This session is concerned with homotopy methods for the efficient solution of Bayesian state estimation problems occurring in information fusion and filtering.
For state estimation in the presence of stochastic uncertainties, the best current estimate is represented by a probability density function. For that purpose, different representations are used including continuous densities such as Gaussian mixtures or discrete densities on continuous domain such as particle sets. Given prior knowledge in form of such a density, the goal is to include new information by means of Bayes' theorem. Typically, the resulting posterior density is of higher complexity and difficult to compute. In the case of particle sets, additional problems such as particle degeneracy occur. Hence, an appropriate approximate posterior has to be found. For recursive applications, this approximate posterior should be of the same form as the given prior density (approximate closedness). To cope with this challenging approximation problem, a well-established technique is to gradually include the new information instead of using it in one shot, which is achieved by a homotopy.
For this session, manuscripts are invited that cover any aspect of homotopy methods for state estimation. This includes both theoretically oriented work and applications of known methods.
Topics of interest
- Homotopy-based estimation methods for continuous and discrete densities
- derivations of flow regimes
- specific homotopy schedules
- modification of representation capabilities during flow
- new ideas on processing details
- comparisons of existing methods
- applications of homotopy estimation
Homotopy, particle flow, density flow, transport, Monge-Kantorovich transport, curse of dimensionality, progressive updating, gradual inclusion of information, progressive Bayesian estimation, nonlinear Bayesian state estimation
Special Session Organizers
- Uwe D. Hanebeck, Karlsruhe Institute of Technology (Germany)
- Fred Daum, Karlsruhe Institute of Technology (Germany)