Error Propagation in Aided Discrete 2D Accelerometry

Abstract

Closed form solutions for open and closed loop error propagation are available in the form of the convolution integrals and factorization solutions to the Riccati equation respectively. However, these are often not very illuminating unless the integrals and sums are actually carried out and simplified. This report sets out to formulate and validate explicit models of systematic and stochastic error propagation in “accelerometry” - the author’s term for inertial navigation when the influence of gravity can be neglected. Under the assumption that the trajectory is a straight line, it turns out that the solution can be computed in closed form. Furthermore, when terrain relative velocity indications and measurements of heading (derived perhaps from a magnetometer) are available and integrated with a Kalman filter, it is possible to show in closed form their dramatic effect on overall system performance.