Two-stage parameter estimation methods for linear time-invariant continuous-time systems

This paper considers the parameter estimation problems of general linear time-invariant continuous-time systems described by higher-order constant coefficient differentiate equations. This paper derives the two-stage parameter estimation model of the systems, which contains two parameter vectors, one corresponds to the coefficients of the denominator polynomial of the transfer function and the other corresponds to the coefficients of the numerator polynomial of the transfer function. Furthermore, we propose two-stage projection estimation algorithm, two-stage generalized projection estimation algorithm, two-stage stochastic gradient estimation algorithm, two-stage recursive least squares estimation algorithm and their variants. The proposed algorithms can be extended to investigate the parameter estimation of other linear stochastic systems with colored noises.