An accelerometer-only algorithm for determining the acceleration field of a rigid body, with application in studying the mechanics of mild Traumatic Brain Injury

TL;DR

This paper introduces an accelerometer-only algorithm to determine the acceleration field of a rigid body, aiding in bio-mechanics and mTBI studies without requiring gyroscopes or numerical differentiation.

Contribution

The novel AO-algorithm estimates the acceleration field using only accelerometer data, avoiding noise amplification from differentiation and enabling applications in biomechanics and inertial navigation.

Findings

Efficient computation of acceleration magnitude without differentiation.

Ability to estimate both magnitude and direction of acceleration.

Potential applications in bio-mechanics and inertial navigation.

Abstract

We present an algorithm for determining the acceleration field of a rigid body using measurements from four tri-axial accelerometers. The acceleration field is an important quantity in bio-mechanics problems, especially in the study of mild Traumatic Brain Injury (mTBI). The in vivo strains in the brain, which are hypothesized to closely correlate with brain injury, are generally not directly accessible outside of a laboratory setting. However, they can be estimated on knowing the head's acceleration field. In contrast to other techniques, the proposed algorithm uses data exclusively from accelerometers, rather than from a combination of accelerometers and gyroscopes. For that reason, the proposed accelerometer only (AO) algorithm does not involve any numerical differentiation of data, which is known to greatly amplify measurement noise. For applications where only the magnitude of the acceleration vector is of interest, the algorithm is straightforward, computationally efficient and does not require computation of angular velocity or orientation. When both the magnitude and direction of acceleration are of interest, the proposed algorithm involves the calculation of the angular velocity and orientation as intermediate steps. In addition to helping understand the mechanics of mTBI, the AO-algorithm may find widespread use in several bio-mechanical applications, gyroscope-free inertial navigation units, ballistic platform guidance, and platform control.