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In order to account for spatial correlation in residuals in regression models for areal and lattice data, different disciplines have developed distinct approaches. Bayesian spatial statistics typically has used a Gaussian conditional autoregressive (CAR) prior on random effects, while geographers utilize Moran's I statistic as a measure of spatial autocorrelation and the basis for creating spatial models. Recent work in both fields has recognized and built on a common feature of the two approaches, specifically the implicit or explicit incorporation into the linear predictor of eigenvectors of a matrix representing the spatial neighborhood structure. The inclusion of appropriate choices of these vectors effectively reduces the spatial autocorrelation found in the residuals. We begin with extensive simulation studies to compare Bayesian CAR models, Restricted Spatial Regression (RSR), Bayesian Spatial Filtering (BSF), and Eigenvector Spatial Filtering (ESF) with respect to estimation of fixed-effect coefficients, prediction, and reduction of residual spatial autocorrelation. The latter three models incorporate the neighborhood structure of the data through the eigenvectors of a Moran operator. We propose an alternative selection algorithm for all candidate predictors that avoids the ad hoc approach of RSR and selects on both model fit and reduction of autocorrelation in the residuals. The algorithm depends on the marginal posterior density a quantity that measures what proportion of the total variance can be explained by the measurement error. The algorithm selects candidate predictors that lead to a high probability that this quantity is large in addition to having large marginal posterior inclusion probabilities (PIP) according to model fit. Two methods were constructed. The first is based on orthogonalizing all of the candidate predictors while the second can be applied to the design matrix of candidate predictors without orthogonalization. Our algorithm was applied to the same simulated data that compared the RSR, BSF and ESF models. Although our algorithm performs similarly to the established methods, the first of our selection methods shows an improvement in execution time. In addition, our approach is a statistically sound, fully Bayesian method.

This article summarizes the ideas behind a few programs we developed for spatial data analysis in EViews and MATLAB. They allow the user to check for spatial autocorrelation using Moran's I and provide a spatial filtering procedure based on the Gi statistic by Getis and Ord (1992). We have also implemented graphical tools like Moran Scatterplots for the detection of outliers or local spatial clusters.

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In-process turbine monitoring has been a subject of research since the advent of gas turbines; however, it is difficult because it requires precision measurements to be made at high speeds and temperatures. The measurement of turbine blade tips is especially intriguing because of the potential it holds to greatly increase the efficiency of engine operation and maintenance. Tip-to-casing clearance is one of the major sources of inefficiency in a turbine and monitoring of this clearance would allow active tip-clearance control systems to be implemented. Also, analysis of engine wear through vibration monitoring may increase the effectiveness of engine maintenance and repair. A sensor recently developed at Georgia Tech could answer this challenge. The sensor operates by measuring the phase change of reflected microwaves to measure blade tip displacement. It is robust even in the harsh turbine environment. However, in sensor measurements, the microwave beam pattern causes a phenomenon called spatial filtering to occur, which may compromise the precision of measurements. Since the beam is not a thin line reflecting off a single point on the turbine blade, measurements are a weighted average of measurements along the entire surface within the field-of-view of the sensor. The net effect is a blurred measurement. In measuring turbine blades, only the tip is vital, so the blurring in between blades is not extremely detrimental. However, changing measurement geometry affects the amount of spatial filtering and hence the accuracy of the measurement. This thesis presents a detailed analysis of this phenomenon and especially its effect on turbine blade tip clearance measurements. A design of experiments is presented to qualitatively understand the effect of geometric factors on tip measurements. Along with experimentation, a robust, three-dimensional, ray-tracing, electromagnetic model is presented which was developed to further understand spatial filtering and to analyze specific geometric factors in the measurement of turbine blades. The research shows that microwave measurements may still be made to sufficient accuracy even considering the effect of spatial filtering, and by quantifying spatial filtering in measurements, it may be possible in to glean additional useful data from measurements.

Brain-Computer Interface (BCI) offers the opportunity to paralyzed patients to control their movements without any neuromuscular activity. Signal processing of neuronal activity enables to decode movement intentions. Ability for patient to control an effector is closely linked to this decoding performance. In this study, I tackle a recent way to decode neuronal activity: Deep learning. The study is based on public data extracted by Schalk et al. for BCI Competition IV. Electrocorticogram (ECoG) data from three epileptic patients were recorded. During the experiment setup, the team asked subjects to move their fingers and recorded finger movements thanks to a data glove. An artificial neural network (ANN) was built based on a common BCI feature extraction pipeline made of successive convolutional layers. This network firstly mimics a spatial filtering with a spatial reduction of sources. Then, it realizes a time-frequency analysis and performs a log power extraction of the band-pass filtered signals. The first investigation was on the optimization of the network. Then, the same architecture was used on each subject and the decoding performances were computed for a 6-class classification. I especially investigated the spatial and temporal filtering. Finally, a preliminary study was conducted on prediction of finger movement. This study demonstrated that deep learning could be an effective way to decode brain signal. For 6-class classification, results stressed similar performances as traditional decoding algorithm. As spatial or temporal weights after training are slightly described in the literature, we especially worked on interpretation of weights after training. The spatial weight study demonstrated that the network is able to select specific ECoG channels notified in the literature as the most informative. Moreover, the network is able to converge to the same spatial solution, independently to the initialization. Finally, a preliminary study was conducted on prediction of movement position and gives encouraging results.

The usage of Unmanned Aerial Systems (UASs), such as quadcopters and hexacopters, has steadily increased over the past few years in both recreational and commercial use. This increased availability to purchase such systems has also given rise to many safety and security concerns. A common concern is that the misuse of a UAS can cause damage to airplanes and helicopters in and around airports. Another growing concern is the use of UASs for terrorist intentions such as using the UAS as a remote controlled bomb. There is clearly a need to be able to detect the presence of unwanted UASs in restricted areas. This thesis work presents the beginning work towards a method to detect the presence of these UASs using the blade pass frequency (BPF) of the motors and rotors of a home made quadcopter. A low cost uniform linear microphone array is first used to perform a simple delay-and-sum beamformer to spatially filter out noise sources. The beamformer output is then divided into sub-bands using three bandpass filters centered on the expected location of the fundamental BPF and its 2nd and 3rd harmonics. For each sub-band, an adaptive filter called an adaptive line enhancer is used to extract and enhance the narrowband signals. The response of the adaptive filters are then used to detect the quadcopter by looking for the presence of the 2nd and 3rd harmonics of the fundamental BPF. Static tests of the quadcopter out in a field showed promising results for this method with the ability to detect up to the 3rd harmonic 90ft away and the 2nd harmonic 130 ft away. / Master of Science / The usage of Unmanned Aerial Systems (UASs), such as quadcopters and hexacopters, has steadily increased over the past few years in both recreational and commercial use. This increased availability to purchase such systems has also given rise to many safety and security concerns. A common concern is that the misuse of a UAS can cause damage to airplanes and helicopters in and around airports. Another growing concern is the use of UASs for terrorist intentions such as using the UAS as a remote controlled bomb. There is clearly a need to be able to detect the presence of unwanted UASs in restricted areas. This thesis work presents the beginning work towards a method to detect the presence of a home made quadcopter based on the sound it produces. A series of microphone are first used to remove surrounding sounds that could interfere with the quadcopter’s sound. The output of this processes is then divided into smaller sections using three filters centered on the expected location of the most important and information rich parts of the quadcopter’s sound. For each section, a final filter is used to extract and enhance the signals of interest produced by the quadcopter. The response of these filters are then used to detect whether the quadcopter is present or not. Static tests of the quadcopter out in a field showed promising results for this method with the ability to detect the quadcopter 90 to 130 ft away.

Spatial interaction models of the gravity type are widely used to model origindestination flows. They draw attention to three types of variables to explain variation in spatial interactions across geographic space: variables that characterise an origin region of a flow, variables that characterise a destination region of a flow, and finally variables that measure the separation between origin and destination regions. This paper outlines and compares two approaches, the spatial econometric and the eigenfunction-based spatial filtering approach, to deal with the issue of spatial autocorrelation among flow residuals. An example using patent citation data that capture knowledge flows across 112 European regions serves to illustrate the application and the comparison of the two approaches.(authors' abstract)

Thesis. 1976. Sc.D.--Massachusetts Institute of Technology. Dept. of Mechanical Engineering. / Microfiche copy available in Archives and Engineering. / Vita. / Includes bibliographical references. / by Nathan Clay Martin II. / Sc.D.