A Closed-form Solution for the Strapdown Inertial Navigation Initial Value Problem

TL;DR

This paper presents an exact closed-form solution for the initial value problem in strapdown inertial navigation systems, offering significant efficiency and accuracy improvements over traditional numerical integration methods.

Contribution

It introduces a novel closed-form solution leveraging Lie group structure, reducing computational cost and increasing precision in SINS kinematic propagation.

Findings

Exact closed-form solution for SINS initial value problem

Reduces floating point operations by 12 times compared to Runge-Kutta

Applicable to real-time navigation with improved efficiency

Abstract

Strapdown inertial navigation systems (SINS) are ubiquitious in robotics and engineering since they can estimate a rigid body pose using onboard kinematic measurements without knowledge of the dynamics of the vehicle to which they are attached. While recent work has focused on the closed-form evolution of the estimation error for SINS, which is critical for Kalman filtering, the propagation of the kinematics has received less attention. Runge-Kutta integration approaches have been widely used to solve the initial value problem; however, we show that leveraging the special structure of the SINS problem and viewing it as a mixed-invariant vector field on a Lie group, yields a closed form solution. Our closed form solution is exact given fixed gyroscope and accelerometer measurements over a sampling period, and it is utilizes 12 times less floating point operations compared to a single integration step of a 4th order Runge-Kutta integrator. We believe the wide applicability of this work and the efficiency and accuracy gains warrant general adoption of this algorithm for SINS.