system for modeling icing events as u201c faults u201d of the system response as revealed here either of these two approaches u201c direct u201d or u201c dual u201d may be used depending upon the number of measurements available to the observer the u201c dual u201d algorithm for selecting the observer gain matrix f follows since this provides the designer with the widest range of potential aircraft applications although it will be appreciated by one skilled in the art that a u201c direct u201d algorithm application would possibly suffice for a system having a large number of measurements given a desired eigenvector v i which one wishes the observer structure to contain one then picks a suitable associated eigenvalue u03bb i that is approximately three times faster larger than the dominant eigenvalue of the response mode associated with the icing encounter for most aircraft this would be a classical u201c phugoid u201d response mode where the aircraft is primarily influenced by energy tradeoffs between altitude influenced by flight path angle and airspeed these eigenvalue eigenvector combinations are selected in order to span the full n dimensional state vector based upon observations of simulated or actual flight data from an icing encounter two types of eigenvectors are selected u2014 those that represent the aircraft response to an icing event or a particular icing mode such as proprotor icing wing icing or tailplane icing.