An apparatus for estimating a parameter includes: an optical fiber including at least one core configured to transmit an interrogation signal and including a plurality of sensing locations distributed along a measurement length of the optical fiber and configured to reflect light; a reference optical path configured to transmit a reference signal, the reference optical path disposed in a fixed relationship to the at least one core and extending at least substantially parallel to the at least one core, the reference optical path including a reference reflector that defines a cavity length corresponding to the measurement length; a detector configured to receive a reflected return signal; a reference interferometer configured to receive at least a reference signal and generate an interferometric reference signal; and a processor configured to apply the interferometric reference signal to the reflected return signal to compensate for one or more environmental parameters.