An accelerometer-only algorithm for determining the acceleration field of a rigid body, with application in studying the mechanics of mild traumatic brain injury

Determining rigid body motion from accelerometer data through the square-root of a negative semi-definite tensor, with applications in mild traumatic brain injury

“…The presented algorithm has some similarities to the one recently presented by Rahaman et al [27] 1 , which is referred to as the AO (accelerometer-only) algorithm. For reasons that will become clear shortly, we refer to the algorithm that we present in this manuscript as the ?…”

“…We present here an augmented version of that method for computing similar numerical approximations. The primary difference between our method and that presented in [27] is that the estimate for Ppτ q yielded by our method is certain to retain some of the mathematical properties that are expected of Ppτ q based on our theoretical analysis. Specifically, it follows from Lemmas C.1 and C.2 that sym pPpτ qq is a negative semidefinite matrix with its negative eigenvalues, if any, being of even algebraic multiplicities.…”

“…In §3.1 of [27] a method was presented to estimate Ppτ q and qpτ q from the accelerometer measurements corresponding to the time instance τ . Applying that method for each τ in a discrete time sequence yields a numerical approximation for the maps τ Þ Ñ Ppτ q and τ Þ Ñ qpτ q.…”

“…AO al-gorithms is their non-dependence on gyroscopes. For a detailed discussion on why accelerometers are preferable over gyroscopes in the context of mTBI please see §1 in [27]. Briefly, gyroscopes' power requirements are much higher than those of accelerometers (gyroscopes consume approximately 25 times more power than accelerometers [29]), and algorithms that aim to construct descriptors of a rigid body's acceleration using data from gyroscopes add a significant amount of noise to those descriptors [30,31].…”

“…AO algorithms provide complete information of how the body frame is oriented in space. See §1 in [27] for further discussion on the advantages of the AO and the ? AO algorithms over other algorithms that also make use of only accelerometer data.…”