TIME-DOMAIN LINEAR SYSTEM IDENTIFICATION USING MATRIX EXPONENTIALS.

A novel technique for estimation of the unknown parameters in a linear time-invariant dynamic system model is derived and demonstrated on some example problems. The method uses matrix exponentials to calculate the state vector as well as state vector sensitivities to the unknown parameters. Experimental data consist of discrete, state-observable, free, or forced time-domain measurements. Corrections to the unknown parameters are calculated using the matrix exponential sensitivities along with residuals between the integrated solution (using candidate values for the parameters) and the measurements. The results demonstrate that the method is (i) very accurate (perfect if perfect state-observable measurements are available), (ii) not sensitive to initial guessed values of the unknown parameters, and (iii) only slightly sensitive to significant measurement noise.