Consistent estimation of autonomous linear time-invariant systems from multiple experiments

Operational modal analysis from impulse response data can alternatively be viewed as an identification of a stable autonomous linear time-invariant system. For example, earthquake response data of civil engineering structures and impulsive excitation of bridges leads to this problem. Identification from a single experiment, however, does not yield a consistent estimator in the output error setting due to the exponential decay of the noise-free signal. Using data from multiple experiments, on the other hand, is not straightforward because of the need to match the initial conditions in the repeated experiments. Consequently, we consider the identification from arbitrary initial conditions and show that consistent estimation is possible in this case. The computational method proposed in the paper is based on analytic elimination of the initial conditions (nuisance parameter) and local optimization over the remaining (model) parameters. It is implemented in a ready to use software package, available from http://slra.github.io/software.html