Blind System Identification of Noncoprime Multichannel Systems and Its Application to Noninvasive Cardiovascular Monitoring

Abstract

Multichannel blind system identification (MBSI) is a technique for estimating both an unknown input and unknown channel dynamics from outputs measured at different points of the system. MBSI is a powerful tool particularly for the identification and estimation of dynamical systems in which a sensor, for measuring the input, is difficult to place. MBSI algorithms, however, are not applicable unless the transfer functions of individual channels are coprime, i.e., sharing no common dynamics among the channels. This paper presents a MBSI method, called intermediate input identification (IIID), applicable to multichannel, noncoprime systems containing common dynamics. A variable is introduced to split the original multichannel system into coprime multichannel subsystems and the one consisting of common dynamics. A modified MBSI method is used for identifying the coprime distinct channel dynamics, while the common dynamics is identified based on its unforced response. Identifiability conditions using linear complexity are obtained for both known and unknown model structures. Uniqueness and other properties of the solution are examined. The IIID method is then applied to noninvasive monitoring of the cardiovascular system. The arterial network is modeled as a multichannel system where the blood flow generated by the left ventricle is the input and pressure profiles measured at different branches of the artery, e.g., brachial, carotid, and femoral arteries, are the outputs. While the direct measurement of the input requires a catheter to be inserted into the heart, the IIID method does not need invasive catheterization. It would allow us to estimate both the wave form of the input flow and the arterial channel dynamics from outputs obtained with noninvasive sensors placed at different branches of the arterial network. Numerical examples and simulations verify the major theoretical results and the feasibility of the method.