GOALS

Students know some important classes of stochastic processes used to model measured signals and can select suitable models for the most common use cases, understand their properties, and can apply these models e.g. for parameter estimation. Students have acquired subject-specific knowledge of important standard methods of stochastic signal processing (e.g. Kalman filters, adaptive filters, Markov chains and Markov chain Monte Carlo methods) and are able to apply them to known and new problems. Through the exercises and computer exercises (practical exercise), the students are able to practically implement what they have learned in a team, to explain and evaluate solution approaches and to argue for them. The important basic concepts of stochastic signals are also taught in English, so that the students are able to access the international literature in the field of statistical signal processing.

CONTENT

The lecture 'Statistical Signal Processing' introduces stochastic signal models, and some important engineering applications of stochastic signals. First, the most important stochastic processes for signal models, such as white noise, Poisson processes or Markov chains, are discussed. In terms of applications, the lecture focuses on discrete-time optimal filtering methods. Here, the focus is on the Kalman filter, which is derived for the example of one-step prediction. Subsequently, selected methods for processing stochastic signals are discussed: In particular, these include parametric and nonparametric spectral estimation, maximum likelihood estimators, detectors, and adaptive filters (LMS, RLS).

REQUIREMENTS

none

RECOMMENDED KNOWLEDGE

Knowledge of stochastic signals equivalent to that taught in the lecture "System Theorie 3 - Stochastic Signals" in the Bachelor's program in Electrical Engineering and Information Technology.

LI­TE­RA­TURE

1. Kay, Ste­ven M. "Fun­da­men­tals of Sta­tis­ti­cal Si­gnal Pro­ces­sing, Vo­lu­me I: Esti­ma­ti­on Theo­ry", Pren­ti­ce Hall, 1993
2. Kay, Ste­ven M. "Fun­da­men­tals of Sta­tis­ti­cal Si­gnal Pro­ces­sing, Vo­lu­me II: De­tec­tion Theo­ry ", Pren­ti­ce Hall, 1998
3. Kay, Ste­ven M. "Fun­da­men­tals of Sta­tis­ti­cal Si­gnal Pro­ces­sing, Vo­lu­me III: Prac­tical Al­go­rithm De­ve­lop­ment ", Pren­ti­ce Hall, 2013
4. Kay, Ste­ven M. "In­tui­ti­ve Pro­ba­bi­li­ty and Ran­dom Pro­ces­ses using MAT­LAB", Pren­ti­ce Hall, 2005

MISCELLANEOUS

The lecture and exercise materials will be made available via Moodle. Self-enrollment in the course is possible from 10/18/2022 with the password "Kalman".