**Determining Noise Specifications on Accelerometers and Rate Gyros** |[home](index.md.html)|[syllabus](syllabus.md.html)|[assignments](assignments.md.html)|[labs](labs.md.html)|[final project](finalproject.md.html)|[flight data](FlightData.md.html)|[getting certified](RocketryCertification.md.html)| # Rate Gyros The quantities of interest in a rate gyro are - Constant bias or offset error, $\epsilon$. - Standard deviation of white noise, $\sigma$. - Bias instability, BRW. - Temperature effects. - Calibration errors. For our purposes over the time scale of liftoff to apogee/ejection, bias instability can be ignored, and temperature effects and calibration errors can be lumped in with constant bias. The constant bias or offset error, $\epsilon$, can be determined by measuring the output when there is no rotation (or only the earth's rotation) for a sufficiently long time and taking the average or mean. The uncertainty in the bias is given by the usual Students _t_-test method. The standard deviation of the white noise, $\sigma$, can be determined by measuring the output when there is no rotation (or only the earth's rotation) for a sufficiently long time and taking the standard deviation. Since doing so is part of determining the uncertainty in the mean, you can kill two flies with one swat (the [Swedish version](https://sv.wiktionary.org/wiki/slå_två_flugor_i_en_smäll) of the aphorism). Both of these can (and should) be done with the pre-launch data while the rocket is sitting on the pad. Be aware that if you collect too much pre-launch data, you'll have to explicitly account for temperature effects. Although not expected, if you want to get at the bias instability, the method for calculating the Allan Variance is given in detail in Section 5.1 of [IntroToInertialNavigation](PDF/IntroToInertialNavigation.pdf). # Accelerometers The quantities of interest in an accelerometer are - Constant bias or offset error, $\epsilon$. - Standard deviation of white noise, $\sigma$. - Bias instability, BRW. - Temperature effects. - Calibration errors. For our purposes over the time scale of liftoff to apogee/ejection, bias instability can be ignored, and temperature effects and calibration errors can be lumped in with constant bias. The constant bias or offset error, $\epsilon$, is best handled at the same time as calibration. Ideally, the accelerometer would be placed in a rigid precise fixture permitting orientation in a vertical and anti-vertical position. A sufficient quantity of data are acquired first in the vertical, and then in the anti-vertical positions. The mean, and the uncertainty in the mean for each section are calculated (the uncertainty by the usual Students _t_-test method). The local gravitational acceleration should be [determined](https://www.sensorsone.com/local-gravity-calculator/) The span is calculated as the difference between the two means. The span uncertainty is calculated in the uncorrelated or RMS sense. The scale factor is then given by $2 g_{local}$/span. The offset is the average of the two means. The offset uncertainty is also calculated in the least squares sense. Be sure to keep track of and report units on all results The standard deviation of the white noise, $\sigma$, can be determined by measuring the output when there is no motion (or only the earth's motion) for a sufficiently long time and taking the standard deviation. The standard deviation calculation can (and should) be done with the pre-launch data while the rocket is sitting on the pad. Be aware that if you collect too much pre-launch data, you'll have to explicitly account for temperature effects. However, the scale and the offset measurements have to be done off the launch pad. Although not expected, if you want to get at the bias instability, the method for calculating the Allan Variance is given in detail in Section 5.1 of [IntroToInertialNavigation](PDF/IntroToInertialNavigation.pdf).