Chapter 9.4: INERTIAL SYSTEMS TECHNOLOGIES: SYSTEM IMPLEMENTATION MODELS

9.4 SYSTEM IMPLEMENTATION MODELS

9.4.1 One-Dimensional Example

This example is intended as an introduction to INS technology for the uninitiated. It illustrates some of the key properties of inertial sensors and inertial system implementations.

If we all lived in one-dimensional "line land," then there could be no rotation and no need for gyroscopes. In that case, an INS would need only one accelerometer and navigation computer (all one-dimensional, of course), and its implementation would be as illustrated in Fig. 9.15 (in two dimensions), where the dependent variable x denotes position in one dimension and the independent variable t is time.

This implementation for one dimension has many features common to implementations for three dimensions:

Accelerometers cannot measure gravitational acceleration. An accelerometer effectively measures the force acting on its proof mass to make it follow its mounting base, which includes only nongravitational accelerations applied through physical forces acting on the INS through its host vehicle. Satellites, which are effectively in free fall, experience no sensible accelerations.
Accelerometers have scale factors, which are the ratios of input acceleration units to output signal magnitude units (e.g., meters per second squared per volt). The signal must be rescaled in the navigation computer by multiplying by this scale factor.

Accelerometers have output errors, including
(a) Unknown constant offsets, also called biases.
(b) Unknown constant scale factor errors.
(c) Unknown sensor input axis misalignments.
(d) Unknown nonconstant variations in bias and scale factor.
(e) Unknown zero-mean additive noise on the sensor outputs, including quantization noise and electronic noise. The noise itself is not predictable, but its statistical properties may be used in Kalman filtering to estimate drifting scale factor and biases.
Gravitational accelerations must be modeled and calculated in the navigational computer, then added to the sensed acceleration (after error and scale compensation) to obtain the net acceleration x of the INS.
The navigation computer must integrate acceleration to obtain velocity. This is a definite integral and it requires an initial value, x(t₀); that is, the INS implementation in the navigation computer must start with a known initial velocity.
The navigation computer must also integrate velocity (x) to obtain position (x). This is also a definite integral and it also requires an initial value,x(t₀). The INS implementation in the navigation computer must start with a known initial location, too.

Inertial navigation in three dimensions requires more sensors and more signal processing than in one dimension, and it also introduces more possibilities for implementation (e.g., gimbaled or strapdown)

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Chapter 9.4: INERTIAL SYSTEMS TECHNOLOGIES: SYSTEM IMPLEMENTATION MODELS

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