| Performance ranges | ||||
| System or sensor | High | Medium | Low | Units |
| INS |
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NMi/h CEP rate |
| Gyroscopes |
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deg/h drift rate |
| Accelerometers |
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CEP versus RMS
Unfortunately, the probability‐based CEP statistic is not exactly compatible with the RMS statistics used in the Kalman filter Riccati equations 7 for characterizing INS performance. One must assume some standard probability density function (e.g. Gaussian) to convert mean‐squared horizontal position errors to CEPs.
3.8 Summary
1 Inertial navigation accuracy is mostly limited by inertial sensor accuracy.
2 The accuracy requirements for inertial sensors cannot always be met within manufacturing tolerances. Some form of calibration is usually required for compensating the residual errors.
3 INS accuracy degrades over time, and the most accurate systems generally have shortest mission times. For example, ICBMs only need their inertial systems for a few minutes.
4 Performance of inertial systems is commonly specified in terms of CEP rate.
5 Accelerometers cannot measure gravitational acceleration.
6 Both inertial and satellite navigation require accurate models of the Earth's gravitational field.
7 Both navigation modes also require an accurate model of the shape of the Earth.
8 The first successful navigation systems were gimbaled, in part because the computer technology required for strapdown implementations was decades away. That has not been a problem for about four decades.
9 Gimbaled systems tend to be more accurate and more expensive than strapdown systems.
10 The more reliable attitude implementations for strapdown systems use quaternions to represent attitude.
11 Systems traditionally go through a testing and evaluation process to verify performance.
12 Before testing and evaluation of an INS, its expected performance is commonly evaluated using the analytical models of Chapter 11.
3.8.1 Further Reading
Inertial navigation has a rich and growing technology base – more than can be covered in a single book, and certainly not in one chapter – but there is some good open‐source literature on the subject:
1 Titterton and Weston [12] is a good source for additional information on strapdown hardware and software.
2 Paul Savage's two volume tome [13] on strapdown system implementations is also rather thorough.
3 Chapter 5 of [14] and the references therein include some recent developments.
4 Journals of the IEEE, IEE, Institute of Navigation, and other professional engineering societies generally have the latest developments on inertial sensors and systems.
5 The Mathworks file exchange at https://www.mathworks.com/matlabcentral/fileexchange/ includes many m‐file implementations of navigation procedures, including a complete WGS84 geoid model.
6 In addition, the World Wide Web includes many surveys and reports on inertial sensors and systems.
Problems
Refer to Appendix B for coordinate system definitions, and satellite orbit equations.
1 3.1 Which, if any, of the following coordinate systems is not rotating?Northeast–down (NED)East–north–up (ENU)Earth‐centered Earth‐fixed (ECEF)Earth‐centered inertial (ECI)Moon‐centered moon‐fixed
2 3.2 What is the minimum number of two‐axis gyroscopes (i.e. gyroscopes with two, independent, orthogonal input axes) required for inertial navigation?123Not determined.
3 3.3 What is the minimum number of gimbal axes required for gimbaled inertial navigators in fully maneuverable host vehicles? Explain your answer.1234
4 3.4 Define specific force.
5 3.5 An inertial sensor assembly (ISA) operating at a fixed location on the surface of the Earth would measureNo acceleration1 acceleration downward1 acceleration upward
6 3.6 Explain why an inertial navigation system is not a good altimeter.
7 3.7 The inertial rotation rate of the Earth is1 revolution per day15 deg/h15 arc‐seconds per secondNone of the above
8 3.8 Define CEP and CEP rate for an INS.
9 3.9 The CEP rate for a medium accuracy INS is in the order of2 m/s200 m/h2000 m/h20 km/h
10 3.10 Derive the equivalent formulas in terms of (yaw angle), (pitch angle), and (roll angle) for unit vectors 1, 1, 1 in NED coordinates and 1, 1, 1 in RPY coordinates.
11 3.11 Explain why accelerometers cannot sense gravitational accelerations.
12 3.12 Show that the matrix defined in Eq. (3.35) is orthogonal by showing that the identity matrix. (Hint: Use .)
13 3.13 Calculate the numbers of computer multiplies and adds required forgyroscope scale factor/misalignment/bias compensation (Eq. (3.4 with )accelerometer scale factor/misalignment/bias compensation (Eq. (3.4