Читать книгу Global Navigation Satellite Systems, Inertial Navigation, and Integration - Mohinder S. Grewal - Страница 75

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 , where is the physically applied force (not including gravity) and is the mass it is applied to. Specific force is the force per unit mass, , and accelerometers are sometimes called specific force receivers. SI units for specific force are meters per second per second.

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 systems do nothing to physically control the orientation of the ISA, but they do process the gyroscope outputs to keep track of its orientation with respect to navigation coordinates. A strapdown system is usually attached to its host vehicle so it can keep track of its host vehicle orientation with respect to navigation coordinates.

Inertially stabilized systems use their gyroscopes for controlling ISA attitude, as illustrated in Fig 3.2a–c. This shows three alternative structures that have been tried at different times:

Gimbals, also called a Cardan² suspension. This was the most popular implementation using hardware to solve the attitude problem. The US Navy's Electrostatically Supported Gyro Navigator (ESGN) is a gimbaled system, and possibly the most accurate INS for long‐term inertial navigation.

Ball‐joint, which Fritz Mueller called “inverted gimbals” [3]. It is only useful for applications with limited rotational freedom in pitch and roll, such as for ships in lesser sea states. It has not become popular, perhaps because of the difficulties of applying controlled torques about the spherical bearing to stabilize the ISA.

Floated systems, a configuration also called a “FLIMBAL” system, an acronym for floated inertial measurement ball. The advanced inertial reference sphere (AIRS) inertial navigator for the US Air Force LGM‐30G Minuteman III ICBM is a floated system. Despite the difficulties of transferring power, signals, heat, torque, and relative attitude between the housing and the inner spherical ISA, AIRS is probably the most accurate (and expensive) inertial navigator for high‐g rocket booster applications.

In all three cases, the rotation‐isolated ISA is also called an inertial platform, stable platform, or stable element. The IMU in this case may include the ISA, the gimbal/float structure and all associated electronics (e.g. gimbal wiring, rotary slip rings, gimbal bearing angle encoders, signal conditioning, gimbal bearing torque motors, and thermal control).

Commonly used inertially stabilized ISA orientations in terrestrial applications include:

Inertially fixed (non‐rotating), a common orientation for operations in space. In this case, the ISA may include one or more star trackers to correct for any gyroscope errors. However, locally level implementations may also use star trackers for the same purpose.

Locally level, a common orientation for terrestrial navigation. In this case, the ISA rotates with the Earth, and keeps two of its reference axes locally level during horizontal motion over the surface. Some early systems aligned the gyro and accelerometer input axes with the local directions of north, east, and down, because the gimbal angles could then represent the Euler angles for heading (yaw), pitch, and roll of the vehicle. However, there are also advantages in allowing the locally stabilized element to physically rotate about the local vertical direction.

Inertially stabilized systems are generally more expensive than strapdown systems, but their performance is usually better. This is due, in part, to the fact that their gyroscopes and accelerometers are not required to endure high rotation rates.

“Host vehicle” refers to the transportation system using INS for navigation. It could be a spacecraft, aircraft, surface ship, submarine, land vehicle, or pack animal (including humans).

Shock and vibration isolation. High‐frequency dynamic forces acting on the host vehicle (e.g. from propulsion noise, bumpy terrain, turbulence, or impacts) can excite elastic waves and vibrations in the host vehicle that are transmitted through the vehicle frame to the INS through its mounting hardware. The resulting zero‐mean high‐frequency inputs to the inertial sensors should not influence the navigation solution significantly, but they can create numerical errors in the real‐time computer methods used for integrating attitude rates and acceleration, and they can damage the sensors used. These effects can be mitigated at the interface between INS and host by using shock and vibration isolators (generally made from “lossy” elastomers) to dampen the high‐frequency components of contact forces.

Because inertial navigation systems perform integrals of acceleration and attitude rates, these integrals need initial values.

Initialization is a procedure for obtaining an initial value of the navigation solution.

Rotational orientation or attitude refers to the angular pose of a rigid object in three‐dimensional space relative to the axes of a coordinate system.

Alignment is a procedure used for establishing the initial value of the rotational orientation of the ISA relative to navigation coordinates. Inertial systems with sufficiently accurate sensors can perform self‐alignment when the system is sufficiently stationary with respect to the Earth. In that case, the implementation can be divided into two parts:

Leveling uses the accelerometers to measure the upward acceleration required to counter gravity, from which the system can determine the orientation of its ISA relative to local vertical. For inertially stabilized systems, the stable element (ISA) is physically leveled during this process (hence the name).

Gyrocompassing is a procedure for estimating the direction of the Earth's rotation axes with respect to ISA coordinates, using its gyroscopes. This and the direction of the local vertical then determines the north–south direction, so long as the stationary location is not in the vicinity of the poles. Given these two directions, the INS can orient itself relative to its location on the Earth. The term gyrocompassing is a reference to the gyrocompass, an instrument introduced toward the end of the nineteenth century to replace the magnetic compass on iron ships. The gyrocompass uses mechanical means to orient itself relative to north, whereas the INS requires a computer. For some inertially stabilized systems, gyrocompassing physically aligns the ISA with its level sensor axes pointing north and east.

Transfer alignment uses an independent navigation solution for a host vehicle to initialize the navigation solution (including alignment) in another vehicle carried by the host vehicle. This was originally developed for using the INS in a host vehicle to initialize an INS in guided munitions, and it usually requires some amount of maneuvering of the host vehicle to attain observability of the required alignment variables. A version of this makes use of the INS in an aircraft carrier, the roll and pitch of its deck, and the direction of the launch catapult as inputs for aligning the aircraft INS during takeoff.

Magnetic alignment uses the directions of sensed acceleration (from countering gravity) and the local magnetic field to orient itself. This does not work where the magnetic field is close to vertical (near the magnetic poles), and it can be compromised by magnetic materials warping the local magnetic field.