  It is an open challenge to estimate systematically the physical parameters of
neutron star interiors from pulsar timing data while separating spin wandering
intrinsic to the pulsar (achromatic timing noise) from measurement noise and
chromatic timing noise (due to propagation effects). In this paper we formulate
the classic two-component, crust-superfluid model of neutron star interiors as
a noise-driven, linear dynamical system and use a state-space-based
expectation-maximization method to estimate the system parameters using
gravitational-wave and electromagnetic timing data. Monte Carlo simulations
show that we can accurately estimate all six parameters of the two-component
model provided that electromagnetic measurements of the crust angular velocity,
and gravitational-wave measurements of the core angular velocity, are both
available. When only electromagnetic data are available we can recover the
overall relaxation time-scale, the ensemble-averaged spin-down rate, and the
strength of the white-noise torque on the crust. However, the estimates of the
secular torques on the two components and white noise torque on the superfluid
are biased significantly.
