Topics in probabilistic location estimation in wireless networks

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Abstract
In this survey-style paper we demonstrate the usefulness of the probabilistic modelling framework in solving not only the actual positioning problem, but also many related problems involving issues like calibration, active learning, error estim- ation and tracking with history. We also point out some inter- esting links between positioning research done in the area of robotics and in the area of wireless radio networks. I INTRODUCTION The location of a mobile terminal can be estimated using radio signals transmitted or received by the terminal. The problem is called with various names such as location estima- tion, geolocation, location identification, location dete rmina- tion, localization, and positioning. The traditional, geo metric approach to location estimation is based on angle and dis- tance estimates from which a location estimate is deduced us- ing standard geometry. Instead of the geometric approach, we consider the probabilistic approach which is based on probab- ilistic models that describe the dependency of observed signal properties on the location of the terminal, and the motion of the terminal. The models are used to estimate the terminal's location when signal measurements are available. The feasibility of the probabilistic approach in the contex t of wireless networks has already been demonstrated to some extent in a number of recent papers (4, 9, 13, 14, 15, 20). Probabilistic methods have also been extensively used in ro- botics where they provide a natural way to handle uncertainty and errors in sensor data (16, 17). Many of the probabilistic methods developed in the robotics community, in particular those related to map building, location estimation and track- ing, are also applicable in the context of wireless networks . In the following we discuss selected topics in probabilisti c location estimation, many of which are well-known in prob- abilistic modeling, but have received relatively little at tention in the domain of wireless networks. We focus primarily on wireless local area networks, WLANs, but most of the ideas and concepts are applicable to many other wireless networks as well, including those based on GSM/GPRS, CDMA or UMTS standards. The rest of the paper is organized as follows: In Section II we discuss calibration, the process of obtaining a model of the signal properties at various locations. The actual location estim ation and tracking phase following calibration is considered in Sec- tions III and VI. Issues related to the optimal choice of cal- ibration measurements are discussed in Section IV. In many cases, it is useful to complement a location estimate with in- formation on its accuracy; in Section V we describe methods for error estimation and visualization. Conclusions are su m- marized in Section VII. II CALIBRATION

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