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Multistation estimating of GPS signal atmospheric delays by undifferenced observations

Precise RTK positioning is usually performable only on short length bases, to limit distance correlated biases, as atmosphere and ephemerides. However, it is possible to recover some residual biases also over long distance using appropriate area models, improving the performances of long base RTK positioning up to 100 km base length. Permanent reference station networks are used to estimate the bias model in surveying type applications requiring centimeter accuracy, reducing the worth of traditional single baseline methods. The well known advantages provided by reference station network information include improved modeling of the residual tropospheric, ionospheric and orbit biases. The system state vector, including the parameters of the bias model, is evaluated via Kalman filtering from the undifferenced observation equations. On the rover side, corrections are applied to the observations as single differences, then the model estimates and recovers the undifferentiated residual biases. 1. MOTIVATION Continuous operating reference stations, tracking GPS or GLONASS, and in the future also Galileo, can be coordinated in static and also real time networks. Real time networks provide the support for surveying type applications, as for reference frame realization and maintenance, weather and space-weather forecasting, physical and geophysical type applications. The network properties can be defined under different aspects: • Provided products and services and their broadcasting infrastructure. • Network extension, density and distribution of the reference stations. • Network architecture, number and interconnection of the master stations, communication network. • Mathematical models and algorithms. • Integration of different source data, as meteo, radar, VLBI, laser ranging, etc. The paper focus on bias estimating and surveying type applications. To overcome the limitations of standard RTK systems, reference networks of permanent operating GPS stations can provide Network RTK (NRTK) services, broadcasting network based state parameters to the mobile user, who is then enabled to operate in Multi Reference Station or Virtual Reference Station mode. Network parameter broadcasting is limited in the RTCM 2.x standards, but is now included in the new RTCM 3.0 standard. Standardisation discussion within RTCM in the new version design, has targeted the interoperability between reference station systems and rover receivers from various manufacturers. However, the obstacles in network parameters broadcasting with RTCM 2.x are overcame by the manufacturers by means of proprietary formats, sometimes largely accepted and used as FKP corrections included in RTCM message type 59, sometimes available in proprietary solutions only. The use by different manufacturers of the same proprietary formats, is due to the fact that interoperability is needed urgently. Moreover, the interoperability issues, are related to the creation and proper description of the models used for deriving the biases. The paper presents some remarks about NRTK techniques, taking account of results obtained by professional dual frequency and also low cost single frequency receivers. Data processing simulates NRTK procedures, using a self made software named ALARIS. This software performs one-way estimation of biases, real time static or kinematic positioning, by using different Kalman filtering techniques. 2. DEFINITIONS In NRTK a master station estimates atmospheric biases over a network of permanent reference stations; then the rover station applies to his observations the corrections broadcasted by the master station. This positioning technique will be largely diffused in future for many applications in engineering, cartography, cadastre, GIS and so on. For all this applications, that usually don’t require very high precisions, the use of low cost single frequency receivers is quick and economic (Cina, Manzino, Roggero, ISPRS VI/3, 2003). The proposed technique can be applied mainly in real time positioning and satellite navigation, but also in weather forecasting, ionospheric and tropospheric tomography on regional scale, time transfer, signal propagation and geomagnetic activity monitoring. To perform real time multistation estimating of GPS biases, the parameterisation in the state space domain is applied. For the state space approach the use of undifferenced observations is recommended, since this allows the estimation of clock parameters as well as the separation of atmospheric delays. It also makes the modelling of error processes easier, compared to approaches based on double differences. However, using undifferenced observations we must correctly model some physical parameters, such as the corrections related to the receiver measurement style (cross-correlation or Z-tracking), satellite and receiver antenna phase centre, constant and periodic relativistic corrections, polar motion and tidal earth. State space vector is estimated by Kalman filtering and include the receiver dependent parameter (receiver clock) and the satellite dependent parameters (carrier phase ambiguities, ionospheric and tropospheric delays). Due to the low redundancy of the system, some parameters as orbit errors, satellite clock estimation errors and multipath are neglected. 3. EQUATIONS FOR BIASES CORRECTION Undifferenced equations are suitable for use in bias estimation, necessary to build the bias model and then broadcast the network parameters, to correct the observations in the rover station. A refined way to calculate the GPS signal biases is to estimate every single bias from undifferenced equations: all the error sources that is possible to model, are estimated in the reference station by Kalman filter, applying deterministic and stochastic models in the observation and in the parameter space. This procedure is named one way biases estimation. The observation equations in the reference station, identified by the subscript k, are: