On robust estimation of the location parameter

Imaging the Universe during the first hundreds of millions of years remains one of the exciting challenges facing modern cosmology. Observations of the redshifted 21 cm line of atomic hydrogen offer the potential of opening a new window into this epoch. This will transform our understanding of the formation of the first stars and galaxies and of the thermal history of the Universe. A new generation of radio telescopes is being constructed for this purpose with the first results starting to trickle in. In this review, we detail the physics that governs the 21 cm signal and describe what might be learnt from upcoming observations. We also generalize our discussion to intensity mapping of other atomic and molecular lines.

https://iopscience.iop.org/article/10.1088/0034-4885/75/8/086901/pdf

21 cm cosmology in the 21st century

1. Introduction 2. Radial velocities 3. Astrometry 4. Timing 5. Microlensing 6. Transits 7. Imaging 8. Host stars 9. Brown dwarfs and free-floating planets 10. Formation and evolution 11. Interiors and atmospheres 12. The Solar System Appendixes References Index.

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The Exoplanet Handbook

In traditional radio-based localization methods, the target object has to carry a transmitter (e.g., active RFID), a receiver (e.g., 802.11x detector), or a transceiver (e.g., sensor node). However, in some applications, such as safe guard systems, it is not possible to meet this precondition. In this paper, we propose a model of signal dynamics to allow tracking of transceiver-free objects. Based on radio signal strength indicator (RSSI), which is readily available in wireless communication, three tracking algorithms are proposed to eliminate noise behaviors and improve accuracy. The midpoint and intersection algorithms can be applied to track a single object without calibration, while the best-cover algorithm has potential to track multiple objects but requires calibration. Our experimental test-bed is a grid sensor array based on MICA2 sensor nodes. The experimental results show that the best side length between sensor nodes in the grid is 2 meters and the best-cover algorithm can reach localization accuracy to 0.99 m

An RF-Based System for Tracking Transceiver-Free Objects

Code pseudorange measurements of the Chinese GNSS BeiDou reveal variations which result in code---phase divergences of more than 1 m. We have analyzed these delay variations based on observation data of the International GNSS Service and its Multi-GNSS Experiment campaign. Our results confirm that these code variations are elevation-dependent when observed by receiving antennas on the earth's surface. In addition, we found significant differences between two groups of satellites and among carrier frequencies. These delay variations have only little effects on absolute BeiDou positioning using broadcast ephemerides due to the limited accuracy of the obtainable positions. But, all precise applications which use code measurements are severely affected. These applications include, e.g., certain algorithms used in Precise Point Positioning (PPP), especially PPP ambiguity fixing and single-frequency PPP based on the ionosphere-free code---carrier combination. We developed a correction model and determined correction parameters in order to accommodate these symptoms. Application examples demonstrate the successful mitigation of these code pseudorange variations.

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BeiDou satellite-induced code pseudorange variations: diagnosis and therapy

This reference and handbook describes theory, algorithms and applications of the Global Positioning System (GPS/Glonass/Galileo/Compass). It is primarily based on source-code descriptions of the KSGsoft program developed at the GFZ in Potsdam. The theory and algorithms are extended and verified for a new development of a multi-functional GPS/Galileo software. Besides the concepts such as the unified GPS data processing method, the diagonalisation algorithm, the adaptive Kalman filter, the general ambiguity search criteria, and the algebraic solution of variation equation reported in the first edition, the equivalence theorem of the GPS algorithms, the independent parameterisation method, and the alternative solar radiation model reported in the second edition, the modernisation of the GNSS system, the new development of the theory and algorithms, and research in broad applications are supplemented in this new edition. Mathematically rigorous, the book begins with the introduction, the basics of coordinate and time systems and satellite orbits, as well as GPS observables, and deals with topics such as physical influences, observation equations and their parameterisation, adjustment and filtering, ambiguity resolution, software development and data processing and the determination of perturbed orbits.

GPS: Theory, Algorithms and Applications

The GPS orbit precision of the IGS ultra-rapid predicted (IGU-P) products has been remarkably improved since 2007. However, the satellite clock offsets of the IGU-P products have not shown sufficient high-quality prediction to achieve sub-decimeter precision in real-time precise point positioning (RTPPP), being at the level of 1---3 ns (30---90 cm) RMS in recent years. An improved prediction model for satellite clocks is proposed in order to enhance the precision of predicted clock offsets. First, the proposed prediction model adds a few cyclic terms to absorb the periodic effects, and a time adaptive function is used to adjust the weight of the observation in the prediction model. Second, initial deviations of the predictions are reduced by using a recomputed constant term. The simulation results have shown that the proposed prediction model can give a better performance than the IGU-P clock products and can achieve precision better than 0.55 ns (16.5 cm) in real-time predictions. In addition, the RTPPP method was chosen to test the efficiency of the new model for real-time static and kinematic positioning. The numerical examples using the data set of 140 IGS stations show that the static RTPPP precision based on the proposed clock model has been improved about 22.8 and 41.5 % in the east and height components compared to the IGU-P clock products, while the precisions in the north components are the equal. The kinematic example using three IGS stations shows that the kinematic RTPPP precision based on the proposed clock model has improved about 30, 72 and 44 % in the east, north and height components.

Real-time clock offset prediction with an improved model

Enhancing the positioning precision is the primary pursuit of global positioning system (GPS) users. To achieve this goal, most studies have focused on the relationship between GPS receiver clock errors and GPS positioning precision. This study utilizes undifferentiated phase data to calculate GPS clock errors and to compare with the frequency of cesium clock directly, to verify estimated clock errors by the method used in this paper. The frequency stability calculated from this paper (the indirect method) and measured from the National Standard Time and Frequency Laboratory (NSTFL) of Taiwan (the direct method) match to 1.5 × 10 −12 (the value from this study was smaller than that from NSTFL), suggesting that the proposed technique has reached a certain level of quality. The built-in quartz clocks in the GPS receivers yield relative frequency offsets that are 3‐4 orders higher than those of rubidium clocks. The frequency stability of the quartz clocks is on average two orders worse than that of the rubidium clock. Using the rubidium clock instead of the quartz clock, the horizontal and vertical positioning accuracies were improved by 26‐78% (0.6‐3.6 mm) and 20‐34% (1.3‐3.0 mm), respectively, for a short baseline. These improvements are 7‐25% (0.3‐1.7 mm) and 11% (1.7 mm) for a long baseline. Our experiments show that the frequency stability of the clock, rather than relative frequency offset, is the governing factor of positioning accuracy.

https://ir.nctu.edu.tw:443/bitstream/11536/7050/1/000267294000012.pdf

Determination of global positioning system (GPS) receiver clock errors: impact on positioning accuracy

The Keplerian laws of planetary motion are solutions of the two-body gravitational problem. Solar oblateness resulting from the rotation of the Sun distorts the gravitational force acting on a planet and disturbs its Keplerian motion. An analytic solution of a planetary orbit disturbed by the solar gravitational oblateness is derived. In addition to short- and long-periodic disturbances there are secular disturbances, which lead to a perihelion precession and a nodal regression as well as to a mean-motion advance. The magnitude of the short-periodic perihelion precession could disturb observations of the secular effect if the survey is shorter then one Julian year. Transformation of formulae from the solar equatorial plane to the ecliptic plane is discussed. Numerical estimates of the secular perihelion precessions of Mercury, Venus and Mars are in good agreement with published results, confirming our theory. Inversely, the solar oblateness could be determined through observation of the perihelion precession of a planet. The solution is also valid for satellite orbits in the solar gravitational field.

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Solar oblateness and Mercury's perihelion precession

Ground-based GNSS-R (global navigation satellite system reflectometry) can provide the absolute vertical distance from a GNSS antenna to the reflective surface of the ocean in a common height reference frame, given that vertical crustal motion at a GNSS station can be determined using direct GNSS signals. This technique offers the advantage of enabling ground-based sea level measurements to be more accurately determined compared with traditional tide gauges. Sea level changes can be retrieved from multipath effects on GNSS, which is caused by interference of the GNSS L-band microwave signals (directly from satellites) with reflections from the environment that occur before reaching the antenna. Most of the GNSS observation types, such as pseudo-range, carrier-phase and signal-to-noise ratio (SNR), suffer from this multipath effect. In this paper, sea level altimetry determinations are presented for the first time based on geometry-free linear combinations of the carrier phase at low elevation angles from a fixed global positioning system (GPS) station. The precision of the altimetry solutions are similar to those derived from GNSS SNR data. There are different types of observation and reflector height retrieval methods used in the data processing, and to analyze the performance of the different methods, five sea level determination strategies are adopted. The solutions from the five strategies are compared with tide gauge measurements near the GPS station, and the results show that sea level changes determined from GPS SNR and carrier phase combinations for the five strategies show good agreement (correlation coefficient of 0.97–0.98 and root-mean-square error values of <0.2 m).

Guochang Xu

Papers

GPS: Theory, Algorithms and Applications

Real-time clock offset prediction with an improved model

Determination of global positioning system (GPS) receiver clock errors: impact on positioning accuracy

Solar oblateness and Mercury's perihelion precession

Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR