Journal
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
Volume 65, Issue 10, Pages 8603-8615Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TVT.2015.2508501
Keywords
Bias analysis; frequency difference of arrival (FDOA); localization; nonlinear weighted least squares (WLS); time difference of arrival (TDOA)
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Funding
- National Natural Science Foundation of China [61201099, 61571249, 61401231]
- Zhejiang Open Foundation of the Most Important Subjects of Information and Communication Engineering [xkx11401]
- Open Foundation of the State Key Laboratory of Integrated Services Networks, Xidian University [ISN16-05]
- K. C. Wong Magna Fund in Ningbo University
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We address the source localization problem by using both time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements. We solve this problem in two steps, and in each step, we formulate a nonlinear weighted least squares (WLS) problem followed by a bias reduction scheme. In the first step, we formulate a nonlinear WLS problem using TDOA measurements only and derive the bias of the WLS solution, which is then used to develop an unbiased WLS solution by subtracting the bias from the WLS solution. In the second step, we formulate another nonlinear WLS problem by combining the results in the first step and the FDOA measurements. To avoid the potential risk of local convergence, this WLS problem is reduced to an approximate WLS problem, for which the globally optimal solution can be obtained. The bias of the WLS solution is also derived and then subtracted from the WLS solution to reduce the bias. Simulation results show that the bias of the proposed method is reduced and that the Cramer-Rao lower bound accuracy is also achieved.
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