Stochastic modeling of high-stability ground clocks in GPS analysis
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ORIGINAL PAPER
Stochastic modeling of high-stability ground clocks in GPS analysis Kan Wang · Markus Rothacher
Received: 21 June 2012 / Accepted: 22 January 2013 / Published online: 19 March 2013 © Springer-Verlag Berlin Heidelberg 2013
Abstract In current global positioning system (GPS) applications, receiver clocks are typically estimated epoch-wise in the data analyses even for clocks with high performance like Hydrogen-masers (H-maser). Applying an appropriate clock model for high-stability receiver clocks should, in view of the strong correlation between the station height and the clock parameters, significantly improve the positioning results. Recent experiments have shown that modeling the deterministic behavior of high-quality receiver clocks can improve the kinematic precise point positioning considerably. In this paper, well-behaving ground clocks are studied in detail applying constraints between subsequent and near-subsequent clock parameters. The influence of different weights for these relative clock constraints on the positioning quality, especially on the height, is investigated. For excellent clocks, an improvement of up to a factor of 3 can be obtained for the repeatability of the kinematic height estimates. This may be essential to detect small but sudden changes in the vertical component (e.g., caused by earthquakes). Troposphere zenith path delays (ZPD) are also heavily correlated with the receiver clock estimates and station heights. All these parameters are usually estimated simultaneously. We show that the use of relative clock constraints allows for a higher time resolution of the ZPD estimates (smaller than 2 h) without compromising the quality of the kinematic height estimates. Keywords Stochastic clock model · GPS kinematic PPP · High-performance atomic clock · Troposphere K. Wang (B) · M. Rothacher Institute of Geodesy and Photogrammetry, ETH Zurich, Schafmattstr. 34, 8093 Zurich, Switzerland e-mail: [email protected] M. Rothacher e-mail: [email protected]
1 Introduction In the present-day analyses of global navigation satellite system (GNSS) data, the receiver clocks and satellite clocks are typically estimated as independent parameters for each measurement epoch in the least-squares adjustment. The resulting large number of clock parameters are strongly correlated with troposphere Zenith Path Delays (ZPD) parameters and the station height (Dach et al. 2003; Rothacher and Beutler 1998). It can be expected that, if the quality of the high-performance receiver clocks could be fully exploited with an appropriate deterministic and stochastic model, the solutions of other parameters, especially the kinematic station height estimates, should become more stable and more accurate because of the strong correlation between the clock parameters and the station height. The idea of a detailed stochastic modeling of receiver and satellite clocks is not really new. During the 1980s, colleagues at Jet Propulsion Laboratory (JPL) modeled clock and troposphere parameters using different stochastic
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