Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binarys nature and inspiral kinematics. Using the lalinference_mcmc Markov-chain Monte Carlo parameter estimation code, we use two fiducial examples to illustrate how the geometry and kinematics are encoded into the modulated gravitational wave signal, using coordinates well-adapted to precession. Even for precessing binaries, we show the performance of detailed parameter estimation can be estimated by effective estimates: comparisons of a prototype signal with its nearest neighbors, adopting a fixed sky location and idealized two-detector network. We use detailed and effective approaches to show higher harmonics provide nonzero but small local improvement when estimating the parameters of precessing BH-NS binaries. That said, we show higher harmonics can improve parameter estimation accuracy for precessing binaries ruling out approximately-degenerate source orientations. Our work illustrates quantities gravitational wave measurements can provide, such as reliable component masses and the precise orientation of a precessing short gamma ray burst progenitor relative to the line of sight. Effective estimates may provide a simple way to estimate trends in the performance of parameter estimation for generic precessing BH-NS binaries in next-generation detectors. For example, our results suggest that the orbital chirp rate, precession rate, and precession geometry are roughly-independent observables, defining natural variables to organize correlations in the high-dimensional BH-NS binary parameter space.
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