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The purpose of this paper is to perform a comparative study of two propagation models and a prediction of proximity distances among the space objects based on the two-line element set (TLEs) data, which identifies potentially risky approaches and is used to compute the probability of collision among the spacecrafts.

At first, the proximities are estimated for the mentioned satellites using a precise propagation model and based on a one-month simulation. Then, a study is performed to determine the probability of collision between two satellites using a formulation which takes into account the object sizes, covariance data and the relative distance at the point of closest approach. Simplifying assumptions such as a linear relative motion and normally distributed position uncertainties at the predicted closest approach time are applied in estimation.

For the case of Iridium-Cosmos collision and the prediction of a closest approach using available TLE orbital data and a propagation model which takes into account the effects of the earth’s zonal harmonics and drag atmospheric, the maximum probability of about 2 × 10 −6 was obtained, which can indicate the necessity of enacting avoidance maneuvers regarding the defined a probability threshold by satellite’s owner.

The contribution of this paper is to analyze and simulate the 2009 prominent collision between the Cosmos2251 and Iridium33 satellite by modeling their orbit propagation, predicting their closest approaches and, finally, assessing the risk of the possible collision. Moreover, an enhanced orbit determination can be effective to achieve an accurate assessment of the ongoing collision threat to active spacecrafts from orbital debris and preventing, if necessary, the hazards thereof.

For the measurement of large-scale components in aircraft assembly, the evaluation of coordinate transformation parameters between the coordinate frames of individual measurement systems to the assembly frame is an essential task, which is usually completed by registration of the enhanced reference system (ERS) points. This paper aims to propose an analytical method to evaluate the uncertainties of transformation parameters considering both the measurement error and the deployment error of ERS points.

For each measuring station, the measured coordinates of ERS points are first roughly registered to the assembly coordinate system using the singular value decomposition method. Then, a linear transformation model considering the measurement error and deployment error of ERS points is developed, and the analytical solution of transformation parameters’ uncertainties is derived. Moreover, the covariance matrix of each ERS points in the transformation evaluation is calculated based on a new uncertainty ellipsoid model and variance-covariance propagation law.

For the transformation of both single and multiple measuring stations, the derived uncertainties of transformation parameters by the proposed analytical method are identical to that obtained by the state-of-the-art iterative method, but the solution process is simpler, and the computation expenses are much less.

The proposed uncertainty evaluation method would be useful for in-site measurement and optimization of the configuration of ERS points in the design of fixture and large assembly field. It could also be applied to other registration applications with errors on both sides of registration points.

The purpose of the study is focused on implementation of Global Navigation Satellite System (GLONASS) technique in civil aviation for recovery of aircraft position using Precise Point Positioning (PPP) method in kinematic mode.

The aircraft coordinates of Cessna 172 plane in XYZ geocentric frame were obtained based on GLONASS code and phase observations for PPP method. The numerical computations were executed in post-processing mode in the RTKPOST module in RTKLIB program. The mathematical scheme of equation observation of PPP method was solved using Kalman filter in stochastic processing.

In paper, the average accuracy of aircraft position is about 0.308 m for X coordinate, 0.274 m for Y coordinate, 0.379 m for Z coordinate. In case of the mean radial spherical error (MRSE) parameter, the average value equals to 0.562 m. In paper, the accuracy of aircraft position in BLh geodesic frame were also showed and described.

The PPP method can be applied for determination the coordinates of receiver, receiver clock bias, Zenith Wet Delay (ZWD) parameter and ambiguity term for each satellite.

The PPP method is a new technique for aircraft positioning in air navigation. The PPP method can be also used in receiver autonomous integrity monitoring (RAIM) module in aircraft-based augmentation system (ABAS) system in air transport. The typical accuracy for recovery the aircraft position is about cm ÷ dm level using the PPP method.

The paper is destined for people who work in area of geodesy, navigation, aviation and air transport.

The work presents the original research results of implementation the GLONASS satellite technique for recovery the aircraft position in civil aviation. Currently, the presented research PPP method is used in precise positioning of aircraft in air navigation based on global positioning system and GLONASS solutions.

The purpose of this paper is to propose an innovative method to extend the operating range of the laser tracking system and improve the accuracy and automation of boresighting by designing a measurement instrument. Boresighting is a process that aligns the direction of special equipment with the aircraft reference axis. Sometimes the accurate measurement and adjustment of the equipment and the aircraft are hard to achieve.

The aircraft is moved by an automatic adjustment system which consists of three numerical control positioners. For obtaining the position of the bore axis, an instrument with two measurement points is designed. Based on the multivariate normal distribution hypothesis, an uncertainty evaluation method for the aiming points is introduced. The accuracy of the measurement point is described by an uncertainty ellipsoid. A compensation and calibration method is proposed to decrease the effect of manufacturing error and deflection error by the finite element analysis.

The experimental results of the boresighting measurement prove that the proposed method is effective and reliable in digital assembly. The measurement accuracy of the angle between the bore axis and the reference axis is about ±0.004°. In addition, the measurement result is mainly influenced by the position error of the instrument.

The results of this study will provide a new way to obtain and control the installation deviation of part in aircraft digital assembly and will help to improve the precision and efficiency. This measurement method can be applied to obtain the axis of a deep blind hole.

The purpose of this paper is based on implementation of Global Navigation Satellite System (GNSS) technique in civil aviation for recovery of aircraft position using Single Point Positioning (SPP) method in kinematic mode.

The aircraft coordinates in ellipsoidal frame were obtained based on Global Positioning System (GPS) code observations for SPP method. The numerical computations were executed in post-processing mode in the Aircraft Positioning Software (APS) package. The mathematical scheme of equation observation of SPP method was solved using least square estimation in stochastic processing. In the experiment, airborne test using Cessna 172 aircraft on September 07, 2011 in the civil aerodrome in Mielec was realized. The aircraft position was recovery using observations data from Topcon HiperPro dual-frequency receiver with interval of 1 second.

In this paper, the average value of standard deviation of aircraft position is about 0.8 m for Latitude, 0.7 m for Longitude and 1.5 m for ellipsoidal height, respectively. In case of the Mean Radial Spherical Error (MRSE) parameter, the average value equals to 1.8 m. The standard deviation of receiver clock bias was presented in this paper and the average value amounts to 34.4 ns. In this paper, the safety protection levels of Horizontal Protection Level (HPL) and Vertical Protection Level (VPL) were also showed and described.

In this paper, the analysis of aircraft positioning is focused on application the least square estimation in SPP method. The Kalman filtering operation can be also applied in SPP method for designation the position of the aircraft.

The SPP method can be applied in civil aviation for designation the position of the aircraft in Non-Precision Approach (NPA) GNSS procedure at the landing phase. The typical accuracy of aircraft position is better than 220 m for lateral navigation in NPA GNSS procedure. The limit of accuracy of aircraft position in vertical plane in NPA GNSS procedure is not available.

This paper is destined for people who works in the area of aviation and air transport.

The work presents that SPP method as a universal technique for recovery of aircraft position in civil aviation, and this method can be also used in positioning of aircraft based on Global Navigation Satellite System (GLONASS) code observations.

This paper aims to present the problem of the integration of the global positioning system (GPS)/global navigation satellite system (GLONASS) data for the processing of aircraft position determination.

The aircraft coordinates were obtained based on GPS and GLONASS code observations for the single point positioning (SPP) method. The numerical computations were executed in the aircraft positioning software (APS) package. The mathematical scheme of equation observation of the SPP method was solved using least square estimation in stochastic processing. In the research experiment, the raw global navigation satellite system data from the Topcon HiperPro onboard receiver were applied.

In the paper, the mean errors of an aircraft position from APS were under 3 m. In addition, the accuracy of aircraft positioning was better than 6 m. The integrity term for horizontal protection level and vertical protection level parameters in the flight test was below 16 m.

The paper presents only the application of GPS/GLONASS observations in aviation, without satellite data from other navigation systems.

The presented research method can be used in an aircraft based augmentation system in Polish aviation.

The paper is addressed to persons who work in aviation and air transport.

The paper presents the SPP method as a satellite technique for the recovery of an aircraft position in an aviation test.

The purpose of this paper is to study the implementation of GNSS technique in aviation for recovery of aircraft’s position using Precise Point Positioning (PPP) method.

The aircraft’s coordinates in ellipsoidal frame were obtained based on GPS code and phase observations for PPP method. The numerical computations were executed in post-processing mode in the CSRS-PPP and magicPPP online services. The mathematical scheme of PPP method was development using indifference equations of Ionosphere-Free linear combination. In the experiment, airborne test using Cessna 172 aircraft on June 01, 2010 in the military airport in Deblin was realized. The aircraft’s position was determined using data from GNSS receiver (Topcon HiperPro with interval of 1 s).

In this paper, the accuracy of aircraft’s position is better than 0.07 m for CSRS-PPP service and better than 0.27 m for magicPPP service. In case of the Mean Radial Spherical Error parameter, the average value for CSRS-PPP service equals to 0.01 m, whereas for magicPPP, it is about 0.38 m. The values of vertical coordinate of Cessna 172 aircraft were also checked with results of Real Time Kinematic–On The Fly technique.

In this paper, the analysis of aircraft positioning is focused on the application of the PPP method in post-processing mode. In near real time, the PPP method still has limitations, especially in the area of ambiguity resolution and also instrumental biases (e.g. Narrow Lane Hardware Delays).

The PPP method can be applied in aviation in post-processing mode for verification of true aircraft coordinates and elimination of blunder errors from adjustment processing of GNSS observations. The Zenith Wet Delay term as a product of troposphere delay and receiver clock bias as a product of precise time transfer can be obtained in the PPP method.

The paper presents that the PPP method is an alternative solution for the recovery of aircraft’s position in aviation, and this method can be also applied in the positioning of aircraft based on GLONASS or GPS/GLONASS data.

The absolute GPS positioning technique, especially precise point positioning (PPP), has been widely applied in a variety of engineering fields. Since the requirements for horizontal and vertical components of positioning standard deviations vary greatly in different applications, it is necessary to study the method of estimating the horizontal and vertical components of positioning standard deviation. In present paper, under the assumption of approximately superseding the Geoid with the WGS-84 ellipsoid surface, the authors analyze the real implications of the horizontal and vertical components of positioning standard deviation in absolute GPS positioning, then derive the estimate formulae for the horizontal and vertical components of positioning standard deviation by using Bursa-Wolf transformation as well as variance-covariance propagation law. Finally, a calculation example is presented.

In aircraft wing–fuselage assembly, the distributed multi-point support layout of positioners causes fuselage to deform under gravity load, leading to assembly difficulty and assembly stress. This paper aims to propose a hybrid force position control method to balance aerodynamic shape accuracy and deformation of assembly area, thereby correcting assembly deformation and reducing assembly stress.

Force and position control axes of positioners are selected based on screw theory and ellipsoid method. The position-control axes follow the posture trajectory to align the fuselage posture. To exert force on the fuselage and correct the deformations, the force-control axes follow the contact force derived by using orthogonal experiments and partial least squares regression (PLSR). Finite element simulation and one-dimension deformation correction experiment are conducted to verify the validity of this method.

Simulation results indicate that hybrid force position control method can correct assembly deformation and improve the wing–fuselage assembly quality significantly. Experiment on specimen verifies the effect of this method indirectly.

The proposed method gives a solution to solve the deformation problem during aircraft wing-fuselage assembly, thereby reducing assembly stress and improving assembly quality.

This paper aims to propose a reasonable method to evaluate uncertainty of measurement of industrial robots’ orientation repeatability and solve the non-linear problem existing in its evaluation procedure.

Firstly, a measurement model of orientation repeatability, based on laser tracker, is established. Secondly, some factors, influencing the measurement result of orientation repeatability, are identified, and their probability distribution functions are modelled. Thirdly, based on Monte Carlo method, an uncertainty evaluation model and algorithm of measurement of industrial robot’s orientation repeatability are built. Finally, an industrial robot is taken as the research object to validate the rationality of proposed method.

Results show that the measurement model of orientation repeatability of industrial robot is non-linear, and the proposed method can reasonably and objectively estimate uncertainty of measurement of industrial robots’ orientation repeatability.

This paper, based on Monte Carlo method and experimental work, proposes an uncertainty evaluation method of measurement of industrial robots’ orientation repeatability which can solve the non-linear problem and provide a reasonable and objective evaluation. And the stochastic ellipsoid approach is firstly taken to model the repeatability of laser tracker. Additionally, this research is beneficial to decide whether the orientation repeatability of the industrial robot meets its requirements.