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We analyze the statistical performance of identification of stochasticdynamical systems with non-linear measurement sensors. This includes stochasticWiener systems, with linear dynamics, process noise and measured by anon-linear sensor with additive measurement noise. There are many possiblesystem identification methods for such systems, including the MaximumLikelihood (ML) method and the Prediction Error Method (PEM). The focus hasmostly been on algorithms and implementation, and less is known about thestatistical performance and the corresponding Cram\'er-Rao Lower Bound (CRLB)for identification of such non-linear systems. We derive expressions for theCRLB and the asymptotic normalized covariance matrix for certain Gaussianapproximations of Wiener systems to show how a non-linear sensor affects theaccuracy compared to a corresponding linear sensor. The key idea is to takesecond order statistics into account by using a common parametrization of themean and the variance of the output process. This analysis also leads to a MLmotivated identification method based on the conditional mean predictor and aGaussian distribution approximation. The analysis is supported by numericalsimulations

Algorithms and Performance Analysis for Stochastic Wiener System Identification