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The acquisition of attitude, velocity, and position is an essential task inthe field of inertial navigation, achieved by integrating the measurements frominertial sensors. Recently, the ultra-precision inertial navigation computationhas been tackled by the functional iteration approach (iNavFIter) that drivesthe non-commutativity errors almost to the computer truncation error level.This paper proposes a computationally efficient matrix formulation of thefunctional iteration approach, named the iNavFIter-M. The Chebyshev polynomialcoefficients in two consecutive iterations are explicitly connected through thematrix formulation, in contrast to the implicit iterative relationship in theoriginal iNavFIter. By so doing, it allows a straightforward algorithmicimplementation and a number of matrix factors can be pre-calculated for moreefficient computation. Numerical results demonstrate that the proposediNavFIter-M algorithm is able to achieve the same high computation accuracy asthe original iNavFIter does, at the computational cost comparable to thetypical two-sample algorithm. The iNavFIter-M algorithm is also implemented ona FPGA board to demonstrate its potential in real time applications.

iNavFIter-M: Matrix Formulation of Functional Iteration for Inertial Navigation Computation