SS14 - Homotopy Methods for Progressive Bayesian Estimation

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 

Keywords

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)

Special Session Contact

• Uwe D. Hanebeck ()
• Fred Daum ()