Satellite-Clock Modeling in Single-Frequency PPP-RTK Processing

Abstract

The real-time kinematic precise point positioning (PPP-RTK) technique enables integer ambiguity resolution by providing singlereceiver users with information on the satellite phase biases next to the standard PPP corrections. Using undifferenced and uncombined observations, rank deficiencies existing in the design matrix need to be eliminated to form estimable parameters. In this contribution, the estimability of the parameters was studied in single-frequency ionosphere-weighted scenario, given a dynamic satellite-clock model in the network Kalman filter. In case of latency of the network corrections, the estimable satellite clocks, satellite phase biases, and ionospheric delays need to be predicted over short time spans. With and without satellite-clock models incorporated in the network Kalman filter, different approaches were used to predict the network corrections. This contribution shows how the predicted network corrections responded to the presence and absence of satellite-clock models. These differences in the predicted network corrections were also reflected in the user positioning results. Using three different 1-Hz global positioning system (GPS) single-frequency data sets, two user stations in one small-scale network were used to compute the positioning results, applying predicted network corrections. The latency of the network products ranges from 3 to 10 s. It was observed that applying strong satellite-clock constraints in the network Kalman filter (i.e., with the process noise of 1 or 0.5 mm per square root of second) reduced the root-mean squares (RMS) of the user positioning results to centimeters in the horizontal directions and decimeters in the vertical direction for latencies larger than 6 s, compared to the cases without a satellite-clock model. individual papers. This paper is part of the Journal of Surveying Engineering, © ASCE, ISSN 0733-9453. © ASCE 04018003-1 J. Surv. Eng. J. Surv. Eng., 2018, 144(2): 04018003 Downloaded from ascelibrary.org by Technische Universiteit Delft on 03/04/19. Copyright ASCE. For personal use only; all rights reserved. © ASCE 04018003-2 J. Surv. Eng.

Single-station PPP-RTK: correction latency and ambiguity resolution performance

“…The spectral density of the clock and ionospheric acceleration parameters ∂ 2 b s r ,i are given by σ 2 ∂ 2 ρ and σ 2 ∂ 2 ι , respectively. In case of the satellite clocks, the spectral density σ 2 ∂ 2 ρ may vary between 1 and 7 [mm 2 /sec 3 ], whereas the ionospheric spectral density σ 2 ∂ 2 ι may vary from fractions of [mm 2 /sec 3 ] to several [mm 2 /sec 3 ], depending on the location and time of the receiver data collection (Wang et al 2018b).…”

Precision analysis of troposphere sensing using GPS single-frequency signals

“…1 and 2) and the spatial ionospheric constraints (Eq. 4) can be reformulated with the estimable parametersτ r , dt r , dt s ,ι s r ,δ r,j ,δ s ,j ,d r,j andã s r,j given in Table 1 (Wang et al 2018):…”

“…Estimable parameters in Eqs. 5 and 6 in single-frequency ionosphere-weighted scenario (Wang et al 2018). The satellite hardware biases and ambiguities are assumed to be constant, and the receiver hardware biases and ZWD increments are assumed to be linked in time (SF Network A)…”

The Benefits of Receiver Clock Modelling in Satellite Timing

“…In 2014, Lyu et al [ 14 ] achieved covariance with white frequency modulation (WFM) noise, random walk frequency modulation (RWFM) noise and the correlation between the clock and ambiguity parameter and obtained better results in mitigating day boundaries. Some scholars have verified that clock modelling improves the accuracy of height direction [ 8 , 15 , 16 ]. As demonstrated by the abovementioned work, showing two state clock models involving WFM and RWFM noise that are frequently employed in Kalman filter covariance.…”