Statistically robust Pseudo Linear Identification

Abstract

It is common to assume that the noise disturbing measuring devices is of a Gaussian nature. But this assumption is not always fulfilled. A few examples are the cases where the measurement device fails periodically, the data transmission from device to microprocessor fails or the A/D conversion fails. In these cases the noise will no longer be Gaussian distributed, but rather the noise will be a mixture of Gaussian noise and data not related to the physical process. This posses a problem for estimators derived under the Gaussian assumption, in the sense L that these estimators are likely to produce highly biased estimates in a non Gaussian environment.

This thesis devises a way to robustify the Pseudo Linear Identification algorithm (PLID) which is a joint parameter and state estimator of a Kalman filter type. The PLID algorithm is originally derived under a Gaussian noise assumption. The PLID algorithm is made robust by filtering the measurements through a nonlinear odd symmetric function, called the mb function, and let the covariance updating depend on how far away the measurement is from the prediction. In the original PLID the measurements are used unfiltered in the covariance calculation.