A two-step approach for offset and position estimation from pseudo-ranges applied to multilateration tracking

In multilateration tracking, an object, e.g., an airplane, emits a known reference signal, which is received by several base stations (sensors) located at known positions. The receiving times of the signal at the sensors correspond to the times of arrival (TOA) plus an unknown offset, because the emission time is unknown. Usually, for estimating the position of the object, the receiving times are converted to a larger number of time differences of arrival (TDOA) in order to eliminate the unknown offset. To avoid this conversion, the proposed approach directly uses the receiving times. This is achieved by 1. determining the optimal offset from the redundant measurements in closed form and 2. by considering a modified measurement equation. As a result, position estimation can be performed by optimal stochastic linearization.