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


Lecturer(s) :

Guerrier Stéphane
Skaloud Jan




Every 3 years


Next time: Spring 2023 Block course


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.


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


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:

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.



Applied Time Series Analysis with R:
An Introduction to Statistical Programming Methods with R:
Moodle: (TBD)


Freely accessible website with 'tutorial / exercises' and slides.

Moodle Link

In the programs

Reference week

      Exercise, TP
      Project, other


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