A Spectral Representation Method For Continuous-Time Stochastic System Estimation Based On Analog Data Records

Abstract

In this paper a novel and effective maximum likelihood type method for the estimation of physically meaningful continuous-time stochastic systems from analog data records is introduced. The method utilizes the ARMAX canonical form and block-pulse function spectral representations, through which the problem is shown to be transformed into that of estimating an induced and special-form discrete stochastic system from spectral data. The proposed method is based on a number of key structural and probabilistic properties that this discrete system is shown to possess, including stationarity, invertibility, and the bijective transformation nature of its mapping relationship with the original continuous-time system.Unlike previous schemes, the proposed method utilizes analog data without depending upon estimates of signal derivatives or prefilters, avoids errors due to direct discretizations associated with instantaneous sampling, and is characterized by a linear transformation relationship between the discrete and the original continuous-time system parameters. This leads to additional important advantages, such as the elimination of sensitivity problems associated with highly non-linear mappings, the capability of incorporating a priori system information, and reduced computational complexity. The effectiveness of the method is verified via numerical experiments with a number of stochastic systems.