  Inertial navigation computation is to acquire the attitude, velocity and
position information of a moving body by integrating inertial measurements from
gyroscopes and accelerometers. Over half a century has witnessed great efforts
in coping with the motion non-commutativity errors to accurately compute the
navigation information as far as possible, so as not to compromise the quality
measurements of inertial sensors. Highly dynamic applications and the
forthcoming cold-atom precision inertial navigation systems demand for even
more accurate inertial navigation computation. The paper gives birth to an
inertial navigation algorithm to fulfill that demand, named the iNavFIter,
which is based on a brand-new framework of functional iterative integration and
Chebyshev polynomials. Remarkably, the proposed iNavFIter reduces the
non-commutativity errors to almost machine precision, namely, the
coning/sculling/scrolling errors that have perplexed the navigation community
for long. Numerical results are provided to demonstrate its accuracy
superiority over the state-of-the-art inertial navigation algorithms at
affordable computation cost.
