Analytical solutions for passive source positioning and Geometric Dilution of Precision

This paper provides a closed form analytical solution for TDOA three dimensional (3D) acoustic source localization with four synchronized ultrasonic generators or receivers. Then a pure analytical solution for Geometric Dilution of Precision (GDOP) with four signal generators or receivers is derived instead of a least square solution. The proposed GDOP model removes the effect of time clock drift, which shows the character of Geometric Dilution of Precision more directly.