Sampled-Data Kalman Filtering and Multiple Model Adaptive Estimation for Infinite-Dimensional Continuous-Time Systems

Kalman filtering and multiple model adaptive estimation (MMAE) methods have been applied by researchers in several engineering disciplines to a multitude of problems featuring a linear (or mildly nonlinear) model based on finite-dimensional differential (or difference) equations perturbed by random inputs. However, many real-world systems are more naturally modeled using an infinite-dimensional continuous-time linear systems model, such as those most naturally modeled as partial differential equations or time-delayed differential equations along with a possibly infinite-dimensional measurement model. The Kalman filtering technique was extended to encompass infinite-dimensional continuous-time systems with sampled-data measurements and a technique to approximate an infinite-dimensional continuous-time system model with an essentially equivalent finite-dimensional discrete-time model upon which a filtering algorithm could be based was developed. The tools developed during this research were demonstrated using an estimation problem based on a stochastic partial differential equation with an unknown noise environment

Maximum Likelihood Estimation of Wave Front Slopes using a Hartmann-type Sensor

Current methods for estimating the wave front slope at the pupil of a telescope equipped with a Hartmann-type wave front sensor (H-WFS) are based on a simple centroid calculation of the intensity distributions (spots) recorded in each subaperture of the H-WFS. The centroid method does not include any knowledge concerning correlation properties of the slopes over the subapertures or the amount of light collected by the telescope and diverted to the H-WFS for wave front reconstruction purposes. This thesis devises a maximum likelihood (ML) estimation of the spot centroids by incorporating statistical knowledge of the spot shifts. The light level in each subaperture and the relative spot size is also employed by the shift estimator. The shift estimator is found to be unbiased and is upper bounded by the mean squared error performance exhibited by the classical centroid technique

Maximum a posteriori estimation of wavefront slopes using a Shack-Hartmann wavefront sensor

Current methods for estimating the wavefront slope at the pupil of a telescope using a Shack-Hartmann wavefront sensor (SH--WFS) are based on a simple centroid calculation of the irradiance distributions (spots) recorded in each subaperture. The centroid calculation does not utilize knowledge concerning the correlation properties of the slopes over the subapertures or the amount of light collected by the SH--WFS. This paper presents the derivation of a maximum a posteriori (MAP) estimation of the irradiance centroids by incorporating statistical knowledge of the wavefront tilts. Information concerning the light level in each subaperture and the relative spot size is also employed by the estimator. The MAP centroid estimator is found to be unbiased and the mean squared error performance is upper bounded by that exhibited by the classical centroid technique. This error performance is demonstrated using Kolmogorov wavefront slope statistics for various light levels. 1 Introduction Atmosph..