# Fault Diagnosis and Prognosis of Satellites and Unmanned Aerial Vehicles: A Review
## 4 Diagnostics
### Model-Based Methods
From Equation (5), Markov processes are described by the quality of their transition probability from one state to another solely depending on the current state of the system, irrespective of how it arrived at its current state. For demonstration, Figure 9 depicts a Markov chain of a fault-prone system with a transition probability matrix of \(P= \begin{bmatrix}p_{11}&p_{12}\\ p_{21}&p_{22}\end{bmatrix} \). [PERSON] et al. [13] utilized the idea of jump Markov processes by presenting a Jump Markov Regularized Particle Filter (JMRPF) for nonlinear Inertial Navigation Sensor (INS) fault identification used in longitudinal control of a fixed-wing UAV. The jump Markov approach was introduced into a regularized PF to address the transitions of the system between faulty and nominal modes based on the Markov property. The proposed scheme of [PERSON] et al. does not require predefined fault models to operate. Instead, estimation is carried out for additive abrupt and incipient faults with unexpected dynamics and amplitudes. A Kalman correction strategy is also incorporated into the proposed scheme, which distributes the particle states in the more probable state-space areas to enhance the state and malfunction estimation further. Under numerical simulations, JMRPF showed 77% less root-mean-square error in estimation than a regularized PF while exhibiting shorter convergence times and more robustness to faults with larger amplitudes. [PERSON] et al. [99] developed a model-based method for actuator FDII of a Hex-rotor UAV. Faults are classified as total actuator failures and gain faults attributed to the actuator lift factor's deviations from the nominal condition. The diagnosis model includes a set of EKF-based fault observers whose output is employed to achieve fault reconstruction. The  
Figure 9: A schematic inspired by [98] of how a dynamic system abiding by a simple Markov process transitions between nominal and faulty modes. proposed methodology of [PERSON] et al. surpasses the accuracy of sliding mode observers in attitude angle tracking. [PERSON] et al. [42] developed an enhanced high gain observer for FDII of angular rate sensors in quadrotor UAVs to further address UAV sensor health monitoring. The proposed model is tested under incipient, oscillatory, and intermittent fault conditions, and its results are compared with the integral chain differentiator and basic high-gain observer techniques. The accuracy rate of the proposed approach significantly surpasses that of traditional techniques while being less computationally intensive and providing fast diagnostics. [PERSON] et al. [43] proposed a novel dynamic Event-Triggered Mechanism (ETM) for fault detection in UAV actuators to achieve minimal communication resource usage and remove correlations between generated residuals and dynamic event-triggered transmission errors while circumventing the Zeno phenomenon. Zeno phenomenon refers to the existence of an infinite number of events in a finite time interval, making ETMs prone to errors. The dynamic ETM approach employed by [PERSON] et al. is based on the \(H_{i}/H_{\infty}\) optimization problem, which is solved using the Riccati recursion method. Their fault detection scheme also utilized a new residual evaluation and thresholding method. The simulation results indicate that the proposed dynamic ETM detection scheme outperforms the static variant in terms of accuracy, requiring at least 13% less event transmission information. [PERSON] et al. also expressed that the next steps in this research would be to evaluate the effect of the dynamic ETM on quantitative fault inspection and examine the effect of closed-loop control systems on faults' noticeability. [PERSON] et al. [36] used a stochastic-model-based method for FDII of actuators onboard tilt-rotor UAVs. Their employed methodology consists of several EKF observers, each assigned to a single corresponding actuator.