  Continuous phase estimation is known to be superior in accuracy as compared
to static estimation. The estimation process is, however, desired to be made
robust to uncertainties in the underlying parameters. Here, homodyne phase
estimation of coherent and squeezed states of light, evolving continuously
under the influence of a second-order resonant noise process, are made robust
to parameter uncertainties using a robust fixed-interval smoother, designed for
uncertain systems satisfying a certain integral quadratic constraint. We
observe that such a robust smoother provides improved worst-case performance
over the optimal smoother and also performs better than a robust filter for the
uncertain system.
