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Transdimensional Data Assimilation for dynamic model selection problems

Márk Somogyvári, Sebastian Reich

Abstract

In this paper we combine the non-linear filtering capabilities of particle filters with the transdimensional inference of the reversible-jump Markov chain Monte Carlo method for a data assimilation methodology over dynamic problems with variable dimensionality. By using transdimensional MCMC steps for the rejuvenation of the particle filter, the algorithm could change the number of state space parameters on the fly and can be applied for transdimensional data assimilation purposes. Classic inversion methodologies use pre-defined models, and only changes the individual parameter values during interpretation. This is often not feasible when the optimal model parametrization is not known a priori or when the model resolution needs to change with time. The proposed transdimensional particle filter algorithm, combines the advantages of particle filters and the transdimensional MCMC methods, and provides an easily implementable data assimilation algorithm that could tackle such problems. The methodology could also improve the computational efficiency of particle filters as it could inherently optimize the model complexity in a data-driven way. We demonstrate the capabilities of the enhanced algorithm on two simple model examples.

Transdimensional Data Assimilation for dynamic model selection problems

Abstract

In this paper we combine the non-linear filtering capabilities of particle filters with the transdimensional inference of the reversible-jump Markov chain Monte Carlo method for a data assimilation methodology over dynamic problems with variable dimensionality. By using transdimensional MCMC steps for the rejuvenation of the particle filter, the algorithm could change the number of state space parameters on the fly and can be applied for transdimensional data assimilation purposes. Classic inversion methodologies use pre-defined models, and only changes the individual parameter values during interpretation. This is often not feasible when the optimal model parametrization is not known a priori or when the model resolution needs to change with time. The proposed transdimensional particle filter algorithm, combines the advantages of particle filters and the transdimensional MCMC methods, and provides an easily implementable data assimilation algorithm that could tackle such problems. The methodology could also improve the computational efficiency of particle filters as it could inherently optimize the model complexity in a data-driven way. We demonstrate the capabilities of the enhanced algorithm on two simple model examples.

Paper Structure

This paper contains 8 sections, 20 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Bootstrap particle filter
  4. Transdimensionally-extended particle filter
  5. Model examples
  6. Fourier analysis
  7. Object tracking
  8. Conclusions

Figures (9)

  • Figure 1: Evolution of the exemplary frequency model over time. The upper row shows the observed signal, the lower row shows the underlying state space model at timesteps t=0,25,50 and 75.
  • Figure 2: Reconstructions of the Fourier signals. The upper row shows the reconstructed signals with colored lines and the observed reference signal in black on top. The lower row shows the mean of the reconstructed state space vectors. The depicted timesteps are t=0,25,50 and 75.
  • Figure 3: Convergence of the transdimensional particle filter (TDPF) versus the standard bootstrap filter (sPF).
  • Figure 4: Concept of the object tracking model example (flying planes within a 3-D domain - top), and its observation model (2-D radar image - bottom).
  • Figure 5: Snapshots of radar images from the object tracking example.
  • ...and 4 more figures