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Objectives:
This course on Electrical
Engineering and Computer Science addresses problems of estimation in
the presence of stochastic processes, heavily based on Kalman filtering
concepts. This series of lectures is suitable for post-graduate
students in science and engineering and is strongly based on a
first-year graduate-level course given in the past at MIT by Prof.
Michael Athans. The study of new
directions of research in nonlinear estimation for dynamic systems will
complement the classical approach.
Summary
A central topic in science and engineering
applications is the extraction of (static or dynamic) relevant
information from uncertain (noisy) measurements and data. In the
static case, this corresponds to the problem of parameter
estimation. The problem is even harder in the case of stochastic
random processes, where multivariable system dynamics play a key
role. The key problem is to estimate, and perhaps predict into
the future, the state variables of a dynamic system on the basis of
past incomplete noisy measurements from one or more sensors (the sensor
fusion problem).
Since the 1960´s, the Kalman filter methodology,
and its extensions to nonlinear dynamics, has been the workhorse of
such stochastic dynamic estimation and prediction problems. There
have been thousands of applications related to navigation,
surveillance, process control, and econometrics to mention just a few.
We shall provide a complete exposition of this methodology for both
discrete-time and continuous-time dynamic systems, subject to one or
more stochastic inputs and including noisy measurements from one or
more sensors, including the associated algorithms for practical
applications.
New directions of
research have been pursued by the scientific community, with the main
focus on the stability of the observers obtained. Some of the more
relevant results will be briefly presented during the last phase of the
course namely: H∞ filtering, nonlinear observer design resorting to
Lyapunov methods, linear matrix inequalities (LMIs) and linearly
parametrically varying (LPVs) based nonlinear observers, and nonlinear
observers with linearizable error dynamics.
See the table of contents for a
more detailed list of topics.
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