Joint Clock Parameter and Transmitter Position Estimation using TDOA in One Way Packet Transmission

Abstract

This paper investigates a source localization problem using time difference of arrival (TDOA) measurements in the presence of non-ideal clock parameters between sensors. A joint estimation of the clock offset and of the clock skew of an imperfect clock of an asynchronous receiver under the assumption of affine clock model is proposed. To achieve synchronization among sensors, we opt for a receiver to receiver synchronization based on received signal measurement. The Minimum Variance Unbiased Estimator (MVUE) for the clock skew and the clock offset is derived assuming a known reference transmitter position. The performance of these MVUEs is compared against the corresponding Cram\'er Rao Lower Bounds (CRLB) that are derived for both cases of reference transmitter absent or present. Performance of the estimators is evaluated by means of the Root Mean Squared Error (RMSE). Prior to estimating the position of an unknown target transmitter, an appropriate correction to the clock is applied. The CRLB is also derived for the transmitter position assuming the clocks have been properly corrected.