Online hidden Markov model parameter estimation and minimax robust quickest change detection in uncertain stochastic processes

Stochastic (or random) processes are inherent to numerous fields of human endeavour including engineering, science, and business and finance. This thesis presents multiple novel methods for quickly detecting and estimating uncertainties in several important classes of stochastic processes. The significance of these novel methods is demonstrated by employing them to detect aircraft manoeuvres in video signals in the important application of autonomous mid-air collision avoidance.

Estimates on the coverage of parameter space using populations of models

In this paper we provide estimates for the coverage of parameter space when using Latin Hypercube Sampling, which forms the basis of building so-called populations of models. The estimates are obtained using combinatorial counting arguments to determine how many trials, k, are needed in order to obtain specified parameter space coverage for a given value of the discretisation size n. In the case of two dimensions, we show that if the ratio (Ø) of trials to discretisation size is greater than 1, then as n becomes moderately large the fractional coverage behaves as 1-exp-ø. We compare these estimates with simulation results obtained from an implementation of Latin Hypercube Sampling using MATLAB.

Analysis of parameter uncertainty and sensitivity in PCPF-1 modeling for predicting concentrations of rice herbicides

This paper demonstrates the procedures for probabilistic assessment of a pesticide fate and transport model, PCPF-1, to elucidate the modeling uncertainty using the Monte Carlo technique. Sensitivity analyses are performed to investigate the influence of herbicide characteristics and related soil properties on model outputs using four popular rice herbicides: mefenacet, pretilachlor, bensulfuron-methyl and imazosulfuron. Uncertainty quantification showed that the simulated concentrations in paddy water varied more than those of paddy soil. This tendency decreased as the simulation proceeded to a later period but remained important for herbicides having either high solubility or a high 1st-order dissolution rate. The sensitivity analysis indicated that PCPF-1 parameters requiring careful determination are primarily those involve with herbicide adsorption (the organic carbon content, the bulk density and the volumetric saturated water content), secondary parameters related with herbicide mass distribution between paddy water and soil (1st-order desorption and dissolution rates) and lastly, those involving herbicide degradations. © Pesticide Science Society of Japan.

Efficient parameter estimation in longitudinal data analysis using a hybrid GEE method

The method of generalized estimating equations (GEEs) provides consistent estimates of the regression parameters in a marginal regression model for longitudinal data, even when the working correlation model is misspecified (Liang and Zeger, 1986). However, the efficiency of a GEE estimate can be seriously affected by the choice of the working correlation model. This study addresses this problem by proposing a hybrid method that combines multiple GEEs based on different working correlation models, using the empirical likelihood method (Qin and Lawless, 1994). Analyses show that this hybrid method is more efficient than a GEE using a misspecified working correlation model. Furthermore, if one of the working correlation structures correctly models the within-subject correlations, then this hybrid method provides the most efficient parameter estimates. In simulations, the hybrid method's finite-sample performance is superior to a GEE under any of the commonly used working correlation models and is almost fully efficient in all scenarios studied. The hybrid method is illustrated using data from a longitudinal study of the respiratory infection rates in 275 Indonesian children.

A novel approach to 6-DOF adaptive trajectory tracking control of an AUV in the presence of parameter uncertainties

In this paper, the trajectory tracking control of an autonomous underwater vehicle (AUVs) in six-degrees-of-freedom (6-DOFs) is addressed. It is assumed that the system parameters are unknown and the vehicle is underactuated. An adaptive controller is proposed, based on Lyapunov׳s direct method and the back-stepping technique, which interestingly guarantees robustness against parameter uncertainties. The desired trajectory can be any sufficiently smooth bounded curve parameterized by time even if consist of straight line. In contrast with the majority of research in this field, the likelihood of actuators׳ saturation is considered and another adaptive controller is designed to overcome this problem, in which control signals are bounded using saturation functions. The nonlinear adaptive control scheme yields asymptotic convergence of the vehicle to the reference trajectory, in the presence of parametric uncertainties. The stability of the presented control laws is proved in the sense of Lyapunov theory and Barbalat׳s lemma. Efficiency of presented controller using saturation functions is verified through comparing numerical simulations of both controllers.