  In a recent paper (hep-th/0103228) a new initial value formulation of
fermionic QFT was presented that is applicable to an arbitrary observer in any
electromagnetic background. This approach suggests a consistent particle
interpretation at all times, with the concept of `radar time' used to
generalise this interpretation to an arbitrarily moving observer. In the
present paper we extend this formalism to allow for gravitational backgrounds.
The observer-dependent particle interpretation generalises Gibbons' definition
to non-stationary spacetimes. This allows any observer to be considered,
providing a particle interpretation that depends {\it only} on the observer's
motion and the background, not on any choice of coordinates or gauge, or on
details of their particle detector. Consistency with known results is
demonstrated for the cases of Rindler space and deSitter space. Radar time is
also considered for an arbitrarily moving observer in an arbitrary 1+1
dimensional spacetime, and for a comoving observer in a 3+1 dimensional FRW
universe with arbitrary scale factor $a(t)$. Finite volume measurements and
their fluctuations are also discussed, allowing one to say with definable
precision where and when the particles are observed.
