  Atom interferometers offer excellent sensitivity to gravitational and
inertial signals but have limited dynamic range. We introduce a scheme that
improves on this trade-off by a factor of 50 using composite fringes, obtained
from sets of measurements with slightly varying interrogation times. We analyze
analytically the performance gain in this approach and the trade-offs it
entails between sensitivity, dynamic range, and temporal bandwidth, and we
experimentally validate the analysis over a wide range of parameters. By
combining composite-fringe measurements with a particle-filter estimation
protocol, we demonstrate continuous tracking of a rapidly varying signal over a
span two orders of magnitude larger than the dynamic range of a traditional
atom interferometer.
