This thesis deals with the modeling of structured signals under different sparsity constraints. Many phenomena exhibit an inherent structure that may be exploited when setting up models, examples include audio waves, radar, sonar, and image objects. These structures allow us to model, identify, and classify the processes, enabling parameter estimation for, e.g., identification, localisation, and tracking.In this work, such structures are exploited, with the goal to achieve efficient localisation and tracking of a structured source signal. Specifically, two scenarios are considered. In papers A and B, the aim is to find a sparse subset of a structured signal such that the signal parameters and source locations maybe estimated in an optimal way. For the sparse subset selection, a combinatorial optimization problem is approximately solved by means of convex relaxation, with the results of allowing for different types of a priori information to be incorporated in the optimization. In paper C, a sparse subset of data is provided, and a generative model is used to find the location of an unknown number of jammers in a wireless network, with the jammers’ movement in the network being tracked as additional observations become available.
|Tilldelningsdatum||2022 nov. 25|
|Status||Published - 2022 nov. 1|
Bibliografisk informationDefence details
Place: Lecture hall MA 3, Centre of Mathematical Sciences, Sölvegatan 20, Faculty of Engineering LTH, Lund University, Lund. The dissertation will be live streamed but part of the premises is to be excluded from the live stream.
Name: Jaldén, Joakim
Affiliation: KTH Royal Institute of Technology, Stockholm.
- Source localization
- Cramér-Rao bounds
- Convex Optimization