An Efficient Direct Position Determination Algorithm Combined with Time Delay and Doppler
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The conventional passive location methods such as Taylor series and two-step weighted least square are usually implemented by first estimating related parameters and then solving equations to get the target position. However, the parameters used for location estimation are only estimates and represent an unnecessary intermediate step in the process, which also cannot guarantee to match the real location information. This separation between the parameter estimation algorithm and the location estimation algorithm may lead to information loss. By utilizing a combination of time delay and Doppler, this paper proposes an improved direct position determination algorithm to improve the estimation accuracy. A novel maximum likelihood estimator is used to transform the problem into one of searching for the largest eigenvalue of a Hermitian matrix of position information. Calculation is simplified since the part of nonzero eigenvalues remains unchanged after the matrix is transposed. The target’s position estimation is then determined by searching the space of two-dimensional geographic grids. Simulation results show that the performance of proposed algorithm is closer to the Cramér–Rao lower bound than the original direct position determination algorithm and traditional two-step method based on time delay and Doppler.
KeywordsDirect position determination Maximum likelihood Passive location Eigenvalue decomposition
The authors would like to thank the Editor-in-Chief, Prof. M. N. S. Swamy, and the associate editor for their helpful suggestions in revising and improving our paper. This work has been supported by National Natural Science Foundation of China under Grant 61201381 and the authors wish to acknowledge the help from Professor Anthony J. Weiss at Tel Aviv University in Israel.
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