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.

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.