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Research on developing new algorithms to improve information on brain functionality and structure is ongoing. Studying neural activity through dipole source localization with electroencephalography (EEG) and magnetoencephalography (MEG) sensor measurements can lead to diagnosis and treatment of a brain disorder and can also identify the area of the brain from where the disorder has originated. Designing advanced localization algorithms that can adapt to environmental changes is considered a significant shift from manual diagnosis which is based on the knowledge and observation of the doctor, to an adaptive and improved brain disorder diagnosis as these algorithms can track activities that might not be noticed by the human eye. An important consideration of these localization algorithms, however, is to try and minimize the overall power consumption in order to improve the study and treatment of brain disorders. This thesis considers the problem of estimating dynamic parameters of neural dipole sources while minimizing the system's overall power consumption; this is achieved by minimizing the number of EEG/MEG measurements sensors without a loss in estimation performance accuracy. As the EEG/MEG measurements models are related non-linearity to the dipole source locations and moments, these dynamic parameters can be estimated using sequential Monte Carlo methods such as particle filtering. Due to the large number of sensors required to record EEG/MEG Measurements for use in the particle filter, over long period recordings, a large amounts of power is required for storage and transmission. In order to reduce the overall power consumption, two methods are proposed. The first method used the predicted mean square estimation error as the performance metric under the constraint of a maximum power consumption. The performance metric of the second method uses the distance between the location of the sensors and the location estimate of the dipole source at the previous time step; this sensor scheduling scheme results in maximizing the overall signal-to-noise ratio. The performance of both methods is demonstrated using simulated data, and both methods show that they can provide good estimation results with significant reduction in the number of activated sensors at each time step.
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.