Hours:
20 hours (5 credits)

Room:
Aula Riunioni del Dipartimento di Ingegneria dell’Informazione, Via G. Caruso 16, Pisa – Ground Floor

Short Abstract:
Modern ICT applications are increasingly asking for systems with a relevant level of autonomy. Applications for Industry 4.0, for Internet of Things (IoT) or for service robotics, to mention a few, are gaining more and more attention nowadays. The ability to carry out complex tasks is critically related to the ability to retrieve meaningful information coming from the available sensors. To this end, it is mandatory to understand how a measurement process can be analytically described and how the sensorial data can be manipulated to extract the quantities of interest with the highest possible precision, i.e. the best estimate. This problem becomes even more challenging in dynamic environments when multiple systems interact together, e.g. robotic teams. In this course, the notions needed to correctly model a measurement process will be firstly introduced. Then, an introduction to Bayesian and non-Bayesian classic estimators will be given. Two of the most popular estimators will be studied in details for linear and nonlinear systems: the Weighted Least Squares and the Kalman Filter. Examples of clock synchronisation, state estimation for Smart Grid as well as localisation for single or multiple robots will be presented. Finally, a discussion on other state-of-the-art solutions for localisation as well as on implications for closed-loop systems in the presence of uncertainty will be offered.

Course Contents in brief:

• Background on Statistics: Probability, Random variables, Multivariate Pdfs, Conditional and Marginal pdfs, Propagation of error, stochastic processes
• Data analysis and estimation algorithms (Maximum Likelihood (ML), Least Squares (LS), Maximum A Posteriori (MAP), Minimum Mean Squared Error (MMSE))
• Linear and nonlinear Weighted Least Squares and Kalman filtering, with applications to automation and robotics
• Distributed estimation for team of robots with distributed Kalman Filters

Schedule:

Day I – 20/02/2018 – Morning (4h), 9:00 – 13:00:
Recap on Statistics: Probability, Random variables, Multivariate Pdfs, Conditional and Marginal pdfs, Propagation of errors, White processes, Markovian processes
Data Analysis: Regression for sensor calibration, Statistics of measurement processes

Day I – 20/02/2018 – Afternoon (3h), 14:00 – 17:00:
Estimation Algorithms: Examples of Maximum Likelihood (ML), Least Squares (LS), Maximum A Posteriori (MAP), Minimum Mean Squared Error (MMSE)
Matlab: Examples and Exercises

Day II – 21/02/2018 – Morning (4h), 9:00 – 13:00:
A non-Bayesian Estimator: The (Non-linear) Weighted Least Squares
Matlab: Application of the Least Squares in Distributed Systems - Clock synchronisation example
Application of the Non-linear Least Squares: Smart grid state estimation example
A Bayesian Estimator: The (Extended) Kalman Filter

Day II – 21/02/2018 – Afternoon (3h), 14:00 – 17:00:
Matlab: Robotic vehicles localization
Collaborative localisation: Observability analysis and cross-covariance issue, observability issues and consistency for Kalman filters in collaborative localisation

Day III – 22/02/2018 – Morning (4h), 9:00 – 13:00:
Distributed systems: Linear Consensus Theory

Day III – 22/02/2018 – Afternoon (3h), 14:00 – 17:00:
Distributed estimators: Distributed WLS and distributed Kalman filter
Matlab: Distributed target localization for WSNs

Teaching Notes and Source Code:

https://www.dropbox.com/sh/tlbz0uulw2hiu88/AAD1aLVlqOZH48uOmHmiMTv5a?dl=0