## 1 Introduction  
With the rapid development of aerospace technology, the importance of space in the civil and military fields has become increasingly prominent and, thus, has become a strategic fulcrum for competition among countries. Space technology is an essential basis for developing and utilizing space resources and safeguarding national security. Satellites are some of the most important tools for human exploration and space applications. Due to the high cost of satellite construction and the high cost of launching and in-orbit maintenance, once a failure occurs, it will cause considerable losses. In recent years, on-orbit fault diagnosis technology has made remarkable progress, which has effectively improved the on-orbit operation status and life of satellites. Over the years, studies on fault diagnoses of spacecraft have attracted extensive attention from scholars, and lots of valuable research results have emerged in both the theoretical and engineering fields [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. Research such as that on fault detection and diagnosis [1, 2, 3, 4, 5, 6], reconfigurability analysis [7, 8, 9], life or fault prediction [10, 11, 12, 13], and fault tolerance [14, 15, 16, 17, 18, 19] improves the security and reliability of satellite on-orbit operation from different perspectives. Fault diagnosis is a significant means of achieving high-precision, long-life, and high-reliability on-orbit operation of satellite systems, and it is of great significance. However, existing research has mainly focused on the design of diagnostic algorithms, and there have been few studies on fault diagnosability. According to the definition of fault diagnosability [20], diagnosability includes detectability and isolability. Diagnosability is the key to fast and accurate fault detection and isolation in dynamic systems, and it is also the basis of the design of fault diagnosis methods. Without analyzing the diagnosability of faults, blindly designing fault diagnosis algorithms will inevitably consume personnel and material resources and may not achieve satisfactory results. Therefore, research on fault diagnosability is of great significance. Most of the existing diagnosability research on general control systems only considers the situation of linear system faults [21, 22, 23]; research on nonlinear systems and nonlinear faults can usually only achieve qualitative evaluation [24; 25]. There have been few relatively studies on the diagnosability of satellite systems. For example, [PERSON] [26] studied the fault diagnosability of a satellite momentum wheel based on the idea of if the transfer function from fault to output was zero and if the transfer functions between faults were different. [PERSON] and [PERSON] used the distribution probability of fault vectors and the cosine similarity between different fault vectors in [27] to design a quantitative evaluation method for diagnosability based on directional similarity, which was verified by a satellite attitude determination system. In [28], the authors described a satellite control system as a class of affine nonlinear models by using the invariant minimum dual distribution to give the diagnosability evaluation, which included the qualitative and quantitative evaluation index of detectability and isolability. This paper proposes a method of system diagnosability evaluation based on information geometry theory. The diagnosability problem of the system is described as a distance judgment problem of a multivariate distribution in statistics, and the Fisher information distance is used to quantify the diagnosability of system faults. A fault detectability index and fault isolation index are designed. The designed indexes have explicit and intuitive geometric significance, and they are real distance measures without the problem of index asymmetry. The principle and algorithm process of the method to realize diagnosability judgment are given.