Stochastic modelling of residual tropospheric delays / by Hassan Elobeid Ibrahim

Real-time and near real-time precise point positioning (PPP) requires shorter solution convergence time. Residual tropospheric delay, which exists as a result of the limitations of current tropospheric correction models, is a limiting factor for fast PPP convergence. To overcome the limitations of existing tropospheric models, we proposed a new approach. In this approach, the bulk of the tropospheric delay is accounted for using an empirical model, while the residual component is accounted for stochastically. The analysis of many daily tropospheric residuals data series for stations spanning North America shows that the residual component can be accounted for using an exponential cosine model. A random walk (RW) model was also developed and used along with the NOAA tropospheric corrections with Vienna Mapping Function 1. It is shown that the RW improved the accuracy of station coordinates within the PPP convergence time by a few centimetres.

Stochastic modelling of residual tropospheric delays / by Hassan Elobeid Ibrahim

Real-time and near real-time precise point positioning (PPP) requires shorter solution convergence time. Residual tropospheric delay, which exists as a result of the limitations of current tropospheric correction models, is a limiting factor for fast PPP convergence. To overcome the limitations of existing tropospheric models, we proposed a new approach. In this approach, the bulk of the tropospheric delay is accounted for using an empirical model, while the residual component is accounted for stochastically. The analysis of many daily tropospheric residuals data series for stations spanning North America shows that the residual component can be accounted for using an exponential cosine model. A random walk (RW) model was also developed and used along with the NOAA tropospheric corrections with Vienna Mapping Function 1. It is shown that the RW improved the accuracy of station coordinates within the PPP convergence time by a few centimetres.

Mitigation of Atmospheric Artefacts in Multi Temporal InSAR: A Review

The complexity of the atmosphere renders the modelling of the atmospheric delay in multi temporal InSAR difficult. This limits the potential of achieving millimetre accuracy of InSAR-derived deformation measurements. In this paper we review advances in tropospheric delay modelling in InSAR, tropospheric correction methods and integration of the correction methods within existing multi temporal algorithms. Furthermore, we investigate ingestion of the correction techniques by different InSAR applications, accuracy performance metrics and uncertainties of InSAR derived measurements attributed to tropospheric delay. Spatiotemporal modelling of atmospheric delay has evolved and can now be regarded as a spatially correlated turbulent delay with varying degree of anisotropy random in time and topographically correlated seasonal stratified delay. Tropospheric corrections methods performance is restricted to a case by case basis and ingestion of these methods by different applications remains limited due to lack of their integration into existing algorithms. Accuracy and uncertainty assessments remain challenging with most studies adopting simple statistical metrics. While advances have been made in tropospheric modelling, challenges remain for the calibration of atmospheric delay due to lack of data or limited resolution and fusion of multiple techniques for optimal performance.

Quantitative assessment to the impact of InSAR ionospheric and tropospheric corrections on source parameter modelling: application to the 4th nuclear test, North Korea

SUMMARY Although many studies have revealed that the atmospheric effects of electromagnetic wave propagation (including ionospheric and tropospheric water vapour) have serious impacts on Interferometric Synthetic Aperture Radar (InSAR) measurement results, atmospheric corrections have not been thoroughly and comprehensively investigated in many well-known cases of InSAR focal mechanism solutions, which means there is no consensus on whether atmospheric effects will affect the InSAR focal mechanism solution. Moreover, there is a lack of quantitative assessment on how much the atmospheric effect affects the InSAR focal mechanism solution. In this paper, we emphasized that it was particularly important to assess the impact of InSAR ionospheric and tropospheric corrections on the underground nuclear explosion modelling quantitatively. Therefore, we investigated the 4th North Korea (NKT-4) underground nuclear test using ALOS-2 liters-band SAR images. Because the process of the underground nuclear explosion was similar to the volcanic magma source activity, we modelled the ground displacement using the Mogi model. Both the ionospheric and tropospheric phase delays in the interferograms were investigated. Furthermore, we studied how the ionosphere and troposphere phase delays could bias the estimation of Mogi source parameters. The following conclusions were drawn from our case study: the ionospheric delay correction effectively mitigated the long-scale phase ramp in the full-frame interferogram, the standard deviation decreased from 1.83 to 0.85 cm compared to the uncorrected interferogram. The uncorrected estimations of yield and depth were 8.44 kt and 370.33 m, respectively. Compared to the uncorrected estimations, the ionospheric correction increased the estimation of yield and depth to 9.43 kt and 385.48 m, while the tropospheric correction slightly raised them to 8.78 kt and 377.24 m. There were no obvious differences in the location estimations among the four interferograms. When both corrections were applied, the overall standard deviation was 1.16 cm, which was even larger than the ionospheric corrected interferogram. We reported the source characteristics of NKT-4 based on the modelling results derived from the ionospheric corrected interferogram. The preferred estimation of NKT-4 was a Mogi source located at 129°04′22.35‘E, 41°17′54.57″N buried at 385.48 m depth. The cavity radius caused by the underground explosion was 22.66 m. We reported the yield estimation to be 9.43 kt. This study showed that for large-scale natural deformation sources such as volcanoes and earthquakes, atmospheric corrections would be more significant, but even if the atmospheric signal did not have much complexity, the corrections should not be ignored.

Analysis on the Impacts of Slant Tropospheric Delays on Precise Point Positioning

Tropospheric delay is one main factor affecting the accuracy of precise point positioning (PPP) ambiguity-float and fixed solutions. Investigations mainly focused on evaluating the contributions of tropospheric corrections to the accuracy and reliability of PPP solutions. The tropospheric corrections generally contained the zenith tropospheric delay (ZTD) and the horizontal gradients estimated from relative positioning or PPP. However, the estimated tropospheric delays can be partly absorbed by the carrier phase residuals if the stochastic model is not well-defined. Therefore, along with the ZTD and horizontal gradients, the carrier phase residuals from PPP backward filter are considered to reconstruct slant tropospheric delay (STD). Based on the proposed STD model, its marginal effects on GPS PPP were investigated. Results indicated that the consideration of carrier phase residuals for STD modeling can improve the three-dimensional accuracy to 0.5 cm/1 cm/1.2 cm in the South/North/Up (N/E/U) components. Then, the effects of internal and external STD corrections on PPP float and fixed solutions were analyzed. Compared to the ZTD + gradients augmentation, STD corrections from the same station could improve the PPP accuracy by 51%/51%/60%; the large improvements were because the multipath error and observation noise were eliminated. In comparison, the improvement was 14%/28%/31% using external STD corrections, which indicated the effects of unmodeled tropospheric errors in the phase residuals. The ambiguity-fixing results indicated that the fixing rate of PPP ambiguity was increased by 30% with STD augmentation. As the BeiDou System (BDS) suffered longer convergence than that of GPS, the benefits of STD modeling to the BDS observations were also validated. Overall, the results validated the performance of STD-augmented PPP, which demonstrated the potential application of high-accuracy troposphere products.