An Imaging Compensation Algorithm for Correcting the Impact of Tropospheric Delay on Spaceborne High-Resolution SAR

Troposphere Delay Remote Sensing Using Single GPS Receiver

Global Navigation Satellite System (GNSS) are one of the promising fields of applied astronautics. They give coordinates and time high quality measurements supporting land, sea, air and space applications. In the article, the possible sources of errors in the algorithm for calculating the navigation parameters are analyzed and algorithm for calculating the navigation parameters of the GNSS receiver using raw measurements is introduced. The influence of the troposphere on the GNSS signals is manifested in the form of an additional delay that add to time the signal passing from the satellite to the receiver is taking, this delay depends on temperature, pressure, humidity, as well as on the antennas of the transmitter and receiver. The main feature of the troposphere is that it is a non-dispersive medium to electromagnetic waves up to 15 GHz, thus, tropospheric effects do not change with the frequency of the GNSS signals. Tropospheric delays are usually calculated using Neil mapping function, which has its drawbacks. Thus, this article considers a new algorithm for tropospheric delay estimation by using a genetic algorithm for calculating the navigation parameters of a stationary GNSS receiver. Genetic algorithm, as an effective method of search and optimization, is used to improve the characteristics of the GNSS, reduce the total calculation time and achieve faster convergence to the optimal solution. In the article, a genetic algorithm for tropospheric delay estimation based on the iterative least squares method is presented. In the final part, the results of the genetic algorithm are presented and a comparison of the results of the algorithm with the Niell mapping function.

<p>InSAR derived Atmospheric Phase Screens (APSs) contain the difference between the atmospheric delay along the SAR sensor line-of-sight of two acquisition epochs: the slave and the master epochs. Using estimates of the atmospheric state at the master epoch, coming from independent sources, the APSs can be transformed into maps of tropospheric Zenith Total Delay (ZTD), that is related to the columnar atmospheric water vapor content. Assimilation experiments of such products into numerical weather prediction (NWP) models have shown a positive impact in the prediction of convective storms.</p><p>In this work, a systematical comparison between various APS and ZTD products aims at determining the optimal procedure to go from APSs to InSAR-derived absolute ZTD maps, i.e. to estimate the master delay map. Two different approaches are compared.</p><p>The first is based on a stack of ZTD maps produced with the assimilation of GNSS ZTD observations into an NWP model. This acts as a physically based interpolator of the GNSS values, which have a spatial resolution much coarser than the InSAR APS one.</p><p>The second is based on a stack of ZTD maps derived by an Iterative Tropospheric Decomposition (ITD) model, as implemented in the GACOS service. In this case, the high-resolution ZTD maps are obtained by an iterative interpolation of a global atmospheric circulation model values and GNSS values where available.</p><p>The results of the comparisons and sensitivity tests on the number of ZTD maps needed to derive the unknown master delay map are shown.</p><p> </p><p> </p><p> </p><p><strong> </strong></p><p><strong> </strong></p>

This paper shows effects of tropospheric delay models and mapping functions among delay features occurred when GPS code signal is transferred for GPS Time Transfer. GPS time transfer uses CGGTTS as the international standard format. For geodetic GPS receiver, ROB has provided r2cggtts software which generates CGGTTS data from RINEX data and all laboratories participated in TAI link use this software and send the CGGTTS results periodically. Though Saastamoinen zenith path model and Niell mapping function are commonly used in space geodesy, r2cggtts software applied NATO zenith path model and CHAO mapping function to the tropospheric delay model. Hence, this paper shows effects of two tropospheric delay models by implementing Saastamoinen model and Niell mapping function for the time offset.

When processing code- and carrier-phase ranges sampled at individual epochs, the control baseline of a pair of reference receivers can bring forth relative integer-valued ambiguities and tropospheric delays. The estimates are usually so accurate that they may act as constraints, when a roving user who operates in the network of references requires instantaneous position solutions. This paper has the objective of taking advantage of a tropospheric zenith delay surface for the user’s ranging corrections. A local network of six reference stations was used to study the single-epoch position estimation, which revealed that with the increased reliability of ambiguity resolution on both L1 and L2 carriers, global positioning system-derived height accuracy was refined by more than 60%.

In recent years, geodesy based on spaceborne microwave remote sensing has gained significant advances. However, whether the observations from the Global Navigation Satellite System (GNSS) or Interferometric Synthetic Aperture Radar (InSAR), the results are inevitably influenced by atmospheric tropospheric delay. Although the tropospheric zenith total delay (ZTD) can be estimated through the gridded meteorological data products and empirical models provided by the ERA5 reanalysis product, its accuracy is still insufficient to meet the needs of modern geodesy. To overcome this challenge, we propose leveraging machine learning techniques to learn local spatio-temporal patterns of tropospheric delay for inferring total zenith delay (ZTD) and zenith wet delay (ZWD) at any location within the learning area.Our findings indicate that artificial neural networks can establish a robust mapping between ZTD estimated by empirical models and GNSS-measured ZTD. Then employing the ensemble learning strategy and the time series dynamics model, the ZTD at any location within the sample area can be inferred. To evaluate our approach, we conducted tests during the active water vapor season in the Tübingen region of Baden-Württemberg, Germany, from June 25 to July 9, 2022. In comparative experiments with the root mean square error (RMSE) of Zenith Total Delay (ZTD) derived from ERA5, our proposed method yielded a significant reduction in RMSE, decreasing it from 16.4292mm to 7.2108mm. This reflects a remarkable accuracy improvement of 56.11%.The proposed approach holds promise for enhancing the precision of GNSS positioning, InSAR earth observation, and generating more dependable water vapor products.

A strategy to realize the tropospheric delay correction in satellite based augmentation systems is presented. The tropospheric delay is one of the major error sources of the GNSS signals. It is attempted to generate the correction information from the numerical weather prediction data to realize the tropospheric delay correction in real-time for mobile positioning. To introduce the correction information into the satellite based augmentation system, the amount of the correction data must be minimized without degrading the correction accuracy. In this paper, through several statistical evaluations using the long-term observation data, the appropriate contents and the data amount of the correction message are investigated. It is shown that the correction message should consist of the information of the tropospheric zenith delay and its average gradient in height. The amount of the correction data is also successfully minimized, and users in the region of Japan can receive the sufficient correction information by receiving only 3 messages. The results of the analyses clearly show the feasibility of the presented strategy.

GNSS zenith delays and gradients in the analysis of VLBI Intensive sessions

Slow-light mesophotonic waveguides have gained increasing interest in the recent years owing to their potential for time-delay control of optical signals, crucial for all-optical circuitry, as well as EM energy storage and field enhancement which is important for driving a stronger light-matter interaction. Yet, the design of such systems has hitherto been predominantly directed by modal-type of analyses in frequency domain. We discuss here why frequency domain analysis fails for real systems, leading to mistaken predictions for the effective propagation speed of the EM signal. In particular, by utilizing a time-domain analysis we demonstrate a slow-light paradigm waveguide system which contradicts the widespread notion that the group-index is generally a good measure of the light's speed effective slow-down factor within the waveguide. In particular, our counterexample shows that it is entirely possible when two modes are compared that it would be the one with the lower group index to yield effectively the larger light slow-down factor. We analyze the salient characteristics of the modes with the higher light slow-down-factor merit to understand how to enable slow light in practical platforms. Our results suggest that in order for a large group index to practically effect a large slowdown factor it should be accompanied by a large modal index bandwidth. This can occur when both the group velocity and the group-velocity dispersion are simultaneously near-zero.

<title>Abstract</title> This paper proposes a residual tropospheric error modeling methodology for terrestrial radio navigation systems used for civil aviation. The functional scope of this methodology ranges from elevation angles above 0.2° to zenith and aircraft distances up to 250 km. The tropospheric residual error model for aviation applications based on global navigation satellite systems (GNSS) employs a global constant to model only the variance of the zenith tropospheric delay error and is not directly applicable for terrestrial ranging. The proposed model encompasses errors from tropospheric mapping functions, zenith delay models, and atmospheric effects such as ducting. In addition, the residual error model variance is derived to consider the variability of tropospheric delay as a function of elevation angle and aircraft range. For a proposed tropospheric delay compensation model for terrestrial ranging, the resulting residual error model is still conservative and is accurate to 0.74 mm/km for elevation angles down to 0.2°, which will enable terrestrial systems to support increasingly demanding performance-based navigation systems.

An odd number of digital not-gates connected in a closed loop circuit will produce a relatively stable free running oscillator. The frequency of oscillation is determined by the number and type of not-gates, the circuit supply voltage, and the total length of connection wire used between the not-gates. Measuring the frequency for various lengths of connection wire enables the speed of the digital signals in the wire to be calculated. The method is sensitive enough to reveal that signals traveling in 22 gauge insulated copper wire propagate about 5% slower than those in 22 gauge bare copper wire. The speed in insulated wire is (2.87±0.03)×108 m/s and the speed in bare wire is (3.03±0.02)×108 m/s. This experiment has been found to be a very popular undergraduate laboratory due to its low cost, straightforward theory, and relatively high (∼1%) precision. The absence of a light source eliminates complicated optics and impresses students with the fact that visible light is not the only thing that travels with the speed of light!

The article describes the possibility of using the passive satellite measurements of the atmosphere to investigate the vertical patterns of pressure, temperature and relative humidity and simulate the altitude dependence of the refractive index of air. The seasonal parameters were determined for the exponential model showing the tropospheric refraction over observation points IRKM (Irkutsk), ULAZ (Ulan-Ude) and BADG (Badary). Post-processing of the input GPS data was conducted to ensure the highest positioning accuracy. In addition to high-precision geodesy, the global positioning method was used for determining the total tropospheric zenith delays (ZTD), which values are used to solve the problems of radio physics and meteorology. The angles of refraction and the true distances were estimated and compared in different seasons of the year. This study shows that the angles of refraction at the observation points located in the Baikal zone do not differ significantly in order of magnitude from the values estimated for other climatic zones.

&amp;lt;p&amp;gt;The snow water equivalent (SWE) is a key parameter in hydrology. In the past years, the signals of Global Navigation Satellite System (GNSS) receivers were discovered to be very attractive for SWE monitoring. The set-up of GNSS-based SWE monitoring typically consists of two GNSS receivers, whereas one is placed on the ground to sense the signal attenuation and time delay being caused by the snow pack. A second receiver is placed above the snow and serves as reference receiver. The measurements of both receivers are differenced to eliminate the common effect of errors in the satellite orbits and clocks, satellite phase and code biases and atmospheric errors, while the information on the snow is kept.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;In this talk, we discuss the replacement of the reference receiver by a virtual reference station (VRS). The VRS is a virtual GNSS reference station, whose corrections are obtained by interpolation of the corrections from multiple surrounding reference stations to achieve a higher accuracy at the user location. The concept of VRS was first developed by Trimble and is widely used in today's real-time kinematic (RTK) positioning receivers. The concept of VRS is also attractive for snow monitoring, since the GNSS reference receiver could be avoided resulting in a lower power consumption and less costs. Moreover, this could be a big advantage for applications in slopes, which are, e.g., potentially avalanche prone. Within the hardware setup of our GNSS SWE sensors, an internet communication link for the reception of the corrections from the VRS corrections at the SWE monitoring site is already available.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;However, there are also two challenges: First, the SWE monitoring stations in Alpine areas are typically at a significantly different altitude than the geodetic reference receivers. The differential tropospheric zenith delay is not negligible for altitudinal differences of more than 100 m. Therefore, the differential tropospheric delay needs to be considered either in the determination of VRS corrections or alternatively in the SWE determination. For altitudinal differences of less than 1000 m, the differential tropospheric zenith delay could be approximated by a model with sufficient accuracy. The residual modelling error is projected to the SWE estimate. Second, the use of a VRS instead of a conventional GNSS reference station requires a stronger data link, since the GNSS raw data (pseudoranges, carrier phases and carrier-to-noise power ratio measurements from all tracked satellites) need to be transmitted besides the final SWE results. However, an LTE link is totally sufficient.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Besides the methodology, we will also focus on specific hardware implementations.&amp;lt;/p&amp;gt;

National satellite control points, or any fixed points determined rel- ative to a known control point, can serve as monitoring stations when equipped with dual-frequency global positioning system (GPS) receivers. The available mon- itoring station coordinates are used to advantage to derive time-varying ionospheric and tropospheric path delays from the observed carrier phase data. Distinguishing atmospheric parameters from geometric positions is necessary in many cases be- cause the relative tropospheric zenith delays are strongly correlated with the inter- station height differences. In addition, GPS users may work with the single-fre- quency receivers that track satellite signals for only a few minutes at a time. The algorithm in this paper is based on the cosine functions of double-difference carrier phase measurements. After removing the first-order temporal and spatial iono- spheric effects, the relative tropospheric delays are found to have correlation co- efficients of up to 0.85, with the Saastamoinen model delays using some standard values for atmospheric pressure, temperature, and humidity. When comparing the 19 GPS-derived orthometric heights with the independently leveled heights, in a 5.5 3 4.0 km 2 area, the use of GPS-monitored atmospheric path delays led to an improved root-mean-square height error of 61.48 cm.

Real-time kinematic (RTK) positioning with Global Navigation Satellite System (GNSS) signals is widely used, e.g., for surveying, agriculture, and potentially for autonomous vehicles and unmanned air vehicles in the future. In this paper, an extended RTK positioning for significant height differences between two low-cost GNSS receivers with patch antennas is presented. In this case, the classical model for double difference measurements needs to be extended, i.e., a differential tropospheric zenith delay and pseudorange multipath errors need to be estimated besides the baseline and carrier phase integer ambiguities. The increased number of unknowns results in an ill-conditioned system of observation equations and a substantial correlation between the state estimates. We introduce prior information on the differential tropospheric zenith delay based on the differential air pressure and exploit the temporal correlation of pseudorange multipath errors. Moreover, a criterion for the integer ambiguity candidate vector selection is provided, which is robust over phase multipath and unavoidable errors in the float ambiguity covariance matrix. The proposed method is validated with two low-cost GNSS modules that were placed at the Zugspitzplatt (2601 m a.s.l.) and Eibsee (1018 m a.s.l.). The obtained estimates for the baseline and differential tropospheric zenith delay show a high repeatability over several independent ambiguity fixings. The residuals of the fixed carrier phase measurements are within 2 cm for almost all satellites, which confirms both the measurement model and the ambiguity fixing.