QUASINORM REGRESSION FOR LOCALIZATION ESTIMATION

Embargo until
2024-12-01
Date
2022-11-29
Journal Title
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Publisher
Johns Hopkins University
Abstract
This dissertation is about improving security through signal-agnostic localization of uncooperative RF sources in an indoor environment. The work focuses on utilizing classical signal processing measurements through data-informed and sparse machine learning approaches. Data analysis for purpose of generating approximate performance bounds through Cram'er-Rao bound analysis shows that the indoor RF measurements exhibit significant outliers well outside the standard assumptions of Gaussian distributions. These outliers are a product of both the propagation channel and the sensors. The channel affects measurements through multipath, shadowing, and absorption of the target signals. Similarly, artifacts arise in the sensor processing due to the lack of a priori waveform information precluding the use of optimal methods such as match filtering. Therefore, different approaches are investigated to improve the traditional fingerprinting-based localization algorithms which are sensitive to the non-Gaussian outliers as seen in the measurements. This sensitivity is a result of the inherent distance or comparison functions within the algorithms that utilize L_2 or Euclidean norms. One approach is the generalization of the standard distance function from a L_2-norm to a L_p-norm where p<1, i.e., a quasinorm. We show that there is significant improvements in the localization estimation algorithms whether via quasinorm kernel data transformation prior to linear regression; or, via the application of a quasinorm distance function within the popular and effective k-NN algorithm. More generally, the use of quasinorm is potentially applicable for regression in the general sense against heavy tail error distributions. Another approach is the suppression of outliers via a sparse sensing approach. The basic precept is if outliers are minimized then the performance of the localization approaches will improve. Indeed, it is shown that this is the case though performance is not as substantial as the use of quasinorms. In summary, the contributions of this work include a publicly available open-source measurements database; an extension on the Cram'er-Rao bound calculations via a non-i.i.d. approach; the application of quasinorms to address non-Gaussian distributions in regression; and application of sparse sensing to represent and remove outliers.
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Keywords
quasinorm, indoor localization, kernel methods, k-NN
Citation