This dissertation was presented to the Faculty of the Graduate School of The University of Texas at Austin in partial fulfillment of the requirements for the degree of

Ph.D. in Electrical Engineering

There is a critical need to accurately measure land surface topography over large areas around the world. Topographic data are required for a wide range of civilian, government, and military applications, including assessing the threat and impact of natural hazards such as flooding and planning military operations. Imaging radars have been used extensively to map terrain. They can operate in the microwave portion of the electromagnetic spectrum, which enables them to image during the day or night and under most weather conditions.

Interferometric synthetic aperture radar (INSAR) provides the best overall capability for measuring topography over areas of 10 km² and larger. For many application though, the resolution and accuracy of INSAR is insufficient. This is especially true if the surface is covered with vegetation. INSAR observations do not provide direct measurements of the true surface topography in vegetated areas, but instead yield a height that depends on the sensor characteristics, the surface elevation, and the vegetation. Laser altimeter (LIDAR) sensors can be used to obtain topographic measurements with an order of magnitude better resolution and accuracy than INSAR, but are generally restricted to areas of less than 10 km² because of limited coverage.

In this dissertation, I develop a data fusion framework for the statistically optimal combining of complementary data sets. I apply the framework to fusing INSAR and LIDAR data to produce improved estimates of topography. Neither INSAR nor LIDAR data strictly represents bare surface heights in the presence of vegetation, so prior to the data fusion, bare surface elevations and vegetation heights are estimated from the data by modeling the interactions between the incident energy from the sensors and the vegetation.

The transformed data sets are then combined to exploit the coverage of INSAR and resolution of LIDAR. The data fusion is performed using adaptive multiscale estimation to efficiently capture statistical correlation in the data across many scales. I extend a recently developed multiscale estimation method to allow adaptive estimation of non-stationary spatial processes.

The contributions of this work include (1) combining physical modeling with multiscale estimation to accommodate nonlinear measurement-state relationships, (2) extending multiscale estimation techniques to adaptively estimate non-stationary processes, and (3) improving estimates of ground elevations and vegetation heights for remote sensing applications.