Decentralized Localization Based on Wave Fields Particle Filters and Weiss-Weinstein Error Bounds

A key-challenge in wireless sensor networks is the development of decentralized signal processing and algorithms, i.e. without the central fusion center. More specific, in my dissertation I have contributed to the localization of acoustic sources in acoustic wave fields. It contains three elements: The physical model in terms of the acoustic wave equation is continuous and has to be discretized and decentralized. I utilize a stochastic model to incorporate noise and the lack of knowledge. On top of this model, I use a decentralized maximum a-posteriori particle filter as an estimator. It supports the non-Gaussianity and non-linearity of my model. For the final global consensus of the source location, I additionally present a consensus algorithm. Non-Gaussian and discrete distributions with finite support demand for general analytic Bayesian performance bounds to benchmark estimators. Thus, I derive the analytic sequential Weiss-Weinstein lower bound on the error variance of any estimator for a linear model and probability distributions: Gaussian distributions, discrete / continuous uniform distributions, exponential distributions, Laplace distributions, and discrete distributions with finite alphabet. Eventually, I join these elements and, moreover, consider the perturbed communication between sensors. On that account, I generalize the sequential Weiss-Weinstein bound for my non-linear model.