Mohinder S. Grewal - Global Navigation Satellite Systems, Inertial Navigation, and Integration

Velocity . Zero, by definition.

Position . From GNSS, if available, otherwise from local sources – e.g. signs or local auxiliary sensors (see Section 3.5.1.3).

Gyrocompassing . Gyrocompass alignment of stationary vehicles uses the sensed direction of acceleration to determine the local vertical and the sensed direction of rotation to determine north, as illustrated in Figure 3.13.

Using auxiliary sensors . Non‐gyroscopic attitude sensors can also be used as aids in alignment. These include the following:

Figure 3.13Gyrocompassing determines sensor orientations with respect to east, north, and up.

Magnetic sensors are used primarily for coarse heading alignment, to speed up INS alignment.

Star trackers are used primarily for space‐based or near‐space applications. The Snark cruise missile and the U‐2 spy plane used inertial‐platform‐mounted star trackers to maintain INS alignment on long flights, an idea attributed to Northrop Aviation.

Optical alignment systems have been used on some systems prior to launch. Some use Porro prisms mounted on the inertial platform to maintain optical line‐of‐sight reference through ground‐based theodolites to reference directions at the launch complex.

Quasi magnetostatic sensors have been used in virtual reality systems for determining the attitude and position of the headset relative to its environment. These use three orthogonal and independently coded low‐to‐medium frequency magnetic dipole sources to illuminate the local area where rotational and locational orientation data is required, and three‐axis AC magnetic sensors as receivers.

Gyrocompass alignment is not necessary for integrated GNSS/INS navigation, although many INSs may already be configured for it.

A rough rule‐of‐thumb for gyrocompass alignment accuracy is

(3.15)

where

is the minimum achievable root‐mean‐square (RMS) alignment error in radians,

is the RMS accelerometer accuracy in 's,

is the RMS gyroscope accuracy in degrees per hour,

15 deg/h is the rotation rate of the Earth, and

is the latitude at which gyrocompassing is performed.

Alignment accuracy is also a function of the time allotted for it, and the time required to achieve a specified accuracy is generally a function of sensor error magnitudes (including noise) and the degree to which the vehicle remains stationary.

Gimbaled implementation . Gyrocompass alignment for gimbaled systems is a process for aligning the inertial platform axes with the navigation coordinates using only the sensor outputs while the host vehicle is essentially stationary. For systems using ENU navigation coordinates, for example, the platform can be tilted until two of its accelerometer inputs are zero, at which time both input axes will be horizontal. In this locally leveled orientation, the sensed rotation axis will be in the north–up plane, and the platform can be slewed about the vertical axis to null the input of one of its horizontal gyroscopes, at which time that gyroscope input axis will point east–west. That is the basic concept used for gyrocompass alignment, but practical implementation requires filtering 5 to reduce the effects of sensor noise and unpredictable zero‐mean vehicle disturbances due to loading activities and/or wind gusts.

Strapdown implementation . Gyrocompass alignment for strapdown systems is a process for “virtual alignment” by determining the sensor cluster attitude with respect to navigation coordinates using only the sensor outputs while the system is essentially stationary.

Error‐free implementation . If the sensor cluster could be firmly affixed to the Earth and there were no sensor errors, then the sensed acceleration vector in sensor coordinates would be in the direction of the local vertical, the sensed rotation vector would be in the direction of the Earth rotation axis, and the unit column vectors

(3.16)

(3.17)

(3.18)

would define the initial value of the coordinate transformation matrix from sensor‐fixed coordinates to ENU coordinates:

(3.19)

Practical implementation . In practice, the sensor cluster is usually mounted in a vehicle that is not moving over the surface of the Earth, but may be buffeted by wind gusts or disturbed during fueling and loading operations. Gyrocompassing then requires some amount of filtering (Kalman filtering, as a rule) to reduce the effects of vehicle buffeting and sensor noise. The gyrocompass filtering period is typically on the order of several minutes for a medium‐accuracy INS but may continue for hours, days, or continuously for high‐accuracy systems.

This method is generally faster than gyrocompass alignment, but it requires another INS on the host vehicle and it may require special maneuvering of the host vehicle to attain observability of the alignment variables. It is commonly used for in‐air INS alignment for missiles launched from aircraft and for on‐deck INS alignment for aircraft launched from carriers. Alignment of carrier‐launched aircraft may also use the direction of the velocity impulse imparted by the steam catapult.

This is an issue in GNSS/INS integration, which is covered in Chapter 12. In this case it must also estimate the INS orientation and velocity, the observability of which generally depends on the host vehicle trajectory.

Knowing the instantaneous rotational orientations of the inertial sensor input axes with respect to navigational coordinates is essential for inertial navigation to work. The integration of accelerations for maintaining the navigation solution for velocity and position depends on it.