- Heiko Bruckmeyer
In many fields of engineering, a time-invariant system is approached to be estimated based on noisy observations. A widespread model for this task of system identifi- cation is the state-space approach which captures all relevant information of the physical system in a state vector. The state-space model is generally characterized by two mathematical functions: The system equation which describes the temporal process of the state vector and the observation equation which models the relation between the state vector and the observation. For many practical applications, the assumption of affine functions for the system and the observation equation is a poor approximation and we have to consider nonlinear state-space approaches to model distortions, for example created by miniaturized loudspeaker in mobile phones. This leads to nonlinear mathematical relations and no closed-form solution for the minimum mean square error (MMSE) estimation of the state vector can be found. To approximate the MMSE solution, we can employ numerical sampling methods like the Gaussian particle filter (GPF) proposed in [J.H. Kotecha et al., 2003]. The fundamental idea of numerical sampling is to represent the probability density function of a random variable by a finite number of samples (particles) and corresponding likelihoods (weights).The goal of this thesis is a comparison between the classical GPF proposed in [J.H. Kotecha et al., 2003] and an elitist GPF.