This thesis focuses on the comprehensive and thorough studies on the geospatial processing of airborne (full) waveform lidar data, including waveform modeling, direct georeferencing, and precise georeferencing with self-calibration.<div><br></div><div>Both parametric and nonparametric approaches of waveform decomposition are studied. The traditional parametric approach assumes that the returned waveforms follow a Gaussian mixture model where each component is a Gaussian. However, many real examples show that the waveform components can be neither Gaussian nor symmetric. To address the problem, this thesis proposes a nonparametric mixture model to represent lidar waveforms without any constraints on the shape of the waveform components. To decompose the waveforms, a fuzzy mean-shift algorithm is then developed. This approach has the following properties: 1) it does not assume that the waveforms follow any parametric or functional distributions; 2) the waveform decomposition is treated as a fuzzy data clustering problem and the number of components is determined during the process of decomposition; 3) neither peak selection nor noise floor filtering prior to the decomposition is needed; and 4) the range measurement is not affected by the process of noise filtering. In addition, the fuzzy mean-shift approach is about three times faster than the conventional expectationmaximization algorithm and tends to lead to fewer artifacts in the resultant digital elevation model. <br></div><div><br></div><div>This thesis also develops a framework and methodology of self-calibration that simultaneously determines the waveform geospatial position and boresight angles. Besides using the flight trajectory and plane attitude recorded by the onboard GPS receiver and inertial measurement unit, the framework makes use of the publically accessible digital elevation models as control over the study area. Compared to the conventional calibration and georeferencing method, the new development has minimum requirements on ground truth: no extra ground control, no planar objects, and no overlap flight strips are needed. Furthermore, it can also solve the problem of clock synchronization and boresight calibration simultaneously. Through a developed two-stage optimization strategy, the self-calibration approach can resolve both the time synchronization bias and boresight misalignment angles to achieve a stable and correct solution. As a result, a consistency of 0.8662 meter is achieved between the waveform derived digital elevation model and the reference one without systematic trend. Such experiments demonstrate the developed method is a necessary and more economic alternative to the conventional, high demanding georeferencing and calibration approach, especially when no or limited ground control is available.<br></div>

在許多實際情形下，傳統的統計檢定方法是不足以應付的。故本論文提出模糊檢定方法，我們定義出模糊樣本期望值與模糊樣本變異數的計算方法，再針對不同的模糊資料，分別提出不同的檢定方法，去解決最實際需要解決的問題，其中包括推廣古典的統計檢定方法與自創的檢定方法。 關鍵字：隸屬度函數，模糊樣本取樣，模糊樣本期望值，模糊樣本變異數，人性思考，t檢定，F檢定，模糊常態分配。 / In many expositions of fuzzy methods, fuzzy techniques are described as an alternative to a more traditional statistical approach. In this paper, we present a class of fuzzy statistical decision process in which testing hypothesis can be naturally reformulated in terms of interval-valued statistics. We provide the definitions of fuzzy mean, fuzzy distance as well as investigation of their related properties. We also give some empirical examples to illustrate the techniques and to analyze fuzzy data. Empirical studies show that fuzzy hypothesis testing with soft computing for interval data are more realistic and reasonable in the social science research. Finally certain comments are suggested for the further studies. We hope that this reformation will make the corresponding fuzzy techniques more acceptable to researchers whose only experience is in using traditional statistical methods. Key words: Membership function, fuzzy sampling survey, fuzzy mean, human thought, t-test, F-test, normally distributed.