December 17, 8:00 pm EST
Acquiring the attitude, velocity and position information is fundamental to any motion body manipulation. Inertial navigation is a self-contained method to achieve this goal by integrating inertial measurements from triads of gyroscopes and accelerometers. Over half a century has witnessed tremendous efforts in designing advanced inertial navigation algorithms for strapdown systems so as not to compromise the quality of inertial sensors. This lecture will review the inertial navigation algorithm development history and demonstrate by analyses and examples how the present-day INS algorithm is not always able to deliver the target precision of the well-known DARPA PINS project as a result of fundamental limitations in handling the motion-induced noncommutativity errors (due to nonlinearity). A new approach of functional iteration could bring down the noncommutativity errors to almost machine precision at affordable cost. The approach paves a promising algorithmic road for the forthcoming ultra-precision INS of meter-level accuracy, and the existing dynamic applications as well. It might be useful as well for accurately solving the general ordinary differential equations.