We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the consistency and asymptotic normality of the maximum likelihood (ML) estimator. Then, we devise an estimator that owns the same asymptotic property as the ML one. Specifically, we prove that the negative log-likelihood function converges to a function, which has a unique minimum and positive definite Hessian at the true source’s position. Hence, it is promising to execute local iterations, e.g., the Gauss-Newton (GN) algorithm, following a consistent estimate. The main issue involved is obtaining a preliminary consistent estimate. To this aim, we construct a linear least-squares problem via algebraic operation and constraint relaxation and obtain a closed-form solution. We then focus on deriving and eliminating the bias of the linear least-squares estimator, which yields an asymptotically unbiased and further consistent estimate. Noting that the bias is a function of the noise variance, we further devise a consistent noise variance estimator that involves a 3-order polynomial rooting. Based on the preliminary consistent location estimate, a one-step GN iteration suffices to achieve the same asymptotic property as the ML estimator. Simulation results demonstrate the superiority of our proposed algorithm in the large sample case.

Publication:

IEEE Transactions on Information Theory (Volume: 70, Issue: 4, April 2024)

https://doi.org/10.1109/TIT.2023.3343347

Author:

Guangyang Zeng

School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China; State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China; Department of Automation, University of Science and Technology of China, Hefei, China

Biqiang Mu

Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Email: bqmu@amss.ac.cn

Ling Shi

Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Hong Kong, China

Jiming Chen

College of Control Science and Engineering and the State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China

Junfeng Wu

School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China