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

TL;DR

This paper introduces a matrix-based reformulation of the functional iteration method for inertial navigation, enabling efficient, high-accuracy computations suitable for real-time FPGA implementation.

Contribution

It presents the iNavFIter-M, a matrix formulation that simplifies implementation and enhances computational efficiency of the functional iteration approach in inertial navigation.

Findings

Achieves the same high accuracy as the original method.

Computational cost is comparable to standard two-sample algorithms.

Successfully implemented on FPGA for real-time applications.

Abstract

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