Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction
- Part I Inverse Problems
- 1 Bayesian Inverse Problems andWell-Posedness
- 2 The Linear-Gaussian Setting
- 3 Optimization Perspective
- 4 Gaussian Approximation
- 5 Monte Carlo Sampling and Importance Sampling
- 6 Markov Chain Monte Carlo
- Exercises for Part I
- Part II Data Assimilation
- 7 Filtering and Smoothing Problems and Well-Posedness
- 8 The Kalman Filter and Smoother
- 9 Optimization for Filtering and Smoothing: 3DVAR and 4DVAR
- 10 The Extended and Ensemble Kalman Filters
- 11 Particle Filter
- 12 Optimal Particle Filter
- Exercises for Part II
- Part III Kalman Inversion
- 13 Blending Inverse Problems and Data Assimilation
- References
- Index
9 - Optimization for Filtering and Smoothing: 3DVAR and 4DVAR
Published online by Cambridge University Press: 27 July 2023
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction
- Part I Inverse Problems
- 1 Bayesian Inverse Problems andWell-Posedness
- 2 The Linear-Gaussian Setting
- 3 Optimization Perspective
- 4 Gaussian Approximation
- 5 Monte Carlo Sampling and Importance Sampling
- 6 Markov Chain Monte Carlo
- Exercises for Part I
- Part II Data Assimilation
- 7 Filtering and Smoothing Problems and Well-Posedness
- 8 The Kalman Filter and Smoother
- 9 Optimization for Filtering and Smoothing: 3DVAR and 4DVAR
- 10 The Extended and Ensemble Kalman Filters
- 11 Particle Filter
- 12 Optimal Particle Filter
- Exercises for Part II
- Part III Kalman Inversion
- 13 Blending Inverse Problems and Data Assimilation
- References
- Index
Summary
This chapter demonstrates the use of optimization, namely the 3DVAR and 4DVAR methodologies, to obtain information from the filtering and smoothing distributions. We emphasize that the methods we present in this chapter do not provide approximations of the filtering and smoothing distributions; they simply provide estimates of the signal, given data, in the filtering (on-line) and smoothing (off-line) data scenarios.
- Type
- Chapter
- Information
- Inverse Problems and Data Assimilation , pp. 125 - 132Publisher: Cambridge University PressPrint publication year: 2023