Earth-fixed Coordinate System Research Articles

An Earth-fixed observer to ship waves

This work deals with the linear surface waves generated by a vessel advancing at a constant forward speed. These waves, known as ship waves, appear stationary to an observer on the vessel. Rather than exploring the well-studied stationary ship waves, this work delves into the physical properties of ship waves measured at Earth-fixed locations. While it might have been expected that analysing these waves in an Earth-fixed coordinate system would be a straightforward transformation from existing analytical theories in a moving coordinate system, the reality proves to be quite different. The properties of waves measured at fixed locations due to a passing ship turn out to be complex and non-trivial. They exhibit unique characteristics, being notably unsteady and short crested, despite appearing stationary to an observer on the generating vessel. The analytical expressions for the physical properties of these unsteady waves are made available in this work, including the amplitude, frequency, wavenumber, direction of propagation, phase velocity and group velocity. Based on these newly derived expressions and two-point measurements, an inverse method has been presented for determining the advancing speed and the course of motion of the moving ship responsible for the wave generation. The results from this study can be used in a wide range of applications, such as interpreting data from point measurements and assessing the roles of ship waves in transporting ocean particles.

Dual-UAV Collaborative High-Precision Passive Localization Method Based on Optoelectronic Platform

Utilizing the optical characteristics of the target for detection and localization does not require actively emitting signals and has the advantage of strong concealment. Once the optoelectronic platform mounted on the unmanned aerial vehicle (UAV) detects the target, the vector pointing to the target in the camera coordinate system can estimate the angle of arrival (AOA) of the target relative to the UAV in the Earth-centered Earth-fixed (ECEF) coordinate system through a series of rotation transformations. By employing two UAVs and the corresponding AOA measurements, passive localization of an unknown target is possible. To achieve high-precision target localization, this paper investigates the following three aspects. Firstly, two error transfer models are established to estimate the noise distributions of the AOA and the UAV position in the ECEF coordinate system. Next, to reduce estimation errors, a weighted least squares (WLS) estimator is designed. Theoretical analysis proves that the mean squared error (MSE) of the target position estimation can reach the Cramér–Rao lower bound (CRLB) under the condition of small noise. Finally, we study the optimal placement problem of two coplanar UAVs relative to the target based on the D-optimality criterion and provide explicit conclusions. Simulation experiments validate the effectiveness of the localization method.

Pseudolites to Support Location Services in Smart Cities: Review and Prospects

The location service is an important part of the smart city. A unified location service for outdoor and indoor/overground and underground activity will assist the construction of smart cities. However, with different coordinate systems and data formats, it is difficult to unify various positioning technologies on the same basis. Global navigation satellite system (GNSS)-based positioning is the only way to provide absolute location under the Earth-centered, Earth-fixed coordinate system (ECEF). Increasing indoor and underground human activity places significant demand on location-based services but no GNSS signals are available there. Fortunately, a type of satellite that is indoors, known as pseudolite, can transmit GNSS-like ranging signals. Users can obtain their position by receiving ranging signals and their resection without adding or switching other sensors when they go from outdoors to indoors. To complete the outreach of the GNSS indoors and underground to support the smart city, how to adapt the pseudolite design and unify coordinate frames for linking to the GNSS remain to be determined. In this regard, we provide an overview of the history of the research and application of pseudolites, the research progress from both the system side and the user side, and the plans for pseudolite-based location services in smart cities.

A THREE-DIMENSIONAL APPROACH TO IMPROVE THE INTERNATIONAL REFERENCE IONOSPHERE (IRI) MODEL

Abstract. A three-dimensional model based on time and location is introduced to enhance the accuracy of vertical total electron content (VTEC) global ionosphere maps (GIMs) of ionosphere empirical models. The chosen empirical model is the International Reference Ionosphere 2016 (IRI-2016) model and observations are the GIMs VTEC values from Center for Orbit Determination in Europe (CODE). For this purpose, IRI-2016 is considered as a background model and the VTECs from GIMs are considered as the correction term. The correction term is modelled using spherical harmonics expansion base functions with a degree equal to 15 in Earth-fixed coordinate system with a polynomial B-spline base function for time resolution. The improved VTEC maps are constructed on 1st January 2018 with a Kp index of 4. The root mean square error (RMSE) improvements range from 1.65 TECU to 2.81TECU about 70 percent to 85 percent and the bias improvements are from 0.28 TECU to 1.00 TECU with an average of 0.75 TECU, respectively.

Формирование вращающейся электродинамической космической тросовой системы с использованием скользящего режима управления

The paper considers the process of imparting rotation at a given angular velocity to an electrodynamic space tether system in a near-Earth orbit. The tether system is a linear cluster of three microsatellites connected by insulated conductive cables. Initially the system is gravitationally stabilised in the approximate vertical direction. Electromagnetic forces generated in the conductive cables by the geomagnetic field impart rotation to the system. We stated the equations of motion for the system in the Earth-fixed coordinate system, taking into account distributed load produced by gravitational and electromagnetic forces. The system is moving in a fairly high, almost circular orbit, so aerodynamic forces are not taken into account. Adjusting the current will reduce the strain in the tethers. The model under consideration represents those as a set of material points connected by unilateral elastic links. We propose a feedback current controller based on sliding mode control. The system variables lie on a single surface, moving across which ensures asymptotic stability of the control process. We used a simplified system motion model to synthesise the controller parameters. We analysed the angular motion of microsatellites with respect to the tether direction while rotation is imparted to the system. Numerical examples confirm the efficiency of our approach to setting up a rotating space tether system

Earth-Fixed Books Reduce Motion Sickness When Reading With a Head-Mounted Display

There are concerns that viewing two-dimensional (2D) content such as web pages on a head-mounted display (HMD) in the car may aggravate motion sickness. This is because when 2D content is fixed to a head-fixed coordinate system, the appearance of the content does not change even when the body moves; therefore, it is impossible to visually perceive the movement of one’s body, resulting in a sensory conflict between the visual and vestibular senses. A method for reducing motion sickness when displaying 3D content on an HMD has been investigated; however, when displaying 2D content, no such method has been investigated. Therefore, this study aims to verify to the possibility of reducing motion sickness from the change of appearance caused by fixing 2D content to the earth-fixed coordinate system when viewing it with an HMD in a moving environment. Participants sat on a seat that was mounted on a vibrating device and moved in the pitch direction while reading a book on the HMD. Consequently, the severity of motion sickness was significantly lower when the book was fixed to the earth-fixed coordinate system than when fixed to the head-fixed coordinate system. This result suggests that by fixing the content to the earth-fixed coordinate system, motion sickness can be reduced because the movement of one’s body can be perceived through changes in the appearance of the content, and the sensory conflict between visual and vestibular sensations can be resolved.

Projection and integration of connected-infrastructure LiDAR sensing data in a global coordinate

Recently, roadside Light Detection and Ranging (LiDAR) has been deployed for different transportation applications such as high-resolution-micro-traffic data collection, vehicle–pedestrian safety evaluation, and driver’s behavior analysis. An ideal LiDAR-enhanced traffic infrastructure system needs multiple LiDAR sensors deployed around intersections and along road segments, which generate a seamless coverage of intersections or arterials. To obtain continuous and complete traffic data, the integration method is much more important to extend the data range and improve the density of scanned points. In this research, an innovative approach based on the GPS mapping method was present to automatically integrate data collected by different LiDAR sensors in a global coordinate. In this method, the raw data collected by multiple LiDAR sensors are used as input, at least 4 reference points collected by GPS devices are needed for each LiDAR sensor, then a transformation step is applied to transform all the LiDAR points into the Earth-centered, Earth-fixed coordinate system. After obtaining all the LiDAR points in the global coordinate system, an Iterative Closest Point (ICP) method was used to reduce the errors caused by data collection and calculation. The sensitivity analysis part provided the best number for the reference points collection. At last, the data collected at two sites (Evans & McCarran intersection and Blue parking lot of University of Nevada, Reno (UNR) were selected to verify the method. The testing results showed that the proposed method has a high level of automation and improved accuracy.

A broadcast ephemeris design of LEO navigation augmentation satellites based on the integration-type ephemeris model

Low Earth orbit (LEO) satellites are a promising type of navigation augmentation satellite for current global navigation satellite systems. Aiming at the navigation function, an effective broadcast ephemeris model needs to be designed for LEO satellites. An enhanced integration-type broadcast ephemeris model is proposed in this study. First, the short-term periodical variation characteristics of LEOs’ accelerations in the Earth-centered Earth-fixed coordinate system are analyzed. The Chebyshev polynomials and harmonic functions are then applied to represent the variation perturbation of accelerations. Tests using simulated and real data from LEO satellites at altitudes from 600 to 1400 km are conducted to evaluate the fit accuracy of the proposed models in terms of arc length, integration method, integration step length, orbital altitude, inclination, eccentricity, etc. The fit accuracy is dramatically improved compared to that of the current GLONASS integration-type broadcast model, where fit errors less than 10 cm are achieved with an arc length of 20 min.

Experimental Verification of a Pulsar-Based Positioning System Using L-Band Measurements

This paper discusses the observability analysis, the estimation algorithm, the numerical simulation, and the experimental verification of a pulsar-based positioning system. This positioning system relies on the unscented Kalman filter and several open source pulsar timing software libraries to estimate the observatory position in an Earth-fixed coordinate system. Monte Carlo analysis was used to numerically verify the filter implementation. Pulsar time-of-arrival data obtained from L-band measurements were used for the experimental verification. The result of this research indicates that a root-sum-square positioning accuracy of can be achieved after processing 3.5 h of archival data.

A Föld alakja és a geodinamika

Az 1960-as évek végén az ELTE Geofizikai Tanszékén megalakult Űrkutató Csoport és a Budapesti Műszaki Egyetem bázisán, nagyrészt diákköri munka keretében kezdődtek meg a hazai Doppler-geodéziai mérések, melyek célja földfelszíni pontoknak a Föld tömegközéppontjához rögzített koordináta-rendszerben történő helymeghatározása volt, műholdas jelek vételével. A jelen munkában összefoglalt kutatás eredményeként a mérési pontok helymeghatározásának pontossága ugyanabba a nagyságrendbe esett és alig maradt el a NASA által ugyanebben az évtizedben az amerikai űrprogram földi követőállomásainak hasonló módszerrel elvégzett helymeghatározásához képest. Ez a munka jelentette Horváth Ferenc kutatói pályafutásának kezdetét. Cikkünk végén bemutatjuk, hogy az űrgeodézia már ebben az időszakban is kapcsolódott a Föld dinamikai szerkezetének megértéséhez.

EMLR for multiple radars on a mobile platform

Aiming at the problem of radar sensor registration on a mobile platform, this study uses multiple radars to estimate the biases of the radar under the earth-centred earth-fixed coordinate system, which provides more accurate information for data fusion. Compared to the maximum likelihood registration (MLR) algorithm, which can only estimate radar offset biases, a novel extended MLR (EMLR) algorithm is proposed. The algorithm could estimate radar-offset biases, attitude biases, and the target real location simultaneously. The simulation results verified that the EMLR algorithm can effectively improve the precision of registration.

Measurement of particle directions in low earth orbit with a Timepix

In Low Earth Orbit (LEO) in space electronic equipment aboard satellites and space crews are exposed to high ionizing radiation levels. To reduce radiation damage and the exposure of astronauts, to improve shielding and to assess dose levels, it is valuable to know the composition of the radiation fields and particle directions. The presented measurements are carried out with the Space Application of Timepix Radiation Monitor (SATRAM). There, a Timepix detector (300 μm thick silicon sensor, pixel pitch 55 μm, 256 × 256 pixels) is attached to the Proba-V, an earth observing satellite of the European Space Agency (ESA). The Timepix detector's capability was used to determine the directions of energetic charged particles and their corresponding stopping powers. Data are continuously taken at an altitude of 820 km on a sun-synchronous orbit. The particles pitch angles with respect to the sensor layer were measured and converted to an Earth Centred Earth Fixed (ECEF) coordinate system. Deviations from an isotropic field are extracted by normalization of the observed angular distributions by a Geant4 Monte Carlo simulation —taking the systematics of the reconstruction algorithm and the pixelation into account.

GEO space debris flux determination based on earth-fixed coordinate system

An analysis is performed on the space debris flux determination of geosynchronous (GEO) orbit based on earth-fixed coordinate system. As part of the examination, flux contribution from different components of space debris is presented here in order to clarify the linkage between orbital characteristic and resulting flux distribution. The analysis of GEO flux determination based on earth-fixed coordinate system reveals several new insights: 1) Near the GEO equatorial plane, average flux mainly centralizes in two azimuth ranges: the higher priority one, local azimuth close to±90°, mainly contributed from objects with relatively larger inclination; the lower priority one, local azimuth close to 0°, mainly contributed from objects with relatively smaller inclination. 2) Impact flux against geostationary satellites is not unified by longitude. Longitude-dependent flux determination based on earth-fixed frame reveals that impact flux against geostationary satellite near the geopotential wells (105°W and 75°E longitude zones) is about two to three times larger than average. 3) The comparison of flux determination against certain targets based on earth-fixed coordinate system and inertially-fixed coordinate system shows significant difference.

LONG-TERM MONITORING OF WATER DYNAMICS IN THE SAHEL REGION USING THE MULTI-SAR-SYSTEM

Abstract. Fresh water is a scarce resource in the West-African Sahel region, seasonally influenced by droughts and floods. Particularly in terms of climate change, the importance of wetlands increases for flora, fauna, human population, agriculture, livestock and fishery. Hence, access to open water is a key factor. Long-term monitoring of water dynamics is of great importance, especially with regard to the spatio-temporal extend of wetlands and drylands. It can predict future trends and facilitate the development of adequate management strategies. Lake Tabalak, a Ramsar wetland of international importance, is one of the most significant ponds in Niger and a refuge for waterbirds. Nevertheless, human population growth increased the pressure on this ecosystem, which is now degrading for all uses. The main objective of the study is a long-term monitoring of the Lake Tabalak’s water dynamics to delineate permanent and seasonal water bodies, using weather- and daytime-independent multi-sensor and multi-temporal Synthetic Aperture Radar (SAR) data available for the study area. Data of the following sensors from 1993 until 2016 are used: Sentinel-1A, TerraSARX, ALOS PALSAR-1/2, Envisat ASAR, RADARSAT-1/2, and ERS-1/2. All SAR data are processed with the Multi-SAR-System, unifying the different characteristics of all above mentioned sensors in terms of geometric, radiometric and polarimetric resolution to a consistent format. The polarimetric representation in Kennaugh elements allows fusing single-polarized data acquired by older sensors with multi-polarized data acquired by current sensors. The TANH-normalization guarantees a consistent and therefore comparable description in a closed data range in terms of radiometry. The geometric aspect is solved by projecting all images to an earth-fixed coordinate system correcting the brightness by the help of the incidence angle. The elevation model used in the geocoding step is the novel global model produced by the TanDEM-X satellite mission. The advantage of the Multi-SAR-System is that it comprises ortho-rectification, radiometric enhancement, normalization and Kennaugh decomposition, independent from sensors, modes, polarizations or acquisition date of SAR data. In addition, optical satellite data can be included as well, to fill gaps where SAR data are missing due to the special normalization scheme. This kind of pre-processing is exclusively implemented at the Earth Observation Center of the German Aerospace Center in Oberpfaffenhofen, Germany. Therefore, the dynamic change of the open water of the Lake Tabalak could be classified over dry and rainy seasons and years, using different SAR data. The study provides a unique database and contributes to a better understanding of wetland systems in the Sahel region influenced by human pressure and climate change.

LONG-TERM MONITORING OF WATER DYNAMICS IN THE SAHEL REGION USING THE MULTI-SAR-SYSTEM

Fresh water is a scarce resource in the West-African Sahel region, seasonally influenced by droughts and floods. Particularly in terms of climate change, the importance of wetlands increases for flora, fauna, human population, agriculture, livestock and fishery. Hence, access to open water is a key factor. Long-term monitoring of water dynamics is of great importance, especially with regard to the spatio-temporal extend of wetlands and drylands. It can predict future trends and facilitate the development of adequate management strategies. Lake Tabalak, a Ramsar wetland of international importance, is one of the most significant ponds in Niger and a refuge for waterbirds. Nevertheless, human population growth increased the pressure on this ecosystem, which is now degrading for all uses. The main objective of the study is a long-term monitoring of the Lake Tabalak’s water dynamics to delineate permanent and seasonal water bodies, using weather- and daytime-independent multi-sensor and multi-temporal Synthetic Aperture Radar (SAR) data available for the study area. Data of the following sensors from 1993 until 2016 are used: Sentinel-1A, TerraSARX, ALOS PALSAR-1/2, Envisat ASAR, RADARSAT-1/2, and ERS-1/2. All SAR data are processed with the Multi-SAR-System, unifying the different characteristics of all above mentioned sensors in terms of geometric, radiometric and polarimetric resolution to a consistent format. The polarimetric representation in Kennaugh elements allows fusing single-polarized data acquired by older sensors with multi-polarized data acquired by current sensors. The TANH-normalization guarantees a consistent and therefore comparable description in a closed data range in terms of radiometry. The geometric aspect is solved by projecting all images to an earth-fixed coordinate system correcting the brightness by the help of the incidence angle. The elevation model used in the geocoding step is the novel global model produced by the TanDEM-X satellite mission. The advantage of the Multi-SAR-System is that it comprises ortho-rectification, radiometric enhancement, normalization and Kennaugh decomposition, independent from sensors, modes, polarizations or acquisition date of SAR data. In addition, optical satellite data can be included as well, to fill gaps where SAR data are missing due to the special normalization scheme. This kind of pre-processing is exclusively implemented at the Earth Observation Center of the German Aerospace Center in Oberpfaffenhofen, Germany. Therefore, the dynamic change of the open water of the Lake Tabalak could be classified over dry and rainy seasons and years, using different SAR data. The study provides a unique database and contributes to a better understanding of wetland systems in the Sahel region influenced by human pressure and climate change.

Time-domain simulation of berthing problem between FPSO and shuttle tanker in waves

A time-domain simulation method based on potential flow model has been developed to investigate the berthing problem between two floating bodies in wave. The boundary value problem is formulated with respect to an earth-fixed coordinate system because the relative positions of the two vessels continuously change during the berthing operation. The classical finite element method is used to solve the Laplace equation in the fluid domain with moving boundary. The linearized free-surface boundary conditions are integrated in time by applying 4th-order Adams–Bashforth–Moulton method. A simple re-mesh algorithm with local and global mesh systems is introduced to update mesh by considering large horizontal movement of the berthing vessel. The developed numerical method is used to investigate the berthing problem between a FPSO and shuttle tanker in waves. The focus is on the wave-induced motion response during the berthing process. The characteristics of the motion responses in berthing operation are examined with various wave frequencies, berthing speeds and wave headings.

Compact North Finding System

The knowledge of orientation of an object with respect to the earth-fixed reference coordinate system is crucial in many applications. For instance, in oil mining, it is very crucial to accurately know the orientation of the drilling equipment under the earth surface to drill through the desired path. In this context, we propose a compact inertial sensor system that estimates the instantaneous orientation of the system using an accelerometer and a gyroscope-derived tilt and azimuth angles. To keep the system size small, we use two-axis accelerometer and one-axis gyroscope. In addition, to avoid high sensor cost, the sensor biases are removed using the indexing method. The proposed system estimates the orientation of the compact system in almost all of the orientations, and, additionally, it also provides the measurement accuracy and integrity values that help in ascertaining the validity of the orientation estimate.

A sequential converted measurement Kalman filter in the ECEF coordinate system for airborne Doppler radar

For an airborne Doppler radar, the carrying platform is moving and has time-varying attitudes. The filtering algorithms applicable to local coordinate system are not suitable anymore. In this paper, we propose a sequential converted measurement Kalman filter (SCMKF) with Doppler, which is based on the earth-centered earth-fixed (ECEF) coordinate system. First, to effectively utilize Doppler measurement with probable correlation with slant range, the correlated Doppler and range are decorrelated by the Cholesky factorization. The range component remains unchanged while the Doppler component is changed. Second, by a series of coordinate transformations with unchanged range component and other observations, the converted position measurement is obtained. Meanwhile, the corresponding error covariance is derived by using Taylor series expansion. With the resulting converted measurement and covariance, the target state is filtered by the converted measurement Kalman filter (CMKF), which is extended to the ECEF system. Finally, the filtered state is updated sequentially with the changed Doppler. Compared with the posterior Cramer–Rao lower bound as well as the CMKF, the proposed SCMKF is shown to be an efficient solution, and is superior to the CMKF. Although the gain brought from low-accuracy Doppler is limited, the introduction of high-accuracy Doppler can improve tracking performance significantly.

GEO objects spatial density and collision probability in the Earth-centered Earth-fixed (ECEF) coordinate system

The geostationary (GEO) ring is a valuable orbital region contaminated with an alarming number of space debris. Due to its particular orbital characters, the GEO objects spatial distribution is very susceptible to local longitude regions. Therefore the local longitude distribution of these objects in the Earth-centered Earth-fixed (ECEF) coordinate system is much more stable and useful in practical applications than it is in the J2000 inertial coordinate system. In previous studies of space debris environment models, the spatial density is calculated in the J2000 coordinate system, which makes it impossible to identify the spatial distribution in different local longitude regions. For GEO objects, this may bring potent inaccuracy. In order to describe the GEO objects spatial distribution in different local longitude regions, this paper introduced a new method which can provide the spatial density distribution in the ECEF coordinate system. Based on 2014/12/10 two line element (TLE) data provided by the US Space Surveillance Network, the spatial density of cataloged GEO objects are given in the ECEF coordinate system. Combined with the previous studies of “Cube” collision probability evaluation, the GEO region collision probability in the ECEF coordinate system is also given here. The examination reveals that GEO space debris distribution is not uniform by longitude; it is relatively centered about the geopotential wells. The method given in this paper is also suitable for smaller debris in the GEO region. Currently the longitudinal-dependent analysis is not represented in GEO debris models such as ORDEM or MASTER. Based our method the further version of space debris environment engineering model (SDEEM) developed by China will present a longitudinal independent GEO space debris environment description in the ECEF coordinate system.

Hydrodynamic interaction between two barges during berthing operation in regular waves

In this study, the berthing problem in waves is numerically investigated by a time-domain simulation method based on a potential flow model. The boundary value problem for a berthing operation is formulated with respect to an earth-fixed coordinate system. The Laplace equation of a moving boundary problem is solved using the finite element method by adopting an efficient re-mesh algorithm. The developed numerical method is applied to investigate the berthing problem between two rectangular barges, with particular focus on the hydrodynamic forces acting on the barges during the berthing process. It is assumed that the two barges correspond to installation and transportation barges. To simplify the berthing problem, the transportation barge is assumed to approach the installation barge along a straight path at constant speed. The hydrodynamic force responses during berthing operation are investigated via a series of numerical computations. Further, the effects of wave heading and wave frequency are investigated. To validate present numerical results, model tests were conducted in the Ocean Engineering Basin of KRISO. The berthing tests were performed using two barge models under the head and beam sea conditions. Fairly good agreement is observed between the numerical simulation and experimental results.