Abstract
In this paper we introduce a recursive subspace system identification algorithm for MIMO linear parameter varying systems driven by general inputs and a white noise time varying parameter vector. The new algorithm is based on a convergent sequence of linear deterministic-stochastic state-space approximations, thus considered a Picard based method. Such methods have proven to be convergent for the bilinear state-space system identification problem. The key to the proposed algorithm is the fact that the bilinear term between the time varying parameter vector and the state vector behaves like a white noise process. Using a linear Kalman filter model, the bilinear term can be efficiently estimated and then used to construct an augmented input vector at each iteration. Since the previous state is known at each iteration, the system becomes linear, which can be identified with a linear-deterministic subspace algorithm such as MOESP, N4SID, or CVA. Furthermore, the model parameters obtained with the new algorithm converge to those of a linear parameter varying model. Finally, the dimensions of the data matrices are comparable to those of a linear subspace algorithm, thus avoiding the curse of dimensionality. © 2007 EUCA.

Abstract

Abstract

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Abstract
The fast development of field, data processing equipment and software has allowed the use of geophysical methods to an ever increasing range of applications. Hence nowadays it is much easier to conduct massive field surveys combining different methods, to obtain more accurate and denser data, so that complex modeling and interpretation at limited costs can be carried out. Landfills have been targeted by geophysical methods in order to investigate their environmental impacts. In fact, landfills have been the classic way to deposit domestic and industrial waste and have generated a large range of negative environmental impacts in groundwater and soils. These problems often persist even after the effective use of the landfills and subsequent recovery processes. Owing to their characteristics, landfills are difficult to access and because of the general lack of accurate information regarding the shape, nature of the refuse, history and development of the landfill, non-invasive, nondestructive methods and sometimes autonomous data acquisition devices must be used to monitor impacts and to investigate and prevent groundwater and soil contamination. Geophysical methods can be applied to investigate a wide range of aspects related with the assessment of the environmental impact of landfills. Problems such as geometry definition, geological settings, contamination plume location and monitoring investigation of internal structure and refuse zoning, determination of fluid flow direction and paths or the determination of sealing conditions and leakage may be more successfully evaluated if a carefully chosen geophysical survey is part of any investigation program. Because of the nature and complexity of the problems to investigate, only multidisciplinary approaches, involving geophysics, hydrochemical, hydrogeological and geological information, can provide meaningful results for a thorough assessment of the landfills impact on the environment. This work intends to demonstrate the application of geophysical methods in the investigation of the environmental impacts, as described above, of industrial and domestic landfills during their life time and after closure. Thus, several examples will be discussed illustrating the use of 2D, 3D and time lapse resistivity, electromagnetic, ground probing radar, self-potential, magnetic, gravity surveys and airborne thermal mapping. Most of the geophysical data will be presented and shortly discussed together with information from boreholes, geology, hydrogeology and hydrochemical data. As it will be shown, it is clear that only a judicious combination of methods and information from different nature can provide tools for the diagnosis and assessment of the impact of landfills in the environment, for the investigation of the best engineering solutions to remediate them and for the possible recovery of refuse with economic interest.