(757c) Robust M-Estimators for On-Line State Estimation of Dynamic Systems With Gross Measurement Errors

Authors: 
Nicholson, B., Illinois Institute of Technology
Lopez-Negrete, R., Carnegie Mellon University
Biegler, L. T., Carnegie Mellon University



State estimation is a crucial part of the monitoring and/or control of all chemical processes. While there are many ways to approach this problem, moving horizon estimation (MHE) has the advantage of directly incorporating nonlinear dynamic models and can be formulated as a nonlinear programming (NLP) problem. However, large-scale MHE formulations can take a significant amount of computational time to solve which poses a problem for performing on-line state estimation. To solve this problem we consider an extension of MHE called Advanced Step Moving Horizon Estimation (asMHE). With asMHE, the dynamic optimization problem is divided into a background calculation using a prediction of the next measurement, and a fast on-line update step based on NLP sensitivity. asMHE has the benefit of calculating state estimates on-line that are significantly faster than MHE. However, computational time is not the only concern in state estimation; we also want our estimates to be robust to measurement errors. Sensors can fail or be contaminated in such a way that the measurements they report are vastly different from the true values of the states being measured. In this study we investigate the performance of the MHE and asMHE formulations when our measurements are contaminated with large errors. We apply robust M-Estimators, specifically Huber’s fair function and Hampel’s redescending estimator, as ways to mitigate the bias of these gross errors on our state estimates. This approach is demonstrated on dynamic models of a CSTR and a distillation column. Based on the performance details of this comparison we conclude that the asMHE formulation with the redescending estimator can be used to get fast and accurate state estimates, even in the presence of significantly many gross measurement errors.

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