Finite difference identification of noisy distributed systems using scanning measurements

Most of the present-day literature concerned with identification theory and techniques is directed toward lumped parameter systems, and many comprehensive surveys of the field are available, (see Refs. 1 and 2) for example(s)). Relatively little has appeared in the literature concerning distributed identification, and even more noticeable is the scarcity of papers dealing with systems described by the one-dimensional wave equation. Perdeauville and Goodson (Ref. 3) were perhaps the first researchers with a workable but time consuming method for the identification of coefficients of the wave equation. Fairman and Shen (Raf. 4) also considering the wave equation, used the technique of finite differencing to approximate spatial derivatives, and Poisson filter chains to approximate temporal derivatives.