  Atomic accelerometers and gravimeters are usually based on freely-falling
atoms in atomic fountains, which not only limits their size, but also their
robustness to environmental factors such as tilts, magnetic fields or
vibrations. Such limitations have precluded their broad adoption in the field,
for geophysics, geology, and inertial navigation. More recently, atom
interferometers based on holding atoms in an optical lattice have been
developed. Such gravimeters also suppress the influence of vibrations in the
frequency range of ~1 Hz and above by several orders of magnitude relative to
conventional atomic gravimeters. Here, we show that such interferometers are
robust to tilts of more than 8 mrad with respect to the vertical and can
suppress the effect of even strong environmental magnetic fields and field
gradients by using atoms in the F=3,4 hyperfine ground states as
co-magnetometers, potentially eliminating the need for shielding. We
demonstrate gravimeter sensitivity of $0.7~\rm{mGal}/\sqrt{\rm Hz}$ ($1~{\rm
mGal}=10~\mu\rm{m/s}^2$) in a compact geometry where atoms only travel over mm
of space.
