Ultra-Wideband Aided Carrier Phase Ambiguity Resolution in Real-Time Kinematic GPS Relative Positioning

E. Broshears, S. Martin, D. Bevly

Abstract:	This research paper presents results that show incorporating the accurate range measurements from ultra-wideband radios into the baseline-constrained LAMBDA method of the RTK algorithms helps improve the time-to-fix of the carrier phase integer ambiguities. The higher frequency and accuracy of the UWBs also help the robustness of the position solution by detecting faulty signals and cycle slips. The results show quicker time-to-fix with the UWB measurements than the standard LAMBDA method would get alone. This research can be applied to any sort of dynamic situation in which two GPS receivers and two UWBs are coupled parallel to each other and are within a relatively close proximity. Ever since GPS was first implemented, it has been used to aid navigation. Accuracy of the position solutions limit GPS usage to certain navigation applications. Typical accuracy of position solutions for raw GPS signals is around 5-10 meters. Atmospheric errors are among the biggest contributors to the degradation of the GPS signal; but for relatively close distances, these atmospheric errors are highly correlated and can be differenced out between two different GPS receivers. Mitigating these common errors between receivers can bring the accuracy of the relative positioning between receivers down to less than 1 meter. However, some additional differential corrections can be made if the relative carrier phase integer ambiguities between the receivers are found. Once these integer ambiguities are resolved, the position solution accuracy can get down to less than 3 centimeters. The objective of the research in this work is to integrate the range measurements from ultra-wideband (UWB) radios into the differential GPS positioning algorithms to help resolve the carrier phase ambiguities quicker and more reliably. Relative positioning is especially important in navigation, so the ability to gain extremely accurate global positioning measurements is critical for certain applications; examples of such applications could include: an autonomous helicopter landing on an aircraft carrier, an unmanned aerial vehicle airborne refueling, or a leader-follower autonomous driving scenario. Resolving these ambiguities is no trivial task, especially if using lower cost single-frequency GPS receivers. Luckily, the researchers at the Delft University of Technology, headed by Peter Teunissen, have created what is now known as the Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) method. This algorithm decorrelates the covariance of the errors to the receivers common satellites and creates a more efficient search space to look for the integer ambiguities. The LAMBDA method has been around for several decades, and new improvements are continually being researched to add to this method. One of the additions to this method is a baseline-constrained LAMBDA, or C-LAMBDA, which can take a priori knowledge of the baseline between GPS receivers and integrate it into the LAMBDA method to reduce the search space for the integer ambiguities. Applications for the C-LAMBDA method include scenarios in which the GPS antennas are mounted onto a platform on a vehicle. If three antennas are mounted in a triangle at known distances, then the attitude of the vehicle can be determined. This baseline constraint can resolve the ambiguities quicker than the typical LAMBDA method and also adds an element of robustness to the method to protect it against multi-path and other errors that affect the GPS signal that cannot be differenced out between receivers. Ultra-wideband radios are a relatively new type of technology that unlike radios, which use sinusoidal frequency transmissions, use a quick impulse sent out over a wide range of frequencies. When two or more UWBs are placed in close proximity, approximately less than 100 meters, they can calculate the time-of-flight between antennas and derive a range measurement that is centimeter-level accurate. With a frequency of up to about 30 Hz, UWBs also have a much higher frequency than most GPS receivers. This technology is being researched to aid small convoys of autonomous aerial and ground vehicles. The objective of this paper is to successfully integrate the range measurements from the UWBs into the C-LAMBDA method, essentially treating the UWB measurements as a baseline constraint. Several implications have been considered when integrating the UWBs into the C-LAMBDA method. Aside from the UWB ranging measurements being used in the C-LAMBDA method to resolve the integer ambiguities, the UWBs could also be used as a validation on the normal LAMBDA method. This would allow for the UWBs to check for cycle slips or GPS measurement fault detection. The wavelength of the L1 GPS signal is about 19 centimeters, so the accuracy required of the range measurements to successfully detect cycle slips will be investigated. If the UWB measurement accuracy is below the length altered by a single cycle slip, then it should be able to be used as a cycle slip detector. Results include a quicker time-to-fix for the carrier phase integer ambiguities. With a single-frequency GPS receiver, this time-to-fix can take up to ten minutes, sometimes longer. Dual-frequency GPS receivers can usually resolve the ambiguities within 30 seconds, depending on the conditions and dynamics of the receivers. The integer ambiguities must be reset every time a satellite is acquired or dropped and also when a cycle slip is detected. Because of this, a shorter time-to-fix can be crucial for a dynamic situation when the ambiguities are frequently being reset. As long as the UWBs provide centimeter-level accuracy, using the UWB ranging measurements should help to improve the time-to-fix of the ambiguities consistently.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	1277 - 1284
Cite this article:	Broshears, E., Martin, S., Bevly, D., "Ultra-Wideband Aided Carrier Phase Ambiguity Resolution in Real-Time Kinematic GPS Relative Positioning," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1277-1284.
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