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
7 - Filtering and Smoothing Problems and Well-Posedness
Published online by Cambridge University Press: 27 July 2023
- 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
In this chapter we introduce data assimilation problems in which the model of interest, and the data associated with it, have a time-ordered nature.We distinguish between the filtering problem (on-line) in which the data is incorporated sequentially as it comes in, and the smoothing problem (off-line) which is a specific instance of the inverse problems that have been the subject of the preceding chapters.
- Type
- Chapter
- Information
- Inverse Problems and Data Assimilation , pp. 101 - 111Publisher: Cambridge University PressPrint publication year: 2023