Abstract
The paper examines the anchorless direction estimation problem using signal measurements of time difference of arrival (TDOA) from multiple far-field sources in 3D space. A systematic solution involving coordinate frame construction is proposed to jointly estimate source directions and sensor positions through low-rank matrix approximation. The number of unknown parameters to be estimated is reduced by QR decomposition of the mixing matrix to determine the relevant parameters. Pseudolinear and iterative estimators are developed for the solution through norm constraints. We study the property of TDOA-based anchorless direction estimation, discuss the necessary number of sources and sensors, and derive the constrained Cramér–Rao bound for performance evaluation. Additionally, an exception treatment strategy is proposed in the complex case for pseudolinear estimator. A simulation conducted to validate the proposed solution's effectiveness showed that the solution's estimation accuracy was high, indicating its feasibility and effectiveness.
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