  This dissertation explores the topics of parameter estimation and model
reduction in the context of quantum filtering. Chapters 2 and 3 provide a
review of classical and quantum probability theory, stochastic calculus and
filtering. Chapter 4 studies the problem of quantum parameter estimation and
introduces the quantum particle filter as a practical computational method for
parameter estimation via continuous measurement. Chapter 5 applies these
techniques in magnetometry and studies the estimator's uncertainty scalings in
a double-pass atomic magnetometer. Chapter 6 presents an efficient feedback
controller for continuous-time quantum error correction. Chapter 7 presents an
exact model of symmetric processes of collective qubit systems.
