This book presents a simple unknown input estimation technique using generalized matrix inverse. The full order observer constructed by g-inverse is extended and implemented for this purpose. The necessary and sufficient condition has been introduced for existence of such an estimator. The proposed method is illustrated by numerical example (Two loop autopilot in pitch plane) and the MATLAB simulation results. A detailed comparison between the estimation results of unknown inputs of a linear time invariant system using projection operator approach and using the method of generalized matrix inverse have been discussed. The full order observer constructed using projection operator approach has been extended and implemented for this purpose.