# Coursebooks

## Inference for large-scale time series with application to sensor fusion

#### Lecturer(s) :

Guerrier Stéphane
Skaloud Jan

English

Every 3 years

#### Remark

Next time: Spring 2023 Block course

#### 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.

https://gmwm.netlify.com

### Reference week

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German