Absolute measures of time-difference-of-arrival positioning error in underwater acoustic telemetry setups

This brief communication presents two solutions for calculating absolute measures of error from time-difference-of-arrival (TDOA) positioning in underwater acoustic telemetry arrays. First, a Monte Carlo estimation of TDOA positioning error is derived. Next, a computationally inexpensive, approximate solution to the Monte Carlo method is presented. This approximate solution is achieved by solving the Jacobian of a closed-form TDOA positioning model. The positioning error covariance matrix returned from either method can then be used to report the accuracy of TDOA positions or utilized in state-space positioning models. Finally, calculations of the expected radial error are shown which serves as a simple summary statistic for reporting positioning error in real units.