  Gravitational wave searches for continuous-wave signals from neutron stars
are especially challenging when the star's spin frequency is unknown a priori
from electromagnetic observations and wanders stochastically under the action
of internal (e.g. superfluid or magnetospheric) or external (e.g. accretion)
torques. It is shown that frequency tracking by hidden Markov model (HMM)
methods can be combined with existing maximum likelihood coherent matched
filters like the F-statistic to surmount some of the challenges raised by spin
wandering. Specifically it is found that, for an isolated, biaxial rotor whose
spin frequency walks randomly, HMM tracking of the F-statistic output from
coherent segments with duration T_drift = 10d over a total observation time of
T_obs = 1yr can detect signals with wave strains h0 > 2e-26 at a noise level
characteristic of the Advanced Laser Interferometer Gravitational Wave
Observatory (Advanced LIGO). For a biaxial rotor with randomly walking spin in
a binary orbit, whose orbital period and semi-major axis are known
approximately from electromagnetic observations, HMM tracking of the
Bessel-weighted F-statistic output can detect signals with h0 > 8e-26. An
efficient, recursive, HMM solver based on the Viterbi algorithm is
demonstrated, which requires ~10^3 CPU-hours for a typical, broadband (0.5-kHz)
search for the low-mass X-ray binary Scorpius X-1, including generation of the
relevant F-statistic input. In a "realistic" observational scenario, Viterbi
tracking successfully detects 41 out of 50 synthetic signals without spin
wandering in Stage I of the Scorpius X-1 Mock Data Challenge convened by the
LIGO Scientific Collaboration down to a wave strain of h0 = 1.1e-25, recovering
the frequency with a root-mean-square accuracy of <= 4.3e-3 Hz.
