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.
3.3 Inertial Sensor Technologies
3.3.1 Gyroscopes
The French physicist Léon Foucault (1819–1868) gave them this name (from the Greek for “rotation sensor” or something like that) in the mid‐nineteenth century. The technology has developed considerably since then. The following is but a sampling from a vast reservoir of technological approaches to inertial sensing.
3.3.1.1 Momentum Wheel Gyroscopes (MWGs)
Foucault used one to measure the rotation rate of the Earth3 in 1852, this one featuring a spinning brass wheel passively isolated from disturbing torques by using two nested gimbals.
Bearing Technologies
A limiting design factor in momentum wheel gyroscope (MWG) performance has been bearing torque, which has been addressed by going from sleeve bearings to jewel bearings, to ball bearings, to air bearings, and to electrostatic