Short-term temporal variability of GPS receiver's differential code biases (DCB): retrieving and modeling
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The satellite and receiver differential code biases (DCB) combined, account for the main error budget of GPS-based ionosphere investigations. As the space environment onboard the GPS satellites is quite constant, the long-term stability of GPS satellite DCB has been observed. At the same time, continuous GPS data collection from receivers of global coverage makes it possible to estimate GPS satellite DCB with high accuracy. These two facts, however, do not hold true for a variety of receivers' DCB. As a result of various operating environments as well as distinct firmware versions, receiver DCB may experience short-term variations over time. Precise modeling of receiver DCB's variation can raise the reliability of ionosphere products determined from GPS data, as well as ensure the correctness of conclusions drawn based on these products when investigating atmosphere/space effects and geodetic phenomena. Given zero/short-baseline GPS data, the customary scheme used to retrieve receiver DCB is further modified as follows: 1) Precise point positioning (PPP) has been implemented, respectively, using GPS data collected by each of the receiver that forms the baseline. The slant ionosphere delays biased by satellite and receiver DCB, and the undifferenced, float-valued ambiguities can be estimated, among other parameters. 2) Those undifferenced ambiguities are then combined so as to form an independent set of double-differenced ambiguities that are fixable. 3) After taking these fixed ambiguities into consideration, the slant ionosphere delays determined by means of PPP can be further refined. The between-receiver, single-differenced values of these delays are then used to retrieve a time series of receiver DCB, the time resolution of which is equal to that of GPS observations in use. In addition, the ionosphere-fixed model with estimable receiver DCB has been derived. By characterizing the dynamic model of receiver DCB as random walk, the consistency between both the estimated and the formerly retrieved receiver DCB forms a basis to identify an optimal empirical value of the STD of the process noise. Numerical tests make use of multiple days' dual-frequency GPS data collected by 4 co-located receivers that form a total of one zero-baseline and two short-baselines, with a maximum separation of 15 m. The main conclusions include: 1) The modified scheme outperforms the customary one, as being able to determine a time series of receiver DCB less affected by low-frequency code noise and multipath effects; 2) The intra-day variations of receiver DCB determined from the zero-baseline is less than 1 TECu, without apparent day-to-day repeatability. A random walk with STDs of process noise between 1.0 and 1.5 mm is sufficient to characterize different days' variation behaviors; 3) The size of receiver DCB variation corresponding to one of the short-baselines can exceed 12 TECu (roughly 2 m) during one day. To model it with random walk, the empirical STD of the process noise should be set no less than 2 mm. The proposed methods in this paper may serve as new ways to routinely monitor and calibrate receiver DCB.
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