Identification of continuous-time linear dynamic stochastic systems (Q1175870)

The problem dealt with in the paper is the estimation of parameters in linear stochastic differential equations of the form: \(A(p)y(t)=B(p)u(t)+v(t)\), \(t\in\mathbb{R}\), where \(p\) is the derivative operator \(\left(py(t)={dy(t)\over dt}\right)\), \(A(p)\) and \(B(p)\) are polynomials in \(p\), and \(y(t)\), \(u(t)\) and \(v(t)\) are the output, input and disturbance functions, respectively. First, the authors show that a direct application of the least-squares algorithm is inadequate as it is quite sensitive to small variations in the numerical implementation procedure. Then, some auxiliary integral transformations of the original model are introduced and an instrumental variable-based estimation method is advocated. The convergence of the instrumental variable technique is established under a number of conditions whose frequency-domain interpretation is also provided.