A synthesizable VHDL model of the exact solution for three-dimensional hyperbolic positioning system

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.