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The single and double-differencing operation of GPS observations is effectively used to eliminate nuisance parameters of receiver-and satellite-specific biases. According to the theorem of equivalent representation, we develop the simplified equations that equivalently represent the single and double-differenced observation equations using corresponding pseudo-observations in single or multi-baseline solutions. The transformation of the covariance matrix of original observables is no longer necessary. Therefore, the algorithms are very convenient for programming and efficient in computation. The unbiased estimate of the variance of unit weight is also derived from equivalent observation equations. The simplified equations are verified by numerical examples.

Spaceborne GNSS-R (global navigation satellite system reflectometry) is an innovative and powerful bistatic radar remote sensing technique that uses specialized GNSS-R instruments on LEO (low Earth orbit) satellites to receive GNSS L-band signals reflected by the Earth's surface. Unlike monostatic radar, the illuminated areas are elliptical regions centered on specular reflection points. Evaluation of the spatiotemporal resolution of the reflections is necessary at the GNSS-R mission design stage for various applications. However, not all specular reflection signals can be received because the size and location of the GNSS-R antenna's available reflecting ground coverage depends on parameters including the on-board receiver antenna gain, the signal frequency and power, the antenna face direction, and the LEO's altitude. Additionally, the number of available reflections is strongly related to the number of GNSS-R LEO and GNSS satellites. By 2020, the Galileo and BeiDou Navigation Satellite System (BDS) constellations are scheduled to be fully operational at global scale and nearly 120 multi-GNSS satellites, including Global Positioning System (GPS) and Global Navigation Satellite System (GLONASS) satellites, will be available for use as illuminators. In this paper, to evaluate the future capacity for repetitive GNSS-R observations, we propose a GNSS satellite selection method and simulate the orbit of eight-satellite LEO and partial multi-GNSS constellations. We then analyze the spatiotemporal distribution characteristics of the reflections in two cases: (1) When only GPS satellites are available; (2) when multi-GNSS satellites are available separately. Simulation and analysis results show that the multi-GNSS-R system has major advantages in terms of available satellite numbers and revisit times over the GPS-R system. Additionally, the spatial density of the specular reflections on the Earth's surface is related to the LEO inclination and constellation construction.

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Abstract: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).

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.