Development of accurate state estimation with observer models from process sensor measurements are often limited by noisy measurements typically resulting from sensor fidelity, process disturbances and variables correlations. The estimation of state variables of dynamic systems with noisy output measurements, are traditionally modelled with Gaussian white noise. Noisy measurements of industrial dynamic processes are expressed as gross error additions to bounded expected sensor measurements. This noise treatment targets the design of filters using a combination of GSVD factorization of error covariance and gross error identification. The resulting output measurement model is illustrated on the simplified Tennessee Eastman Process application, where it is successfully applied for accurate state estimation.