Zero difference geometrical precise orbit determination of low flying satellites with GPS-SST observations

SST (Satellite to Satellite Tracking) observations between GPS and LEO (Low Earth Orbiter) play an important role to determine precise 3D orbits of LEO satellites. The Zero difference technique has been proven to be very efficient for this task. Zero difference means that the observations between the GPS satellites and the LEO satellite must be used without any differencing (in time or in position). In this work, as a first step to determine precise LEO orbits, initial LEO positions have been estimated based on the Bancroft method with an accuracy of a few meters. These positions can be used subsequently as initial values for LEO positions based on pseudo-range ionosphere free observations. Then the position differences between two sequential epochs can be estimated with an accuracy of approximately 1 cm based on ionosphere free carrier phase observations. The absolutely estimated positions and position differences can be used afterwards to estimate the final absolute positions of a LEO satellite at every epoch, if a sufficient number of GPS satellites i.e. equal or more than four are available

Pure Geometrical Precise Orbit Determination of a LEO Based on GNSS Carrier Phase Observations

The interest in a precise orbit determination of Low Earth Orbiters (LEOs) especially in pure geometrical mode using GNSS observations has been grown rapidly. Conventional GNSS-based strategies rely on the GNSS observations from a terrestrial network of ground receivers (IGS network) as well as the GNSS receiver on-board LEO in double difference (DD) or in triple difference (TD) data processing modes. With the advent of precise orbit and clock products at centimeter level accuracy provided by the IGS centers, the two errors associated with broadcast orbits and clocks can be significantly reduced. Therefore, higher positioning accuracy can be expected even when only a single GNSS receiver is used as zero difference (ZD) procedure. In this paper, the zero difference procedure has been applied to CHAMP high-low SST observations then the solution denoted as Geometrical Precise Orbit Determination (GPOD). The determination of absolute positions based on only carrier phase observations has the disadvantage that the ambiguity term must be determined in addition, but the advantage with respect to the positioning accuracy is significant. The estimated geometrical orbit of CHAMP is point-wise and its accuracy relies on the geometrical status of the GNSS satellites and on the number of tracked GNSS satellites as well as on the GNSS measurement accuracy in the data processing. The position accuracy of 2-3 cm of CHAMP based on high-low GPS carrier phase observations with zero difference procedure has been realized. These point-wise absolute positions can be used to estimate kinematical orbit of the LEOs

Geometrical LEO Precise Orbit Determination (POD) with only sequential time differenced GPS SST carrier phase observations

High-low GPS LEO (Low Earth Orbiter) SST (Satellite to Satellite Tracking) observations play an important role to determine geometrical, precise, 3D orbits of LEO satellites. The ambiguity parameters in the Zero difference technique aren’t integer any more, and the carrier phase observations have to be solved in the float mode. If the difference between two sequential epochs has been built, and the observation rate is small then on the one hand, the ambiguity parameters have been canceled out (if there aren’t any cycle slips in the carrier phase observations), on the other hand many errors in the ZD observations can be eliminated (e.g. antenna phase centre offsets and its variations, multi-path, etc.). Therefore, the sequential time differenced carrier phase observation has been proven to be very efficient for the LEO precise orbit determination. In this paper, as a first step to determine geometrical LEO precise orbits, initial LEO absolute positions have been estimated based on the Bancroft method with an accuracy of a few meters. These absolute positions can be used subsequently as initial values for LEO positions based on pseudo-range ionosphere free observations. To avoid cycle slips in the carrier phase observations, at first, 15 elevation cut-off angle has been applied to the observations, secondly, with the estimated positions in the code pseudo-range process and with the help of the receiver clock offset between two sequential epochs, the cycle slips have been eliminated in the iterative process. It is clear that in this method, the estimated LEO orbit is point-wise (geometrical, not kinematical) and the geometrical configuration (DOP) of GPS satellites plays an important roll in the data processing

A proposal for an orbit determination procedure for short arcs of LEO with GPS SST observations

Precise orbit determination of LEO (Low Earth Orbiter) satellites plays an important role in satellite geodesy. In this work, a technique for a precise determination of short arcs (ca. 30 minutes) of low flying satellites is proposed. The procedure is based on the solution of Newton’s equation of motion solved as a boundary value problem. The technique allows determining kinematical orbits without any force function information as well as semi-dynamic with partial force function information or dynamic orbits with full information of the forces acting on the satellites. Furthermore, the procedure allows a computation in the space domain as well as in the spectral domain. To accelerate the convergence of the solution in the spectral domain, special polynomials (i.e. Euler-Bernoulli polynomial) have to be used to avoid Gibbs’ effects at the boundaries of the arcs. The precisely determined short arcs can be used for regional as well as for global gravity field recovery tasks

How important is the dynamical information in determination of LEO orbits

The interest in a precise orbit determination of Low Earth Orbiters (LEOs) using GNSS observations to recover of the Earth's gravity field has been grown rapidly. With the advent of precise orbit and clock products at centimeter level accuracy provided by the IGS analysis centers and the geometrical connections between GNSS satellites and LEOs, the orbit of LEOs can be estimated based on only a single GNSS receiver onboard LEOs. The determined LEO orbit is based on only geometrical configuration between GNSS and LEO. This procedure is known as Geometrical Precise Orbit Determination (GPOD). The ephemerides of point-wise LEO positions can be derived by this method at every observation epochs. Kinematical Precise Orbit Determination (KPOD) is another estimation procedure, which is based on the geometrical information too. Based on a new proposed method, the kinematical orbit is represented by a sufficient number of approximation parameters, including boundary values of the LEO arc. This kind of orbit representation not only allows to determine arbitrary functional (e.g. velocity and acceleration) of the satellite arc's, but it is also possible to use dynamical observations for the determination of orbit parameters. It should be mentioned that in the geometrical and kinematical orbit determination procedures, no dynamical (force) information is used at all. Because of the close relation of the estimated kinematical parameters with the force function model, the orbit determination can be designed as a pure kinematical orbit determination on the one hand, and a pure dynamical orbit determination on the other hand. In other words, this formulation of the orbit determination allows a smooth transition from a kinematical to dynamical orbit determination. At the one end, the orbit parameters are determined without any force (dynamical) information at all, and the other extreme end, all orbit representing parameters are functions of the force model. If only weak dynamical restrictions are introduced to the estimation procedure, then a reduced-kinematical orbit results. In this poster, the new proposed orbit determination concept will be introduced and the effect of the dynamical information in the orbit determination procedures will be presented for the GOCE mission as a case study based on the simulated data. The various possibilities with the corresponding results of GOCE based on GNSS observations will be presented