Nonlinear Bayesian Estimationfor the Wiener Model

Abstract

This thesis addresses the challenge of autonomous bathymetric mapping, the process of creat-ing topographical maps of the ocean floor, using an Autonomous Underwater Vehicle (AUV).Conventional surveys rely on expensive crewed vessels and often fail to exploit the underlyingstatistical patterns of the collected bathymetric data. This work proposes a model-drivenestimation framework that treats bathymetric mapping as a nonlinear system identification problem.

Using properties of the underlying state-space model and by representing the seabed through alinear combination of known basis functions, a novel estimation algorithm is derived. The pro-posed method formulates a dual Bayesian state-parameter estimator in which affine MinimumMean Square Error (MMSE) estimators are constructed for both the unknown model param-eters and the latent system states. By alternating between these closed-form estimators ina fixed-point iteration, the algorithm progressively reduces state-induced uncertainty andimproves parameter estimation accuracy.

Finally, a filtering extension of the dual state-parameter estimator is introduced. This exten-sion enables scalable processing of large data sets by operating online, while incurring a limitedloss in accuracy compared to the batch formulation. The proposed estimators are evaluatedin Monte Carlo experiments and benchmarked against a state-of-the-art methods. The resultsshow that the proposed methods consistently outperform existing estimation algorithms interms of accuracy and computational complexity.