Parameter estimation for stochastic linear hereditary systems

Given the response covariance of a linear heredity system and a parameterized model, a model error method is developed to estimate unknown system parameters. It is assumed that the system is linear and time-invariant, but not necessarily finite-dimensional. A characterization of the time-invariant property in terms of the response covariance function leads to a simplified error functional to estimate the unknown parameters. Numerical results are presented illustrating agreement between the estimated model and the data. Robustness of the methods to errors in the covariance function is discussed