Expectation Maximization Algorithm for Simultaneous Tracking and Sparse Calibration of Sensor Networks

Sensor networks are everywhere around us. Developments in sensor technology and advances in hardware miniaturization open up brand-new application areas. In the future networks of cheap and small sensor nodes will be deployed for a variety of purposes. Military needs have been a major motivation for the development in the past, but today it has changed. Other applications such as traffic monitoring, security threat detection, ecology and environmental protection are the new driving forces behind further development.The thesis considers the problem of calibration of ground sensor networks. In order to perform its operational tasks – detection, classification and tracking ofobjects of interest, the network has to be correctly calibrated. Improper calibration might result in a degraded performance, problems with data association and appearance of multiple track instances representing one object.In order to find the unknown calibration parameters (biases), in most cases we need to use reference targets with known positions. If such targets are not available, one has to use opportunistic targets and simultaneously estimate both target positions and bias parameters. In this thesis, the expectation maximization algorithm is applied to that problem, where the unknown states are treated as latent (unknown) variables in the process of bias estimation.Next, the problem of estimating a large number of calibration parameters is tackled. In the case when the measurement data is not informative enough – due to a limited range of sensors or a small number of samples – standard approaches such as the least squares algorithm might provide unreliable results. One solution to the problem is to apply a regularization (or prior in a Bayesian case). In this thesis, the problem of selecting the parameters (the so called hyper-parameters) for the regularization process, based on the set of measurements, is considered. The solution is provided through the evidence approximation method, where both the bias parameters and the hyper-parameters are estimated simultaneously. As a result, one obtains a robust algorithm that, thanks to the application of Occam’s razor, allows to find the good trade-off between model complexity and its fit to the data.Finally, both methods are combined together, in order to provide a robust and accurate algorithm for the calibration of sensor networks using targets of opportunity.The applicability of algorithms was also verified during field trials with good final outcome, confirming the expected performance.