Development of accurate state estimation with observer models from typical sensor measurements are often limited bynoisy measurements typically resulting from sensor fidelity, process disturbances and variables correlations. Theestimation of state variables of the dynamical systems with noisy output measurements, are traditionally modelled withGaussian white noise. With zero-mean noise assumptions, Kalman filter structured observer models have beenintroduced for optimal statistical estimation of dynamic state variables, however this limits their efficacy for applicationsin practice where noise is more unpredictable and chaotic. In order to overcome this limitation, the system output measurements have been previously modeled with generalizedlinear model containing colored noise contributions to sensor measurements. This model was used for direct staticestimation from measurements by error minimization and principal components analysis with generalized singularvalue decomposition. Here, the non-Gaussian measurement errors are approximated using Edgeworth series expansion to obtain Gaussianerror approximations in a generalized linear model. With the proposed filter, progressive noisy observations can bereduced to a Gaussian white noise approximation using the noise distribution of the output measurements. Noisymeasurements in typical industrial dynamic processes are expressed as gross error additions to expected sensormeasurements. By defining acceptable measurement deviations from expected measurements with continuousmonitoring, gross errors are grouped into noisy measurement models: outliers - instantaneous rare deviations, bias -continuous varying deviations, or drift - continuous growing deviations. These deviations are reduced to whiteGaussian approximations with the Edgeworth series model. The resulting output measurement model is used for accurate static state estimation through error minimization withgeneralized singular value decomposition. Static state estimates with this method are stable and consistent in following process variable evolution with minimalerror. They are employed for development of reduced order dynamic observer models with the Extended Kalman filterframework for optimum estimation. The numerical illustrations of a simple Biochemical process and the simplifiedTennessee Eastman process are used as examples to showcase the performance of the developed approach.