Identification of a Two-Input System: Variance Analysis

This paper examines the identification of a single-output two-input system. Motivated by an experiment design problem(should one excite the two inputs simultaneously or separately), we examine the effect of the (second) input signal on the variance of the various polynomial coefficients in the case of FIR, ARX, ARMAX, OE and BJ models. A somewhat surprising result is to show that the addition of a second input in an ARMAX model reduces the variance of all polynomials estimates.