Cold atom interferometers are among the most sensitive instruments in measuring inertial forces, such as gravity, gravity gradients, accelerations, and rotations. High performance operation outside the lab is generally challenging due to limited dynamic range and systematic effects. We will present new approaches to atom interferometry that tackle these limitations, including simultaneous quadrature-phase detection, extension of dynamic range by orders of magnitude using new, composite, interferometric fringes as in a Moiré-like effect, and scale-factor stabilization in point-source interferometry using correlation with fringe contrast. We study all these schemes and demonstrate them experimentally in static and dynamic conditions.