This paper addresses the issue of spacecraft pursuit and evasion, considering factors such as incomplete information and attitude deviations in space. From the perspective of the pursuing spacecraft, five state estimation strategies are proposed, along with an optimal control law for this scenario. Initially, a finite-time differential game model under complete information is established, which serves as the control strategy for the escaping spacecraft, thereby circumventing an infinite-dimensional game scenario. Subsequently, the impact of incomplete information on the payoff function of the pursuing spacecraft and the influence of attitude deviation on the pursuit and evasion game task are analyzed. The control error resulting into attitude deviation is compensated by the proposed state estimation algorithm. The simulation analysis validates the efficacy of the five state estimation methods examined in this study. Additionally, these algorithms have been evaluated with respect to speed, stability, and energy consumption. The results indicate that the proposed techniques can ensure successful execution of pursuit tasks, effectively mitigating losses attributed to incomplete data and attitude deviations. Furthermore, these methods demonstrate potential applicability to other space-related tasks such as proximity tracking, space rendezvous and docking, and the management of uncontrollable spacecraft.