hydraulic conductivity and porosity) and state variables (piezometric head and concentration) of a groundwater flow and contaminant transport problem. A synthetic experiment is used to demonstrate the capability of the EnKF to estimate hydraulic conductivity and porosity by assimilating dynamic head and multiple concentration data in a transient flow and transport model. In this work the worth of hydraulic conductivity, porosity, piezometric head, and concentration data is analyzed in the context of aquifer characterization and prediction uncertainty reduction. The results indicate that the characterization of the hydraulic conductivity and porosity fields is continuously improved as more data are assimilated. Also, groundwater flow and mass transport predictions are improved as more and different types of data are assimilated. The beneficial impact of accounting for multiple concentration data is patent.
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