Proceedings of the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2008)
The inter-frequency bias (IFB) is present in all dual frequency combinations of GPS pseudorange and carrier phase observables. It is caused by the path dependent signal delays in both the satellite and receiver. That delay can be directly measured for a space vehicle prior to launch, or for a ground based receiver prior to its being used in the field. However the bias is known to drift, and monitoring the delay estimate by direct measurement is time consuming for ground based receivers and impossible for deployed space vehicles. Hansen (2002) examined the observability of IFB through a global model of ionosphere total electron content (TEC). Variation in the receiver portion of the IFB can also be observed in receivers with antennae in a zero-baseline configuration. This is referred to as an inter-receiver bias (IRB). In this study a Kalman filter is formulated to observe IFBs and IRBs. Process noise is used to allow the filter to track changes in the IFBs and IRBs. The filter also implements constraints to reflect the fact that a given IRB is not linearly independent of the IFBs. Because the receivers are distributed on a global scale, the Kalman filter requires a globally observable phenomenon by which to tie the IFBs. In this case ionosphere delay provides such a phenomenon. The filter was applied to observations collected by GPS monitor stations that comprise the National Geospatial- Intelligence Agency Monitor Station Network (MSN). Each monitor station contains two geodetic quality receivers in a zero-baseline configuration and continuously collects GPS observations. The GPS observations collected by this network are used to produce both precise ephemeris and the broadcast ephemeris. GPS observations made through the network are incorporated into the GPS Master Control Station (MCS) Kalman filter of the Operational Control System (OCS) (Wiley, 2006). The Kalman filter in the OCS estimates the orbital parameters that are transmitted via the navigation message. If estimated effectively, knowledge of the receiver portion of the IFB can aid in achieving better ionosphere models. IFBs are made observable using a global ionosphere delay model. A ninth order spherical harmonic model derived by Y.C. Chao (1997) was used in this study for ionosphere delay. Chao used this spherical harmonic model to capture ionospheric variations that occurred over a smaller global region in his IFB estimation process. In this study a similar model was used but was verified using observations that span a global coverage. The receiver portion of the IFB is observed precisely using the IRB. In this study error terms were introduced into the Kalman filter design to realign the IRB estimates to the IFB estimates produced for each of the two receivers in a zero baseline configuration. For a nominal epoch of measurement, there were 198 noisy measurements used each epoch to generate twelve monitor station specific IRBs. The IRB estimates showed small, decimeter level dynamic variation over the period of a day. The quality of the IFB estimate directly affects the quality of the ionospheric model formed during the estimation process. Results verify that the filter is operating properly. The ionosphere model, though simple, demonstrates that the total electron content (TEC) peaks during local noon and is at a minimum during local night. IRB estimates are roughly constant over time and have a magnitude of less than 2.5 meters. Similar estimates are formed for the IFBs, however when processing one day of observations, the IFB estimates are less stable than those of the IRBs. Future effort will involve tuning the filter, and establishing criteria for its convergence.