Apparent-gravity camera frame

If $g$ is gravitational acceleration and $a$ is the camera's acceleration, the locally felt upward vector is $U=a-g$. Choose the travel unit vector $X$, set $W=U-(U\cdot X)X$, and, when $W\ne 0$, take $Z=W/\Vert W\Vert$ and $Y=Z\times X$. These form an orthonormal basis with $U$ in the $XZ$ plane. If $U$ is parallel to $X$, the condition leaves the roll angle free even when $U\ne 0$; transport a previous transverse axis or choose a well-conditioned coordinate axis and project it into $X^{\perp }$.