  Inertial navigation applications are usually referenced to a rotating frame.
Consideration of the navigation reference frame rotation in the inertial
navigation algorithm design is an important but so far less seriously treated
issue, especially for ultra-high-speed flying aircraft or the future
ultra-precision navigation system of several meters per hour. This paper
proposes a rigorous approach to tackle the issue of navigation frame rotation
in velocity/position computation by use of the newly-devised velocity/position
integration formulae in the Part I companion paper. The two integration
formulae set a well-founded cornerstone for the velocity/position algorithms
design that makes the comprehension of the inertial navigation computation
principle more accessible to practitioners, and different approximations to the
integrals involved will give birth to various velocity/position update
algorithms. Two-sample velocity and position algorithms are derived to
exemplify the design process. In the context of level-flight airplane examples,
the derived algorithm is analytically and numerically compared to the typical
algorithms existing in the literature. The results throw light on the problems
in existing algorithms and the potential benefits of the derived algorithm.
