Inference for large-scale time series with application to sensor fusion
CIVIL-606 / 2 credits
Teacher(s): Guerrier Stéphane, Skaloud Jan
Language: English
Remark: Next time: Spring 2025, block course
Frequency
Every 3 years
Summary
Large-scale time series analysis is performed by a new statistical tool that is superior to other estimators of complex state-space models. The identified stochastic dependences can be used for sensor fusion by Bayesian (e.g. Kalman) filtering or for studying changes in natural/biological phenomena.
Content
Linear dynamic systems
- state-space notation and propagation of errors
- modeling of sensor errors and state vector augmentation
- the need for stochastic model identification and parameter estimation in Bayesian filtering
Time series fundamentals
- measuring dependence, examples
- stationarity and fundamental representation
- ARMA models
Properties of estimators
- extremum estimators
- Maximum Likelihood
- Generalized Method of Moments
- consistency and asymptotic normality
Allan Variance
- Allan Variance definition, properties and estimation
- Allan Variance-based estimation of stochastic parameters
Generalized Method of Wavelet Moments (GMWM)
- wavelet variance
- GMWM estimator and its properties
- model selection
GMWM Extensions
- covariate-dependent models and examples
- multivariate-based modeling
GMWM usage
- ‘R’ and its GMWM package with documentation
- on-line computational platform
- examples
Keywords
Statistics, modeling, estimation, sensor-fusion, time-series, Bayesian/Kalman filtering, state-space models
Learning Prerequisites
Required courses
Linear algebra, basic signal processing, basic statistics, basic programming
Learning Outcomes
By the end of the course, the student must be able to:
- Calculate Allan/Wavelet variances from time time-series data
- Identify structure of latent stochastic processes within a time series
- Estimate model parameters together with its confidence intervals
- Apply estimated models in state-space estimation
Expected student activities
The lectures alternates with labs during 2 week block. Students then work on a 32h project (distributed data or -after an agreement - their own data). The evaluation is based on written project report that is presented first orally before its due date - 1.5 month after block end.
Resources
Bibliography
Applied Time Series Analysis with R: https://smac-group.github.io/ts/
An Introduction to Statistical Programming Methods with R: https://smac-group.github.io/ds/
Moodle: (TBD)
Notes/Handbook
Freely accessible website with “tutorial / exercises” and slides.
Websites
Moodle Link
In the programs
- Exam form: Oral presentation (session free)
- Subject examined: Inference for large-scale time series with application to sensor fusion
- Lecture: 12 Hour(s)
- Exercises: 8 Hour(s)
- Practical work: 10 Hour(s)
- Type: optional