Theoretical facts on RSSI-based geolocation

Joseph S. Picard, Anthony J. Weiss

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We address the problem of locating a stationary emitter using the Received Signal Strength (RSS) at receivers with known locations. The Maximum Likelihood estimator for the emitter location requires the minimization of a non-convex cost function. Since this cost function exhibits numerous local minima, its global minimization is usually realized by means of a grid search and is therefore computationally expensive. In this document, we prove three novel theoretical properties of RSS-based cost functions for Maximum Likelihood localization. First, we show that local maxima of RSS-based cost functions occur at receivers locations. Thus, unlike local minima, the locations of local maxima are a-priori known since the receivers locations are known. Second, we show that the smallest local maximum is necessarily closer to the global minimum than any other local minimum. Third, we show that the global minimum of the non-convex cost function lies within a triangular area defined by the smallest local maxima. Combining these theoretical facts, we propose a procedure for delimiting a small geographical area that contains the global minimum of the cost function, with high probability. Therefore, localization can be achieved by grid search over this reduced area only, which significantly reduces computational costs.

Original languageEnglish
Title of host publication2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012
DOIs
StatePublished - 2012
Event2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012 - Eilat, Israel
Duration: 14 Nov 201217 Nov 2012

Publication series

Name2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012

Conference

Conference2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2012
Country/TerritoryIsrael
CityEilat
Period14/11/1217/11/12

Keywords

  • Emitter Localization
  • Indoor Positioning
  • Maximum Likelihood
  • Received Signal Strength

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