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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 super high-speed flying vehicles or the future ultraprecision navigation system of several meters per hour. A rigorous approach is proposed 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 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 with the typical algorithms that exist in the literature. The results throw light on the problems in existing algorithms and the potential benefits of the derived algorithm.