for CEP rate determinations.
INS Performance Categories
In the 1970s, before GPS became a reality, the US Department of Defense established the following categories of INS performance:
High accuracy systems have free inertial CEP rates in the order of 0.1 nautical miles per hour (
Medium accuracy systems have free inertial CEP rates in the order of 1 nautical mile per hour (
Low accuracy systems have free inertial CEP rates in the order of 10 nautical miles per hour (
Comparable Sensor Performance Ranges
Order‐of‐magnitude ranges for the inertial sensor errors in these INS performance categories are summarized in Table 3.1. Inertial sensors below tactical grade are sometimes called commercial grade or consumer grade.
Table 3.1 INS and inertial sensor performance ranges.
| Performance ranges | ||||
| System or sensor | High | Medium | Low | Units |
| INS |
|
|
|
NMi/h CEP rate |
| Gyroscopes |
|
|
|
deg/h drift rate |
| Accelerometers |
|
|
|
|
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
