Geolocation by time difference of arrival using hyperbolic asymptotes

The paper proposes a new simplified algorithm to estimate the location of an emitter by utilizing time difference of arrival (TDOA) measurements. This is achieved by recasting the estimation problem in prolate spheroidal coordinates. Prolate spheroidal coordinates greatly simplify the TDOA equations, producing a set of linear equations in the far field limit. The set of linear equations corresponds to the hyperbolic asymptotes of the TDOA measurements. We also develop a systematic approach that associates the hyperbolic asymptotes with the emitter. In the near field, the far field solution can be used to "seed" the iterative maximum likelihood (ML) estimate, enabling convergence to the ML solution.