Quantification of state estimator performance in presence of model plant mismatch for multivariate system

This article proposes a data driven technique for quantifying the performance of state estimators in the presence of a mismatch between plant dynamics and the model used for estimation. A two step approach is proposed in which Hurst exponent of posteriori error (difference between plant measurement, 𝑦 𝑘 and updated estimator outputs 𝑦^) is calculated which is then used as feature vector. This feature vector can quantify mismatch for univariate 𝑘|𝑘 systems but for multivariate systems correlation in between variables can be taken into account by calculating Mahalanobis distance of the Hurst exponents. Mahalanobis distance of feature vector (Hurst exponent) provide a metric which can quantify the model plant mismatch. This two steps technique can be applied to estimated states also when enough measurements are not provided by process. The procedure is tested on two non-linear systems and simulation results reveal that the technique serves as a tool that (i) can quantify the performance of a state estimator in a multivariate system, (ii) is independent of computation theory of estimators