Systematic biases in the on-board navigation solution of a CubeSat GNSS payload board

In December 2018 and April 2019, two 3-unit cube satellites of the company Astrocast were launched into orbit. Both satellites are equipped with our low-cost single-frequency multi-GNSS payload board, which provides almost continuous on-board receiver solutions containing the position from GNSS code observations and the velocity from Doppler measurements. We make use of these independent observation types (positions and velocities) to identify and analyse systematic biases in the receiver solution. Therefore, we estimate the parameters of a dynamic orbit model using three different approaches: fitting the orbit model (1) to the positions only, (2) to the velocities only and (3) to both, positions and velocities.

After removing outliers, the position residuals from the position-only approach are at a level of about 5 m, the velocity residuals from the velocity-only approach at about 15 cm/s. When computing the positions with the velocity-only approach, however, the residuals are much larger and show a once-per revolution periodicity with amplitudes of up to 40 m. Besides that, we identify two offsets in the residuals which are independent of the observation type: a radial position bias of -3 m and an along-track velocity bias of -1.2 cm/s. Additionally, we observe two offsets which are dependent on the observation type: an along-track offset of 13 m in the position residuals when using the velocity-only approach and a radial offset of 1.3 cm/s in radial velocities when using the position-only approach.

The periodicity in radial and along-track direction is related to the orbit eccentricity and may be due to a general deficiency, when using velocities to estimate geometric orbit parameters. When comparing the orbits from the position-only and the velocity-only approach, we find an offset in the right ascension of the ascending node, which corresponds to a maximum cross-track position difference of 40 m at the equator. We show that this effect is caused by a periodic bias in the velocity solutions with a maximum at the poles. A possible cause for such a periodicity in the velocity solutions may be dynamic effects in the receiver tracking loops related to the LEO satellite velocity relative to the GNSS constellation, which can vary strongly within one revolution.

Our results show that both, the radial position offset and the along-track velocity offset are dependent on the altitude of the satellite and are likely to be caused by ionospheric refraction. The explanation for the along-track position offset and the along-track velocity offset, however, is not that obvious. We found that these two offsets are geometrically related and, thus, must have the same physical cause. Based on the combined position-and-velocity approach we demonstrate that they originate from a velocity bias rather than from a position bias. To explain the physical cause of such a radial velocity offset, we will study the ionospheric effects on GNSS code and Doppler measurements in more detail, where we use a 3D-ionosphere model and take also the altitude of the two satellites into account.