Estimation of External Forces from Noisy State Measurements

A technique is presented for the estimation of unknown forces which might be acting on a dynamic system. The method may use for input noisy measurements of any observable set of functions of the system states (including, trivially, the states themselves). The estimate is obtained from the solution of a two-point boundary-value problem, and is in the form of an unmodeled disturbance versus time trajectory. In this paper, the method is derived and discussed, and then illustrated by estimating several unknown forcing functions acting on a simple vibrating system.