Design of Gaussian inputs for Wiener model identification

We develop a tractable algorithms for finding the optimal power spectral density of the Gaussian input excitation for identifying a Wiener model. This problem is known as a difficult problem for two reasons. Firstly, the estimation accuracy depends on the higher order joint moments of the potentially infinitely many past samples of the input signal. In addition, the covariance matrix of the parameter estimates is thought to be a highly non-convex function of the power spectral density function. In this contribution we show that under Gaussian assumption it is possible to completely parameterize the set of all admissible information matrices with only a finite number of parameters. We present a convex algorithm to solve the D-optimal design problem. This idea can be extended further to design Gaussian mixture designs.