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Interpolating Reference Data: Kinematic Positioning Using Public GNSS Networks

Torben Schüler
High-accuracy users of public GNSS reference archives don’t always have access to data that matches the high sampling frequencies needed for real-time kinematic techniques. This column proposes a method for interpolating GNSS observation residuals so as to produce data that can be used in kinematic applications.

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Kinematic GNSS data processing algorithms are constantly being improved to work over long inter-station distances.  Within the GNSS community some users have a need for publicly available data for high-frequency (equal to or greater than one hertz) kinematic applications. These applications may be separated into two classes: those using post-processed data and those requiring real-time or near real-time data.

A variety of commercial and public GNSS service providers offer reference data derived from GNSS satellite broadcasts and archived in near real-time, which can be used for long-baseline kinematic applications. Several commercial vendors provide reference data through satellite-based channels at relatively high frequency rates (up to one Hertz).

A number of public service providers, however, offer data free of charge via the Internet, notably the International GNSS Service (IGS) Tracking Network with approximately 350 stations distributed globally. The IGS network has a relatively high density over North-America and Europe. Further densifications exist regionally, such as the National Continuously Operating Reference Stations (CORS) Network supported by the U.S. National Geodetic Survey, the EUREF Permanent Network in Europe, and the Shenzehn CORS network in southeastern China.

Consequently, publicly available GNSS reference station data are becoming more and more attractive for use in kinematic applications. Unfortunately, these archived data normally exhibit sampling intervals as large as 30 seconds, whereas kinematic positioning requires sampling frequencies in the range of 1 to 20 Hz or even higher. For instance, only sites belonging to the IGS Low Earth Orbit (LEO) network — a subset of the IGS tracking network — provide 1 Hz data. There are many scientific applications, such as hydrographic surveying or airborne photogrammetry, and gravimetry, that can benefit from using publicly available, “freeware data” to generate 1 Hz data.

The decision of the U.S. government to turn off S/A (Selective Availability) in May 2000 opened the door for accurate densification of reference station data, but this opportunity has not received proper attention yet. In the future, the availability of the future Galileo system, combined with existing GPS and GLONASS satellite constellations, will further improve the positioning performance.

For the time being, however, in using the low-frequency public reference network data the need to interpolate reference station measurements in the time domain arises, because both rover and reference station data must be available with the same temporal resolution (and synchronously).  This article will discuss techniques by which low-frequency reference station data can be used to generate higher sampling rates for use in kinematic applications, both post-processed and in real-time.

The Algorithm
In this article, GNSS data interpolation is not carried out on the measurements directly. Instead, the known orbit information is used to compute observation residuals that will be interpolated afterwards. This procedure is slightly more complicated than a direct interpolation of the measurements — for example, using high-order polynomials — but it is still easy to implement.

. . .

Positioning Tests
Positioning experiments were carried out on the campus area of the University FAF Munich, Germany, in order to demonstrate the feasibility of this interpolation approach.

. . .

Real-Time Aspects
Although this article focuses on data interpolation for post-processing (or near real-time) applications, many readers might also be interested in true real-time applications.

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Summary and Conclusions
Interpolation of GNSS measurements is a task often undertaken by users who want to exploit publicly available data in high-frequency kinematic scenarios. We presented an algorithm for precise data interpolation that reduces the original measurements with the help of orbit information and applies linear interpolation to the slowly varying observation residuals.

The loss of accuracy is rather marginal when interpolated carrier-phases from data sampled each 5 seconds are used compared to the positions obtained from original data. Even for 10-second data the agreement between original and interpolated data is still within 1 millimeter for the horizontal position and 1.5 millimeter for the vertical coordinate.

These results indicate that reference station data do not necessarily need to be archived with the nominal sampling frequency (often 1 Hz). Instead, an optimal trade-off between storage capacity and sampling interval would be between 5 and 10 seconds. This statement is in agreement with 5-second sampling interval recommended by L. Wanninger in the work cited in the Additional Resources section as well as J. Wickert et al. who recommended 10-second sampling intervals for ground station data used for CHAMP radio occultation measurements.

Data sampled every 30 seconds tends to be a bit too sparse for interpolation when the highest precision is required in kinematic applications. Unfortunately, this is the commonly used output interval of publicly available GPS reference networks. It is therefore recommended to enhance the output interval to at least 15 seconds (or better 10 seconds) in order to offer useful data to more users, thus expanding the idea of real multipurpose networks.

For the complete article, including figures and graphs, please download the PDF at the top of the page.

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Equipment used for test trials included a Z-Sensor base station, from Thales Navigation (now Magellan Navigation, Inc.) San Dimas, California USA, and, as the rover unit, the RTK GPS 5800 from Trimble, Sunnyvale, California USA.

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