The arrangement of the accelerometers and gyroscopes is generally the same in all INS used for navigation. The common approach is to use three single axis accelerometers and gyroscopes, with an accelerometer and gyroscope placed with its input axis along each of three mutually orthogonal axes. The collection of sensors used is referred to as the instrument cluster. The surface on which the instrument cluster is placed is referred to as the platform.
The use of a platform is common to all INS and the separation of configurations is found through how the platform is used in the determination of position. The platform is normally either suspended in a set of gimbals, referred to as a gimballed or stabilized platform system, or placed directly upon the body to which it is to reference, known as a strapdown or analytical platform system. The platform system and its housing are referred to as the IMU. Each IMU has differing methods of sensing rotations and correspondingly the computation process is different in each circumstance. The use of accelerometers is common in both circumstances however the function of gyroscopes is different in gimballed and strapdown configurations.
Gimballed platforms require numerous parts in order to maintain the platform in the correct orientation. The major components required include:
· The instrument cluster – held in a fixed orientation.
· The gimbals – used as the divider between the instrument cluster and the case to which motion is referenced. The gimbal has two orthogonal pivot axes which attach to outward and inward pivot axes.
· The bearings – used to allow the motion of the gimbals, found at the pivot axes of all gimbals.
· The gimbal motors – used to help maintain the orientation of the platform. There exists one motor for each gimbal which is located next to the bearing.
· The pickoffs – used to measure the angular rates of the gimbals. The pickoffs are located at the opposite pivot point to the gimbal motor.
Strapdown platforms have few extra components when compared to the gimballed configurations. The strapdown system does not attempt to preserve a fixed alignment like gimballed systems. Instead the platform is attached to the body of the vehicle to which it is to reference. The IMU in strapdown configurations is normally placed so the axes of the IMU are parallel to the axes of the vehicle. The basic principle of an IMU is the same for gimballed and strapdown configurations, to provide a measure of the acceleration and rotation rate in three defined axes. The gimballed system provides the defined axes in a mechanical method, maintaining an orientation, whereas strapdown systems compute the axes orientation mathematically, calculating the separation of the current state to the original defined axes, effectually replacing the mechanical gimbal set with a mathematical one.
Gimballed systems attempt to keep the platform perpendicular to the gravity vector, which changes at each point. Schuler tuning refers to the process that is applied to keep the platform vertical. The process is defined through the period of the Schuler pendulum. The Schuler pendulum is a concept that states that a pendulum of length from the platform to the centre of the earth would be insensitive to the accelerations felt by the platform. The period of oscillation of the Schuler pendulum is approximately 84 minutes when close to the earth’s surface. The application of such a pendulum is impractical, however, the system can be ‘tuned’ to exhibit the properties of such a pendulum, referred to as Schuler tuning. The platform is now insensitive to accelerations of the platform, is not directly rotated by the accelerations that are incident upon it.
The second aspect of Schuler tuning is the platform alignment with the gravity vector, achieved through rotation of the platform based on the velocity of the IMU in each of the east and north directions separately. The rate at which the platform is rotated, called the angular torquing rate, is equal to the linear velocity in the east and north direction divided by the separation of the platform from the centre of the earth.
The errors created from torquing the platform are best shown in the consideration of a stationary gimballed system. The stationary platform is, for some reason, placed a tilt and correspondingly measures a component of the gravity in the north accelerometer. This is interpreted as acceleration in the north direction, which is converted to a velocity used to torque the platform to reduce the tilt. The platform is now tilted in the opposite direction and the process repeats with the opposite direction of the initial direction. The result is that the velocity and position oscillate at the Schuler frequency.
Effects of Initial Tilt Errors
Gyroscope drift error is another error which excites a Schuler oscillation. The effect of a gyro drift causes a tilt to build up in the platform, resulting in an oscillatory acceleration error. The velocity and position oscillate at the Schuler frequency, however this time the velocity does not oscillate about zero, so the position error is now a Schuler oscillation superimposed on a ramp function.
Gyro Drift Errors from King (1998)
Each platform has advantages and problems which separate the uses for which each platform is suitable for use. This line is decreasing with the constant technological advancements that occur.
The advantages of gimballed systems include:
· They can operate with vehicle rotation rates greater than 1000 degrees per second, due to the ability of the pickoff
· They can self align by gyro-compassing
· They can calibrate the sensors by platform rotations
· Gyro torquer errors do not lead to attitude error
· Require simpler gyroscopes. The sensor platform only needs to rotate at the small rates required to keep it level, meaning that the gyroscopes do not need a large dynamic range. The lack of gyroscope rotation means that there are no angular acceleration error present in the accelerometers and gyroscopes.
· Higher accuracy. The accelerometer axes are always well defined and the horizontal accelerometers measure no component of gravity, measuring only the inertial accelerations.
There are also problems with the gimballed system that need to be considered, including:
· They are mechanically complicated. The gimbal structure and bearings have to be as rigid as possible to ensure that the axes remained defined under vibrations and large forces. The bearings also have to have as little friction as possible. The result is that he device is complex and correspondingly difficult to create
· They are larger, more expensive and have lower reliability than strapdown. The reliability of gimballed systems is compromised by the numerous parts that are needed to function and the stress placed on components such as the bearings.
· Gimbal requirements. Each gimbal must have a pickoff and a torquer to enable alignment, if either leak a magnetic field it could disrupt the operation of the accelerometers and gyroscopes.
The advantages of the strapdown system are generally related to the advantages that this system exhibits over gimballed systems, most likely as a result of being a later development. Strapdown systems are lighter, cheaper, simpler, rugged and more easily configured for odd shaped spaces, they also are more reliable than strapdown systems. Most of the advantages are due to the replacement of mechanical gimbals with a computer which is smaller, lighter and more reliable.
For all the advantages that removing the gimbals have for strapdown systems it also creates some problems including:
· Sensors cannot be easily calibrated so must be stable. Strapdown platforms can be difficult to align as they are not easily moved
· System rotation can induce sensor errors such as output angular accelerations and torquer errors
· Accelerometer bias errors accumulate and all accelerometers may be subjected to components of gravity reducing their accuracy and exciting cross-axis errors.
· Require gyroscopes to measure large rates. As the platform rotates at the same rate as the vehicle the gyroscope must have a dynamic range capable of measuring the total range of rate experienced.