Abstract: Vetting location information of an unknown mobile node is a key point of locating service in the ubiquitous computing environment. The errors due to locating an triangular area was studied in the 2-D space as a pervasive computing environment. And the theorem of a locating unit deployment(LUD) was presented. Based on the finding,a new physical property parameter of coverage, coverage base, was defined and introduced for the first time. And, the deployment issue between locating units was also studied, as a result, the theorem of coverage base about locating units was proposed in minimum error condition. hhe simulation tests indicate that the locating unit deployment theorem can meet the requirement of ubiquitous terminal's real-time localization and possesses the preferable localization precision.

Key words: Ubiquitous computing, Locating unit, Locating unit deployment, Coverage base