# Fault Diagnosis and Prognosis of Satellites and Unmanned Aerial Vehicles: A Review
## 2 Preliminaries and Definitions
The visual representation of the mentioned process is depicted in Figure 2. Nevertheless, the intricate details of fault-tolerant methods and the literature related to them fall beyond the scope of this paper. FDP methodologies mostly monitor the health state of satellites, spacecraft, and UAVs through model-based and data-driven methods. Model-based techniques rely on high-fidelity models of systems and estimators to evaluate fault-sensitive states, analyze them, and compare the results with the model of the system operating nominally. Model-based methods comprise deterministic and stochastic strategies. Stochastic estimation schemes account for the added process and measurement noise while estimating states. Among stochastic schemes, Kalman Filter (KF) are utilized for linear models with added Gaussian noise, and Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) for  
Figure 2: FDP and fault-tolerant control schemes. nonlinear models with added Gaussian noise. When several faults are involved, interacting multiple model (IMM) methods could be used which employ several interacting filters to classify different fault modes [13]. Meanwhile, the Particle Filter (PF) class is reliable for estimation in nonlinear models with non-Gaussian noise. All in all, the main drawback of using model-based methods is their requirement for precise models that are not always available and are difficult to derive for every application. Essentially, the family of KFs can estimate the internal states of a linear or nonlinear dynamic system in the presence of known parameters and noisy processes and measurements. They could also be used to estimate the parameters instead of states, considering only states, and the process and measurement noises are known. Keep in mind that in this text, states refer to the dynamical representation of systems that tend to exhibit rapid changes. In contrast, parameters are virtually time-invariant elements closely tied to the system's characteristics. System state estimation is used to study the deviations of the system's dynamical behavior from nominal conditions. However, the system's parameters, as opposed to states, could also indicate a system's health, especially when it is undergoing degradation. There are also approaches for simultaneously estimating the states and parameters of a system, namely, dual and joint estimation. On the other hand, parameter estimation is usually, but not necessarily, associated with time delays, restricting their usage to offline health monitoring and not accommodating online monitoring requirements [14]. Model-based methods usually utilize residual-based algorithms to diagnose faults in control systems. To clarify the practicality of residual-based algorithms in fault diagnosis, an example of their use in a general discrete linear system along with a linear KF was outlined in [15]. Accordingly, the linearized system model in state-space form is represented by  
\[\left\{\begin{array}{l}X_{k}=A_{k-1}X_{k-1}+\Gamma_{k-1}w_{k-1}\\ Z_  
When a threshold is surpassed, a fault is identified, and depending on the context, it may be isolated and described based on where and the extent to which the threshold has been surpassed. Residual-based algorithms have the flexibility to employ different residual definitions, but they fundamentally share the same concept as exemplified in [15]. However, using constant thresholds could yield unsatisfactory results or cause divergence, especially when they are poorly defined and when the nonmeasurable parameters of the system undergo abrupt changes [16]. To avoid this problem, adaptive thresholding methods have been utilized in the literature. Data-driven methods are another popular approach for health monitoring in nonlinear systems. Data-driven techniques encompass a broad spectrum of Machine Learning (ML) and Artificial Intelligence (AI) algorithms that can learn and extract patterns from datasets.