Posts Tagged ‘gps improvement’

How GPS Bends Time

Saturday, July 16th, 2011

Equation section, WIRED magazine:


Einstein knew what he was talking about with that relativity stuff. For proof, just look at your GPS. The global positioning system relies on 24 satellites that transmit time-stamped information on where they are. Your GPS unit registers the exact time at which it receives that information from each satellite and then calculates how long it took for the individual signals to arrive. By multiplying the elapsed time by the speed of light, it can figure out how far it is from each satellite, compare those distances, and calculate its own position.

For accuracy to within a few meters, the satellites’ atomic clocks have to be extremely precise—plus or minus 10 nanoseconds. Here’s where things get weird: Those amazingly accurate clocks never seem to run quite right. One second as measured on the satellite never matches a second as measured on Earth—just as Einstein predicted.

According to Einstein’s special theory of relativity, a clock that’s traveling fast will appear to run slowly from the perspective of someone standing still. Satellites move at about 9,000 mph—enough to make their onboard clocks slow down by 8 microseconds per day from the perspective of a GPS gadget and totally screw up the location data. To counter this effect, the GPS system adjusts the time it gets from the satellites by using the equation here. (Don’t even get us started on the impact of general relativity.)



GPS: Techniques to improve accuracy

Sunday, May 25th, 2008


Augmentation methods of improving accuracy rely on external information being integrated into the calculation process. There are many such systems in place and they are generally named or described based on how the GPS sensor receives the information. Some systems transmit additional information about sources of error (such as clock drift, ephemeris, or ionospheric delay), others provide direct measurements of how much the signal was off in the past, while a third group provide additional navigational or vehicle information to be integrated in the calculation process.

Examples of augmentation systems include the Wide Area Augmentation System, Differential GPS, Inertial Navigation Systems and Assisted GPS.

Precise monitoring

The accuracy of a calculation can also be improved through precise monitoring and measuring of the existing GPS signals in additional or alternate ways.

After SA, which has been turned off, the largest error in GPS is usually the unpredictable delay through the ionosphere. The spacecraft broadcast ionospheric model parameters, but errors remain. This is one reason the GPS spacecraft transmit on at least two frequencies, L1 and L2. Ionospheric delay is a well-defined function of frequency and the total electron content (TEC) along the path, so measuring the arrival time difference between the frequencies determines TEC and thus the precise ionospheric delay at each frequency.

Receivers with decryption keys can decode the P(Y)-code transmitted on both L1 and L2. However, these keys are reserved for the military and “authorized” agencies and are not available to the public. Without keys, it is still possible to use a codeless technique to compare the P(Y) codes on L1 and L2 to gain much of the same error information. However, this technique is slow, so it is currently limited to specialized surveying equipment. In the future, additional civilian codes are expected to be transmitted on the L2 and L5 frequencies (see GPS modernization, below). Then all users will be able to perform dual-frequency measurements and directly compute ionospheric delay errors.

A second form of precise monitoring is called Carrier-Phase Enhancement (CPGPS). The error, which this corrects, arises because the pulse transition of the PRN is not instantaneous, and thus the correlation (satellite-receiver sequence matching) operation is imperfect. The CPGPS approach utilizes the L1 carrier wave, which has a period 1000 times smaller than that of the C/A bit period, to act as an additional clock signal and resolve the uncertainty. The phase difference error in the normal GPS amounts to between 2 and 3 meters (6 to 10 ft) of ambiguity. CPGPS working to within 1% of perfect transition reduces this error to 3 centimeters (1 inch) of ambiguity. By eliminating this source of error, CPGPS coupled with DGPS normally realizes between 20 and 30 centimeters (8 to 12 inches) of absolute accuracy.

Relative Kinematic Positioning (RKP) is another approach for a precise GPS-based positioning system. In this approach, determination of range signal can be resolved to a precision of less than 10 centimeters (4 in). This is done by resolving the number of cycles in which the signal is transmitted and received by the receiver. This can be accomplished by using a combination of differential GPS (DGPS) correction data, transmitting GPS signal phase information and ambiguity resolution techniques via statistical tests—possibly with processing in real-time (real-time kinematic positioning, RTK).

GPS time and date

While most clocks are synchronized to Coordinated Universal Time (UTC), the atomic clocks on the satellites are set to GPS time. The difference is that GPS time is not corrected to match the rotation of the Earth, so it does not contain leap seconds or other corrections which are periodically added to UTC. GPS time was set to match Coordinated Universal Time (UTC) in 1980, but has since diverged. The lack of corrections means that GPS time remains at a constant offset (19 seconds) with International Atomic Time (TAI). Periodic corrections are performed on the on-board clocks to correct relativistic effects and keep them synchronized with ground clocks.

The GPS navigation message includes the difference between GPS time and UTC, which as of 2006 is 14 seconds due to the leap second added to UTC December 31st of 2005. Receivers subtract this offset from GPS time to calculate UTC and specific timezone values. New GPS units may not show the correct UTC time until after receiving the UTC offset message. The GPS-UTC offset field can accommodate 255 leap seconds (eight bits) which, at the current rate of change of the Earth’s rotation, is sufficient to last until the year 2330.

As opposed to the year, month, and day format of the Gregorian calendar, the GPS date is expressed as a week number and a day-of-week number. The week number is transmitted as a ten-bit field in the C/A and P(Y) navigation messages, and so it becomes zero again every 1,024 weeks (19.6 years). GPS week zero started at 00:00:00 UTC (00:00:19 TAI) on January 6, 1980 and the week number became zero again for the first time at 23:59:47 UTC on August 21, 1999 (00:00:19 TAI on August 22, 1999). To determine the current Gregorian date, a GPS receiver must be provided with the approximate date (to within 3,584 days) to correctly translate the GPS date signal. To address this concern the modernized GPS navigation messages use a 13-bit field, which only repeats every 8,192 weeks (157 years), and will not return to zero until near the year 2137.

GPS modernization

Having reached the program’s requirements for Full Operational Capability (FOC) on July 17, 1995, the GPS completed its original design goals. However, additional advances in technology and new demands on the existing system led to the effort to modernize the GPS. Announcements from the U.S. Vice President and the White House in 1998 initiated these changes, and in 2000 the U.S. Congress authorized the effort, referring to it as GPS III.

The project aims to improve the accuracy and availability for all users and involves new ground stations, new satellites, and four additional navigation signals. New civilian signals are called L2C, L5 and L1C; the new military code is called M-Code. Initial Operational Capability (IOC) of the L2C code is expected in 2008. A goal of 2013 has been established for the entire program, with incentives offered to the contractors if they can complete it by 2011.