New Methodology of Designation the Precise Aircraft Position Based on the RTK GPS Solution

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.

Determination of the geodetic latitude and height by spatial geocentric coordinates

The authors propose to derive the formulas given in [1, 2] for determining the height and latitude based on the Cartesian rectangular coordinates X, Y, Z, giving an accuracy for the geodetic height H of 1 mm for heights up to 50 km and for geodetic latitude B of 0,0001 arc seconds for H < 10 km. The formulas proposed in [1, 2] apply to all values of latitude and longitude (B and L). In [3], we propose two new formulas for H and B. In this paper, it is shown that the formulas proposed in [3] apply to points of ellipsoid surface and points with geodetic latitude of 0° and 90°. For the same formulas proposed in [3], the corrections are derived to ensure an accuracy of H of 1 mm at H ≤ 10 km, which apply to all values of B and L. Basing on the presented geometric conclusions, calculations and analyzes, a new solution for H and B respectively is proposed for given X, Y, Z, which provides an accuracy for H less than 1 mm for H ≤ 100 km and for B of 0,0001 arc seconds for H ≤ 50 km.

Getchell’s method for conversion of Cartesian-geocentric to geodetic coordinates – Its properties and Newtonian alternative

The paper concentrates on the iterative Getchell’s method (formulated in 1972) and its alternative Newtonian implementation for conversion of Cartesian geocentric coordinates into geodetic coordinates. The same basic equation formulated in the Getchell’s method is used in both cases. The equation has a stable form in the whole range of argument (latitude) variation \langle -\pi /2,\pi /2\rangle . The original Getchell’s method (somehow “forgotten”) has a simple geometric interpretation and its applications turn out to be particularly effective. Many studies on iterative algorithms usually omit theoretical proofs of convergence replacing them with conclusions based on numerical examples. This paper presents theoretical proofs of algorithms convergence both for the Getchell’s method and the Newton procedure. The convergence parameter and numerical error of results were estimated in each case. Numerical tests were carried out for a set of points distributed on the Earth’s space, also for extreme h values. For typical practical applications of the Getchell’s method, sufficiently accurate results are obtained after 1–3 iterations, while in the Newton procedure already after one iteration, assuming the same numerical error and initial conditions. The accuracy of the geodetic coordinates determinations meets all practical requirements with some margin. For example an absolute numerical error for latitude is approx. 0.4\cdot {10^{-13}} [rad] i. e. about 0.00026 mm in the length of the meridian arc. The proposed methods were compared with other methods (algorithms), including in terms of stability and non-singularity in the entire usable space of the Earth, but excluding the near geocenter, which has no practical significance. Both the modification of the Getchell method and its Newtonian alternative are very good determined in this area (in the Earth’s poles, the final solution is directly the starting value of iterative algorithms). The discussed algorithms were implemented in the form of procedures in DELPHI language.

New Strategy for Improving the Accuracy of Aircraft Positioning Based on GPS SPP Solution

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.

Aircraft positioning using DGNSS technique for GPS and GLONASS data

Purpose The purpose of this paper is to present the problem of implementation of the differential global navigation satellite system (DGNSS) differential technique for aircraft accuracy positioning. The paper particularly focuses on identification and an analysis of the accuracy of aircraft positioning for the DGNSS measuring technique. Design/methodology/approach The investigation uses the DGNSS method of positioning, which is based on using the model of single code differences for global navigation satellite system (GNSS) observations. In the research experiment, the authors used single-frequency code observations in the global positioning system (GPS)/global navigation satellite system (GLONASS) system from the on-board receiver Topcon HiperPro and the reference station REF1 (reference station for the airport military EPDE in Deblin in south-eastern Poland). The geodetic Topcon HiperPro receiver was installed in Cessna 172 plane in the aviation test. The paper presents the new methodology in the DGNSS solution in air navigation. The aircraft position was estimated using a “weighted mean” scheme for differential global positioning system and differential global navigation satellite system solution, respectively. The final resultant position of aircraft was compared with precise real-time kinematic – on the fly solution. Findings In the investigations it was specified that the average accuracy of positioning the aircraft Cessna 172 in the geocentric coordinates XYZ equals approximately: +0.03 ÷ +0.33 m along the x-axis, −0.02 ÷ +0.14 m along the y-axis and approximately +0.02 ÷ −0.15 m along the z-axis. Moreover, the root mean square errors determining the measure of the accuracy of positioning of the Cessna 172 for the DGNSS differential technique in the geocentric coordinates XYZ, are below 1.2 m. Research limitations/implications In research, the data from GNSS onboard receiver and also GNSS reference receiver are needed. In addition, the pseudo-range corrections from the base stations were applied in the observation model of the DGNSS solution. Practical implications The presented research method can be used in a ground based augmentation system (GBAS) augmentation system, whereas the GBAS system is still not applied in Polish aviation. Social implications The paper is destined for people who work in the area of aviation and air transport. Originality/value The study presents the DGNSS differential technique as a precise method for recovery of aircraft position in civil aviation and this method can be also used in the positioning of aircraft based on GPS and GLONASS code observations.

Determination of the Precise Coordinates of the GPS Reference Station in of a GBAS System in the Air Transport

This paper presents results of research concerning determination of the GPS reference station coordinates located on the grounds of an EPDE airport in Deblin. The study uses a mathematical model of the PPP measurement technique in order to determine the coordinates of the reference station using the real GPS code-phase observations. The computations of the coordinates of the GPS reference station were carried out in numerical applications CSRS-PPP, APPS and GAPS. In this research was found that the accuracy of finding solutions to the XYZ geocentric coordinates of the reference station REF1 between solutions CSRS-PPP, APPS and GAPS ranges from 0.01m to 0.13m. In addition, the accuracy of determining the XYZ geocentric coordinates from the PPP method related to the GPS differential solution ranged from 0.01m to 0.11m.

Accuracy Assessment of Aircraft Positioning Using the Dual-Frequency GPS Code Observations in Aviation

This study publishes results of tests with regard to determination of the aircraft positioning accuracy by means of the GPS navigation in aviation. The research exploits the mathematical model of the linear combination "IonosphereFree" in order to designate the coordinates of an aircraft. The research uses the actual GPS code observations, recorded by a satellite receiver mounted in the Cessna 172, at the time of the experiment for the EPDE military aerodrome in Dęblin. The computations of the position of the Cessna 172 aircraft for the linear combination "Ionosphere-Free" were made in the APS Toolbox v.1.0.0. programme. Within evaluation of accuracy of the GPS positioning in aviation, the determined coordinates of the aircraft Cessna 172 from the APS programme were compared to an accurate reference position from the solution derived by the PPP measurement technique. In the research, the authors obtained an average positioning accuracy of approximately 5 m in the geocentric XYZ coordinates and approximately 4 m in the ellipsoidal BLh coordinates. In addition, the 3D-error parameter is lower than 7 m for the XYZ geocentric coordinates.

Improving geodetic support in construction taking into account zones of tectonic disturbances and application of topocentric coordinates

During the construction and operation of buildings and structures, it is extremely important to ensure the accuracy of their geometrical parameters in nature. At the same time, accuracy requirements are constantly increasing. At the same time, studying such issues as consideration of geological factors, for example, consideration of the structural features of the buildings and structures foundations has remained virtually in the same state for decades. In the guidelines for observing the deformations of the basements and foundations of buildings and structures the earth’s surface is taken as homogeneous array, and it is recommended when observing deformations, to carry out laying initial benchmarks for industrial and civil objects at a distance of 50–100 m. A number of studies show that a homogeneous array should be considered as a special case. In fact, in the construction of various objects, heterogeneity of the soil massif in the form of stratification, as well as the presence of zones of tectonic disturbances are often encountered. The latter, in the form of faults and geopathic zones, are already taken into account in urban planning activities, medicine, and other areas. Without taking them into account, the creation of a geodetic center base during construction can lead to significant errors, due to the uneven deformation of the structure near fault zones. There is a need to assess the impact of these zones during construction and their consideration when creating a geodetic center base. Here it is necessary to emphasize the fact that ensuring the removal of the structure’s geometrical parameters into nature is the task of the geodetic service in any circumstances. The next important point in construction is to minimize the error of projecting geocentric coordinates onto a plane. This is especially true when using satellite coordinates. In the traditional approach, the coordinate basis for construction is normatively oriented to the use of the Gauss-Kruger projection. With extended objects in the latitudinal direction and remoteness from the axial meridian of the six-degree zone, the use of this projection causes transformation errors. When creating a geodesic framework according to satellite coordinates determinations, it is highly advisable to use local to-center topocentric flat surfaces, which allow a significant reduction in the distortion of the transformation. The authors discuss the solution of identified issues and provide specific examples.