# Fault Diagnosis and Prognosis of Satellites and Unmanned Aerial Vehicles: A Review
## 4 Diagnostics
### Model-Based Methods  
Model-based methodologies have been a staple of fault diagnostic strategies, specifically ACS diagnostics, for many years. Their capacity to carry out precise and timely FDII using high-fidelity models has made them reliable techniques for time-sensitive missions. On top of that, the interpretability present in the outputs provided by model-based methods is conducive to making appropriate judgments and taking remedying fault-tolerant measures. This section discusses their applicability in a broad spectrum of satellite and UAV diagnostic case studies. [PERSON] and [PERSON] [45] utilized a second-order nonlinear sliding mode observer for FDII in a tetrahedron RW assembly. [PERSON] and [PERSON] indicated that due to the over-actuatedness of the RW assembly and redundant RWs, no more than two in-phase faults could be fully diagnosed, and postprocessing is needed to perform isolation and identification. However, even with two concurrently occurring faults, isolating their locations proved challenging since several permutations of faulty RWs could have the same effect on the generated residuals. [PERSON] and [PERSON] worked around this problem by taking measures to make distinctions between the different possibilities. [PERSON] and [PERSON] [41] utilized a two-stage EKF to estimate satellite actuator and sensor faults. The focal point of their study is estimating both multiplicative and additive faults while modeling actuator faults as multiplicative and additive and sensor faults as additive. [PERSON] and [PERSON] represented multiplicative faults as control effectiveness parameters and additive faults as added amplitudes. Their proposed model was also tested using the telemetry data of an on-orbit satellite, and the faults were successfully estimated. Another work addressing the problem of diagnosing multiplicative faults is the study by [PERSON] et al. [11], which presents an adaptive model-based methodology applicable to Lipschitz nonlinear systems. The proposed methodology performs fault detection and identification simultaneously. It involves an adaptive state observer leveraging a robust adaptive law effective against unknown faults, measurement, and modeling uncertainties. The scheme was tested on a single-link flexible joint robot arm and displayed rapid convergence and better accuracy rates than a similar existing fault estimation scheme. To accommodate the adaptivity requirements in satellite ACS diagnosis applications, [PERSON] et al. [19] used Adaptive Unscented Kalman Filter (AUKF) techniques for fault detection of RWs. They expanded upon them by combining them with the Particle Swarm Optimization (PSO) method. The PSO method is used to circumvent the complicated procedure of setting up the AUKF for parameter estimation and making it more precise and efficient. The model-based methodology is based on a high-fidelity RW model developed by [PERSON] [94]. It is indicated by [PERSON] et al. that for more rigorous results, a more sophisticated implementation of the PSO and AI manipulation is required. Furthermore, [PERSON] et al. addressed the fault diagnosis of RW assemblies in [95] by introducing a model-based hierarchical approach for FDII of RWs onboard satellites. Their three-step proposed methodology consists of (1) an AUKF for detection, (2) multiple UKFs along with Bayes' probability theorem and probability distributions for isolation, and (3) dual-state and parameter estimation using UKFs for identification. The methodology's accuracy rate in detecting, isolating, and identifying faults was determined by simulations to be 89.5% on average. During their research on enhancing AUKFs for single RW usages, [PERSON] et al. [16] also presented the Covariance-based Adaptive Unscented Kalman Filter (CAUKF), a variant of the AUKF with the aim of refining parameter estimation. The model-based method incorporates adaptive covariance matrices of states and parameters to be robust to sudden fluctuations in nonmeasurable parameters of the system.