Earth-fixed Coordinate System Research Articles

The method and experiment analysis of two-way common-view satellite time transfer for compass system

Time synchronization between ground and satellites is a key technology for satellite navigation system. With dual-channel satellite, a method called Two-Way Common-View (TWCV) satellite time transfer for Compass system is proposed, which combines both characteristics of satellite common-view and two-way satellite-ground time transfer. By satellite-ground two-way pseudo-range differencing and two stations common-view differencing, this TWCV method can completely eliminate the influence of common errors, such as satellite clock offset, ephemeris errors, troposphere delay and station coordinates errors. At the same time, ionosphere delay related to signal frequency is also weakened significantly. So the precision of time transfer is improved much more greatly than before. In this paper, the basic principle is introduced in detail, the effect of major errors is analyzed and the practical calculation model in the Earth-fixed coordinate system for this new method is provided. Finally, experiment analysis is conducted with actual Compass observing data. The results show that the deviation and the stability of the satellite dual channel can be better than 0.1 ns, and the accuracy of the two-way common-view satellite time transfer can achieve 0.4 ns. All these results have verified the correctness of this TWCV method and model. In addition, we compare this TWCV satellite time transfer with the independent C-band TWSTFT (Two-Way Satellite Time and Frequency Transfer). It shows that the result of the TWCV satellite time transfer is in accordance with the C-band TWSTFT result, which further suggests that the TWCV method is a remote high precision time transfer technique. The research results in this paper are very important references for the development and application of Compass satellite navigation system.

Estimation fusion with radar and ADS-B for air traffic surveillance

The surveillance sensor that has been mainly used for target tracking in air traffic control (ATC) environment is radar. The automatic dependent surveillance - broadcasting (ADS-B), which is based on the technologies of global navigation satellite systems (GNSS), is recently participating in ATC systems for more accurate and reliable surveillance. Although ADS-B provides more accurate and a wider variety of measurements than does radar, it needs careful considerations for the application of the ATC systems. This is due to the fact that the reliability of ADS-B measurements is dependent upon each aircraft whereas that of radar is not. This study proposes a practical system for the estimation fusion of multiple heterogeneous sensors, which includes radar and ADS-B, whose measurements and sensor characteristics are different from one another. A centralized fusion architecture for the data that are received asynchronously from multiple sensors is adopted for the optimum estimation fusion. The three-dimensional earth-centered earth-fixed (ECEF) coordinate system is used for the common coordinates for preprocessing and filtering in order to avoid the registration errors, which can occur in two-dimensional coordinates with a stereographic projection at the system center. In case of the ADS-B, the validity of the sensor data for each aircraft is primarily checked using the accuracy and integrity information of the aircraft. Another important validation for the ADS-B is performed using a comparison of the ADS-B data with the radar data because the ADS-B validation information from each aircraft may not be fully reliable. Furthermore, additional measurements from the downlinked aircraft parameters (DAP), which are available in mode-S radar and ADS-B, are incorporated into state estimation. A variable-sized measurement vector and matrix are used for the tracking filter in order to dynamically reflect the availability of the additional measurements. The simulation results indicate that the proposed fusion system can improve the tracking performance with the advantages of different types of surveillance sensors.

Tracking a Maneuvering Target in Clutter by Asynchronous and Heterogeneous Sensors on Single Airborne Platform

A new algorithm is proposed for tracking a maneuvering target in clutter using heterogeneous sensors, such as active and passive sensors, which are carried on single moving airborne platform and report their observations asynchronously. The algorithm combining interacting multiple model (IMM) with probabilistic data association filter (PDAF) is sequentially implemented to cope with asynchronous reports. In addition, in order to close to practice, the algorithm is based on Earth-centered Earth-fixed (ECEF) coordinate system while it considers the effect of the platform’s attitude. So the algorithm extends previous algorithms from synchronous case to asynchronous case, from fixed station to moving airborne platform, and from local Cartesian coordinates to general ECEF coordinates. The simulation results show that the proposed algorithm has a broader and more practical scope while being slightly worse than existing algorithm which only be applied under synchronous case.

An Optimal Resolution Steering Method for Geosynchronous Orbit SAR

For satellites in geosynchronous orbit (GEO) using synthetic aperture radar (SAR), the direction of the satellite velocity vector in the Earth-centered, Earth-fixed (ECEF) coordinate system varies widely in one orbital period. When the velocity vector is approximately parallel to the range direction at equatorial latitudes, the 2-D sidelobes of the generalized ambiguity function (GAF) on the ground are non-orthogonal, which results in a significant deterioration in the ground resolution. To improve the ground resolution, this study investigates an optimal resolution steering (ORS) method for GEO SAR. The ORS method differs from the total zero Doppler steering (TZDS) method, which attempts to minimize the Doppler centroid. In the ORS method, a beam pointing direction is derived based on the constraints of optimal ground resolution. Then, a 2-D roll-pitch strategy is derived to obtain small steering angles, and the beam is steered to the optimal beam pointing direction. Finally, the ORS method is verified with simulations.

Three-dimensional adjustment of integrated geodetic observables in Earth-centred and Earth-fixed coordinate system

The demand for integrated adjustment of different geodetic observables arose from practical reasons. The popular basic concept of the seventies and sixties was reconsidered. A new procedure was developed for the adjustment of precise geodetic observables, by which the astro-gravimetric data—geoid undulations and deflections of the vertical—can be taken into account in different ways. New “quasi-linear” observation equations were introduced for geodetic total stations measurement, which have a more convenient numerical advantage with respect to traditional approach. The method is tested and demonstrated by field measurements. Rotational residuals and additional parameters—scale differences and antenna phase centre offsets—can be used to handle the outliers of GNSS baseline components aided by proper statistical tests. The common application of GNSS baselines and levelled height differences proved to be an efficient tool to improve the height component of local 3D networks. If the deflections of the vertical are comparable to the accuracy of geodetic total station measurements the integrated adjustment is preferable.

Relativistic time transfer in the vicinity of the Earth and in the solar system

The algorithms for relativistic time transfer in the vicinity of the Earth and in the solar system are derived. The concepts of proper time and coordinate time are distinguished. The coordinate time elapsed during the transport of a clock and the propagation of an electromagnetic signal is analysed in three coordinate systems: an Earth-Centred Inertial (ECI) coordinate system, an Earth-Centred Earth-Fixed (ECEF) coordinate system and a barycentric coordinate system. The timescales of Geocentric Coordinate Time (TCG), Terrestrial Time (TT) and Barycentric Coordinate Time (TCB) are defined and their relationships are discussed. Some numerical examples are provided to illustrate the magnitudes of the effects.

CHARGED PARTICLES AND THE ELECTRO-MAGNETIC FIELD IN NONINERTIAL FRAMES OF MINKOWSKI SPACE–TIME II: "APPLICATIONS: ROTATING FRAMES, SAGNAC EFFECT, FARADAY ROTATION, WRAP-UP EFFECT"

We apply the theory of noninertial frames in Minkowski space–time, developed in the previous paper, to various relevant physical systems. We give the 3 + 1 description without coordinate singularities of the rotating disk and the Sagnac effect, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system. Then we study properties of Maxwell equations in noninertial frames like the wrap-up effect and the Faraday rotation in astrophysics.

Use of body-fixed coordinate system in analysis of weakly nonlinear wave–body problems

When a weakly nonlinear wave–body problem is considered in an inertial coordinate system, high-order derivatives appear in the higher-order body boundary conditions and make it difficult to get convergent and accurate results, especially for bodies with sharp corners or high surface curvatures. In this paper, a new method taking the advantage of the accelerated body-fixed coordinate system is proposed to avoid derivatives of the velocity potential on the right-hand side of the body boundary conditions. A domain decomposition method is applied with the use of the body-fixed coordinate system in the inner domain and the Earth-fixed coordinate system in the outer domain. The second-order radiation and diffraction of bodies with and without sharp corner are studied in the time domain and verified. A numerical beach is applied. Unlike the other methods which transfer the high-order derivatives to lower-order ones by using Stokes-like theorems, it is straightforward to generalize the present method to higher than second-order radiation problems and to the nonlinear wave–body analysis when the forward speed or current is included.

CHARGED PARTICLES AND THE ELECTRO-MAGNETIC FIELD IN NONINERTIAL FRAMES OF MINKOWSKI SPACE-TIME I: ADMISSIBLE 3 + 1 SPLITTINGS OF MINKOWSKI SPACE-TIME AND THE NONINERTIAL REST FRAMES

By using the 3 + 1 point of view and parametrized Minkowski theories we develop the theory of noninertial frames in Minkowski space-time. The transition from a noninertial frame to another one is a gauge transformation connecting the respective notions of instantaneous three-space (clock synchronization convention) and of the three-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the noninertial rest-frame one. We show that every isolated system can be described as an external decoupled noncovariant canonical center of mass (described by frozen Jacobi data) carrying a pole–dipole structure: the invariant mass and an effective spin. Moreover we identify the constraints eliminating the internal three-center of mass inside the instantaneous three-spaces.In the case of the isolated system of positive-energy scalar particles with Grassmann-valued electric charges plus the electro-magnetic field, we obtain both Maxwell equations and their Hamiltonian description in noninertial frames. Then by means of a noncovariant decomposition we define the noninertial radiation gauge and we find the form of the noncovariant Coulomb potential. We identify the coordinate-dependent relativistic inertial potentials and we show that they have the correct Newtonian limit.In the second paper we will study properties of Maxwell equations in noninertial frames like the wrap-up effect and the Faraday rotation in astrophysics. Also the 3 + 1 description without coordinate-singularities of the rotating disk and the Sagnac effect will be given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.

Nonlinear Dynamic Simulation of a Tethered Aerostat: A Fidelity Study

Full-scale flight tests of an instrumented TCOM 71M tethered aerostat conducted by the U.S. Army provide a database for determining the fidelity of the TCOM nonlinear dynamic simulation. Six global position system sensors, accurate to ±5 cm, determined the position and attitude of the aerostat, and winds were measured using a three-axis anemometer mounted on the aerostat's fin near the tip. A 32-min window of data was selected for comparison with the simulation, using the recorded winds to derive a turbulence table. This required correcting the winds for aerostat velocity and transforming to an Earth-fixed coordinate system aligned with the mean aerostat heading. Best results were obtained when the turbulence was propagated through the reference point with uniform flow over the aerostat, rather than the segmented hull with nonuniform flow

Satellite geodesy on curved space-time manifolds. Earth-fixed charts

The reformulation of geodetic measurement processes within the framework of general relativity is discussed. The metric tensor plays an important role in general relativity and has to be represented with respect to a set of appropriate charts. Almost every quantity of interest in geodetic or geophysical applications refers to a geocentric, Earth-fixed coordinate system (chart), therefore they are of great importance in geodesy and geophysics. The space–time metric with respect to an Earth-fixed chart is derived at first post-Newtonian order. The field equations determining the terrestrial gravitational field are derived and its explicit representation is outlined. The impact of the results on the modelling of geodetic measurement processes including space–time positioning scenarios as well as the high-precision gravitational field estimation is outlined.

Sensor alignment with Earth-centered Earth-fixed (ECEF) coordinate system

In this work, we formulate the multiple sensor alignment problem in an Earth-centered Earth-fixed (ECEF) coordinate system. The alignment algorithm maps the sensor measurements to the ECEF coordinates using a geodetic transformation, and attributes the discrepancies in the Earth-referenced system reported by each sensor to the sensor biases. Sensor biases are then estimated using the least squares (LS) technique. Simulated and real-life radar data are used to evaluate the performance of the proposed algorithm. Comparisons are made to those algorithms based on the standard stereographic projection.

Performance of sensor alignment with earth-referenced coordinate systems for multisensor data fusion

We consider the problem of sensor alignment for multisensor data fusion. A least squares (LS) sensor alignment algorithm is formulated using the earth-centered earth-fixed (ECEF) coordinate system. Perturbation analysis is carried for the ECEF-LS algorithm in the presence of sensor elevation measurement errors. A modified generalized least squares (MGLS) alignment approach is proposed that is applicable to 2-D sensor fusion systems and a computationally stable algorithm is developed to obtain the MGLS solution. Computer simulations are used to show the effectiveness of the proposed alignment algorithm.

How to Compute Interval Inclusions of Geodetic Coordinates from Interval Inclusions of Cartesian Coordinates

In satellite geodesy the position of a point P is usually determined by computing its coordinate vector x with respect to an earth-fixed Cartesian coordinate system S. S is chosen such that a rotational ellipsoid E, closely approximating the surface of the earth, has normal form with respect to S. Since the geodetic coordinates of P with respect to E (ellipsoidal latitude ϕ, ellipsoidal longitude λ, and ellipsoidal height h) describe the location of P with respect to the surface of the earth much better than x, a frequently appearing problem is to compute ϕ, λ, and h from x.

Digital Technique for Generating Synthetic Aperture Radar Images

This paper describes a digital processing method applicable to a synthetic aperture radar, to be carried by the space shuttle or by satellites. The method uses an earth-fixed coordinate system in which corrective procedures are invoked to compensate for errors introduced by the satellite motion, earth curvature, and wavefront curvature. Among the compensations discussed are those of the coordinate system, skewness, roll, pitch, yaw, earth rotation, and others. The application of a Fast Fourier Transform in the numerical processing of the two-dimensional convolution is discussed in detail.

Parallel and perpendicular electric fields in an aurora

Previously reported results of a rocket borne electric field experiment flown near local midnight from Andenes, Norway have been transformed to an Earth-fixed coordinate system and compared with plasma temperature and density measurements, energetic particle fluxes, and perpendicular electric field variations, to strengthen the earlier conclusion that ∼10 mV/m electric fields existed parallel to the magnetic field line during the flight. Perpendicular electric field measurements made as the rocket crossed six auroral arc boundaries indicated that the mean electric field strength did not vary across the boundary of an arc but that the boundary was often characterized by charge oscillations having periods of a few seconds.

Re-entry wake in an earth-fixed coordinate system

Re-entry wake in an earth-fixed coordinate system