This paper addresses the key question that when faults occur either the aircraft system dynamics changes due to the fault or these dynamics are unknown (precisely). This question is addressed for the important case of Air Data Sensor failures, due to e.g. icing, for fixed wing aircraft operating in a nominal fight condition. The solution to this question uses basic ideas from subspace Identification to cast this problem in linear least squares problem with convex constraints (nuclear norm and 1-norm constraints). The latter are relaxations of a rank and cardinality constraint. The presented solution is validated using real-life fight test data.