GPS / INS for Airborne Mapping Applications
By James Thompson

GPS
Most people are now familiar with GPS (Global Positioning System) given its broad use in vehicle and hand-held navigation systems. Although these systems are impressive, they do not deliver the centimeter-level accuracy required for airborne mapping applications such as LiDAR and Digital Imagery. So how is GPS and GPS/INS (Inertial Navigation Systems) used for high-accuracy applications?

First, let's discuss how GPS works. GPS receivers measure the travel-time of signals broadcast from the GPS satellites. Each GPS satellite broadcasts its position and its own unique code. The receiver generates a replica of each satellite's code and calculates the travel-time based on how much the replica code must be shifted to match the satellite's actual incoming code (Figure 1).

Figure 1: Determining signal travel-time with code

The travel-times are converted to distances ("ranges") by multiplying by the speed of light. Given the distances to the satellites, and each satellite's position, the receiver performs a 3-dimensional "trilateration" (intersection) to determine its own position.

The term "position" typically refers to a 3-dimensional coordinate, consisting of Latitude, Longitude and Height. Since we have 3 "unknowns", we need 3 equations (satellites) to solve for position, yet experienced GPS users will tell you at least 4 satellites are required, why is this?

A GPS receiver's clock is not synchronized to "GPS time" (the time system all the satellites are synchronized to). This difference, between "receiver time" and "GPS time", is called the "clock offset". An "extra" (4th) satellite is required to solve for this difference in time systems. If you are only interested in your horizontal position (Latitude and Longitude) only 3 satellites are required.

So far we have discussed how typical in-car or hand-held GPS receivers work. These systems typically provide accuracies of a few meters in real-time, which is fine for way-finding applications. Airborne mapping applications, however, require much higher accuracies, so how are they achieved?

To achieve centimeter-level accuracy, a technique called Differential GPS (DGPS) is employed (Figure 2). In this scenario (at least) two GPS datasets are collected simultaneously: One over a known ground control point ("base station"), and the other in the aircraft ("remote station"). The data is combined in special "post-processing" software after the flight to yield a high-accuracy solution, but how?

Figure 2: Airborne DGPS

When we began our discussion we mentioned that each GPS satellite broadcasts its own unique code. We went on to explain that the receiver compares its replica code with the actual incoming satellite's code to measure the signal's travel-time. But how did the code get to the receiver? The code is of course "carried" on a wave. By exploiting some unique properties of the so called "carrier phase", DGPS is able to achieve centimeter-level accuracy.

In DGPS the measurements from the base and remote stations are subtracted or "differenced" (hence the name Differential GPS) in post-processing. This differencing has two big advantages:

  1. A differenced carrier-phase measurement is produced.
  2. Errors common to both datasets conveniently cancel in the difference.
To expand on Point 1, the differenced carrier-phase measurement can be thought of as a very accurate measure of change in position. Therefore, if the software can accurately determine the receiver's "start" position, a high-accuracy trajectory can be determined from that point forward. The process of determining (or re-determining) this accurate start position is called "Ambiguity Resolution". Ambiguity Resolution is crucial for accuracy but is beyond the scope of this paper, suffice it to say: The closer you are to the base station, the easier ambiguity resolution becomes. With proper GPS equipment, flight planning, and field procedures, DGPS provides the centimeter-level accuracies required for airborne mapping applications.

GPS/INS
As described in the previous section, DGPS can provide fantastic position accuracies for airborne sensors. However, this GPS-only solution is deficient in two ways:
  1. It does not contain any information about how the airborne sensor was pointing (i.e. the sensor's roll, pitch, and heading - its "attitude").
  2. The GPS positions exist only every second, or half-second, along the trajectory.
To expand on Point 1, Inertial Navigation Systems (INS) measure attitude using a device called an Inertial Measurement Unit (IMU). The IMU contains 3 gyroscopes (gyros) and 3 accelerometers. The gyros measure angular rates, and the accelerometers measure acceleration. We have mentioned previously that it is position and attitude that are important for airborne mapping, so what good are these angular rates and accelerations coming from the IMU?

The INS is an "integrating" system. Integration is just a fancy word meaning "to sum up over time". It is through integration that the IMU data is converted to the information we really need. For example, if we know our "start" heading is 180 degrees (we are pointing South) and some time later the heading-gyro outputs an angular rate of 1 degree per second for 90 seconds, we know our heading has changed +90 degrees and we are now heading West (270 degrees). But how far have we traveled? Knowing the attitude (from the gyro data), the INS also integrates the accelerometer data to keep track of our velocity and distance from the "start" position. Note that the "start" attitude and position mentioned in the example above are accurately determined during the INS "alignment" process.

The problem with integrating systems is this: As the measurements are summed over time, so too are the measurement errors. This means that as time passes the INS solution becomes less and less accurate, eventually becoming unusable. This phenomenon is referred to as "drift" and is solved by combining GPS with INS. This combination brings about many benefits as illustrated in Table 1.

Table 1: Navigation Solution Pros and Cons
Solution Type Pro Con
GPS only
  • Uniform high accuracy
  • No attitude information
  • Possible gaps in solution due to losses of satellite lock
  • Comparatively low data-rate
INS only
  • Attitude included
  • High data-rate
  • High short-term accuracy
  • Self-contained
  • Solution accuracy degrades over time
Combined GPS/INS
  • High accuracy, high data-rate, continuous position and attitude navigation solution
  


Figure 3 illustrates how the GPS/INS solution is actually created. First the GPS data is differentially processed. Then the resulting DGPS solution is combined with the inertial data to produce the final navigation solution.

Figure 3: GPS/INS Processing Workflow

Summary
We have learned that Airborne Mapping Applications typically use GPS/INS systems to achieve high-accuracy navigation solutions. The airborne GPS data is combined with base station data and post-processed after the flight. The inertial data is then blended with the post-processed GPS to yield a navigation solution that (now) contains attitude and position information at the high data-rate and accuracy required.

References
Pflug, H., Aerogravimetry - a Geotechnology in Motion, Potsdam, Germany, http://www.gfz-potsdam.de/pb1/pg3/aero/introduction_e.html (last date accessed: Nov 21, 2007)

Rizos, C., Principles and Practice of GPS Surveying, Sydney, Australia, http://www.gmat.unsw.edu.au/snap/gps/gps_survey/principles_gps.htm (last date accessed: Nov 21, 2007)

Sun, H., February 2006, Introduction to GPS/IMU Integration, Photogrammetric Engineering & Remote Sensing, 90-92

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