In recent years, with the development of micro-satellite clusters and large-scale satellite constellations, the likelihood of multiple spacecraft engaging in orbital pursuit–evasion games has increased. This paper establishes a novel interception domain theory for planar orbital multi-player “encirclement-capture” differential games, and it proves the partitioned structure and classification properties of Nash equilibrium solutions. The main contributions of our study are the following: (1) Proposing the first rigorous definition of interception domains in orbital pursuit–evasion games, proving their convexity, developing computational methods for domain intersections, and establishing a complete classification of equilibrium for planar multi-pursuer interception games, which establishes a theoretical foundation for analyzing multi-spacecraft orbital pursuit–evasion games. (2) Analyzing Nash equilibrium properties for “encirclement-capture” differential games with two, three, or more pursuers, classifying degenerate/non-degenerate scenarios via spatial inclusion relationships. The equilibrium results indicate that as the number of pursuers increases, the game tends toward a degenerate scenario where the likelihood of redundant pursuers (whose actions do not affect the game outcome) rises.

Recent advancements in satellite optical reconnaissance have elevated the sun angle to a critical factor in orbital pursuit-evasion games. The stringent imaging constraints imposed by sun angle and relative distance induce non-smoothness in the terminal region of such differential games, significantly complicating equilibrium-solution derivation. To address this challenge, we formulated a novel differential game model where the pursuer minimizes the time-to-entry into the evader’s effective imaging region. We first constructed a sequence of low-dimensional manifolds that collectively cover the terminal region, solving the differential game with this sequence to yield the Nash equilibrium. Subsequently, we approximated the terminal region using a smooth manifold of identical dimensions, enabling a computationally efficient approximate solution. Both methodologies demonstrate broad applicability to orbital differential games featuring non-smooth terminal regions. Simulation results confirm that the approximation error becomes pronounced only under extreme initial sun angles, though this error remains acceptable for practical space reconnaissance applications.

Deep learning (DL) methods have shown great potential for remote sensing image change detection recently, but still suffer from several limitations. Within the identical semantic concept, significant but irrelevant changes in surface texture, color and spatial shifting of building objects resulted from variations in imaging physical factors, causes feature inconsistency of building objects in bitemporal sences. Conventional DL methods lack the capability to effectively distinguish real changes from irrelevant changes, leading to some false detections. This letter propose a novel framework, the multi-scale residual alignment transformer (AlignFormer), to mitigate the above issues. Specifically, inspired by deformable attention mechanism, we firstly design an adaptive feature alignment module (AFAM) to suppress the inconsistency of feature pairs, where the regions of building can be adaptively focused on and the spatial-temporal dependencies of relevant building objects in feature pairs effectively captured, via scheme of flexibly sampling Keys/Values for each given Query. Besides, we utilize an extremely tiny Swin Transformer as the backbone of differencing-based framework for obtaining hierarchical features. Moreover, inspired by residual learning strategy, three AFAMs are integrated into the framework to form the multi-scale residual architecture for the coarse-to-fine alignment of the paired features. Experimental results confirm the superiority of our proposed method over several state-of-the-art algorithms. Our code will be released at https://github.com/lilei-aircas/AlignFormer_CD.