## UFIHE Algorithm

For the purpose of Fault Detection and Isolation (FDI), we propose a robust hybrid estimation algorithm for a class of hybrid system with unknown fault input. The algorithm is named as the **Unknown Fault Input Hybrid Estimation (UFIHE)** algorithm. Normally, an estimation algorithm for a hybrid system with unknown fault inputs typically has more discrete states than the nominal system, because the resulting hybrid system has extra discrete states representing individual faults. However, it has been shown that too many discrete states (multiple models) degrade the estimation accuracy rapidly in the multiple-model-based hybrid estimation algorithm. Our algorithm excels the existing algorithms in that it reduces the number of the estimators running in parallel. We do not model each fault as a discrete state. We consider the transition of the nominal (normal) hybrid system only. This goal is achieved by decoupling the unknown fault input from the continuous dynamics corresponding to each discrete state. We apply the algorithm to state estimation of VTOL aircraft with changing flight mode (see also Figure 4). Simulation results show that our algorithm give better estimation results than the conventional hybrid estimation algorithms.

Figure 4: Flight mode transition of a VTOL aircraft

Figure 5: Estimation performance of the UFIHE algorithm and the IMM algorithm

(Monte Carlo simulation with 100 runs)

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