GEODESY, CARTOGRAPHY AND AERIAL PHOTOGRAPHY

The aim of this work is to evaluate the accuracy of determining the wet component of zenith tropospheric delay (ZTD) from GNSS-measurements and the accuracy of determining the hydrostatic component according to the Saastamoinen model in comparison with the radio sounding data as well. Zenith tropospheric delay is determined mainly by two methods - traditional, using radio sounding or using atmospheric models, such as the Saastamoinen model, and the method of GNSS measurements. Determination of the hydrostatic component of the zenith tropospheric delay was performed by radio sounding data obtained at the aerological station Praha-Libus in 2011-2013 and in 2018. Data were processed for the middle decades of January and July of each year at 0h o’clock of the Universal Time. The wet component was calculated from GNSS observations. By a significant number of radio soundings at the Praha-Libus aerological station, hydrostatic and wet components of zenith tropospheric delay (ZTD) and the same number of ZTD values derived for the corresponding time intervals from GNSS measurements at the GOPE reference station were determined. The values of the wet component of ZTD were determined and compared with the corresponding data obtained from radio soundings. We found that the error of the hydrostatic component in winter does not exceed 10 mm in absolute value, and in summer it is approximately 1.5 times smaller. This is due to differences in the stratification of the troposphere and lower stratosphere in winter and summer. As for the wet component of ZTD, its errors do not exceed: in winter 15 mm, in summer – 35 mm. The resulting differences in summer have a negative sign, indicating a systematic shift, and in winter – both negative and positive. Today, there are many studies aimed at improving the accuracy of determining zenith tropospheric delay by both Ukrainian and foreign authors, but the problem of the accuracy of the hydrostatic component remains open. The study provides recommendations for further research to improve the accuracy of zenith tropospheric delay.

Development and evaluation of the refined zenith tropospheric delay (ZTD) models

The tropospheric delay is a significant error source in Global Navigation Satellite System (GNSS) positioning and navigation. It is usually projected into zenith direction by using a mapping function. It is particularly important to establish a model that can provide stable and accurate Zenith Tropospheric Delay (ZTD). Because of the regional accuracy difference and poor stability of the traditional ZTD models, this paper proposed two methods to refine the Hopfield and Saastamoinen ZTD models. One is by adding annual and semi-annual periodic terms and the other is based on Back-Propagation Artificial Neutral Network (BP-ANN). Using 5-year data from 2011 to 2015 collected at 67 GNSS reference stations in China and its surrounding regions, the four refined models were constructed. The tropospheric products at these GNSS stations were derived from the site-wise Vienna Mapping Function 1 (VMP1). The spatial analysis, temporal analysis, and residual distribution analysis for all the six models were conducted using the data from 2016 to 2017. The results show that the refined models can effectively improve the accuracy compared with the traditional models. For the Hopfield model, the improvement for the Root Mean Square Error (RMSE) and bias reached 24.5/49.7 and 34.0/52.8 mm, respectively. These values became 8.8/26.7 and 14.7/28.8 mm when the Saastamoinen model was refined using the two methods. This exploration is conducive to GNSS navigation and positioning and GNSS meteorology by providing more accurate tropospheric prior information.

Kinematic Zenith Tropospheric Delay Estimation with GNSS PPP in Mountainous Areas

The use of global navigation satellite systems (GNSS) precise point positioning (PPP) to estimate zenith tropospheric delay (ZTD) profiles in kinematic vehicular mode in mountainous areas is investigated. Car-mounted multi-constellation GNSS receivers are employed. The Natural Resources Canada Canadian Spatial Reference System PPP (CSRS-PPP) online service that currently processes dual-frequency global positioning system (GPS) and Global’naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) measurements and is now capable of GPS integer ambiguity resolution is used. An offline version that can process the above and Galileo measurements simultaneously, including Galileo integer ambiguity resolution is also tested to evaluate the advantage of three constellations. A multi-day static data set observed under open sky is first tested to determine performance under ideal conditions. Two long road profile tests conducted in kinematic mode are then analyzed to assess the capability of the approach. The challenges of ZTD kinematic profiling are numerous, namely shorter data sets, signal shading due to topography and forests of conifers along roads, and frequent losses of phase lock requiring numerous but not always successful integer ambiguity re-initialization. ZTD profiles are therefore often only available with float ambiguities, reducing system observability. Occasional total interruption of measurement availability results in profile discontinuities. CSRS-PPP outputs separately the zenith hydrostatic or dry delay (ZHD) and water vapour content or zenith wet delay (ZWD). The two delays are analyzed separately, with emphasis on the more unpredictable and highly variable ZWD, especially in mountainous areas. The estimated delays are compared with the Vienna Mapping Function 1 (VMF1), which proves to be highly effective to model the large-scale profile variations in the Canadian Rockies, the main contribution of GNSS PPP being the estimation of higher frequency ZWD components. Of the many conclusions drawn from the field experiments, it is estimated that kinematic profiles are generally determined with accuracy of 10 to 20 mm, depending on the signal harshness of the environment.

GEODESY, CARTOGRAPHY, AND AERIAL PHOTOGRAPHY

The purpose of this work is to build 3D models of components of zenith tropospheric delay (ZTD) according to the surface measurements of meteorological values obtained at 100 points, which is almost evenly distributed throughout Ukraine. Method. Saastamoinen formulas calculated dry and wet components of the zenith tropospheric delay. According to the obtained results, the fields of dry and wet components of tropospheric delay were compiled, the fields of their change were constructed using a different number of studied points. Also, with the help of a graphic editor, 3D models of the magnitude one-moment distribution of dry and wet components of the zenith tropospheric delay for the territory of Ukraine were built. Results. Built 3D models of ZTD components; constructed zenith tropospheric delay fields for the territory of Ukraine; a comparison of the distribution of delay components for the specified area and its change during the day are the results of this work. It is established that the dry component becomes more important in the southern and central territory of Ukraine, where the observation points are lower in height and where there is a higher atmospheric pressure, which dominates in the calculation of this component. Accordingly, the wet component is also higher in the southern part of Ukraine, but this is due to higher relative humidity. As a result of the compaction of the network to 100 points, more accurate models of component distribution were obtained, which allowed Ukraine to assess in more detail the value of tropospheric delay for the territory of Ukraine. Further compaction of the network for the territory of Ukraine did not lead to the expected increase in the accuracy of tropospheric delay, as the location of meteorological stations in the country is not uniform enough, and some values of meteorological magnitudes are obtained not by direct measurements but by interpolation. It is necessary to compact the model with reliable meteorological measurements evenly and to control the calculation of components by integrating according to the aerological soundings carried out at individual points to obtain a more detailed model. Scientific novelty and practical significance. The scientific novelty is to build 3D models of tropospheric delay components for the territory of Ukraine at a certain point in time. The practical significance of the performed research is that they can be used as an initial step to build a Spatio-temporal model of tropospheric delay, reflecting the spatial changes of the delay in real-time for a particular area.

A New GPT2w Model Improved by PSO-LSSVM for GNSS High-Precision Positioning

Tropospheric delay is an important error affecting GNSS high-precision navigation and positioning, which will decrease the precision of navigation and positioning if it is not well corrected. Actually, tropospheric delay, especially in the zenith direction, is related to a series of meteorological parameters, such as temperature and pressure. To estimate the zenith tropospheric delay (ZTD) as accurately as possible, the paper proposes a new fused model using the least squares support vector machines (LSSVM) and the particle swarm optimization (PSO) to improve the precision and temporal resolution of meteorological parameters in global pressure and temperature 2 wet (GPT2w). The proposed model uses the time series of meteorological parameters from the GPT2w model as the initial value, and thus, the time series of the residuals can be obtained between the meteorological parameters from meteorological sensors (MS) and the GPT2w model. The long time series of meteorological parameters is the evident periodic signal. The GPT2w model describes its dominant frequency (harmonics), and the residuals thus can be seen as the short-period signal (nonharmonics). The combined PSO and LSSVM model (PSO-LSSVM) is used to predict the specific value of the short-period signal. The new GPT2w model, in which the meteorological parameter value is obtained by combining the estimated meteorological parameters residuals and the GPT2w-derived meteorological parameters, can be acquired. The GNSS network stations in Hong Kong throughout 2017-2018 are processed by the GNSS Processing and Analysis Software (GPAS), which is developed by the Chinese Academy of Surveying & Mapping, to estimate the zenith tropospheric delay and station coordinates using the new GPT2w model. Statistical results reveal that the accuracy of the new GPT2w model-derived ZTD was improved by 60% or more compared with that of the GPT2w-derived ZTD. In addition, the positioning accuracy of the GNSS station has been effectively improved up to 44.89%. Such results reveal that the new GPT2w model can greatly reduce the influence of nonharmonic components (short-period terms) of the meteorological parameter time series and achieve better accuracy than the GPT2w model.