With the continuous development of space technology, an increasing number of spacecraft have been launched into near-Earth orbit. According to a report by the Union of Concerned Scientists, as of May 2021, over 35 countries operate more than 5000 satellites, with an additional 750000 fragments larger than 1 cm also present in orbit. This proliferation of space assets and debris significantly increases the risk of collisions, posing threats to space safety and efficient orbital resource management. Therefore, rapid and accurate initial orbit determination (IOD) of space targets is crucial for ensuring space security. Traditional IOD methods, such as Laplace’s and Gauss’s methods, often struggle under short arc observational conditions due to their sensitivity to measurement errors. To address these challenges, we explore the application of spatial filtering velocimetry to enhance the accuracy and robustness of IOD under limited observational data and significant error conditions.

In this paper, we integrate the principles of spatial filtering velocimetry with IOD algorithms to achieve accurate orbit determination of space targets. Spatial filtering velocimetry utilizes a uniformly distributed grating to measure a target’s angular velocity. A detailed mathematical formulation of the method is included, supplemented by imaging simulations to evaluate the influence of observational errors on IOD accuracy. The simulation platform employed features an i5-12500H processor @3.10 GHz with 32 GB of RAM. Observational parameters and scenarios (Tables 1 and 2) are meticulously designed to replicate real-world conditions. During simulations, targets are observed over 20 s, approximately 1/276 of an orbital period. Gaussian noise with varying standard deviations (0″, 5″, 10″, 15″, 20″, and 25″) is introduced to simulate angular errors. In addition, a sinusoidal grating with an appropriate period is used to modulate the target’s brightness, enabling the extraction of frequency information to calculate angular velocity and acceleration. The proposed method is compared with traditional IOD techniques, including Laplace’s method, Gauss’s method, Gooding’s method, and the AURORAS method. Comparative analysis focuses on accuracy and robustness under varying observational error conditions.

The results demonstrate that the relative errors in distance measurements using the spatial filtering velocimetry method are 0.83%, 4.32%, 1.23%, 1.42%, 3.19%, and 1.32% for six targets under ideal conditions (Table 3). When the standard deviation of observational error increases to 25″, the relative errors remain stable at 0.77%, 4.24%, 1.27%, 1.43%, 3.21%, and 1.33%, respectively. While the method shows higher absolute errors compared to others under ideal conditions, it exhibits superior robustness, with minimal error fluctuation as measurement noise increases (Fig. 10). In contrast, other methods experience significant degradation in accuracy. The robustness of spatial filtering velocimetry arises from its direct measurement of angular velocity, which reduces the coupling between angular position errors and angular motion. In addition, we also analyze the influence of spectral bandwidth on orbit determination accuracy by varying the window length of the short-time Fourier transform function (Fig. 12). Results indicate that distance error decreases initially with increasing window length but rises once becomes too large. The behavior is attributed to the trade-off between spectral signal bandwidth and the resolution of frequency changes, affecting the accuracy of angular velocity extraction.

In this paper, we propose a novel method for initial orbit determination of space targets based on spatial filtering velocimetry. By directly measuring angular velocity using a uniformly distributed grating, the method minimizes the coupling between angular position errors and angular motion, thus enhancing robustness under significant observational errors. The accuracy of the method and its performance under varying observational error conditions are evaluated through imaging simulations. The results indicate that, while the method’s distance measurement accuracy is relatively low under ideal conditions, remarkable robustness, and stability are demonstrated as measurement errors increase. To further enhance orbit determination accuracy, efforts will focus on extending the sampling time, refining time-domain spectral analysis techniques, achieving orbit correlation, and introducing additional constraints. Furthermore, observational experiments will be conducted to validate the effectiveness of these methods, providing robust support for space situational awareness and the determination and prediction of space debris orbits.