Non-linear Models

Filtering algorithms for non-linear models.

Xiao-Li Hu, Thomas Schön, Lennart Ljung

Particle filters is a recent and much used approach to estimate the states of a non-linear dynamical model with stochastic disturbances. It plays a crucial role in many of MOVIII's  Information Integration projects. Essentially, particle filtering can be seen as a Monte-Carlo method where many possible solutions to the equations are generated and their agreement with observed output is the basis of how to propagate and enhance the simulated solutions. In the project we are investigating convergence aspects of this approach. An apparently new convergence result has been proven recenty.

Identification on manifolds.

Henrik Ohlsson, Jacob Roll, Lennart Ljung

In some cases the observed data for an estimation problem are confined to surfaces of lower dimension in the observation space. If this surface is a linear subspace, many well known methods of PCA (principal components analysis) character apply. For non-linear manifolds, the problem is more complex. The problem has been studied recently by many authors, typically in connection with medical data analysis/imaging. We investigate how these approaches can be applied to dynamical systems modeling.