  We apply a Gaussian state formalism to track fluctuating perturbations that
act on the position and momentum quadrature variables of a harmonic oscillator.
Following a seminal proposal by Tsang and Caves [Phys. Rev. Lett. 105, 123601
(2010)], Einstein-Podolsky-Rosen correlations with the quadrature variables of
an ancillary harmonic oscillator are leveraged to significantly improve the
estimates as relevant sensor variables can be arbitrarily squeezed while
evading adverse effects from the conjugate, anti-squeezed variables. Our
real-time analysis of the continuous monitoring of the system employs a hybrid
quantum-classical description of the quantum probe and the unknown classical
perturbations, and it provides a general formalism to establish the
achievements of the sensing scheme and how they depend on different parameters.
