  We consider the simultaneous and continuous measurement of qubit observables
$\sigma_z$ and $\sigma_z\cos\varphi + \sigma_x\sin\varphi$, focusing on the
temporal correlations of the two output signals. Using quantum Bayesian theory,
we derive analytical expressions for the correlators, which we find to be in
very good agreement with experimentally measured output signals. We further
discuss how the correlators can be applied to parameter estimation, and use
them to infer a small residual qubit Hamiltonian arising from calibration
inaccuracy in the experimental data.
