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VLSI Design
Volume 15 (2002), Issue 2, Pages 507-520

A Synthesizable VHDL Model of the Exact Solution for Three-dimensional Hyperbolic Positioning System

Department of Electrical and Computer Engineering, New Jersey Center for Wireless and Telecommunication, New Jersey Institute of Technology, Newark 07102, NJ, USA

Received 1 August 2001; Revised 3 October 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a synthesizable VHDL model of a three-dimensional hyperbolic positioning system algorithm. The algorithm obtains an exact solution for the three-dimensional location of a mobile given the locations of four fixed stations (like a global positioning system [GPS] satellite or a base station in a cell) and the signal time of arrival (TOA) from the mobile to each station. The detailed derivation of the steps required in the algorithm is presented. A VHDL model of the algorithm was implemented and simulated using the IEEE numeric_std package. Signals were described by a 32-bit vector. Simulation results predict location of the mobile is off by 1 m for best case and off by 36 m for worst case. A C + + program using real numbers was used as a benchmark for the accuracy and precision of the VHDL model. The model can be easily synthesized for low power hardware implementation.