A Spectral Representation Method for Continuous-Time Stochastic System Estimation based on Analog Data Records

In this paper a novel and effective Maximum Likelihood type method for the estimation of 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 transformed into that of estimating an induced discrete system from spectral data. The proposed method is based on a number of key properties that this discrete system is shown to possess, such as stationarity, invertibility, and the bijective transformation nature of its mapping relationship with the original continuous-time system. Unlike previous schemes, the proposed method can use analog data without depending on explicit estimates of signal derivatives or prefilters, avoids significant errors associated with direct discretizations, and is characterized by a linear transformation relationship between the discrete and the original continuous-time system parameters that leads to low computational complexity, circumvents sensitivity problems associated with non-linear transformations, and allows for the straightforward incorporation of a-priori system information.