3.2 Terminology
Much of the terminology for inertial navigation evolved when the technology was highly classified and being developed by independent design teams, the result of which has been considerable diversity. The terminology used throughout the book, listed in the following text, generally follows a standardized terminology for inertial sensors [1] and systems [2].
Inertia is the propensity of bodies to maintain constant translational and rotational velocity, unless disturbed by forces or torques, respectively (Newton's first law or motion).
Inertial reference frames are coordinate frames in which Newton's laws of motion are valid. They cannot be rotating or accelerating. They are not necessarily the same as the navigation coordinates, which are typically dictated by the navigation problem at hand. We live in a rotating and accelerating environment here on Earth, and that defines an Earth‐fixed locally level coordinate system we already feel comfortable with – even though it is accelerating (to counter gravity) and rotating. These rotations and accelerations must be taken into account in the practical implementation of inertial navigation.
Navigation coordinates are those used for representing the position of the inertial sensors with respect to its environment. In GNSS/INS integration, this will generally be the same as that used by the GNSS, representing the near‐Earth environment. See Appendix B (www.wiley.com/go/grewal/gnss) for descriptions of navigation coordinates and the transformations involved.
The navigation solution for inertial navigation includes the instantaneous values of position, velocity, and rotational orientation of the inertial sensors with respect to navigation coordinates. It must be sufficient for propagating the solution forward in time, given the inertial sensor outputs.
Inertial sensors measure inertial accelerations and rotations, both of which are vector‐valued variables.
Accelerometers measure specific force, the point being that accelerometers do not measure gravitational acceleration. Specific force is modeled by Newton's second law as
Gyroscopes (often shortened to “gyros”) are sensors for measuring rotation.
Displacement gyros (also called whole‐angle gyros) measure accumulated rotation angle, in angular units (e.g. radians or degrees).
Rate gyros measure rotation rates in angular rate units (e.g. radians per second, degrees per hour, etc.).
Inertial navigation depends on gyros for maintaining knowledge of how the accelerometers are oriented in inertial and navigational coordinates.
Input axes of an inertial sensor define which vector component(s) of acceleration, rotation, or rotation rate it measures. These are illustrated by arrows in Figure 3.1, with rotation arrows wrapped around the input axes of gyroscopes to indicate the direction of rotation. Multi‐axis sensors measure more than one component.
Calibration is a process for characterizing sensor input–output behavior from a set of observed input–output pairs. The objective of sensor calibration is to be able to determine its inputs, given its outputs.
Scale factor and bias are the most common sensor error characteristics determined by calibration.
Scale factor is the ratio of sensor output variation to sensor input variation.
Bias is the sensor output with zero input.
Inertial sensor assemblies (ISAs) are ensembles of inertial sensors rigidly mounted to a common base to maintain the same relative orientations, as illustrated in Figure 3.1.
ISAs used in inertial navigation usually contain three accelerometers and three gyroscopes, represented in the figure by lettered blocks with arrows representing their respective input axes, or an equivalent configuration using multi‐axis sensors. However, ISAs used for some other purposes (e.g. dynamic control applications such as autopilots or automotive steering augmentation) may not need as many sensors, and some designs use redundant sensors. Other terms used for the ISA are instrument cluster and (for inertially stabilized implementations) stable element or stable platform.
Figure 3.1 Inertial sensor assembly (ISA) components.
Inertial reference unit (IRU) is a term commonly used for inertial sensor system for attitude information only (i.e. using only gyroscopes). Space‐based telescopes, for example, do not generally need acccelerometers, but they do need gyroscopes to keeping track of orientation.
Inertial measurement units (IMUs) include ISAs and associated support electronics for calibration and control of the ISA. Support electronics may also include thermal control or compensation, signal conditioning and input–output control. An IMU may also include an IMU processor, and – for inertially stabilized systems – the gimbal control electronics.
Inertial navigation systems (INS) measure rotation rates and accelerations, and calculate attitude, velocity, and position. Its subsystems include:
IMUs, already mentioned earlier.
Navigation computers (one or more) to calculate the gravitational acceleration (not measured by accelerometers) and process the outputs of the accelerometers and gyroscopes from the IMU to maintain an estimate of the position of the IMU. Intermediate results of the implementation method usually include estimates of velocity, attitude, and attitude rates of the IMU.
Figure 3.2 Inertially stabilized IMU alternatives.
User interfaces, such as display consoles for human operators and analog and/or digital data interfaces for vehicle guidance and control functions.
Power supplies and/or raw power conditioning for the complete INS.
Implementations of inertial navigation systems include two general types:
Strapdown