## 1 Introduction  
Traditional spacecraft orbit determination primarily employs two methodologies: ground station/survey ship-based tracking and global navigation satellite system (GNSS) receiver measurements. For medium- and low-orbit spacecraft, the L-band autonomous orbit-determination technology utilizing GNSS navigation receivers has proven effective, offering high accuracy while significantly alleviating the operational burden on ground tracking, telemetry and command (TT&C) networks [1]. However, medium- and high-orbit spacecraft encounter limitations with GNSS navigation signal measurements, including a limited number of receivable satellites, weak signal strength, poor geometric configurations and insufficient robustness [2]. Consequently, orbit measurement and determination for medium- and high-orbit spacecraft predominantly rely on ground tracking stations or ships. This approach, while effective, necessitates multiple tracking stations or ships, resulting in a suboptimal efficiency-to-cost ratio. Additionally, the existing orbit-determination system struggles with tracking arcs for overseas spacecraft, leading to constrained orbit-measurement accuracy. A single tracking station often fails to meet the stringent orbit-determination accuracy requirements for spacecraft. Satellite navigation systems such as global positioning system (GPS), GLONASS, Galileo and Beidou have established or demonstrated the functionality of Ka-band inter-satellite links. These links enable various extended users (such as satellites, aircraft, space stations and other spacecraft) to perform distance measurements and data transmissions. Particularly when ground TT&C stations are out of sight, high-precision orbit determination can be achieved through the Ka inter-satellite link [3]. While numerous studies have explored orbit determination via navigation inter-satellite links, the majority focus on applications within navigation constellations, with limited research on extended user orbit determination [4, 5]. For instance, the study in [6], \"Research on the Beidou Clock Difference Observation and Strategy of Autonomous Orbit Determination under the Condition of Inter-Satellite Link\", does not address the challenge of non-high-precision time-frequency extended users achieving time-frequency synchronization, and it only outlines strategies for bidirectional orbit determination between navigation satellites. The paper [7], \"The Preliminary Result and Analysis for BD Orbit Determination with Inter-satellite Link Data\", introduces methods for independent orbit determination using Ka inter-satellite links and joint orbit determination combining inter-satellite Ka measurements with L-band data, demonstrating significant improvements in navigation-measurement orbit determination and time synchronization accuracy for the L-band. The papers [8, 9] describe methods requiring extended users to use bidirectional ranging values for orbit determination, overlooking the practical limitation that in-orbit extended users can only obtain unidirectional ranging values. These studies also demand frequent observation arcs and substantial time slot resources within the navigation inter-satellite link, which are impractical for large-scale user time slot resource applications. This paper proposes a unidirectional orbit-determination method based on the navigation Ka inter-satellite link for extended users without high-precision time-frequency references. Given the limited time slot resources of the navigation inter-satellite link [10, 11], non-atomic clock users collect unidirectional range data according to time slot planning. The clock difference value is deduced and compensated using a clock difference model, achieving high-precision time and frequency synchronization along with bidirectional communication. Because navigation satellites cannot return ranging values to extended users, the latter can only collect unidirectional ranging values post-launch.