Title: Semiparametric Estimation of Target Locations
Advisors: Associate Professor Moulinath Banerjee, Professor George Michailidis
Committee Members: Associate Professor Stilian Stoev, Professor Bin Nan (Biostatistics)
Abstract: Detection, identification and tracking of spatial phenomena are important tasks in various environmental and infrastructure applications. Wireless sensor networks are widely used for monitoring natural phenomena in space and over time, as well as for target detection and tracking. Sensors acquire signals emitted from the target that are corrupted by noise, and then try to detect the location of the target based on the information received. In most cases, the form of the signal generating model is assumed to be known (e.g exponential/polynomial etc) and the subsequent analysis is based on that assumption. But the assumption of a known signal model can be restrictive and quite ambitious, since there may be different types of targets present, whose signals may follow different models. Thus, the inference would be unreliable for a misspecified model. In this proposal, instead of assuming any particular signal model, we introduce a semiparametric model for signal propagation where both the location of the target and the signal generating function are treated as unknown for subsequent inference. Here we try to exploit the fact that the signal strength received by the sensor decreases as its distance from the target increases, which is true in most practical situations. In the proposed model, the parametric part (unknown target location) and the nonparametric part (unknown signal function) are "bundled" together, which makes the problem more challenging. We develop a maximum likelihood estimation procedure based on spline based models and establish its asymptotic properties. The proposed method is illustrated on selected synthetic data.