Statistical Distribution Analysis of Navigation Positioning System Errors-Issue of the Empirical Sample Size

Land and Seabed Surface Modelling in the Coastal Zone Using UAV/USV-Based Data Integration

The coastal zone is an area that includes the sea coast and adjacent parts of the land and sea, where the mutual interaction of these environments is clearly marked. Hence, the modelling of the land and seabed parts of the coastal zone is crucial and necessary in order to determine the dynamic changes taking place in this area. The accurate determination of the terrain in the coastal zone is now possible thanks to the use of Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vehicles (USVs). The aim of this article is to present land and seabed surface modelling in the coastal zone using UAV/USV-based data integration. Bathymetric and photogrammetric measurements were carried out on the waterbody adjacent to a public beach in Gdynia (Poland) in 2022 using the DJI Phantom 4 Real Time Kinematic (RTK) UAV and the AutoDron USV. As a result of geospatial data integration, topo-bathymetric models in the coastal zone were developed using the following terrain-modelling methods: Inverse Distance to a Power (IDP), kriging, Modified Shepard's Method (MSM) and Natural Neighbour Interpolation (NNI). Then, the accuracies of the selected models obtained using the different interpolation methods, taking into account the division into land and seabed parts, were analysed. Research has shown that the most accurate method for modelling both the land and seabed surfaces of the coastal zone is the kriging (linear model) method. The differences between the interpolated and measurement values of the R95 measurement are 0.032 m for the land part and 0.034 m for the seabed part. It should also be noted that the data interpolated by the kriging (linear model) method showed a very good fit to the measurement data recorded by the UAVs and USVs.

Reducing the Uncertainty of the Moving Object Location Measurement with the Method of Quasi-Multiple Measurement in GNSS Technology in Symmetrical Arrangement

The article presents a solution to the problem of limited accuracy of dynamic measurements performed with GNSS receivers. The proposed measurement method is a response to the needs related to the assessment of the measurement uncertainty of the position of the track axis of the rail transport line. However, the problem of reducing the measurement uncertainty is universal for many different situations where high accuracy of positioning of objects is required, especially in motion. The article proposes a new method to determine object's location using geometric constraints of a number of GNSS receivers arranged in symmetric configuration. The proposed method has been verified by comparing signals recorded by up to five GNSS receivers during stationary and dynamic measurements. The dynamic measurement was made on a tram track within the framework of a cycle of studies upon effective and efficient methods to catalogue and diagnose tracks. A detailed analysis of the results obtained with the quasi-multiple measurement method confirms remarkable reduction in their uncertainty. Their synthesis shows the usability of this method in dynamic conditions. The proposed method is expected to find application in measurements requiring high accuracy, and in case of deterioration of the signal quality from satellites by one or more of GNSS receivers due to the appearance of natural obstacles.

Research on the Error of Global Positioning System Based on Time Series Analysis

Due to the poor dynamic positioning precision of the Global Positioning System (GPS), Time Series Analysis (TSA) and Kalman filter technology are used to construct the positioning error of GPS. According to the statistical characteristics of the autocorrelation function and partial autocorrelation function of sample data, the Autoregressive (AR) model which is based on a Kalman filter is determined, and the error model of GPS is combined with a Kalman filter to eliminate the random error in GPS dynamic positioning data. The least square method is used for model parameter estimation and adaptability tests, and the experimental results show that the absolute value of the maximum error of longitude and latitude, the mean square error of longitude and latitude and average absolute error of longitude and latitude are all reduced, and the dynamic positioning precision after correction has been significantly improved.

Analysis of Methods for Determining Shallow Waterbody Depths Based on Images Taken by Unmanned Aerial Vehicles

Hydrographic surveys enable the acquisition and processing of bathymetric data, which after being plotted onto nautical charts, can help to ensure safety of navigation, monitor changes in the coastal zone, and assess hydro-engineering structure conditions. This study involves the measurement of waterbody depth, identification of the seabed shape and geomorphology, the coastline course, and the location of underwater obstacles. Hydroacoustic systems mounted on vessels are commonly used in bathymetric measurements. However, there is also an increasing use of Unmanned Aerial Vehicles (UAV) that can employ sensors such as LiDAR (Light Detection And Ranging) or cameras previously not applied in hydrography. Current systems based on photogrammetric and remote sensing methods enable the determination of shallow waterbody depth with no human intervention and, thus, significantly reduce the duration of measurements, especially when surveying large waterbodies. The aim of this publication is to present and compare methods for determining shallow waterbody depths based on an analysis of images taken by UAVs. The perspective demonstrates that photogrammetric techniques based on the SfM (Structure-from-Motion) and MVS (Multi-View Stereo) method allow high accuracies of depth measurements to be obtained. Errors due to the phenomenon of water-wave refraction remain the main limitation of these techniques. It was also proven that image processing based on the SfM-MVS method can be effectively combined with other measurement methods that enable the experimental determination of the parameters of signal propagation in water. The publication also points out that the Lyzenga, Satellite-Derived Bathymetry (SDB), and Stumpf methods allow satisfactory depth measurement results to be obtained. However, they require further testing, as do methods using the optical wave propagation properties.

Determination of Navigation System Positioning Accuracy Using the Reliability Method Based on Real Measurements

In navigation, the Twice the Distance Root Mean Square (2DRMS) is commonly used as a position accuracy measure. Its determination, based on statistical methods, assumes that the position errors are normally distributed and are often not reflected in actual measurements. As a result of the widespread adoption of this measure, the positioning accuracy of navigation systems is overestimated by 10–15%. In this paper, a new method is presented for determining the navigation system positioning accuracy based on a reliability model where the system’s operation and failure statistics are referred to as life and failure times. Based on real measurements, the method proposed in this article will be compared with the classical method (based on the 2DRMS measure). Real (empirical) measurements made by the principal modern navigation positioning systems were used in the analyses: Global Positioning System (GPS) (168’286 fixes), Differential Global Positioning System (DGPS) (900’000 fixes) and European Geostationary Navigation Overlay Service (EGNOS) (900’000 fixes). Research performed on real data, many of which can be considered representative, have shown that the reliability method provides a better (compared to the 2DRMS measure) estimate of navigation system positioning accuracy. Thanks to its application, it is possible to determine the position error distribution of the navigation system more precisely when compared to the classical method, as well as to indicate those applications that can be used by this system, ensuring the safety of the navigation process.

Improvement of UAV Positioning Performance Based on EGNOS+SDCM Solution

The article presents the results of research on multi-SBAS (multi-satellite-based augmentation system) positioning in UAV (unmanned aerial vehicle) technology. For this purpose, a new solution was developed for combining the UAV position navigation solution from several SBAS systems. In this particular case, the presented linear combination algorithm is based on the fusion of EGNOS (European geostationary navigation overlay service) and SDCM (system of differential correction and monitoring) positioning to determine the resultant UAV coordinates. The algorithm of the mathematical model uses weights of measurements in three ways, i.e., Variant I, the reciprocal of the number of tracked satellites from a single SBAS solution; Variant II, the inverse square of mean coordinate errors from a single SBAS solution; and Variant III, the reciprocal of UAV flight speed from a single SBAS solution. The research experiment used real GNSS (global navigation satellite system) navigation data recorded by the VTOL unmanned platform. The test flight was made in April 2020 in Poland, near Warsaw. Based on the developed research results, it was found that the highest accuracy of UAV positioning was obtained when using the weighting model for Variant II. In the weight model of Variant II, the accuracy of the solution of the UAV position increased by 1–2% for the horizontal components and 19–22% for the vertical component h, concerning the results obtained from the weighing Variants I and III. It is worth noting that the proposed research model significantly improves the results of determining the ellipsoidal height h. Compared to the arithmetic mean model, determining the h component in the Variant II weight model is improved by about 23%. The paper also shows the advantage of EGNOS+SDCM positioning over EGNOS positioning alone in determining the accuracy of the vertical component h. The obtained research results show the significant advantages of the multi-SBAS positioning model in UAV technology.

Consistency of the Empirical Distributions of Navigation Positioning System Errors with Theoretical Distributions-Comparative Analysis of the DGPS and EGNOS Systems in the Years 2006 and 2014

Positioning systems are used to determine position coordinates in navigation (air, land and marine). The accuracy of an object’s position is described by the position error and a statistical analysis can determine its measures, which usually include: Root Mean Square (RMS), twice the Distance Root Mean Square (2DRMS), Circular Error Probable (CEP) and Spherical Probable Error (SEP). It is commonly assumed in navigation that position errors are random and that their distribution are consistent with the normal distribution. This assumption is based on the popularity of the Gauss distribution in science, the simplicity of calculating RMS values for 68% and 95% probabilities, as well as the intuitive perception of randomness in the statistics which this distribution reflects. It should be noted, however, that the necessary conditions for a random variable to be normally distributed include the independence of measurements and identical conditions of their realisation, which is not the case in the iterative method of determining successive positions, the filtration of coordinates or the dependence of the position error on meteorological conditions. In the preface to this publication, examples are provided which indicate that position errors in some navigation systems may not be consistent with the normal distribution. The subsequent section describes basic statistical tests for assessing the fit between the empirical and theoretical distributions (Anderson-Darling, chi-square and Kolmogorov-Smirnov). Next, statistical tests of the position error distributions of very long Differential Global Positioning System (DGPS) and European Geostationary Navigation Overlay Service (EGNOS) campaigns from different years (2006 and 2014) were performed with the number of measurements per session being 900’000 fixes. In addition, the paper discusses selected statistical distributions that fit the empirical measurement results better than the normal distribution. Research has shown that normal distribution is not the optimal statistical distribution to describe position errors of navigation systems. The distributions that describe navigation positioning system errors more accurately include: beta, gamma, logistic and lognormal distributions.