  Qubit noise spectroscopy (QNS) is a valuable tool for both the
characterization of a qubit's environment and as a precursor to more effective
qubit control to improve qubit fidelities. Existing approaches to QNS are what
the classical spectrum estimation literature would call "non-parametric"
approaches, in that a series of probe sequences are used to estimate noise
power at a set of points or bands. In contrast, model-based approaches to
spectrum estimation assume additional structure in the form of the spectrum and
leverage this for improved statistical accuracy or other capabilities, such as
superresolution. Here, we derive model-based QNS approaches using inspiration
from classical signal processing, primarily though the recently developed
Schrodinger wave autoregressive moving-average (SchWARMA) formalism for
modeling correlated noise. We show, through both simulation and experimental
data, how these model-based QNS approaches maintain the statistical and
computational benefits of their classical counterparts, resulting in powerful
new estimation approaches. Beyond the direct application of these approaches to
QNS and quantum sensing, we anticipate that the flexibility of the underlying
models will find utility in adaptive feedback control for quantum systems, in
analogy with their role in classical adaptive signal processing and control.
