Formula 1

where $a_{0}$ is the linear acceleration at some reference point designated the "origin", $\alpha$ is the angular acceleration of the body (assuming it is rigid), $k \in\left(1,2, \ldots, N_{a}\right), i \in\left(1,2, \ldots, n^{*}\right), j \in(x, y, z)$, and $\mathbf{e}_{x}^{T}=[100], \mathbf{e}_{y}^{T}=[010]$, and $\mathbf{e}_{z}^{T}=[001]$ are row selection vectors (as shown assuming accelerometer orientation is aligned per a traditional right hand Cartesian system).

$$\mathbf{e}_{x}^{T}=[100], \mathbf{e}_{y}^{T}=[010]$$

Formula 2

e linear acceleration at some reference point designated the "origin", $\alpha$ is the angular acceleration of the body (assuming it is rigid), $k \in\left(1,2, \ldots, N_{a}\right), i \in\left(1,2, \ldots, n^{*}\right), j \in(x, y, z)$, and $\mathbf{e}_{x}^{T}=[100], \mathbf{e}_{y}^{T}=[010]$, and $\mathbf{e}_{z}^{T}=[001]$ are row selection vectors (as shown assuming accelerometer orientation is aligned per a traditional right hand Cartesian system).

$$\mathbf{e}_{z}^{T}=[001]$$

Formula 3

Parameter $N_{a}$ represents the number of accelerometer measurements (as previously defined) and $n^{*} \leq N_{a}$ the number of measurement locations; e.

$$n^{*} \leq N_{a}$$

Formula 4

, utilization of multi-axis accelerometers results in $n^{*}<N_{a}$.

$$n^{*}<N_{a}$$