# Fault Diagnosis and Prognosis of Satellites and Unmanned Aerial Vehicles: A Review
## 4 Diagnostics
### Model-Based Methods
When addressing a complicated hierarchical system, they converted the representation of the system from an Overlapping Block-Diagonal State Space (OBDSS) to their innovative Constrained-State Block-Diagonal State Space (CSBDSS). The proposed approach can simplify the implementation of KFs in a distributed manner. During Kalman filtering iterations, the constrained-state condition must be met, equivalent to solving local constrained optimization cost functions. Various systems, including power systems and sensor networks, can be addressed with this technique. A hierarchical fault estimation and accommodation approach is proposed in [54]. To minimize the adverse effects of unmodeled dynamics, uncertainty, and disturbances within the SFF, [PERSON], and [PERSON] seek to encourage cooperative interactions across levels and modules. Additionally, they highlighted a crucial finding: centralized estimation schemes exhibit notable drawbacks when faced with unmodeled dynamics, uncertainties, and disturbances. As a result, the cooperative estimation procedure proposed in [54] proves to be a highly applicable method for overcoming the mentioned challenges. An advanced approach to cooperative actuator fault estimation in deep space is presented in [76] that integrates hybrid and switching techniques. Every operational mode represents a distinct cooperative estimation strategy and communication pattern between the localized filters responsible for detecting and estimating the SFF's status. With the help of this approach, fault estimation accuracy is likely to be enhanced in a cooperative and dynamically changing space environment. A cooperative fault accommodation challenge within SFF is explored in [56]. It used absolute rather than relative measurements, like other studies by [PERSON]'s team [45; 52; 55; 57], making the approach applicable to a wide range of SFFs operating in planetary orbits. In this study, collaboration between controllers maximizes the efficiency of supporting a faulty satellite. Therefore, the scope of this study is expanded to include a broader spectrum of SFF based on the cooperative fault accommodation framework. In another study [65], [PERSON] and [PERSON] introduced an innovative, collaborative framework designed to estimate the states of SFF. This framework employed the concept of sub-observers, each dedicated to estimating specific states based on provided input, output, and state information. To maintain estimation errors at a manageable level, they proposed a directed graph representing the interdependencies among subobservers. By carefully selecting the optimal path within these subobservers, a higher-level supervisor gains the ability to thoughtfully choose and configure a set of sub-observers, ensuring accurate estimation of all system states. In cases where unreliable information is introduced due to significant disturbances, noise, or actuator faults, specific subobservers may lose their efficacy. In such scenarios, the supervisor dynamically adjusts the subobserver set by selecting a new path within the subobserver's digraph. This adaptive approach effectively manages and restricts the impact of these uncertainties, ensuring they only influence local estimates of states and faults. Consequently, the spread of uncertainties throughout the estimation process is minimized, preventing extensive performance degradation across the entire SFF [65]. In [64], a particular structure is described by [PERSON] and [PERSON]. The SFF is considered to be a Multiple-Input, Multiple-Output (MIMO) system in this study. By employing this structural approach, the overall formation is optimally managed, and a viable stability analysis can be conducted. One problem, however, is that the MIMO structure is not resilient to local faults. As a result, it is imperative to develop FDI filters capable of detecting such localized faults. FDI filters operating in a local or decentralized capacity were devised and presented to mitigate this vulnerability.