Fundamental issues in Beam-Position-Monitor (BPM)-based beam dynamics observations are studied in this dissertation. The major topic is the Model-Independent Analysis (MIA) of beam centroid dynamics. Conventional beam dynamics analysis requires a certain machine model, which itself often needs to be refined by beam measurements. Instead of using any particular machine model, MIA relies on a statistical analysis of the vast amount of BPM data that often can be collected non-invasively during

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... al machine operation. There are two major parts in MIA. One is noise First of all, I would like to thank my adviser John Irwin. Without him this dissertation would simply not exist. I treasure the enjoyable experience of doing research together, especially during the time when we were trying to make some sense out of seemingly nonsense experimental data and finally established the Model-Independent Analysis (MIA) methods. From time to time, his enthusiasm and intuition sparked me to be creative; his persistence helped me to walk the extra mile when I thought I had got there (maybe because I was exhausted). I am surely grateful for his careful correction of my writing. In addition, I have the memory of his red face when he was frustrated with me for being tired of facing the hassle to obtain machine time, as well as the memory of the nice dinner at his home right after I passed my oral defense.