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Session C6: Terrestrial Signals of Opportunity-Based Navigation Systems

Privacy-Preserving Proximity-Based Positioning with Robustness
Guillermo Hernandez, Shuo Tang, and Pau Closas. Electrical, and Computer Engineering Dept., Northeastern University

As the Global Navigation Satellite System (GNSS) research community continues to explore methods to enhance the position accuracy and improve the integrity of such systems, one particular area that draws attention is the ability to incorporate valuable resources, such as nearby GPS-enabled receivers, to improve the position accuracy of a particular receiver, or a user whose location is unknown. An approach that incorporates these nearby receivers is the proximity-based service (PBS) [1]. This depends on the user whose location is unknown, denoted as the p-th user, and its capability to establish a proximity area. There have been different methods to develop this proximity area, such as using the signal-to-noise ratio (SNR), WiFi, and Bluetooth technologies [2,3,4]. Ideally, within this proximity area there are nearby users who are able to communicate with this p-th user and are willing to participate in the process of obtaining an established position for the p-th user. This process requires the nearby users’ accurate position information to make an estimation for the p-th user position.
There are different methods that the PBS can incorporate to compute an estimated position for the p-th user. Some of these methods include using multilateration and utilizing an estimator to produce the desired estimated results [5]. While using the estimator approach may obtain highly accurate estimated position results, there are two concerns that need to be taken into consideration. The first concern is presented within the observable position measurements given by the nearby users and their impact on the accuracy performance of the PBS. It is desirable that each nearby user provides honest and high-accuracy observable position measurements of their own position, but this may not always be the case. The information given by these nearby users may not always be accurate due to an internal system fault, or there might be a malicious user whose sole objective is to reduce the performance of the proximity-based solution service [5]. Therefore, to account for such outliers a robust estimator can be taken into account; this method was proposed in [5]. The second concern introduced is the privacy concern of each nearby user. This concern arises when the nearby users place themselves in a vulnerable state and make their own position information public and accessible to the PBS in order to compute the position estimation for the p-th user. There are methods that provide a solution that incorporates homomorphic encryption, such as in [6], but this may come at a large computational cost.
To address both concerns simultaneously without requiring a large computational cost, we propose to implement a robust estimator with the capability to produce near-optimal estimated results, in the presence of outliers, while maintaining the privacy of each user who participates in the PBS. To achieve this feature, we depend on the methodologies of differential privacy and its implementation on statistical estimators. Recent works such as [7,8,9,10] have provided different approaches in how to establish estimators that utilize the differential privacy properties. Therefore, the objective of this study is to build upon these ideas and establish an alternative solution to the proximity-based service that accounts for the privacy of each user that participates in the PBS.
As part of our investigation, the proposed solution will be evaluated within a simulated environment that represents a realistic environment. In the simulated environment, a set of sensors (also referred to as users) will be generated around a user whose location is unknown, denoted as the p-th. The environment will consist of having these users that satisfy the proximity-based property, of being within the p-th user’s proximity area, while others will not satisfy this requirement. The presence of the users outside of this proximity area will introduce the scrutiny of having outliers present within the dataset used to compute the p-th user’s position.
In this simulated environment, the distribution properties of how the users’ locations are generated will be known and with this known knowledge the most efficient estimator can be obtained in the sense that it attains the Cramér-Rao Bound (CRB). The CRB will serve as the benchmark to analyze and compare the accuracy performance of the proposed solution. In addition, it will establish the realization if the proposed solution will obtain near-to optimal results. The Root Mean-Squared Error (RMSE) will be used as a metric to evaluate the proposed solution’s accuracy performance.
After evaluating the accuracy performance of the proposed solution, it will also be compared to a standard robust estimator that does not take into account the privacy concerns that are within the PBS, as seen in [5]. This direct comparison will serve as a method of understanding the impact the privacy properties, introduced by the proposed solution, may have on the accuracy performance of the PBS. Therefore, by constructing this comparison any offset in this performance, if any, can come to a realization if there is a need to limit the privacy properties to maintain highly accurate or near-optimal estimated results.
With these two tests, we anticipate the proposed solution will produce near optimal results that are similar to the robust estimator seen in [5]. In addition, we predict that there will be some minor decrease in its accuracy performance due to the privacy properties. The amount of how much this impact may have on the accuracy performance is something that we aim to further understand. Still, we anticipate that the proposed solution will still be able to serve as an alternative solution to the proximity-based service that considers the privacy concern of the users who participate in helping estimate the position of the p-th user.
As the proximity-based service is able to provide near-optimal results with the presence of outliers, the privacy concern is still a common present issue. Therefore, we proposed an alternative solution to the PBS that takes into account this concern, while still maintaining highly accurate estimated results.
References
[1] Dardari, D., Closas, P., & Djuri?, P. M. (2015). Indoor tracking: Theory, methods, and technologies. IEEE transactions on vehicular technology, 64(4), 1263-1278.
[2] Yin, F., Zhao, Y., & Gunnarsson, F. (2015, July). Proximity report triggering threshold optimization for network-based indoor positioning. In 2015 18th International Conference on Information Fusion (Fusion) (pp. 1061-1069). IEEE.
[3] Turgut, Z., Aydin, G. Z. G., & Sertbas, A. (2016). Indoor localization techniques for smart building environment. Procedia computer science, 83, 1176-1181.
[4] Bagosi, T., & Baruch, Z. (2011, August). Indoor localization by WiFi. In 2011 IEEE 7th International Conference on Intelligent Computer Communication and Processing (pp. 449-452). IEEE.
[5] Hernandez, G., Tang, S., & Closas, P. (2024, September). Proximity-Based Location with Robustness to Byzantine Failures. In Proceedings of the 37th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2024) (pp. 2729-2737).
[6] Hernandez, G., LaMountain, G., & Closas, P. (2023, April). Proximity-based positioning scheme with multi-layer privacy. In 2023 IEEE/ION Position, Location and Navigation Symposium (PLANS) (pp. 235-242). IEEE.
[7] Avella-Medina, M. (2021). Privacy-preserving parametric inference: a case for robust statistics. Journal of the American Statistical Association, 116(534), 969-983.
[8] Brown, G., Gaboardi, M., Smith, A., Ullman, J., & Zakynthinou, L. (2021). Covariance-aware private mean estimation without private covariance estimation. Advances in neural information processing systems, 34, 7950-7964.
[9] Liu, X., Kong, W., & Oh, S. (2022, June). Differential privacy and robust statistics in high dimensions. In Conference on Learning Theory (pp. 1167-1246). PMLR.
[10] Alabi, D., Kothari, P. K., Tankala, P., Venkat, P., & Zhang, F. (2023, June). Privately estimating a Gaussian: Efficient, robust, and optimal. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (pp. 483-496).

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