Geometric optimization of a time-of-arrival (TOA) based self-positioning terrestrial system

This work investigates geometric optimization of antenna configuration in lateral geometry for a terrestrial time-of-arrival based self-positioning system, considering optimization confronted by two competing and opposing phenomena, the purely geometric analogy of GPS geometric dilution of precision, and tracking errors in correlation of the pseudorandom sequences, as set by signal-to-noise ratio. We consider coherent tracking, purely LOS propagation from omnidirectional antennas, with simplifying two-dimensional geometry and two antennas, briefly regarding effects of platform dynamics. In contrast to a common supposition, ranging error variances are not assumed equal. Expected value of radial error is chosen for optimization and the possible range of this measure is found to be quite large. We progress from single point optimization to optimization over an area sampled in a matrix. Representative numerical results are found for optimal solutions as well as power requirements to maintain a given error level. The solutions are obtained using Monte Carlo simulation techniques.