The Minimum Expectation Selection Problem

We define the min-min expectation selection problem (resp. max-min expectation selection problem) to be that of selecting k out of n given discrete probability distributions, to minimize (resp. maximize) the expectation of the minimum value resulting when independent random variables are drawn from the selected distributions. We assume each distribution has finitely many atoms. Let d be the number of distinct values in the support of the distributions. We show that if d is a constant greater than 2, the min-min expectation problem is NP-complete but admits a fully polynomial time approximation scheme. For d an arbitrary integer, it is NP-hard to approximate the min-min expectation problem with any constant approximation factor. The max-min expectation problem is polynomially solvable for constant d; we leave open its complexity for variable d. We also show similar results for binary selection problems in which we must choose one distribution from each of n pairs of distributions.Comment: 13 pages, 1 figure. Full version of paper presented at 10th Int. Conf. Random Structures and Algorithms, Poznan, Poland, August 200

Algorithms and Methods for Received Signal Strength Based Wireless Localization

In the era of wireless communications, the demand for localization and localization-based services has been continuously growing, as increasingly smarter wireless devices have emerged to the market. Besides the already available satellite-based localization systems, such as the GPS and GLONASS, also other localization approaches are needed to complement the existing solutions. Finding different types of low-cost localization methods, especially for indoors, has become one of the most important research topics in recent years.One of the most used approaches in localization is based on Received Signal Strength (RSS) information. Specific fingerprints about RSS are collected and stored and positioning can be done through pattern or feature matching algorithms or through statistical inference. A great and immediate advantage of the RSS-based localization is its ability to exploit the already existing infrastructure of different communications networks without the need to install additional system hardware. Furthermore, due to the evident connection between the RSS level and the quality of a communications signal, the RSS is usually inherently included in the network measurements. This favors the availability of the RSS measurements in the current and future wireless communications systems.In this thesis, we study the suitability of RSS for localization in various communications systems including cellular networks, wireless local area networks, personal area networks, such as WiFi, Bluetooth and Radio Frequency Identification (RFID) tags. Based on substantial real-life measurement campaigns, we study different characteristics of RSS measurements and propose several Path Loss (PL) models to capture the essential behavior of the RSS levels in 2D outdoor and 3D indoor environments. By using the PL models, we show that it is possible to attain similar performance to fingerprinting with a database size of only 1-2% of the database size needed in fingerprinting. In addition, we study the effect of different error sources, such as database calibration errors, on the localization accuracy. Moreover, we propose a novel method for studying how coverage gaps in the fingerprint database affect the localization performance. Here, by using various interpolation and extrapolation methods, we improve the localization accuracy with imperfect fingerprint databases, such as those including substantial cover-age gaps due to inaccessible parts of the buildings

Physical Layer Challenges and Solutions in Seamless Positioning via GNSS, Cellular and WLAN Systems

As different positioning applications have started to be a common part of our lives, positioning methods have to cope with increasing demands. Global Navigation Satellite System (GNSS) can offer accurate location estimate outdoors, but achieving seamless large-scale indoor localization remains still a challenging topic. The requirements for simple and cost-effective indoor positioning system have led to the utilization of wireless systems already available, such as cellular networks and Wireless Local Area Network (WLAN). One common approach with the advantage of a large-scale standard-independent implementation is based on the Received Signal Strength (RSS) measurements.This thesis addresses both GNSS and non-GNSS positioning algorithms and aims to offer a compact overview of the wireless localization issues, concentrating on some of the major challenges and solutions in GNSS and RSS-based positioning. The GNSS-related challenges addressed here refer to the channel modelling part for indoor GNSS and to the acquisition part in High Sensitivity (HS)-GNSS. The RSSrelated challenges addressed here refer to the data collection and calibration, channel effects such as path loss and shadowing, and three-dimensional indoor positioning estimation.This thesis presents a measurement-based analysis of indoor channel models for GNSS signals and of path loss and shadowing models for WLAN and cellular signals. Novel low-complexity acquisition algorithms are developed for HS-GNSS. In addition, a solution to transmitter topology evaluation and database reduction solutions for large-scale mobile-centric RSS-based positioning are proposed. This thesis also studies the effect of RSS offsets in the calibration phase and various floor estimators, and offers an extensive comparison of different RSS-based positioning algorithms