Data-driven algorithms are developed to fully automate sensor fault detection in systems governed by underlying physics, with a particular focus on the flight test setting. The proposed machine learning method uses a time series of typical behavior to approximate the evolution of measurements of interest by a linear time-invariant system. Given additional data from related sensors, a Kalman observer is used to maintain a separate real-time estimate of the measurement of interest. Sustained deviation between the measurements and the estimate is used to detect anomalous behavior. A decision tree, informed by integrating other sensor measurement values, is used to determine the amount of deviation required to identify a sensor fault. The method is validated by applying it to three test systems exhibiting various types of sensor faults: commercial flight test data, an unsteady aerodynamics model with dynamic stall, and a model for longitudinal flight dynamics forced by atmospheric turbulence. In the latter two cases, fault detection was tested for several prototypical failure modes. The combination of a learned dynamic model with the automated decision tree accurately detects sensor faults in each case.