## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 8603-8615 |

Number of pages | 13 |

Journal | IEEE Transactions on Vehicular Technology |

Volume | 65 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2016 |

## All Science Journal Classification (ASJC) codes

- Automotive Engineering
- Aerospace Engineering
- Electrical and Electronic Engineering
- Applied Mathematics

## Keywords

- Bias analysis
- frequency difference of arrival (FDOA)
- localization
- nonlinear weighted least squares (WLS)
- time difference of arrival (TDOA)