Laser based underwater triangulation ranging is sensitive to the environmental conditions and laser beam profile. Also, its ranging quality is greatly affected by the algorithm choices for peak detection and for image processing. By utilizing the merging least-squares approximation for laser image processing, it indeed succeeds in increasing quality of triangulation ranging in water; however, this result was obtained on the use of a laser beam with nearly circular cross-section. Therefore, by using an ellipse-like laser beam cross-section for range finding, we are really interested in understanding the quality of range finding with different peak detection algorithms. Besides, the ellipse orientation of the laser spot projected on the image plane would be various. We are also interested in learning about the relationship between the ellipse orientation and the quality of range finding. In this study, peak detection algorithms are investigated by considering four different laser beam cross-sections which are ircle, horizontal ellipse, oblique ellipse, and vertical ellipse. First, we employ polynomial regression for processing laser image to study the effect of polynomial degree on quality of triangulation ranging. It was found that the linear regression achieves the best ranging quality than others. Then, according to this result, the ranging quality associated with peak detection is evaluated by employing three different algorithms which are the illumination center, twice illumination center and the illumination center with principal component analysis. We found that the ranging quality by using the illumination center with principal component analysis is the best, next is twice illumination center, and last the illumination center. This result indicates that the orientation of elliptical laser beam has an influential effect on the quality of range finding. In addition, the ranging quality difference among peak detection algorithms is significantly reduced by implementing the merging least-squares approximation rlaser image processing. This result illustrates that the merging least-squares approximation does reduce the effect of peak detection algorithm on the quality of range finding.

Directors designed for observation and fire control in naval environments consist of a mechanical pedestal moved by two electrical motors. To meet the high demands on director precision, a servo solution based on feedback control is used. The digital servo controller has to be tuned to meet demands on performance and stability. This report presents methods for automatic tuning, intended to replace today’s manual tuning procedures. System identification based on relay feedback and recursive least-squares approximations are combined with the Ziegler-Nichols and AMIGO tuning procedures for PI controllers are evaluated. Evaluations are performed in simulations, for which a SIMULINK model is constructed. Results indicate that the automatic tuning may perform well compared to the manual tuning used today, and that it could bring considerable reduction in the time required for tuning.

This paper attempts to use image processing methods to reduce the influences of ambient light and scattering effect on the performance of an underwater range finder. The Taguchi method, as well, is employed to increase the repeatability of underwater range finding. In this study, the image processing methods of the least-squares approximation, brightness and contrast adjustment, and primary color processing are presented. The illumination center is also used to estimate the position of the laser spot in the image. In addition, a bandpass optical filter at the receiving end is used to investigate the effects of filters on the quality of range finding. To verify the effectiveness of the proposed image processing methods, a series of DOE process runs are carried out to study effects of the design parameters on quality of range finding. For each image processing method, its corresponding control factors and levels are assigned to an inner orthogonal array. To make the proposed image processing methods robust against noises, both environmental illumination and turbidity are forced into the experiments by utilizing an outer orthogonal array. Images for processing are then captured under different noise conditions in accordance with the allocation of the outer noise array. And, according to the layout of the inner array, the S/N ratio of each treatment combination is calculated. After that, the optimum combination of control factors is predicted through the analysis of variance. Then, the confirmation experiments are carried out to verify that the combination of control factors at the perceived best levels is valid. Based on the results of experiments and analyses, it is found that the least-squares approximation is better than other proposed image processing methods for increasing the quality of range finding. Moreover, the effect of increasing quality of range finding by using the least-squares approximation is superior to that of using a bandpass optical filter. Even though a range finding system has incorporated a bandpass optical filter for filtering out unwanted noises, the quality of range finding can still be increased distinctly while the algorithm of the least-squares approximation is employed. As well, the least-squares approximation is feasible to reduce the scattering effects in the laser images if the size of the sparse backscattering light spot is smaller than that of the target light spot.

Data gathering is a constant in human history with ever increasing amounts in quantity and dimensionality. To get a feel for the data, make it interpretable, or find underlying laws it is necessary to fit a function to the finite and possibly noisy data. In this thesis we focus on a method achieving this, namely least squares approximation. Its discovery dates back to around 1800 and it has since then proven to be an indispensable tool which is efficient and has the capability to achieve optimal error when used right. Crucial for the least squares method are the ansatz functions and the sampling points. To discuss them, we gather tools from probability theory, frame subsampling, and $L_2$-Marcinkiewicz-Zygmund inequalities. With that we give results in the worst-case or minmax setting, when a set of points is sought for approximating a class of functions, which we model as a generic reproducing kernel Hilbert space. Further, we give error bounds in the statistical learning setting for approximating individual functions from possibly noisy samples. Here, we include the covariate-shift setting as a subfield of transfer learning. In a natural way a parameter choice question arises for balancing over- and underfitting effect. We tackle this by using the cross-validation score, for which we show a fast way of computing as well as prove the goodness thereof.:1 Introduction 2 Least squares approximation 3 Reproducing kernel Hilbert spaces (RKHS) 4 Concentration inequalities 5 Subsampling of finite frames 6 L2 -Marcinkiewicz-Zygmund (MZ) inequalities 7 Least squares in the worst-case setting 8 Least squares in statistical learning 9 Cross-validation 10 Outlook

This report focus upon implied volatility for American styled Asian options, and a least squares approximation method as a way of estimating its magnitude. Asian option prices are calculated/approximated based on Quasi-Monte Carlo simulations and least squares regression, where a known volatility is being used as input. A regression tree then empirically builds a database of regression vectors for the implied volatility based on the simulated output of option prices. The mean squared errors between imputed and estimated volatilities are then compared using a five-folded cross-validation test as well as the non-parametric Kruskal-Wallis hypothesis test of equal distributions. The study results in a proposed semi-parametric model for estimating implied volatilities from options. The user must however be aware of that this model may suffer from bias in estimation, and should thereby be used with caution.