## 1 Introduction  
With the rapid development of satellite technology, low-Earth orbit (LEO) satellites have emerged as a disruptive innovative technology, playing a key role in multiple fields such as telecommunications, Earth observation, scientific research, and national security [1]. LEO satellites are typically located at an altitude between 160 km and 2000 km. Satellites in this orbit travel around the Earth at extremely high speeds, with the time to complete one orbit ranging from approximately 90 min to 120 min [2]. A critical issue that must be addressed in such high-speed movement for wireless communications is the significant Doppler shift. High Doppler shift and multipath effects lead to two-dimensional fading in the time-frequency domain. To address this issue, the orthogonal time frequency space (OTFS) modulation technique has emerged as a promising solution in recent years. The emerging OTFS modulation [3, 4] has a greater advantage than OFDM over time-frequency dual-selective channels in high-mobility scenarios, which transforms the rapidly varying time-domain channel into a nearly static channel in the delay-Doppler (DD) domain [5, 6]. Channel estimation and data detection in OTFS systems are often conducted in the DD domain. Channel estimation is a critical technique to improve the performance of OTFS systems. However, in LEO satellite communications, the extreme Doppler spread may cause Doppler shifts that exceed the intrinsic resolution limit of OTFSsystems. Therefore, paths of the channel often have non-integer Doppler shifts in practical scenarios. The fractional Doppler shifts make the impact of Doppler paths disperse into all Doppler bins [7], which introduces the inter-Doppler interference (IDI) among data in the DD domain. Additionally, the rapidly varying channel coherence time demands ultra-low-latency estimation algorithms. Therefore, LEO satellite communications require low-complexity algorithms that can achieve accurate channel estimation under fractional Doppler conditions. Current available channel estimation methods [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19] for OTFS systems can be classified into four categories. The first category is channel estimation methods with the embedded pilot in [8; 9; 10; 11]. This algorithm inserts one or more pilot symbols into the data sequence, serving as a commonly used channel estimation scheme for LEO satellite communications [10; 11]. In these methods, the dispersed paths on other Doppler bins due to fractional Doppler shifts are treated as small integer Doppler paths. Due to the limited number of guard symbols, these methods can only estimate a few major bins and cannot account for all of the dispersed Doppler bins. The second category is the correlation-based channel estimation methods, in which the channel response of the pilot signal is correlated with the basis function in the DD domain, as described in [12]. However, in scenarios where a single delay path has multiple non-integer Dopplers paths, the overlapping of dispersed Doppler bins may greatly degrade the performance of correlation processing, which highly increases the errors in channel estimation. To reduce the channel estimation errors, a quasi-Newton method is introduced to iteratively re-estimate the fractional Doppler channel in [13], but the complexity of the channel estimation is significantly increased. The third category is based on the orthogonal matching pursuit (OMP) algorithm. This algorithm was initially applied in the OFDM system [14] and can achieve joint estimation of the frequency offset and channel. However, it is not directly suitable for the Doppler estimation problem in the OTFS system. On this basis, an improved structured sparse adaptive matching pursuit (MSSAMP) algorithm is proposed in [15], which can estimate the Doppler and channel information in the case of unknown channel sparsity. However, the algorithm can only estimate the integer Doppler values and is unable to distinguish fractional Doppler values.