Precise Point Positioning with Fast Ambiguity Resolution - Prerequisites, Algorithms and Performance

L. Mervart, C. Rocken, T. Iwabuchi, Z. Lukes, M. Kanzaki

Abstract:	A number of strategies for the autonomous precise positioning of dual-frequency GNSS receivers have recently been developed. Stemming from the well-known concept of the precise-point positioning (PPP) the new algorithms have introduced the resolution of the initial phase ambiguities on the zero- or single- (between satellites) difference level that ensures the highest resulting accuracy. In order to make the zero-difference ambiguity resolution possible it is necessary to model all biases that influence the GNSS measurements, estimate these biases using a network of reference stations and transmit them to the rovers. The concept is also known as the State-Space Representation and modeling of all individual GNSS error components. For global networks, the ionospheric refraction seems to be the error component that is the most difficult to model mathematically. A possible approach how to avoid this difficulty is to use solely such linear combinations of dual-frequency GNSS measurements that are not affected by the ionospheric refraction. In that case the state-space representation of the error component does not need to include the dispersive (ionospheric) part. Using the Melbourne-Wuebbena (MW) linear combination together with the phase-only ionosphere-free (L3) linear combination of the measurements is an example of this approach. It has been shown that this MW&L3 algorithm can be used for regional as well as global applications and the method has already been implemented successfully under the name PPPAR (PPP with Ambiguity Resolution). The PPPAR technique is providing higher positioning accuracy than standard PPP because resolving the ambiguities decreases the degree of freedom in the client solution. Similar to baseline processing with ambiguity resolution it is primarily the east-west component of the solution that is improved by ambiguity resolution. 1-cm level horizontal positioning of fully kinematic clients is possible with PPPAR. This level of accuracy is needed for the most demanding applications in precision farming, deformation monitoring, GNSS seismology, and surveying. While the PPPAR method provides similar accuracies as baseline processing with real-time-kinematic techniques, its main drawback for some applications may be seen in the fact that it requires a considerable time to fix the initial phase ambiguities on their integer values (and in that way to reach its final highest accuracy). In the basic form of the PPPAR algorithm the problem of the long ambiguity time-to-fix appears not only after the rover receiver cold start but also after any interruption of the GNSS measurements (caused e.g. by obstacles in the receiver's vicinity). At GPS Solutions we have developed two improvements of the original PPPAR method that we presented first at the ION conference in Savannah, GA in 2008. The first improvement is aimed to handle the fast (within seconds) ambiguity fixing after an interruption (gap) in receiver measurements. This approach uses the dual frequency observations of the client receiver to estimate the ionospheric delay in the direction of all observed satellites. Then when the line of sight to a satellite (or to all satellites) is lost because the client passes under an obstruction the ionosphere prior to this obstruction is extrapolated until the GNSS signal to the obstructed satellites is re-acquired. This extrapolated ionosphere is then used as a constraint to quickly re-estimate the ambiguities and quickly return to pre-gap positioning accuracies. This method is (almost) independent on the ionospheric conditions and can thus be used for global applications without the need of providing ionospheric information to the client. The second approach deals with fast (within seconds or at most within a few minutes) ambiguity resolution after the receiver cold start. In this case additional ionospheric information has to be provided to the client. This information can in principle come from ionospheric models such as Klobuchar or NeQuick but we found that these models are not sufficiently accurate to serve as a constraint to aid fast ambiguity fixing. Therefore we model and estimate the ionosphere based on dual frequency observations from a regional GNSS reference network on the server side and transmit these corrections to the client for interpolation. The client determines a satellite specific ionospheric delay with these corrections and uses this delay as a constraint for rapid ambiguity fixing. We call this approach PPP with fast ambiguity resolution (PPPAR_FAR). PPP_FAR is applicable for local and regional services. A global application is presently not possible because of the required density of the reference network. The presentation describes the principles of the two methods mentioned above, discusses the necessary prerequisites like the necessary density of the reference network, and shows the results achieved in both regional (Japan and USA) and global scales. Special attention is paid to the state-space representation components that describe the atmospheric biases - both its dispersive (ionospheric) and non-dispersive (tropospheric) parts, their modeling and estimation (on the server-side) and their interpolation and usage on the rover-side. We show that the interpolation methods based on the algorithms of the so-called triangulated irregular networks provide the optimal utilization of the information gathered during the processing of the reference network and thus contribute to both the highest accuracy of the results and to the reduction of the bandwidth necessary for the transmission link between the reference network server and the rover (client) receiver.
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:	1176 - 1185
Cite this article:	Mervart, L., Rocken, C., Iwabuchi, T., Lukes, Z., Kanzaki, M., "Precise Point Positioning with Fast Ambiguity Resolution - Prerequisites, Algorithms and Performance," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1176-1185.
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