Position estimation error performance model for a minimum configuration 3-D multilateration

Abstract

A multilateration system estimates the position of emitter using time difference of arrival (TDOA) measurements with a lateration algorithm. It involves solving a set of hyperbolic plane equations to determine the position of the emitter given the TDOA measurements that corresponds to the path difference (PD) measurement in distance. A performance model is developed using the relative maximum error bound (RMEB) which relates the plane equation condition number, the relative ground receiving station (GRS) geometry and the PD measurement error to estimate the position estimation (PE) error. By using air traffic monitoring for civil aviation as an application, Monte Carlo simulation verifies the PE error of the performance model for a square GRS configuration. The coverage assumed a 3600 bearing, a range of up to 200 km and a maximum altitude of 15 km. Simulation results also show that the performance model estimates the horizontal position error with a maximum absolute error of 0.1 km up to a range of 200 km at an altitude of 15 km and a minimum absolute error of 0.2 km at an altitude of 15 km.