This thesis develops a hierarchy of Bayesian estimation methods for Wiener-type state-space models, motivated by autonomous underwater vehicle (AUV) bathymetric mapping and related robotic perception problems. The focus is on a class of models in which a known linear dynamical process is observed through an unknown, possibly nonlinear output map whose parameters must be inferred from noisy input-output data. In this setting, the observation model is driven by latent, stochastic system states. The central objective is to design parameter estimators that are both statistically accurate and computationally tractable, enabling their embedding within navigation and mapping pipelines.

The work begins with a maximum a posteriori (MAP) estimator for identifying an unknown output map, formulated as a linear time-varying (LTV) observation-model identification problem. In this setting, the MAP estimation problem is posed over the entire state-parameter trajectory and shown to be non-convex. A semidefinite-programming (SDP) relaxation based on linear matrix inequalities (LMIs) is then derived to obtain a conservative but tractable approximation, whose solution serves as a warm start for quasi-Newton re!nement. Numerical experiments validate the efficacy of the proposed method in terms of estimation accuracy and computational efficiency.... ... Read more

We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches. ... Read more