angles representing vehicle heading (with respect to north), pitch (with respect to horizontal), and roll. Output attitude may also be used to drive cockpit displays such as compass cards or artificial horizon indicators.
Accelerometer Error Compensation and Gyroscope Error Compensation denote the calibrated corrections for sensor errors. These generally include corrections for scale factor variations, output biases, and input axis misalignments for both types of sensors, and acceleration‐dependent errors for gyroscopes.
Gravity denotes the gravity model used to compute the acceleration due to gravity as a function of position.
Coriolis denotes the acceleration correction for Coriolis effect in rotating coordinates.
Leveling denotes the rotation rate correction to maintain locally level coordinates while moving over the surface of the Earth.
Earth Rate denotes the model used to calculate the Earth rotation rate in locally level INS coordinates.
Torquing denotes the servo loop gain computations used in stabilizing the INS in locally level coordinates.
Figure 3.23 Essential navigation signal processing for gimbaled INS.
Not shown in the figure is the input altitude reference (e.g. barometric altimeter or GNSS) required for vertical channel (altitude) stabilization.
3.7 Testing and Evaluation
The final stage of the development cycle is testing and performance evaluation. For standalone inertial systems, this usually proceeds from the laboratory to a succession of host vehicles, depending on the application.
3.7.1 Laboratory Testing
Laboratory testing is used to evaluate sensors before and after their installation in the ISA, and then to evaluate the system implementation during operation. The navigation solution from a stationary system should remain stationary, and any deviation is due to navigation errors. Testing with the system stationary can also be used to verify that position errors due to intentional initial velocity errors follow a path predicted by Schuler oscillations (
Additional laboratory testing may be required for specific applications. Systems designed to operate aboard Navy ships, for example, may be required to meet their performance requirements under dynamic disturbances at least as bad as those to be expected aboard ships under the worst sea conditions. This may include what is known as a “Scoresby test,” used at the US Naval Observatory in the early twentieth century for testing gyrocompasses. Test conditions may include roll angles of
Drop tests (for handling verification) and shake‐table or centrifuge tests (for assessing acceleration capabilities) can also be done in the laboratory.
3.7.2 Field Testing
After laboratory testing, systems are commonly evaluated next in highway testing.
Systems designed for tactical aircraft must be designed to meet their performance specifications under the expected peak dynamic loading, which is generally determined by the pilot's limitations.
Systems designed for rockets must be tested under conditions expected during launch, sometimes as a “piggyback” payload during the launch of a rocket for another purpose. Accelerations can reach around
In all cases, GNSS has become an important part of field instrumentation. The Central Inertial Guidance Test Facility at Holoman AFB was once equipped with elaborate range instrumentation for this purpose, which is now performed at much lower cost using GNSS.
3.7.3 Performance Qualification Testing
The essential performance metric for any navigation system is accuracy, commonly specified in terms of position accuracy. However, because inertial navigation also provides attitude and velocity information, those may also be factors in performance assessments. In the case of integrated GNSS/INS systems, there may be an additional performance metric related to how fast navigational accuracy degrades when GNSS signal reception is lost. INS‐only navigation is called free inertia navigation, and we will start there. Integrated GNSS/INS performance is addressed in Chapter 12.
3.7.3.1 CEP and Nautical Miles
Here, “CEP” stands for “circular error probable” or “circle of equal probability,” specified as the radius of the circle about the navigation solution with a radius such that the true solution is equally likely to be inside or outside of that circle. That radius is usually specified in units of nautical miles (1852 m in SI units6).
3.7.3.2 Free Inertial Performance
“Free” here means unaided by external sensors – except for altimeter aiding required to stabilize altitude errors.
Free Inertial Error Heuristics
Unaided inertial navigators are essentially integrators, integrating sensed accelerations (including sensor noise) to get velocity and integrating velocity to get position. Unfortunately, integration does bad things to zero‐mean random noise. The integral of zero‐mean additive uncorrelated random noise on an accelerometer output is a random walk process, the variance of which grows linearly over time. Integrated twice to get position, we might expect variance to grow quadratically with time, in which case its standard deviation would grow linearly with time. As a consequence, one might expect INS performance to be characterized by how fast an error distance statistic grows linearly with time.
CEP Rates
A common INS performance metric used in military applications is CEP rate, generally calculated over typical INS mission times (a few hours, generally) and originally measured (before GNSS availability) during INS performance qualification trials aboard different military aircraft or surface vehicles on suitably instrumented test ranges. That can now be done using GNSS
