(17e) State Estimation of System Measurements with Edgeworth-Expanded Gross Errors Using Generalized Singular Value Decomposition

Development of accurate state estimation with observer models from typical sensor measurements are often limited by noisy measurements typically resulting from sensor fidelity, process disturbances and variables correlations. The estimation of state variables of the dynamical systems with noisy output measurements, are traditionally modelled with Gaussian white noise. With zero-mean noise assumptions, Kalman filter structured observer models have been introduced for optimal statistical estimation of dynamic state variables, however this limits their efficacy for applications in practice where noise is more unpredictable and chaotic.

In order to overcome this limitation, the system output measurements have been previously modeled with generalized linear model containing colored noise contributions to sensor measurements. This model was used for direct static estimation from measurements by error minimization and principal components analysis with generalized singular value decomposition.

Here, the non-Gaussian measurement errors are approximated using Edgeworth series expansion to obtain Gaussian error approximations in a generalized linear model. With the proposed filter, progressive noisy observations can be reduced to a Gaussian white noise approximation using the noise distribution of the output measurements. Noisy measurements in typical industrial dynamic processes are expressed as gross error additions to expected sensor measurements. By defining acceptable measurement deviations from expected measurements with continuous monitoring, 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 white Gaussian approximations with the Edgeworth series model.

The resulting output measurement model is used for accurate static state estimation through error minimization with generalized singular value decomposition.
Static state estimates with this method are stable and consistent in following process variable evolution with minimal error. They are employed for development of reduced order dynamic observer models with the Extended Kalman filter framework for optimum estimation. The numerical illustrations of a simple Biochemical process and the simplified Tennessee Eastman process are used as examples to showcase the performance of the developed approach.