iNavFIter: Next-Generation Inertial Navigation Computation Based on Functional Iteration
This addresses a long-standing challenge in inertial navigation for applications requiring high accuracy, such as dynamic systems and cold-atom precision navigation, representing a significant advancement rather than an incremental improvement.
The paper tackles the problem of non-commutativity errors in inertial navigation computation, which are critical for high-dynamic and precision systems, by introducing iNavFIter, a new algorithm based on functional iterative integration and Chebyshev polynomials that reduces these errors to near machine precision while maintaining affordable computational cost.
Inertial navigation computation is to acquire the attitude, velocity and position information of a moving body by integrating inertial measurements from gyroscopes and accelerometers. Over half a century has witnessed great efforts in coping with the motion non-commutativity errors to accurately compute the navigation information as far as possible, so as not to compromise the quality measurements of inertial sensors. Highly dynamic applications and the forthcoming cold-atom precision inertial navigation systems demand for even more accurate inertial navigation computation. The paper gives birth to an inertial navigation algorithm to fulfill that demand, named the iNavFIter, which is based on a brand-new framework of functional iterative integration and Chebyshev polynomials. Remarkably, the proposed iNavFIter reduces the non-commutativity errors to almost machine precision, namely, the coning/sculling/scrolling errors that have perplexed the navigation community for long. Numerical results are provided to demonstrate its accuracy superiority over the state-of-the-art inertial navigation algorithms at affordable computation cost.