The problem of estimating an unknown force driving a linear oscillator is
revisited. When using linear measurement, feedback is often cited as a
mechanism to enhance bandwidth or sensitivity. We show that as long as the
oscillator dynamics are known, there exists a real-time estimation strategy
that reproduces the same measurement record as any arbitrary feedback protocol.
Consequently some form of nonlinearity is required to gain any advantage beyond
estimation alone. This result holds true in both quantum and classical systems,
with non-stationary forces and feedback, and in the general case of
non-Gaussian and correlated noise. Recently, feedback enhanced incoherent force
sensing has been demonstrated [Nat. Nano. \textbf{7}, 509 (2012)], with the
enhancement attributed to a feedback induced modification of the mechanical
susceptibility. As a proof-of-principle we experimentally reproduce this result
through straightforward filtering.Comment: 5 pages + 2 pages of Supplementary Informatio
