A GNSS–Cellular Network Hybridization Strategy for Robust Positioning

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors The paper addresses the problem of improving the robustness and accuracy of positioning by combining GNSS and cellular network data. The authors propose a hybridization strategy that uses signal strength, Doppler shift, and GNSS pseudorange measurements to improve localization accuracy in urban environments. The method involves a probabilistic data association (PDA) framework and an extended Kalman filter (EKF) to fuse heterogeneous data sources. Simulation and experimental results are presented to demonstrate the advantages of the proposed approach in terms of robustness and continuity. Topic is timely and relevant due to the increasing demand for reliable and accurate positioning in GNSS-challenged environments such as forest or urban canyons. The manuscript is of interest to the research community working on GNSS enhancement, sensor fusion and positioning algorithms.   The English is generally fluent and comprehensible, although some expressions should be slightly refined to improve clarity and flow.  I suggest the following major points be addressed:     1) There are some typographical and editorial issues, including inconsistent use of acronyms and occasional grammatical slips (e.g., verb tenses, article usage). Examples include:  "GNSS signal can be received" → "GNSS signals can be received" The caption of Fig. 4 is too vague.     2) The experimental section lacks a thorough benchmarking against other robust positioning or hybridization methods. The benefit of the PDA-EKF fusion strategy is only demonstrated in terms of continuity, not precision. Please include a quantitative comparison with established fusion techniques (e.g., GNSS/INS, GNSS/UWB).   3) In the Introduction, when discussing hybrid localization frameworks combining GNSS and auxiliary data sources (e.g., Doppler, signal strength, inertial), the authors may consider including more recent contributions such as [1,2], which explore alternative fusion models and control-oriented approaches to tackle non-Gaussian noise and outlier suppression. These references would improve the contextualization of the proposed contribution.   [1] G. Garraffa et al., "Localization Based on Parallel Robots Kinematics As an Alternative to Trilateration," IEEE Transactions on Industrial Electronics, vol. 69, no. 1, Jan. 2022. [2] Feng et al., "An Adaptive IMU/UWB Fusion Method for NLOS Indoor Positioning and Navigation" IEEE Internet of Things Journal, vol. 10, no. 13, pp. 11414-11428, 1 July1, 2023,   4) The urban scenarios selected appear to favor continuity but not necessarily accuracy in presence of multipath or NLOS. The model does not incorporate any error models for multipath or GNSS degradation. This is a major omission, as robustness to those effects is a key challenge in the field.   5) The simulation section lacks essential details. For example, the placement and type of cellular sources are not described. Are the signal strength maps pre-recorded or simulated? How are Doppler measurements obtained or modeled? Without these details, it is difficult to evaluate reproducibility and generality.   6) The method involves probabilistic association, EKF updates, and Doppler estimation. However, no comment is provided regarding real-time feasibility or computational cost on embedded systems. Please include a basic complexity discussion or runtime profile.   7) The real-world tests are not adequately detailed. What GNSS receiver, Doppler estimator, and cellular signal acquisition system were used? How were cellular features measured or extracted in real-time? What was the sampling frequency?

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The author studied a hybrid localization approach that enables users to independently combine GNSS and 4G/5G data to improve positioning accuracy in cases where satellite signals are weak or unusable, and conducted static positioning tests on this method in three environments. The author has made some contributions to this subject. However, there are still some deficiencies in this article. I hope the following comments can help improve the manuscript.

• Line227, the sequence of formula numbers is incorrect.
• Line278, Line278, the format of the title number 2.2.3 is inconsistent with the context, and the subsequent title number directly changes from 2.2.3 to 2.4.
• The fonts of the secondary and tertiary headings in the article are not uniform.
• In the experimental section, all the experimental result data are in tabular form, which is very inconvenient for comparison and analysis. It is suggested that the experimental results be placed in a graph for better comparison and analysis.
• The accuracy of the experimental results was evaluated by using two types of errors, real positioning errors and standard deviations, but there was a lack of analysis of the real positioning error results.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

The GNSS-cellular network hybridization positioning is an interesting topic that can potentially enhance positioning accuracy in urban environments. The paper analyzes both position-domain and observation-domain approaches, but the theoretical and experimental analyses require further clarification:

1. In Equation (4), does the subscript n denote the observed pseudorange between the user and GNSS/4G base stations within the same epoch, or across different epochs?

2. Please provide detailed method for the accuracy estimation of the n observations in Equation (7) for both GNSS and 4G measurements.

3. The linearized form of Equation (24) should be explicitly derived in the same format as Equation (17) for consistency.

4. The methodology for determining inter-system weights in Equation (27) needs clarification, as this critically impacts positioning performance.

5. In the experimental section:

   • Specify the duration of collected data used for evaluation.
   • Include a time-series analysis of positioning errors to highlight:
     • Instances of large vs. minimal errors across different methods.
     • RMS error statistics to quantitatively compare performance.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The revised version of the paper takes into account the majority of the requested improvements and clarifications. The responses provided are precise and technically sound. I appreciate the efforts made to enhance the reproducibility, and editorial consistency of the work. Below I list a few residual remarks that should be addressed in a final round before publishing:

1) Authors have clearly explained the limitations of GNSS and cellular Network. However, it might be helpful to explicitly state, for example at the beginning of Section 2.2, that the two hybridization approaches operate at different abstraction levels (position vs. measurement) and thus imply different constraints on modeling error sources.

2) While the sampling interval of 15 seconds is indicated, authors should briefly mention whether this rate is a limitation of the logging apps, the network update frequency, or a deliberate choice to emulate low-rate periodic positioning. This would help contextualize the frequency in terms of application scenarios (i.e. static monitoring vs. dynamic tracking).

3) Authors report that the WLS estimation takes 30–50 ms per epoch. While this is sufficient for acceptability, it would be useful to specify the number of base stations and GNSS satellites typically involved in each epoch to help gauge scalability.

4) Improvements to Figure 1 and Figure 4 captions are appreciated. Ensure that all figure captions follow a consistent format, including full terms on first use (e.g., “Base Station (BS)” instead of just “BS”) and specify whether the scenario is simulated or experimental when relevant.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed all the questions

Author Response

We would like to express our sincere gratitude to Reviewer 3 for the time and effort dedicated to reviewing our manuscript.
Their insightful comments and constructive suggestions have greatly contributed to improving the clarity, quality, and scientific depth of the paper.
We are truly grateful for this thoughtful feedback, which has helped strengthen both the presentation and the overall impact of our work.