GPS

Editor's Notes

• #14: How A GPS Receiver Determines Its Position Each satellite transmits what’s called a Navigation Message, which is downloaded by GPS receivers. The NAV Message the following information: GPS constellation status (all the satellites) satellite ephemeris and health data (individual satellites), GPS Time and UTC time transfer parameters, and ionosphere interference correction parameters. The GPS currently uses two frequencies to accomplish data transmission, L1 and L2. The NAV Message and coarse acquisition information are provided on the L1 frequency. Another frequency (L3) is planned for the next generation of satellites to enhance position and navigation precision of GPS receivers. The pseudo random noise (PRN) code is a fundamental part of the GPS. It's a very complicated digital code unique to each satellite. It’s a complex sequence of "on" and "off" digital pulses (see the diagram). The signal looks like random electrical noise (similar to the “snow” you might see on a TV), but is actually a very precise code. Hence the name “pseudo-random noise.” When a GPS receiver acquires a GPS signal it examines the satellite’s incoming PRN and begins generating a matching digital signal to mimic the satellite’s signal. The receiver matches each satellite’s PRN code with an identical copy of the code contained in the receiver’s database. Its next task is to try and determine how long ago the signal was generated by the satellite. But there’s a problem. As explained earlier, each satellite is equipped with atomic clocks; clocks which are constantly monitored for accuracy by the Master Control Station. The GPS receiver on the other hand is equipped only with a single digital clock comparable to a cheap wrist watch. The only way for the receiver to calculate an accurate position is if it can accurately measure the precise travel time of the satellite radio signal. A discrepancy of just a few nanoseconds between satellite and receiver will translate into a large position error on the ground. So the GPS receiver uses a clever technique to calculate the precise time it took for the GPS signal to reach it. By shifting its own generated copy of the satellite’s PRN code in a matching process, and by comparing this shift with its own internal clock, the receiver can calculate how long it took the signal to travel from the satellite to itself. By comparing the time difference between the two, and multiplying that time by the 186,000 miles per second travel speed of the signal, the receiver can roughly determine the distance separating it from the satellite. This process is repeated with every satellite signal the receiver locks on to. The distance between satellite and receiver derived from this method of computing distance is called a pseudo-range (“false range”) because the receiver’s clock is not synchronized with the satellites clocks. Pseudo-range is subject to several error sources, such as delays caused by the atmosphere, and multipath interference. More about that later. Here’s a simplified example of how a GPS receiver synchronizes itself to GPS Time for precise positioning. Imagine that the GPS satellite PRN signal is a song being broadcast by a radio station. The GPS receiver is a record player which is playing the same song, but it’s not synchronized to the broadcast song. Both songs are playing, but at different places in the song and at different speeds. By speeding up or slowing down the turntable, the two songs can be precisely matched. They become synchronized. Similarly, the GPS receiver synchronizes its digital signal to match that of each satellite’s signal. Once the receiver has its internally generated PRN code in synch with the satellite’s code it can determine a pseudo-range distance to the satellite. It does this for every satellite signal it receives. As will be explained later, under ideal conditions four satellites are used to calculate a precise position. Since GPS Time is one of the most important components of the System, it’s important to understand what GPS Time actually is. GPS Time is measured in weeks and seconds from 24:00:00, January 5, 1980 and is adjusted to within one microsecond of Universal Coordinated Time (UTC). Universal Coordinated Time is the international standard for time, and is tied to the earth’s rotation. Because of this it must be periodically adjusted to compensate for the slowing of the earth’s rotation – these adjustments are called leap seconds. But because GPS Time has no leap seconds, it is not adjusted, which puts it ahead of UTC time by several seconds. Universal Coordinated Time is computed from GPS Time using the UTC correction parameters sent by the Master Control Station to the satellite constellation as part of the navigation message. At the transition between 23:59:59 UTC on June 30, 1997 and 00:00:00 UTC on July 1, 1997, UTC time was retarded one additional second, putting GPS Time ahead of UTC time by thirteen seconds. A GPS receiver will use the GPS Time to UTC time correction parameter to provide the user with UTC time on the receiver’s display. It’s important to note that setting an incorrect time zone in a GPS receiver has no effect on the receiver’s ability to provide an accurate position. An incorrect time zone merely provides different time on a receiver’s display, not inaccurate time.
• #20: How a Receiver Determines Its Position Traveling at the speed of light each satellite PRN signal takes a brief, but measurable amount of time to reach a GPS receiver. The difference between when the signal is sent and the time it is received, multiplied by the speed of light, enables a GPS receiver to accurately calculate the distance between it and each satellite, provided that several factors are met. Those factors are: Good satellite signal lock by the GPS receiver (already covered) A minimum of four satellite signals (discussed next) Good satellite geometry (discussed later) When a GPS receiver is turned on it immediately begins searching the sky for satellite signals. If the receiver already has a curent almanac (such as one acquired on a previous outing), it speeds up the process of locating the first satellite signal. Eventually it locates and acquires its first signal. Reading this signal the receiver collects the Navigation Message. If the receiver does not have a current almanac, or was moved more than 300 miles while turned off, it must collect a new almanac, which will take about 12-13 minutes after the first satellite signal is acquired. Why the need for a new almanac if the receiver is moved more than 300 miles while turned off? Beyond 300 miles from its last used location the receiver is presumed to be using different GPS satellites, and therefore should download a new almanac to reflect the new PRN codes. If the receiver is turned on and collecting satellite signals while moving over 300 miles, its almanac is automatically updated. In the above graphic, the GPS receiver calculates a rough location somewhere on this three dimensional sphere, which is actually thousands of miles in diameter. All the receiver can really do at this point is collect system data and search for more satellites.
• #21: How a Receiver Determines Its Position (cont.) In a perfect world, where both satellite and receiver clocks were perfectly synchronized with each other, an accurate position could be determined from just two satellites. However, most receivers are incapable of calculating an accurate position using just two satellites. The dot in the example represents the approximate location of where the receiver thinks it is based on the information provided by two satellites. At least now the receiver knows that it is somewhere at the intersection of those two satellite signals. But that’s the only improvement in its position calculations. The satellite signal spheres should intersect at precisely the receiver’s location, but don’t because the clock in the GPS receiver isn’t yet synchronized with GPS Time. So the receiver estimates a “pseudo-range” to each satellite.
• #22: How a Receiver Determines Its Position (cont.) Three satellites can provide only a two-dimensional (2D) position. Without manually entering the receiver’s exact elevation (most GPS receivers don’t allow elevation to be entered manually), the rendered 2D position may be off by several kilometers on the ground. If the exact elevation of the GPS receiver is known, entering that elevation into a receiver with this capability replaces the need for a fourth satellite signal to allow a receiver to triangulate a precise position. The receiver essentially uses elevation in lieu of a fourth satellite, and makes the appropriate adjustments to trilaterate a reasonably good 3D position. But without manual elevation correction most GPS receivers must rely on a fourth satellite to provide the final clock correction information necessary to calculate a 3D position. Until a fourth satellite signal is acquired the receiver will not be able to determine x and y horizontal, and z vertical positioning (a true 3D position). This is because the fourth satellite signal is used by the receiver not to provide more position data, but, rather, the final time correction factor in its ranging calculations. As a rule, 2D positions should always be avoided whenever possible. Use 2D positioning only when a 3D position is not possible, but be aware of the horizontal error inherent in any 2D position. The inability of a GPS receiver to triangulate a 3D position may be due to a variety of factors, including user error, poor satellite geometry, and harsh landscape conditions (tall buildings, canyons, and dense tree cover among others). As will be shown later in the course, all GPS receivers provide some means for informing the user which mode they are operating in. It’s up to the user to be aware of the errors associated with 2D positioning.
• #23: How a receiver determines its position (cont.) For a GPS receiver to achieve three-dimensional (3D) positioning it needs to acquire four or more satellite signals. A 3D position is comprised of X and Y (horizontal), Z (vertical) positions, and precise time (not varying more than a few hundred nanoseconds). The receiver’s processor uses the fourth satellite pseudo-range as a timing cross check to estimate the discrepancy in its own ranging measurements and calculate the amount of time offset needed to bring its own clock in line with GPS Time (recall the radio station and record player simultaneously playing the same song). Since any offset from GPS Time will affect all its measurements, the receiver uses a few simple algebraic calculations to come up with a single correction factor that it can add or subtract from all its timing measurements that will cause all the satellite spheres to intersect at a single point (x, y, and z). That time correction synchronizes the receiver's clock with GPS Time. Now the receiver essentially has atomic clock accuracy with the time correction factor needed to achieve precise 3D positioning. The pseudo-ranges calculated by the GPS receiver will correspond to the four pseudo-range spheres surrounding the satellites, causing the four spheres to intersect at precisely the receiver’s location (the dot in the diagram).
• #25: the dashed lines show the actual intersection point, and the gray bands indicate the area of uncertainty. the solid lines indicate where the GPS receiver "thinks" the spheres are located. Because of errors in thereceiver's internal clock, these spheres do not intersect at one point. The GPS receiver must change the size of the spheres until the intersection point is determined. The relative size of each sphere has already been calculated, so if the size of one sphere is changed, the other spheres must be adjusted by exactly the same amount.