In this work, several procedures for the fault detection and isolation (FDI) on general aviation aircraft sensors are presented.In order to provide a comprehensive wide-spectrum treatment, both linear and nonlinear, mode~based and data-driven methodologies are considered. The main contributions of the paper are related to the development of both FDI polynomial method (PM) and FDI scheme based on the nonLinear geometric approach (NLGA). As to the PM, the obtained results highlight a good trade-off between solution complexity and resulting performances. Moreover, the proposed PM is especially useful when robust solutions are required for minimising the effects of modelling errors and noise, while maximising fault sensitivity. As to the NLGA, the proposed work is the first development and robust application of the NLGA to an aircraft model in flight conditions characterised by tight-coupled longitudinal and lateral dynamics. In order to verify the robustness of the residual generators related to the previous FDI techniques,the simulation results adopt a typical aircraft reference trajectory embedding several steady-state flight conditions, such as straight flight phases and coordinated turns. Moreover, the simulations are performed in the presence of both measurement and modelling errors. Finally, extensive simulations are used for assessing the overall capabilities of the developed FDI schemes and a comparison with neural networks (NN) and unknown input Kalman filter (UIKF) diagnosis methods is performed.