This article presents a novel method for validating compass devices. To this end, the post-processing method was used, i.e., the previously recorded vessel’s heading from three compass devices was applied. A spectral analysis of the recorded heading in the frequency domain was conducted by applying the fast Fourier transform method. Based on a synthetic summary of the results of spectral analysis in the heading error frequency domain, the factors causing errors of low-frequency compass device indications, manifested by the vessel’s yawing due to the vessel steering errors on the pre-determined course and the external factors causing total drift of the vessel, were eliminated. To this end, the convolution functions in the form of the sum of input signals with an impulse response, i.e., the filter with a finite impulse response (FIR) and with an infinite impulse response (IIR), were used to compare the effectiveness of the methods estimating the vessel’s heading. The final stage of the research process in the methodology applied was the use of state- and time-discrete Markov processes whose task is to determine the matrices of the intensity of transitions between the states of individual compass systems. Full article

The paper presents the results of research on improving the accuracy of aircraft positioning using RTK-OTF (Real Time Kinematic–On The Fly) technique in air navigation. The paper shows a new solution of aircraft positioning for the application of the differential RTK-OTF technique in air navigation. In particular, a new mathematical model is presented which makes it possible to determine the resultant position of an aircraft based on the solution for the method of least squares in a stochastic process. The developed method combines in the process of alignment of GPS (Global Positioning System) observations, three independent solutions of the aircraft position in OTF mode for geocentric coordinates XYZ of the aircraft. Measurement weights as a function of the vector length and the mean vector length error, respectively, were used in the calculations. The applied calculation method makes it possible to determine the resultant position of the aircraft with high accuracy: better than 0.039 m with using the measurement weight as a function of the vector length and better than 0.009 m with the measurement weight as a function of the mean error of the vector length, respectively. In relation to the classical RTK-OTF solution as a model of the arithmetic mean, the proposed method makes it possible to increase the accuracy of determination of the aircraft position by 45–46% using the measurement weight as a function of the vector length, and 86–88% using the measurement weight as a function of the mean error of the vector length, respectively. The obtained test results show that the developed method improves to significantly improve the accuracy of the RTK-OTF solution as a method for determining the reference position in air navigation. Full article

Radio frequency fingerprinting (RFF) methods are becoming more and more popular in the context of identifying genuine transmitters and distinguishing them from malicious or non-authorized transmitters, such as spoofers and jammers. RFF approaches have been studied to a moderate-to-great extent in the context of non-GNSS transmitters, such as WiFi, IoT, or cellular transmitters, but they have not yet been addressed much in the context of GNSS transmitters. In addition, the few RFF-related works in GNSS context are based on post-correlation or navigation data and no author has yet addressed the RFF problem in GNSS with pre-correlation data. Moreover, RFF methods in any of the three domains (pre-correlation, post-correlation, or navigation) are still hard to be found in the context of GNSS. The goal of this paper was two-fold: first, to provide a comprehensive survey of the RFF methods applicable in the GNSS context; and secondly, to propose a novel RFF methodology for spoofing detection, with a focus on GNSS pre-correlation data, but also applicable in a wider context. In order to support our proposed methodology, we qualitatively investigated the capability of different methods to be used in the context of pre-correlation sampled GNSS data, and we present a simulation-based example, under ideal noise conditions, of how the feature down selection can be done. We are also pointing out which of the transmitter features are likely to play the biggest roles in the RFF in GNSS, and which features are likely to fail in helping RFF-based spoofing detection. Full article

This paper presents a PREcise and Fast Method of Ambiguity Reinitialization/Resolution (PREFMAR) for L1 and L2 in GPS measurements. The method determines NL1 and NL2 ambiguities based on the ambiguity functions: Ψ(NL1)NL1NL2 and Ψ(NL2)NL2NL1. These ambiguity functions have been described in detail in this work. The developed method of ambiguity initialization and reinitialization in relative positioning can use Global Positioning System (GPS) measurements from only two satellites and one measurement epoch. To resolve NL1 and NL2 ambiguities, a variance-covariance (VC) matrix of the float solution is not needed. The size of the search area in the PREFMAR method depends on code and phase accuracy as well as on the GNSS signal frequencies. Therefore, the search area is specific for every double or triple Global Navigation Satellite Systems (GNSS) data frequency. However, this part of the research only presents the ambiguity search area for L1 and L2 of GPS measurements. Additionally, a numerical example has been analyzed in detail with the use of the PREFMAR method and a float solution (NL1, NL2). Finally, the elaborated algorithms were successfully tested on real L1 and L2 GPS measurements for instantaneous ambiguity reinitialization. The PREFMAR method allows instantaneous ambiguity reinitialization if all satellites lose contact with a GNSS antenna, for short and long baselines. Therefore, the PREFMAR has a great potential for precise real-time kinematic GNSS navigation. Full article

This paper presents DGNSS network code positioning using permanent geodetic networks, commonly used in GNSS measurements. Using several reference stations at the same time allows for the independent control of GNSS positioning and facilitates the more realistic estimation of accuracy. Test calculations were made on the basis of real GPS data, using one TRIMBLE mobile receiver and four nearest reference stations of the ASG-EUPOS geodetic system. In addition, DGNSS positioning computational simulations were performed for a case where one mobile GNSS receiver would be able to be used with two (e.g., GPS + Galileo or GPS + GLONASS) or four different positioning systems and different GNSS reference station systems at the same time. To reduce the deviations of the DGPS positioning from a true value, the Kalman filtering for horizontal coordinates and vertical ones was used. The result shows a significant improvement in DGPS positioning accuracy. Based on the numerical analysis carried out, it can be seen that when four GNSS systems are used, it is possible to achieve a DGNSS accuracy of 0.1 m and 0.2 m for horizontal and height coordinates, respectively, using only code measurements. Additionally, the paper presents the impact of the DGNSS code positioning accuracy on the effectiveness of determining ambiguities of phase observations on individual measurement epochs, using the L1–L5 observations of the GPS system and the precise and fast method of ambiguity resolution (PREFMAR). The developed DGNSS positioning methodology can be applied for reliable GNSS navigation using at least two independent GNSS systems. Full article

The paper describes and presents a new calculation strategy for the determination of the aircraft’s resultant position using the GPS (Global Positioning System) SPP (Single Point Positioning) code method. The paper developed a concept of using the weighted average model with the use of measuring weights to improve the quality of determination of the coordinates and accuracy of GPS SPP positioning. In this research, measurement weights were used as a function of the number of GPS satellites being tracked, and geometric PDOP (Position Dilution of Precision) coefficient. The calculations were made using navigation data recorded by two independent GPS receivers: Thales Mobile Mapper and Topcon HiPerPro. On the basis of the obtained results, it was found that the RMS (Root Mean Square) accuracy of positioning for XYZ geocentric coordinates was better than 1.2% to 33.7% for the weighted average method compared to a single GPS SPP solution. The proposed approach is therefore of practical application in air navigation to improve the quality of aircraft positioning. Full article

This paper presents the concept of precise navigation based on SBAS technology and CORS stations. In a kinematic test, three rover Global Positioning System (GPS) receivers, properly spaced relatively to each other, were used in order to estimate reliable and redundant GPS/EGNOS positions. Next, the Kalman filter was employed to give the final solution. It was proven that EGNOS positioning allows to obtain an accuracy in the range of about 0.5–1.5 m. The proposed solution involving the use of three mobile receivers and Kalman filtering allowed to reduce the 3D error to a level below 0.3 m. Such an accuracy was achieved using only GPS L1 code observations and EGNOS corrections. Additionally, a reliable monitoring of quality of GPS/EGNOS positioning in the test area based on CORS stations was presented. Full article

The aim of this paper is to present the problem of the implementation of the EGNOS (European Geostationary Navigation Overlay Service) data for the processing of aircraft position determination. The main aim of the research is to develop a new computational strategy which might improve the performance of the EGNOS system in aviation, based on navigation solutions of an aircraft position, using several GNSS (Global Navigation Satellite System) onboard receivers. The results of an experimental test conducted by the Cessna 172 at EPDE (European Poland Deblin) (ICAO (International Civil Aviation Organization) code, N51°33.07’/E21°53.52’) aerodrome in Dęblin are presented and discussed in this paper. Two GNSS navigation receivers with the EGNOS positioning function for monitoring changes in the parameters of the aircraft position in real time during the landing phase were installed onboard a Cessna 172. Based on obtained research findings, it was discovered that the positioning accuracy was not higher than 2.1 m, and the integrity of positioning did not exceed 19 m. Moreover, the availability parameter was found to equal 1 (or 100%); also, no intervals in the continuity of the operation of the EGNOS system were recorded. In the paper, the results of the air test from Dęblin were compared with the parameters of positioning quality from the air test conducted in Chełm (ICAO code: EPCD, N51°04’57.8” E23°26’15”). In the air test in Chełm, the obtained parameters of EGNOS quality positioning were: better than 4.9 m for accuracy, less than 35.5 m for integrity, 100% for availability, and no breaks in continuity. Based on the results of the air tests in Dęblin and Chełm, it was concluded that the parameters of the EGNOS positioning quality in aviation for the SBAS (Satellite Based Augmentation System) APV (Approach to Vertical guidance) procedure were satisfied in accordance with the ICAO (International Civil Aviation Organization) requirements. The presented research method can be utilized in the SBAS APV landing procedure in Polish aviation. In this paper, the results of PDOP (Position Dilution of Precision) are presented and compared to the two air tests in Dęblin and Chełm. The maximum results of PDOP amounted to 1.4 in the air test in Dęblin, whereas they equaled 4.0 in the air test in Chełm. The paper also shows how the EGNOS system improved the aircraft position in relation to the only GPS solution. In this context, the EGNOS system improved the aircraft position from about 78% to 95% for each ellipsoidal coordinate axis. Full article

This paper presents a precise and fast method of ambiguity resolution (PREFMAR) for frequencies L1/E1 and L5/E5a of GPS/GALILEO data. The developed method is designed for precise and fast determination of ambiguities in GNSS phase observations. Ambiguities are chosen based on mathematical search functions. The fact that no variance–covariance matrix (VC matrix) with a so-called float solution is needed proves the innovativeness of the developed method. The developed method enables determination of the ambiguities for short baseline double-difference (DD) observations. The presented algorithms for the developed method enable unique and reliable calculation of the ambiguity if the actual errors of code measurements of DD observations are less than 0.38 m and the relative errors of phase observations are in the range of ±3 cm. The paper presents both mathematical derivations of the functions used in the PREFMAR and numerical calculations based on real double-difference GPS observations (L1-L5). The elaborated algorithms can be easily implemented into GNSS receivers or mobile phones. Therefore, they can be widely used in many geoscience applications, as well as in precise GPS/GALILEO navigation. Full article