Parameter estimation based on sparse modeling

Research Project, 2012 – 2014

Model-Based Signal Processing deals generally with information extraction from measured sensor data. A mathematical model of sensor(s) and signal propagation is usually derived from first principles. The unknown parameters are then found by some kind of fit of the model to available data. Such parameter estimation methods have received much attention, and in most cases their statistical properties are well understood. However, in practical situations the used model captures the dominant phenomena at most. In many cases several possible models are postulated and the correct model may even switch during the data collection. Much less is known regarding how this model uncertainty affects the estimation error, and in particular how the error can be predicted from data only. In this project, we focus on two particular problems related to model uncertainty. One concerns calibration using interpolation and smoothing, and a particular application is antenna array signal processing. The other is tracking of moving targets using multiple motion models. For both these problems, we address the issues of performance prediction and lower bounds for the achievable performance under model uncertainties. If successful, the results will have an impact of how practical antenna arrays and other equipment requiring calibration are designed (and the associated cost), as well as specification and design of tracking systems, for example in vehicle safety applications.

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