GPS Q&A: Industry experts answer reader's GPS questions

Q. What's the difference between real-time code and real-time phase? - A.G. Northbrook, Ill.

A. John C. Bohlke, Sokkia Corp.: Many differences exist between real-time code and real-time phase GPS corrections. Real-time code corrections, often referred to as real-time differential GPS, makes use of the C/A code portion of the GPS signal for achieving meter or submeter-level accuracy while in the field. The standard real-time code message, labeled with the RTCM acronym, is being transmitted by commercial providers, the U.S. Coast Guard and other agencies. Many users choose to purchase a real-time code receiver (and with some providers, a subscription to their service) in order to improve their GPS accuracy whereas others transmit and receive their own correction. In contrast, surveyors use real-time phase corrections, often referred to as the real-time kinematic method, in order to achieve centimeter-level accuracy while in the field. Most users transmit phase corrections from their own dual-frequency receiver using the manufacturers' proprietary format because a popular correction standard like RTCM has not been readily accepted. Unlike the code corrections, real-time phase corrections rely more heavily on constant radio contact and are more limited by the length of distance between the base and roving receiver(s) due to the accuracy of the system.

Chris Dietsch, Trimble Navigation Ltd.: There are three general differences between real-time code and real-time phase. First is the type of observation being made, second is the applications they are associated with and third is the accuracies that the user can expect to achieve. A "Code" measurement is the time delay between the incoming satellite code and a replica of the code being generated by the receiver, times the speed of light and is called a "Pseudo-Range." A phase measurement is the phase of the signal left after the Doppler-shifted satellite carrier is differenced with the constant frequency generated by the receiver.
      Real-time code is more commonly referred to as "Real-Time Differential" and is used in mapping and navigation. Meter level accuracies are normally associated with this application although sub-meter accuracy can be achieved. Real-time phase is usually called "Real-Time Kinematic" and has applications in surveying, mapping and precise positioning. When one speaks of Real-Time Kinematic applications, centimeter level accuracies are assumed.

Andrew Hurley, Leica Inc.: In a scientific sense, real-time can be defined as any action undertaken that results in an instantaneous response. Now, look at your watch. The time displayed is happening in real-time. A GPS receiver will generate a navigated position in real-time, but due to the effects of Selective Availability the real-time position may be in error by as much as 100m. To achieve accuracies at the meter level or down to the centimeter level differential techniques must be employed. We can separate real-time into two distinct modes with very distinct operations:
      1. Real-time differential GPS, which utilizes the code part of the signal structure as generated from the satellites. With the reference station on a known point in the WGS 84 coordinate system and tracking all available satellites it can compute pseudorange corrections for each of the satellites being tracked. These corrections are then transmitted, normally in the RTCM format, to a roving station via a radio link. The roving receiver which is tracking all available satellites takes the pseudorange corrections and applies them accordingly. This generates a corrected position which can be referred to as a range corrected position. This corrected position can vary depending on the grade of the receivers being used. Top of the line receivers should expect to see accuracies in the order of 0.3-0.5m baseline length.
      2. Real-time phase, which utilizes the code and phase part of the signal structure. The reference station is set up on a known WGS 84 coordinate and tracks all available satellites. The rover similarly tracks all available satellites. The reference station transmits via the radio link to the rover all the GPS measurements. The rover will undergo calculations to resolve the ambiguities and yields centimeter accuracy.
      Real-time is fast becoming a widely acceptable tool within the survey industry. As real-time GPS does suffer from certain limitations (radio links, obstructions, etc.) it is worth considering how well and easy it is to integrate the GPS real-time generated positions with conventional survey measuring devices so that productivity on site is not lost.

Bryan Townsend, NovAtel Communications Ltd.: The difference between real-time code and real-time phase positioning is due to the difference in GPS data used to calculate the position. Real-time code positioning uses the pseudorange measurement only where the real-time phase positioning uses the carrier phase measurement or a combination of the psuedorange and carrier phase measurement. The difference to the user is that real-time code positioning can produce meter level positioning accuracy where real-time phase can produce centimeter level positioning accuracy. The cost is that real-time phase requires a better data link and the use of higher end GPS receivers.

Dr. Frank van Diggelen/Bill Martin, Ashtech Inc.: The difference is accuracy. Code means the C/A or P code used by the GPS satellite to modulate the GPS signal. This code is used to determine the pseudorange from the user to the satellite, and so code is synonymous with pseudorange.
      Phase in this context means carrier phase. This is the phase of the carrier wave. The carrier wave is the signal that is being modulated by the code.
      Note that there is room for confusion here, since the code also has its own phase, so it is better to use the term carrier phase, not simply phase, to refer to carrier phase.
      Receivers measure the carrier phase with precision of 0.5 to 1 cm, while the code can only be measured with precision of 0.5 to 1 m. So positions derived from carrier phase (if your receiver and/or post-processing software have that capability) are much more accurate than positions derived only from code.
      Real-time means that the positions are derived in the receiver, in real time. Again there is room for confusion in the use of the words in the question. To remove this confusion use more words, e.g. real-time positions from code, and real-time positions from carrier-phase.

Q. What is least squares? - A.O. St. Louis, Mo.

A. Bohlke: Least squares refers to a mathematical procedure that distributes the total error among observed measurements. Each measurement may receive an equal amount of the total error. Alternatively, the measurement may be weighted thereby receiving some portion of the error that relates to the quality of the measurement. Most GPS users rely on a least squares adjustment for distributing the error in their measurements throughout a network of observations.

Dietsch: Least squares is a mathematical procedure that utilizes redundant observations to produce a "Most Probable Value" for some unknown quantity or quantities by "minimizing the sum of the squares of the residuals." Least squares has many applications in math, science and engineering. In surveying and mapping, least squares is normally used to perform network or traverse adjustments or to estimate the transformation parameters that "Best Fit" a set of observations. Least squares is a flexible tool that can be adapted to any math model and which allows the user to evaluate the mathematical and statistical integrity of the measurements in question.

Hurley: The ultimate aim when using least squares is to adjust a set of observations in such a way that the sum of the squares of the residuals get minimized. This is achieved by taking a set of observations and creating a model, applying a mathematical algorithm to that model and then using statistics to evaluate the adjusted data. The end result will yield the most probable value, a value based on the set of observations that will tend toward the truth. Surveyors use least squares methods to verify the integrity of their measurements, and to "fit" their observations onto known positions.
      Many different adjustment techniques exist today. Most of them are unique to certain applications. Least squares is an adjustment technique that is more general and a systematic procedure that can be used for all situations. Remember it is not an adjustment technique unique to GPS. It is commonly used in geodesy, photogrammetry, surveying and many other areas. Unfortunately, the details and mathematics of least squares are not easily explained in a couple of paragraphs.

Townsend: Least squares is a criteria often used to indicate convergence of a mathematical problem where there are more observations than unknown parameters. Hence, the solution is over determined causing an imperfect fit of observations to parameters. The least squares criteria dictates that the solution has converged when the sum of the squares of the observation residuals is minimized.

van Diggelen/Martin: It is common knowledge to all surveyors that every measurement, whether collected using conventional surveying equipment or GPS equipment, contains error. These errors can be classified as random errors (inescapable errors due to the precision of the equipment being used) and blunders (mistakes in the measurement). It is extremely important that blunders are detected and removed from measured data, otherwise, the results will be unreliable.
      Performing a least squares adjustment has been proven as the best method to detect blunders in survey measurements. Blunder detection is accomplished through statistical analysis of the measured data. These statistical tools help point to data suspected to contain a blunder. Once problem data is discovered, it can be removed from the data set.
      A second advantage of a least squares adjustment is the analysis of precision of the adjusted measurement data. Additional statistical tools present in most least squares adjustment software will enable the user to determine the level of precision attained in the survey.
      Although detection of blunders and survey precision can be performed through other means, using least squares will give users the best tools to ensure that final adjusted measurements are devoid of blunders, instilling confidence in the reliability and precision of their surveys.
      An alternative answer to the question may be: Least squares is the fewest number of engineers required to change a light bulb.

About the participants:
John C. Bohlke serves as GPS technical product manager for Sokkia Corp. in Overland park, Kan. He may be reached at 913-492-4900 or 800-4-SOKKIA in the U.S. (phone) or 913-492-0188 (fax). Chris Dietsch is a product test engineer for Trimble Navigation Ltd. in Sunnyvale, Calif. He may be reached at 408-481-8502 (phone) or 408-481-8699 (fax). Andrew Hurley is a GPS product specialist at Leica Inc. in Englewood, Colo. He may be reached at 303-799-9453 (phone) or 303-799-4809 (fax). Bill Martin is a marketing manager, Survey, at Ashtech Inc. in Sunnyvale, Calif. He may be reached at 408-524-1508 (phone), 408-524-1500 (fax), or e-mail: [email protected] Bryan Townsend is a GPS specialist with NovAtel Communications Ltd. in Alberta Canada. He may be reached at 1-800-280-2242 (toll free in North America only), 403-295-4900 (phone), or 403-295-4901 (fax). Dr. Frank van Diggelen is a marketing manager, OEM and Navigation at Ashtech Inc. in Sunnyvale, Calif. He may be reached at 408-524-1508 (phone), 408-524-1500 (fax), or e-mail: [email protected]

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