Multiple-Model Estimation Applied to Unequal, Heterogeneous State Space Models

Abstract

Multiple-model estimation is useful to detect both structural and parametric changes of technical systems and has been used in areas such as target tracking and fault diagnosis. Known approaches to multiple-model estimation, such as Generalized-Pseudo-Bayesian approaches or the Interacting-Multiple-Model approach, apply a stochastic filter for each model and calculate the estimate by appropriately mixing the moments calculated by each filter. However, it has to be taken into account that in the context of fault diagnosis the individual mathematical models often have unequal, heterogeneous state spaces. Thus, multi-model estimation approaches have to be appropriately adapted, otherwise biased estimates will be calculated. In contrast to known multiple-model estimation approaches to unequal, heterogeneous state spaces, where the necessary adaptions are only done for the model conditional means and covariance matrices, we propose an approach, where the model conditional probability density functions are adapted so that non-Gaussian filters can also be used.

This work was funded by the European Union and the federal state of North Rhine-Westphalia, Germany.