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2025-07-31
Fundamental GDOP Bounds and Base Station Deployment in 2D TDOA Positioning Systems
By
Shaohan Feng,

    Mr. Shaohan Feng

    School of Electronics and Information Engineering

    Tiangong University

    China

    Homepage

Weiguang Shi,

    Dr. Weiguang Shi

    School of Electronics and Information Engineering

    Tiangong University

    China

    Homepage

Yongtao Ma,

    Dr. Yongtao Ma

    Tianjin University

    China

    Homepage

Wanru Ning,

    Dr. Wanru Ning

    School of Computer Science

    Peking University

    China

    Homepage

Zihang Meng

    Dr. Zihang Meng

    School of Astronautics

    Harbin Institute of Technology

    China

    Homepage

Progress In Electromagnetics Research B, Vol. 114, 27-35, 2025
doi:10.2528/PIERB25041606 | Google Scholar

Abstract
This paper investigates the theoretical bounds of geometric dilution of precision (GDOP) in two-dimensional time difference of arrival (TDOA) positioning systems. The corresponding base station (BS) deployment for a single mobile terminal (MT) is subsequently derived. Considering the correlation of time difference measurements, a simplified closed-form expression for GDOP is first derived, and it is shown that GDOP is independent of the selection of the reference BS. Theoretical bounds for GDOP are rigorously established, along with the conditions under which these bounds are valid. Based on these boundary conditions, the study demonstrates that optimal deployment occurs when BSs are grouped, and the azimuths of BSs within each group are evenly distributed around a circle centered at the MT. For systems with up to five BSs, the optimal deployment is proven to be unique, whereas non-unique solutions emerge for larger configurations. In contrast, the complete solution set for the worst-case deployment occurs when BSs are collinear and symmetrically aligned along a specific coordinate origin or axis. Numerical simulations validate the theoretical findings, highlighting the superiority of uniform angular distributions. These results provide actionable guidelines for enhancing positioning accuracy in cellular networks and a foundational framework for multi-BS deployment optimization.
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Citation
Shaohan Feng, Weiguang Shi, Yongtao Ma, Wanru Ning, and Zihang Meng, "Fundamental GDOP Bounds and Base Station Deployment in 2D TDOA Positioning Systems," Progress In Electromagnetics Research B, Vol. 114, 27-35, 2025.
doi:10.2528/PIERB25041606
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