Nearest Neighbor Data Association for LEO Satellite Identification

Jennifer Sanderson and Zaher Kassas

Peer Reviewed

Abstract:	A derivation of the conditional probability density functions (PDFs) necessary in the implementation of a probabilistic data association filter (PDAF) for measurements used in opportunistic navigation with low-Earth-orbit (LEO) satellites, specifically Doppler frequency shift measurements, will be performed. Additionally, an appropriate clutter model for opportunistic Doppler frequency shift measurements will be determined. These will then be implemented into a novel PDAF designed specifically for the data association of received opportunistic RF signals with overpassing LEO satellites. The PDAF will leverage a LEO satellite dynamics model to initialize the validation regions and propagate their covariances. The PDAF will be coupled with an Extended Kalman Filter (EKF) which estimates the receiver’s states. The accuracy of the PDAF and navigation performance of this dual filter framework will be evaluated using collected signal data from LEO satellites. GPS is a critical provider of position, navigation, and timing (PNT) information. Unfortunately, due to its low signal strength, openly available signal structure, and low frequency diversity, GPS is vulnerable to unintentional and adversarial jamming and spoofing attacks. To ensure continued safety and success of the many industries which rely on this technology, a research need rooted in the development of alternative navigation systems has emerged. One such system that has gained the attention of the navigation community is the utilization of radio frequency (RF) signals-of-opportunity (SOP). In this alternative navigation system, commonly available RF signals such as the ones generated by cellular communications towers and communication satellites are used for estimating position and velocity of a receiver. These signals, although not intended for navigation purposes, can still be exploited to form a navigation solution using recently developed algorithms [1] [2]. Low-Earth-Orbit (LEO) satellites are good candidates for SOP based navigation systems due to their ubiquity, frequency diversity, and proximity to Earth – qualities that improve their resilience to RF interference. Although a popular topic in scientific literature, there still exists significant gaps in fundamental research that must be investigated before this technology is ready for real-world applications. Recently, SOP-based navigation systems have demonstrated GPS-independent navigation with positioning accuracies on the order of tens of meters [1] [2] [3]. These results come with the assumption that the identity of the signal transmitter is known – a requirement for the navigation system to accurately estimate the receiver’s position. One of the great advantages to SOP-based navigation is its ability to operate passively without the need to fully know a signal’s structure or extract signal data -- data that would include transmitter identification information. As a result, at the time of reception, the source of a received signal is unknown, and the navigator cannot correlate the measurement against reference data to generate a navigation correction. This problem was avoided in published work, and recorded measurements were manually matched with its source prior to navigation analysis using the ground truth data of the receiver’s position and velocity. Manual data association such as this is still dependent on GPS but has yet to be addressed in scientific literature. One approach to solving the problem of signal origination is the use of a probabilistic data association algorithm (PDA). Traditionally used for single target identification in radar or similar applications, PDAs are used to distinguish measurements from clutter and are often paired with a Bayesian-type filter (referred to as a probabilistic data association filter or PDAF) to perform target tracking [4]. Although these algorithms have been well-vetted for radar-type sensor measurements, they have not been applied to the measurements found in opportunistic radio navigation. It is the intention of this paper to apply the theory of PDAFs to the application space of opportunistic navigation with LEO satellites for autonomous transmitter identification which requires only an estimate of the receiver’s states. Several significant differences exist between radar-type applications used by PDAFs and opportunistic navigation applications resulting in the need for further study. They include: (1) the estimation of both the target and sensor’s states, (2) the distribution of clutter in the measurement space, (3) the ratio of number of targets to the number of received measurements, and (4) the understanding of target dynamics. An extension of each of these potential differences will be discussed presently. PDAF-SLAM Fusion Radar-based PDAFs track only target states as the sensor’s states are assumed to be well-defined. In our approach, we intend to use a PDAF to track signal transmitters’ states while also tracking the states of our receiver. This fusion of PDAFs and simultaneous tracking and mapping (SLAM) has been applied in the robotics community [5], but it has yet to be applied to an opportunistic navigation system. Unknown Clutter Model PDAs rely on a data association probability model which is composed of the PDFs of the current state conditioned on each data association event. These PDFs are a function of the following: (1) probability of target detection (2) the probability the measurement exists within the validation region, and (3) the likelihood ratio of the measurement originating from the target rather than clutter. The likelihood ratio relies on an accurate clutter model, commonly a Poisson clutter model for radar-type applications, to distinguish measurements from clutter [4]. There does not exist a study to determine if this clutter model would be appropriate for Doppler frequency shift measurements from LEO satellites. Measurement to Target Ratio In a LEO-based SOP navigation system, the ratio of targets to received measurements differs significantly from that of a radar system. At a given time epoch, a receiver would have no more than a single measurement from each nearby satellite whereas in radar target tracking one would have many measurements originating from a single target. This limiting number of measurements from LEO satellites may cause an increase in the time required to identify a satellite with a specified certainty. Use of Dynamics Models to Aide PDAF Unlike traditional target tracking where targets may have unknown or unpredictable dynamics, LEO satellites dynamics can be estimated through the use of one of a variety of orbital propagators. The most commonly used is the Simplified General Perturbations model (SGP4). Although this model is known to suffer from significant errors [6] the estimates can still be used to limit the potential number of satellites a measurement originated from and establish the validation region surrounding each satellite. Additionally, an even further simplified orbital model such as the J2 acceleration model as it was applied to generic space objects in [7], can be used to propagate the covariance of satellites to be implemented in the data association PDFs. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. ? References [1] Z. M. Kassas, N. Khairallah and S. Kozhaya, "Ad Astra: Simultaneous Tracking and Navigation with Megaconstellation LEO Satellites," IEEE Aerospace and Electronic Systems Magazine, pp. 1-19, 2024. [2] Z. M. Kassas, S. Kozhaya, H. Kanj, J. Saraoufim, S. W. Hayek, M. Neinavaie, N. Khairallah and J. Khalife, "Navigation with Multi-Constellation LEO Satellite Signals of Opportunity: Starlink, OneWeb, Orbcomm, and Iridium," in IEEE/ION Position Location and Navigation Symposium, Monterey CA, 2023. [3] S. Kozhaya, H. Kanj and Z. M. Kassas, "Multi-Constellation Blind Beacon Estimation, Doppler Tracking, and Opportunistic Positioning with OneWeb, Starlink, Iridium NEXT, and Orbcomm LEO Satellites," in ION Position, Location, and Navigation Symposium, Monteray, CA, 2023. [4] Y. Bar-Shalom, F. Daum and J. Huang, "The Probabilistic Data Association Filter," IEEE Control Systems, vol. 29, no. 6, pp. 82-100, 2009. [5] S. L. Bowman, N. Atanasov, K. Daniilidis and G. J. Pappas, "Probabilistic data association for semantic SLAM," in IEEE International Conference on Robotics and Automation (ICRA), Singapore, 2017. [6] D. A. Vallado and P. Crawford, "SGP4 Orbit Determination," American Institute of Aeronautics and Astronautics, Colorado Springs, 2008. [7] X. Zhou, S. Wang and T. Qin, "Multi-Spacecraft Tracking and Data Association Based on Uncertainty Propagation," Applied Sciences, 2022.
Published in:	2025 IEEE/ION Position, Location and Navigation Symposium (PLANS) April 28 - 1, 2025 Salt Lake Marriott Downtown at City Creek Salt Lake City, UT
Pages:	1265 - 1270
Cite this article:	Sanderson, Jennifer, Kassas, Zaher, "Nearest Neighbor Data Association for LEO Satellite Identification," 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), Salt Lake City, UT, April 2025, pp. 1265-1270.
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