 Centripetal subtraction error

Centripetal subtraction error is the residual error left when a modeled centripetal contribution is removed from a rotating accelerometer signal. For the positive magnitude $C=r{\omega }^2$, small errors in radius and angular speed giveThe residual's sign depends on whether the correction is overestimated or underestimated. A correct model also needs synchronized speed information and the appropriate sensor-axis projection; a primary rotating-sensor experiment documents the importance of radial/tangential directions and rotating-frame effects.^[ref]

Using first-order propagation of uncertainty, the standard uncertainty satisfiesThe covariance term must be included when the estimates are correlated.^[ref] For $r=0.020\mathrm{m}$, $\omega =100rad/s$, $u_r=10\mu \mathrm{m}$ and $u_{\omega }=0.1rad/s$, the two uncorrelated contributions have magnitudes0.10 and0.40m/s², giving $u_C\approx 0.4123m/{\mathrm{s}}^2$.

A centripetal timing error can remain even with accurate individual channels. If the speed used for correction lags by $\Delta t$, then $\Delta \omega \approx -\dot{\omega }\Delta t$. At the same radius and speed, acceleration rate $\dot{\omega }=10rad/{\mathrm{s}}^2$ and lag5ms produce correction error approximately $-0.20m/{\mathrm{s}}^2$. Channel timing therefore belongs in the measurement model. These linearized formulas describe small errors; they do not replace accounting for other motion or specific force contributions.