Читать книгу Whole-Angle MEMS Gyroscopes - Doruk Senkal, Andrei M. Shkel - Страница 22

Originally created to analyze frequency stability of clocks and oscillators, Allan Variance analysis is also widely used to represent various noise processes present in inertial sensors, such as gyroscopes [3]. Allan Variance analysis consists of data acquisition of gyroscope output over a period of time at zero rate input and constant temperature. This is followed by binning the data into groups of different integration times:

(1.3)

where is the sampling time, is the sample number, and is the bin size. The uncertainty between bins of same integration times is calculated using ensemble average:

(1.4)

Finally, the calculated uncertainty with respect to integration time () is plotted to reveal information about various noise processes within the gyroscope, Figure 1.3. Sections of the Allan Variance curve and their physical meaning is summarized below [3]:

 Quantization noise is due to the conversion of gyroscope output from analog (continuous) signal to digital (countable) signal by Analog‐to‐Digital Converters (quantization). Quantization noise has a slope of on the Allan variance graph.

 Angle Random Walk (ARW) is caused by white thermomechanical and thermoelectrical noise within the gyroscope, shows up with a slope of . It is usually reported using units (degrees per square root of hour) or (millidegrees per second per square root of hertz).

 Rate Random Walk (RRW) is the random drift term within the gyroscope, shows up with a slope of opposite of ARW.

 Bias instability is the lowest point of the Allan variance curve, shows up with a slope of zero. It represents the minimum detectable rate input within the gyroscope and is reported using units (degrees per hour) or (millidegrees per second). Bias instability is limited by a combination of flicker () noise, ARW, and RRW.Figure 1.3 Sample Allan variance analysis of gyroscope output, showing error in gyroscope output (deg/h or deg/s)with respect to integration time (s).

 Rate ramp, also called the thermal ramp, is caused by temperature changes in the environment, shows up with a slope of .

 Periodic oscillations show up as peaks in the Allan Variance curve with an integration time of (not shown). These oscillations are either caused by a periodic event in sensor electronics or the environment, such as day/night temperature cycles or variations in power supply.