An Approximately Efficient TDOA Localization Algorithm in Closed-Form for Locating Multiple Disjoint Sources With Erroneous Sensor Positions

• Published in: IEEE transactions on signal processing Vol. 57; no. 12; pp. 4598 - 4615
• Main Authors: Le Yang, Ho, K.C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Acoustic sensors; Algorithms; Applied sciences; Closed-form solution; Detection, estimation, filtering, equalization, prediction; Disjoint sources; Estimates; Exact sciences and technology; Exact solutions; Information, signal and communications theory; Localization; Mathematical analysis; Miscellaneous; Noise measurement; Nonlinear equations; Position (location); Position measurement; Sensor arrays; sensor position errors; Sensor systems; Sensors; Signal and communications theory; Signal processing; Signal, noise; Sonar navigation; Studies; Telecommunications and information theory; Time difference of arrival; time difference of arrival (TDOA); Time measurement; localization; Parameter estimation; Nonlinear problems; Algorithm; Joint detection; Arrival time; sensor position errors; Accuracy; Disjoint sources; Algorithm performance; Simulation; Source localization; time difference of arrival (TDOA); Position measurement; Signal processing; Target detection; Cramer Rao inequality
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2027765

This paper considers the problem of time difference-of-arrival (TDOA) source localization when the TDOA measurements from multiple disjoint sources are subject to the same sensor position displacements from the available sensor positions. This is a challenging problem and closed-form solution with good localization accuracy has yet to be found. This paper proposes an estimator that can achieve this purpose. The proposed algorithm jointly estimates the unknown source and sensor positions to take the advantage that the TDOAs from different sources have the same sensor position displacements. The joint estimation is a highly nonlinear problem due to the coupling of source and sensor positions in the measurement equations. We introduce the novel idea of hypothesized source locations in the algorithm development to enable the formulation of psuedolinear equations, thereby leading to the establishment of closed-form solution for source location estimates. Besides the advantage of closed-form, the newly developed algorithm is shown analytically, under the condition that the TDOA measurement noise and the sensor position errors are sufficiently small, to reach the CRLB accuracy. For clarity, the localization of two disjoint sources is used in the algorithm development. The developed algorithm is then examined under the special case of a single source and extended to the more general case of more than two unknown sources. The theoretical developments are supported by simulations.