Abstract
The paper (Stefanski and Sadowski, EURASIP J. Wirel. Commun. Netw. 2018, Article 179) introduces a multilateration algorithm for unsynchronized sensor networks. However, a very similar method has been proposed before that is not cited. Furthermore, in the measurement model of Stefanski and Sadowski (EURASIP J. Wirel. Commun. Netw. 2018, Article 179), an incorrect covariance matrix (Eq. (11) in Stefanski and Sadowski (EURASIP J. Wirel. Commun. Netw. 2018, Article 179)) has been used that leads to inferior results. We summarize the context and explain the measurement methodology proposed in Stefanski and Sadowski (EURASIP J. Wirel. Commun. Netw. 2018, Article 179), while referring to the missing citation. Finally, we derive the correct covariance matrix of the measurement error and demonstrate that the covariance matrix proposed in Stefanski and Sadowski (EURASIP J. Wirel. Commun. Netw. 2018, Article 179) is incorrect.
Highlights
*Correspondence: daniel.frisch@kit.edu Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany sensor’s individual clock offset is canceled. This principle has first been proposed in [2], where always two transmissions were considered in one measurement equation
Multiple local differences of times of arrival (L-DOTA) are calculated by subtracting all pairs of successive time of arrival (TOA). This leads to a dependency of the error in the individual lines in the measurement equation
We derive the measurement equation that connects a sequence of target positions to L-DOTA measurements
Summary
Based on the time of arrival (TOA) of the target’s transmission at each sensor, the target can be located. This principle has first been proposed in [2], where always two transmissions were considered in one measurement equation. We derive the measurement equation that connects a sequence of target positions to L-DOTA measurements. Using the definitions of expected value and covariance, we derive the correct covariance matrix for said measurement equation.
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