THANKS TO THE DEVELOPMENT OF MICROMACHINED SENSORS, the cost of some fairly sophisticated three-axis inertial navigation systems has dropped to a level where they can be seriously considered for use in a variety of demanding civil applications, including general aviation. Inertial systems have been used on commercial and military aircraft as primary navigation instruments for many years but these systems are very expensive and out of reach of most of the general aviation community. Low-cost inertial systems coupled with GPS could benefit general aviation in a number of ways, including: their use in attitude and heading reference systems (AHRS) for advanced perspective displays; aiding of GPS receiver code- and/or carrier-tracking loops to increase interference margins; bridging over short-term GPS outages; and as a stand-alone navigation system after the loss of GPS. However, the errors produced by low-cost inertial systems need to be carefully assessed and contained if these applications are to see the light of day. In this month's column, Drs. Andrey Soloviev and Frank van Graas of Ohio University's Avionics Engineering Center in Athens, Ohio, discuss the potential use of low-cost inertial systems by general aviation and, from a series of simulations and real-world tests, highlight the expected performance of the systems and the implementation challenges.--R.B.L.
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Since November 2001, we have been carrying out a study to integrate GPS with an inertial navigation system (INS) with the aim of developing an autonomous navigation system for general aviation (GA). (General aviation is the term used to describe all aviation except government and scheduled-airline use. In addition to recreational flying, it includes flight training, shipping, surveying, agricultural applications, air taxis, charter passenger service, corporate flying, emergency transport, firefighting and more.)
The study also focuses on a U.S. Department of Transportation (DOT) action plan released on March 7, 2002, that seeks "to maintain the adequacy of backup systems for each area of operation in which the GPS is being used for critical transportation applications." This action plan follows the Volpe GPS vulnerability report that identifies susceptibility of GPS to unintentional interference caused by atmospheric effects, signal blockages from buildings, communication equipment, and potential intentional jamming.
The DOT action plan assumes two options for dealing with the GPS vulnerabilities. The first option consists of using adequate backup systems during GPS outages caused by interference. The second option is to increase the robustness of GPS to intentional or unintentional interference sources. Our work addresses both options through the evaluation of integrated low-cost GPS/INS, as well as the evaluation of accuracy and integrity performance following the loss of GPS for both low-cost and navigation-grade INS.
Our study explores the following potential GA applications of low-cost GPS/INS:
* attitude and heading reference system (AHRS) for advanced (perspective) navigation displays;
* aiding of GPS code- and/or carrier-tracking loops with INS to increase the GPS interference margin by approximately 20-30 dB to mitigate radio frequency interference (RFI);
* bridging over short-term GPS outages by using inertial navigation guidance;
* inertial coasting after the loss of GPS.
For these applications, a low-cost system is defined as an integrated system with a prospective total cost of $3,000-$5,000.
The remainder of this article evaluates the contributions of different error sources into output errors of low-cost inertial systems. We provide an error budget of a typical low-cost INS based on some evaluations we have performed. Next, we describe the enhancement of the low-cost INS accuracy performance by calibrating the INS in flight using GPS data. Finally, we consider the performance characteristics of a calibrated low-cost INS and address the feasibility of different options for the integration of low-cost INS and GPS for potential GA application areas.
Low-Cost System Performance
Our main goal in assessing the performance characteristics of low-cost inertial systems is to evaluate the influence of error sources that significantly contribute to output navigation errors. The evaluation comprises an error sensitivity analysis for low-cost inertial sensors, analysis of sensitivity to errors in initial conditions, and consideration of sensor bandwidth requirements.
The error sensitivity analysis of low-cost inertial sensors evaluates the influence of components of sensor measurement errors for a particular inertial measurement unit (IMU). It is a solid-state, six degree-of-freedom inertial sensing system using three orthogonally mounted, micromachined quartz gyroscopes, and three high-performance linear servo accelerometers in a small, self-contained package. This IMU represents typical low-cost equipment with a projected cost suitable for GA applications (the current cost is approximately $10,000 per unit). In addition, this inertial sensor technology has been utilized in a commercial AHRS that has been certified for aviation use.
The IMU consists of two main sensor types: gyroscopes or "gyros" to measure angular rates and accelerometers to measure velocity rates. Our IMU sensitivity analysis first estimates the gyro and accelerometer measurement error components and then transforms the estimated error components into errors in navigation outputs.
Inertial sensor measurements were collected for a chosen set of motions and post-processed by initial IMU calibration procedures to estimate error components of the gyro and accelerometer measurements. Estimated sensor errors include gyro and accelerometer biases, scale factors, scale-factor non-linearities, misalignment of sensitive axes, noise, and gyro g-sensitive (that is, gravity-sensitive) bias. The IMU calibration platform developed at the Ohio University Avionics Engineering Center was used to generate motion trajectories. The IMU calibration platform provides pitch, roll, and yaw motions, with pitch and roll values varying in the range [+ or -]50 degrees, and yaw changes being continuous and bi-directional. In addition, the platform has freedom in plunge variations. Figure 1 is a photograph of the platform.
[FIGURE 1 OMITTED]
Transformations of estimated components of sensor measurement errors into navigation outputs were carried out analytically with the confirmation of analytical derivations obtained via simulation. Figure 2 exemplifies results of the gyro error analysis by representing components of gyro measurement errors (that include gyro bias, scale factor, misalignment of sensitive axes, noise, and g-sensitive bias) transformed into output position errors. The plots show standard deviation (1-sigma) position errors. Results of the gyro error analysis demonstrate that gyro biases provide the major contribution to inertial output errors. Efforts for enhancing existing low-cost gyro technologies should, therefore, focus on improving the gyro bias performance.
[FIGURE 2 OMITTED]
Figure 3 represents position errors caused by measurement errors of low-cost accelerometers. The results shown in Figure 3 demonstrate that accelerometer bias error dominates all other accelerometer error sources that include accelerometer scale factor, scale-factor non-linearities, misalignment of sensitive axes, and noise. However, accelerometer error sources are shown to be balanced; that is, the different error sources provide similar contributions to the total error.
INS output errors also are influenced by uncertainties in initial conditions (position, velocity, and attitude) as these influence the integration of gyro and accelerometer data to yield the navigation outputs. Specifically, initial tilt errors can significantly degrade INS velocity and position performance characteristics. Figure 4 shows position errors resulting from typical initial tilt errors of a low-cost INS.
[FIGURE 3 OMITTED]
In addition to sensor measurement errors and errors in initial conditions, restricted bandwidth of inertial sensors can significantly degrade performance characteristics of low-cost inertial systems. However, it is important to mention that limited bandwidth is not an important issue for low-cost accelerometers. The reason is high-frequency acceleration components are low-pass filtered by the integration of accelerometer measurements to provide velocity and position navigation outputs. Precise reconstruction of high-frequency accelerations in inertial algorithms is not required. Contrary to low-cost accelerometers, bandwidth limitations can be critical for processing outputs of low-cost gyros. Methods used to process gyro measurements need to be capable of reconstructing high-frequency coning motion components to ensure accurate computation of attitude.
