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

Q. What's an epoch? What's sampling rate? - K.S. Austin, Texas

A. John C. Bohlke, Sokkia Corp.: An epoch represents a specific period in time. In the GPS industry an epoch represents a single GPS measurement because each measurement is tagged with an exact time stamp. The sampling rate is the rate at which the receiver computes a GPS measurement. Typical sampling rates range from several times per second to multiple seconds.

Chris Dietsch, Trimble Navigation: In GPS the term epoch refers to the instant in time when a measurement is made. Sampling rate is the frequency with which measurements are made and is also referred to as the sync rate or the epoch rate. For example, if the sampling rate was set at 15 seconds, as is common for static occupations, a measurement would take place every 15 seconds, the instant of each these measurements would be an individual epoch.

Tom Ford, NovAtel GPS: An epoch is defined as an instance in time. In GPS we usually qualify an epoch to be a specific type. For example, a "measurement epoch" is the time when the measurement occurred, and a "position epoch" is the time for which the position was calculated. The sampling rate is the frequency at which data is reported to the user. On most GPS receivers the sampling rate for positions and raw measurements is user configurable. The sampling rate can be expressed in terms of sample interval or sample frequency.
      The sample interval is the time interval, usually in seconds, between each successive measurement or position. The sample frequency is the number of samples per second. For example, a sample interval of 2 seconds would have sample frequency of 0.5 Hz.

Q.What are the differences between GPS accuracy ratings such as CEP, SEP, 1 Sigma and 2 Sigma? - J.D. Boulder, Colo.

A. Bohlke: Many different ratings exist to represent GPS accuracy. CEP and SEP are used most often for navigational purposes. The Circular Error Probable (CEP) defines the radius of a circle that represents a 50 percent probability of a position lying in that circle. The Spherical Error Probable (SEP) probability is the same except that it represents three-dimensional accuracy because it defines the radius of a sphere. Unlike CEP and SEP, Sigma values are more common in the surveying and mapping market. The value of 1 Sigma indicates a 67 percent confidence value in the positional accuracy and the value of 2 Sigma refers to a 95 percent confidence in the positional accuracy.

Dietsch: The terms CEP (Circular Error Probable), SEP (Spherical Error Probable), 1 Sigma and 2 Sigma are estimates of the probability of an occurrence. CEP refers to a 50 percent probability that the true value of an estimated two-dimensional point lies within a circle centered on the point and of a radius given by the magnitude of the CEP, i.e., ±0.05m. SEP refers to a 50 percent probability that the true value of an estimated three-dimensional point lies within a sphere centered on the point and of a radius given by the magnitude of the SEP, i.e., ±0.05m. 1 Sigma corresponds to a 68.3 percent probability and is also referred to as the standard error or the standard deviation. 2 Sigma translates into a 95.4 percent probability and is often used in surveying and mapping as the level of confidence specified for meeting accuracy requirements. Both the 1 and 2 Sigma probability values given are for a normal distribution of one unknown (univariate). These probability values change if referring to bivariate or multivariate distributions.

Ford: Circular Error Probability (CEP) refers to latitude and longitude (horizontal) position accuracy. A CEP of 1 m means that the average horizontal position error is 1 m. Another way of stating this is the horizontal position error is less than 1 m 50 percent of the time. Spherical Error Probability (SEP) refers to latitude, longitude, and height (3D) position accuracy. It has the same 50 percent probability rating as the CEP.
      The term Sigma is equivalent to the estimated standard deviation of a variable. The probability rating varies according to the number of parameters implicit in the variable. For example, horizontal positioning involves two parameters - latitude and longitude. Vertical positioning relies on only the height component of the position, and therefore only involves one parameter. The table below lists error probabilities of 1 Sigma and 2 Sigma for 1-dimensional (1D), 2-dimensional (2D), and 3-dimensional (3D) positioning.
      The variation in these probability ratings is one of the reasons that CEP and SEP are used more frequently for quoting GPS receiver specifications.

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), 408-481-8699 (fax), or E-mail: [email protected] Tom Ford is a GPS specialist at NovAtel GPS in Calgary, Alberta. He may be reached at 1-800-280-2242 (toll free North America only), 403-295-4900 (phone), 403-295-4901 (fax), or [email protected]

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