Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Asynchronous distributed state estimation for continuous-time stochastic processes

The problem of state estimation of a continuous-time stochastic process using an Asynchronous Distributed multi-sensor Estimation (ADE) system is considered. The state of a process of interest is estimated by a group of local estimators constituting the proposed ADE system. Each estimator is based, e.g., on a Kalman filter and performs single sensor filtration and fusion of its local results wi...

Stochastic Processes in Continuous Time

1 Basic Concepts 3 1.1 Notions of equivalence of stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Sample path properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Properties of filtrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Stopping times . . . . . . . . . . . . . . . . . ....

Sparse Gaussian Processes for Continuous-Time Trajectory Estimation on Matrix Lie Groups

Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot motion, or during with asynchronous sensor measurements. Sparse Gaussian processes (GP) allow for a probabilistic non-parametric trajectory representation th...

Part II CONTINUOUS TIME STOCHASTIC PROCESSES

Bayesian Estimation of Continuous-Time Finance Models

A new Bayesian method is proposed for the analysis of discretely sampled diffusion processes. The method, which is termed high frequency augmentation (HFA), is a simple numerical method that is applicable to a wide variety of univariate or multivariate diffusion and jump-diffusion processes. It is furthermore useful when observations are irregularly observed, when one or more elements of the mu...