AbstractA closed‐form expression for the position dilution of precision (PDOP) in absolute‐range‐based two‐dimensional (2‐D) wireless location systems is derived. Then, using the closed‐form expression, the observation space (OS) required for achieving the lowest PDOP of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$2/\sqrt{N}$ \end{document} is studied, where N is the number of measuring points. The OS is measured by central angle of a sector which covers all measuring points. The target is located at the vertex of the sector. It is shown that, for achieving the lowest PDOP of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$2/\sqrt{N}$\end{document}, the OS is required to be larger than or equal to π/2 while N is even. When N = 3, the OS is instead required to be larger than or equal to 2π/3. It is also shown that the OS of 2π/3 is sufficient to achieve the lowest PDOP of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$2/\sqrt{N}$\end{document} while N is odd. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.