Name
Title | ||
|---|---|---|
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method |
Abstract | ||
|---|---|---|
A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries on the state-space do not in general provide analytical solutions. A widely used numerical approach is the sequential Monte Carlo (SMC) method which relies on stochastic simulations to approximate state densities. For off-line analysis, however, accurate smoothed state density and parameter estimation can become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point-mass filtering methods, but is computationally more advanced and generally applicable. The performance of the FE estimators in relation to SMC and to the resolution of the spatial discretization is examined empirically through simulation. A real-data case study involving fish tracking is also analysed. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.csda.2010.04.018 | Computational Statistics & Data Analysis |
Keywords | Field | DocType |
finite element method,state sequence,state density,numerical approach,unobservable state,state estimation,nonlinear tracking,new approach,nonlinear state estimation,point-mass filter,fe approach,bayesian filter,fe estimator,hidden markov model,diffusion process,approximate state density,sequential monte carlo,stochastic differential equation,fish tracking,data analysis,state space,parameter estimation,stochastic simulation,boundary condition,analytic solution,monte carlo,object tracking,finite element | Discretization,Monte Carlo method,Nonlinear system,Particle filter,Stochastic process,Stochastic differential equation,Finite element method,Numerical analysis,Statistics,Mathematics | Journal |
Volume | Issue | ISSN |
55 | 1 | Computational Statistics and Data Analysis |
Citations | PageRank | References |
3 | 0.63 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. W. Pedersen | 1 | 3 | 0.63 |
| U. H. Thygesen | 2 | 3 | 0.97 |
| H. Madsen | 3 | 4 | 0.99 |