A Study on an Anti-Multiple Periodic Frequency Modulation (PFM) Interference Algorithm in Single-Antenna Low-Earth-Orbit Signal-of-Opportunity Positioning Systems  
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of providing Positioning, Navigation, and Timing (PNT) services for a wide range of applications [1; 2; 3; 4; 5]. However, as GNSS applications increase, its inherent limitations have gradually surfaced. These include weak received signal power, limited frequency diversity, high construction and maintenance costs, and susceptibility to malicious interference, particularly in times of conflict or crisis, which can render services unavailable [6; 7]. Addressing these GNSS deficiencies, especially ensuring reliable and high-precision PNT services in environments where GNSSs are unavailable, has become a key focus for future development [8; 9; 10]. Currently, nations worldwide are actively developing resilient PNT systems to ensure that military equipment can achieve accurate positioning even when GNSS performance is degraded or denied. Notably, the U.S. Department of Defense's 2020 PNT Technology Development Roadmap highlights the use of Signal of Opportunity (SOP) to achieve absolute positioning, thereby complementing GPS functionality and enhancing its availability and robustness. SOP positioning is a technique that utilizes perceivable non-navigation signals--such as acoustic, optical, electromagnetic, and mechanical information--for positioning purposes. Given the abundance of various radio signals in space, the current research primarily focuses on radio-based SOP. SOP typically include both ground-based and space-based radio signals. Ground-based SOP have limited coverage capabilities, making global seamless coverage in regions like deserts, oceans, and polar areas challenging. Space-based SOP mainly refer to signals transmitted by non-navigation/non-cooperative satellites. With the significant development and deployment of Low-Earth-Orbit (LEO) satellites in recent years, SOP positioning using LEO satellites have gradually become a primary focus in navigation and positioning applications [11; 12]. Unlike traditional GNSS-based positioning, SOP positioning using LEO satellites leverages downlink signals, such as those from communication satellites, as radiation sources to achieve ground terminal positioning [13; 14; 15]. Meanwhile, with the rapid development of emerging satellite constellations represented by Starlink and OneWeb, the massive number of LEO satellites provides abundant radiation sources for space-based SOP positioning. In this context, exploring SOP positioning based on LEO constellations has become a research hotspot. Numerous studies have documented various cases of positioning using LEO satellites by different research teams, with achieved positioning accuracy generally reaching the tens of meters level [16; 17; 18; 19; 20; 21; 22; 23; 24]. However, current research on anti-jamming technologies for LEO satellites SOP positioning remains limited, particularly for Periodic Frequency Modulation (PFM) interference, such as Periodic Linear Frequency Modulation (PLFM) and Periodic Sinusoidal Frequency Modulation (PSFM) signals. To date, there has been little in-depth investigation into these interference types both domestically and internationally. However, PFM interference is one of the most common types of interference faced by LEO satellites SOP positioning receivers. This type of interference, typically generated by malicious jammers, radar systems, or civilian radio stations, is characterized by low average power, high peak power, and wide bandwidth.