by the environment.
Error sources in a single axis rate gyroscope can be generalized according to the following formula:
(1.1)
where
(1.2)
Figure 1.2 Micro‐rate integrating gyroscope (MRIG) architectures.
where
1.2.1 Scale Factor Errors
Scale factor (or sensitivity) errors represent a deviation in gyroscope sensitivity from expected values, which results in a nonunity gain between “true” angular rate and “perceived” angular rate. Scale factor errors can be caused by either an error in initial scale factor calibration or a drift in scale factor postcalibration due to a change in environmental conditions, such as a change in temperature or supply voltages, application of external mechanical stresses to the sensing element, or aging effects internal to the sensor, such as a change in cavity pressure of the vacuum packaged sensing element.
1.2.2 Bias Errors
Bias (or offset) errors can be summarized as the deviation of time averaged gyroscope output from zero when there is no angular rate input to the sensor. Aside from initial calibration errors, bias errors can be caused by a change in environment conditions. Examples include a change in temperature, supply voltages or cavity pressure, aging of materials, and application of external mechanical stresses to the sensing element. An additional source of bias errors is external body loads, such as quasi‐static acceleration, as well as vibration.
1.2.3 Noise Processes
Noise in gyroscopes can be grouped under white noise, flicker (
1.2.3.1 Allan Variance
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
(1.4)
Finally, the calculated uncertainty
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.
1.3 Overview
The first part of this book focuses on fundamentals of whole‐angle gyroscopes, dynamics, mathematical framework, and control strategies. In the second part of the book, conventionally micro‐machined 2‐D whole‐angle gyroscope architectures are reviewed. The final part of the book focuses on 3‐D emerging micro‐machining technologies for fabrication of whole‐angle gyroscope architectures.
In Chapter 2, Foucault Pendulum analogy is introduced as a starting point for whole‐angle gyroscope dynamics. Later in the chapter, effects of structural imperfections are introduced, along with requirements for continuous RIG operation.
In Chapter 3, a brief overview of control strategies for CVGs is presented. The remainder of the chapter deals with sustaining oscillation and suppression of error sources in whole‐angle gyroscopes, along with methods for tuning and self‐calibration.
