Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, September 2004. / Thesis Advisor(s): Xiaoping Yun. Includes bibliographical references (p. 59-60). Also available online.

Dissertation (PhD)--University of Stellenbosch, 2006. / Bibliography. Also available via the Internet.

Thesis (MSc)--University of Stellenbosch, 2006. / Bibliography. Also available via the Internet.

Thesis (M.S.) University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (June 26, 2007) Includes bibliographical references.

Bernard C. Levy. / Bibliography: leaves 16-17. / "March 1984" / "ECS-83-12921" "AFOSR-82-0135A"

Ahmed H. Tewfik, Bernard C. Levy, Alan S. Willsky. / Bibliography: leaf 21. / "March 1985." / "...supported in part by the National Science Foundation under Grant ECS-83-12921" "...supported... in part by the Army Research Office under Grant No. DAAG-29-84-K-0005."

Mobile devices with wireless networking capabilities are used in a wide range of environments. Geolocation information increases the value of the data generated by a device and is vital in the development of a wide range of applications from autonomous vehicles to the Internet of things. Systems that generate signals specifically for geolocation have become widely adopted but, due to fundamental constraints, lack coverage and accuracy in complex urban and indoor environments. In addition to this, the reliance on a single signal source is not desirable in many applications that value the integrity of the geolocation estimate. A direction of research aiming to improve geolocation in indoor and urban environments measures signals of opportunity in order to generate a more robust estimate. While this approach improves signal availability, the unpredictable nature of these variable and uncontrolled signals leads to poor geolocation estimates, which are typically not suitable for use in many applications. This project aims to improve on the accuracy, resilience and integrity of a geolocation estimate obtained from signal of opportunity measurements in indoor and urban environments while reducing hardware requirements. This has been achieved by efficiently coupling signals of opportunity within the radio environment with other system signals, such as those from an inertial measurement unit. Research has been carried out to optimise the coupling of these data sources resulting in techniques to allow the identification and removal of key error drivers from both the radio environment and other system sensors. This thesis proposes a specifically designed extended Kalman filter to improve on the signal coupling. The filter aims to optimise the accuracy of radio environment measurements while also providing the ability to identify signal error sources in urban and indoor environments, leading to both greater accuracy and resilience of the geo-location estimate. Further, the proposed extended Kalman filter may use the radio environment as a source of geolocation data. The ability of the filter to recognise and mitigate leading radio environment error sources such as multipath and interference allowed the design of filters to obtain detailed and accurate signal strength and time of arrival information. The thesis also presents a thorough set of simulation and modelling experiments to investigate and optimise the efficiency of the proposed solutions in a range of environments. Validation testing confirmed that in the urban and indoor environments, the average error of geo-location estimates has been reduced from 10 m to 3 m without improvement to the hardware surrounding infrastructure. The improvements presented in this thesis allow networked devices to improve the value of their data by incorporating the context that comes from increased geolocation accuracy and resilience. In turn, this allows the development of a wide range of new location based applications for mobile devises in indoor and urban environments.

In this thesis, we have investigated several computational methods on data assimilation for air quality prediction, especially on the characteristic of sparse matrix and the underlying information of gradient in the concentration of pollutant species. In the first part, we have studied the ensemble Kalman filter (EnKF) for chemical species simulation in air quality forecast data assimilation. The main contribution of this paper is to study the sparse data observations and make use of the matrix structure of the Kalman filter updated equations to design an algorithm to compute the analysis of chemical species in the air quality forecast system efficiently. The proposed method can also handle the combined observations from multiple species together. We have applied the proposed method and tested its performance for real air quality data assimilation. Numerical examples have demonstrated the efficiency of the proposed computational method for Kalman filter update, and the effectiveness of the proposed method for NO2, NO, CO, SO2, O3, PM2.5 and PM10 in air quality data assimilation. Within the third part, we have set up an automatic workflow to connect the management system of the chemical transport model - CMAQ with our proposed data assimilation methods. The setup has successfully integrated the data assimilation into the management system and shown that the accuracy of the prediction has risen to a new level. This technique has transformed the system into a real-time and high-precision system. When the new observations are available, the predictions can then be estimated almost instantaneously. Then the agencies are able to make the decisions and respond to the situations immediately. In this way, citizens are able to protect themselves effectively. Meanwhile, it allows the mathematical algorithm to be industrialized implying that the improvements on data assimilation have directly positive effects on the developments of the environment, the human health and the society. Therefore, this has become an inspiring indication to encourage us to study, achieve and even devote more research into this promising method.

The Kalman Filter has been applied to many fields of hydrology, particularly in the area of flood forecasting. This recursive estimation technique is based on a state-space approach which combines model description of a process with data information, and accounts for uncertainties in a hydrologic system. This thesis deals with applications of the Kalman Filter to ARMAX models in the context of streamflow prediction. Implementation of the Kalman Filter requires specification of the noise covariances (Q, R) and initial conditions of the state vector (x₀, P₀). Difficulties arise in streamflow applications because these quantities are often not known. Forecasting performance of the Kalman Filter is examined using synthetic flow data, generated with chosen values for the initial state vector and the noise covariances. An ARMAX model is cast into state-space form with the coefficients as the state vector. Sensitivity of the flow forecasts to specification of x₀, P₀, Q, R, (which may be different from the generation values) is examined. The filter's forecasting performance is mainly affected by the combined specification of Q and R. When both noise covariances are unknown, they should be specified relatively large in order to achieve a reasonable forecasting performance. Specififying Q too small and R too large should be avoided as it results in poor flow forecasts. The filter's performance is also examined using actual flow data from a large river, whose behavior changes slowly with time. Three simple ARMAX models are used for this investigation. Although there are different ways of writing the ARMAX model in state-space form, it is found that the best forecasting scheme is to model the ARMAX coefficients as the state vector. Under this formulation, the Kalman Filter is used to give recursive estimates of the coefficients. Hence flow predictions can be revised at each time step with the latest state estimate. This formulation also has the feature that initial values of the ARMAX coefficients need not be known accurately. The noise variances of each of the three models are estimated by the method of maximum likelihood, whereby the likelihood function is evaluated in terms of the innovations. Analyses of flow data for the stations considered in this thesis, indicate that the variance of the measurement error is proportional to the square of the flow. In practice, flow predictions several time steps in advance are often required. For autoregressive processes, this involves unknown elements in the system matrix H of the Kalman model. The Kalman algorithm underestimates the variance of the forecast error if H and x are both unknown. For the AR(1) model, a general expression for the mean square error of the forecast is developed. It is shown that the formula reduces to the Kalman equation for the case where the system matrix is known. The importance of this formula is realized in forecasting situations where management decisions depend on the reliability of flow predictions, reflected by their mean square errors. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Understanding the geology and the hydrology of the subsurface is important to model the fluid flow and the behavior of the contaminant. It is essential to have an accurate knowledge of the movement of the contaminants in the porous media in order to track them and later extract them from the aquifer. A two-dimensional flow model is studied and then applied on a linear contaminant transport model in the same porous medium. Because of possible different sources of uncertainties, the deterministic model by itself cannot give exact estimations for the future contaminant state. Incorporating observations in the model can guide it to the true state. This is usually done using the Kalman filter (KF) when the system is linear and the extended Kalman filter (EKF) when the system is nonlinear. To overcome the high computational cost required by the KF, we use the singular evolutive Kalman filter (SEKF) and the singular evolutive extended Kalman filter (SEEKF) approximations of the KF operating with low-rank covariance matrices. The SEKF can be implemented on large dimensional contaminant problems while the usage of the KF is not possible. Experimental results show that with perfect and imperfect models, the low rank filters can provide as much accurate estimates as the full KF but at much less computational cost. Localization can help the filter analysis as long as there are enough neighborhood data to the point being analyzed. Estimating the permeabilities of the aquifer is successfully tackled using both the EKF and the SEEKF.