Joint map estimation and localization using distance measurements to landmarks with unknown location

Andreas Richter*

*Corresponding author for this work

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


In this paper the problem of joint localization and map estimation is studied. The objective is to determine the location of a set of fixed nodes, e.g. access-points or base-stations in a wireless network using only distance measurements acquired by a node moving in the vicinity of the fixed nodes. It is assumed, that no prior information about locations of any of the nodes (fixed or mobile) is available, i.e. no anchor nodes exist. It is shown that, under some mild conditions on the distribution and the number of nodes, the map of the fixed nodes as well as the locations of the mobile node(s) in this map can be identified unambiguously from ranging measurements. A closed form algorithm is derived to estimate the map. Furthermore, the performance of the derived estimator is compared in Monte-Carlo simulations with (i) the Cramér-Rao lower bound (CRLB) and (ii) with the performance of an iterative maximum-likelihood estimator. The derived closed form estimator for the node locations is consistent, but doesn't achieve the CRLB. The ML-estimator achieves the bound if the number of fixed nodes is at least four, and the distance measurements have been obtained at a minimum of six locations.

Original languageEnglish
Title of host publicationConference Record of the 44th Asilomar Conference on Signals, Systems and Computers, Asilomar 2010
Number of pages5
Publication statusPublished - 1 Dec 2010
MoE publication typeA4 Article in a conference publication
EventAsilomar Conference on Signals, Systems & Computers - Pacific Grove, United States
Duration: 7 Nov 201010 Nov 2010
Conference number: 44


ConferenceAsilomar Conference on Signals, Systems & Computers
Abbreviated titleASILOMAR
CountryUnited States
CityPacific Grove

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