Analysis of temperature sensitivity of AFS

7.3 Harmonic and temperature variations

present a clear correlation as PRN-11 (SVN-46) with differences between maximum and mi-nimum beta-angle of 0.2 ns amplitude, for others the correlation is low with differences lower than 0.05 ns as for PRN-17 (SVN-53) or PRN-14 (SVN-41).

It can be concluded that the source of the harmonics is due to thermal variations for the satellites presenting amplitude variations with a clear correlation with the sun beta-angle.

specified by the manufacturer in fractional frequency as±5E-14/^◦C for an expected temperature operation of −10^◦C to 15^◦C [154]. By design, the RAFS can operate up to +15^◦C with a margin up to +20^◦C for the qualification. Some small margins were introduced to warrant good operation also during qualification. If the maximum temperature is reached, the thermal regulation saturates and the thermal coefficient becomes 10 times higher.

In-orbit a clear correlation between frequency and temperature exists with a value of -1.5E-13/^◦C in Figure 7.4. This increased thermal sensitivity with respect to the 5.0E-14/^◦C specifi-cations provided in Table 4.1, is due to the higher temperature outside the designed range with values up to 24^◦C. The higher operational temperature was expected by the satellite manufac-turer and accepted within the objectives of the mission.

Furthermore, the removal of the temperature effects by means of the computed sensitivity and temperature information significantly reduces the observed fluctuations in Figure 7.4(b).

This removal allows the clearer identification of a frequency jump at 3E-13 level around DOY 140.

GIOVE-B

The temperature sensitivity of the PHM is slightly lower than for the RAFS with measured values on ground lower than 3E-14/^◦C [19]. The telemetry sensors trace well the spectrum of changing illumination of the spacecraft during orbital revolution and from solar/lunar eclipses.

PHM and RAFS operate well within their nominal temperature range and the temperature at the PHM location is extremely stable (<0.1^◦C during one orbit).

Correlation with all payload chain temperatures does not reveal any clear contributor in the satellite payload chain [50]. It can be concluded that temperature variations do not justify the oscillation of 0.5 ns amplitude observed in the estimated phase.

GPS

Limited information is available about GPS clock temperature. Temperature stability at the clock location is estimated to vary with the orbital period approximately in the range of±5^◦C for Block IIA and±2.5^◦C for IIR/IIR-M [179]. Even higher variations during eclipse periods up to 6^◦C in 5 hours are also reported by the same author [180].

Typical temperature sensitivities inδf/f/^◦C range between 1.2E-13 and 1.2E-14 for ground cesium clocks [18], 1E-13 for space cesium clocks on board Block IIF [181] and 1E-13 reported for Block IIA Rubidium clocks [11].

Based on the temperature sensitivity of the clock and temperature measurements it is possi-ble to remove the temperature effect as demonstrated offline with GIOVE-RAFS in Figure 7.4.

This concept has been implemented in the Block IIF TKS with a temperature controller loop to reduce the temperature sensitivity of the RAFS in orbit to 1E-14/^◦C [11, 138, 181]. The Block

7.3 Harmonic and temperature variations

(a)GIOVE-A FM5 ’apparent’ clock frequency and RAFS TRP temperature, from May 18 to May 22, 2007. Example of periodic fluctuation and a frequency jump observed on the frequency data.

(b)GIOVE-A FM5 ’apparent’ clock frequency (red dots) and residuals after removal of frequency periodic fluctuation (orange dots)

Fig. 7.4: GIOVE-A RAFS correlation with temperature during eclipse. Source: [65]

IIF Rubidium clock has a temperature coefficient of 2E-13/^◦C without the benefit of the base temperature controller which improves the temperature coefficient by a factor better than 50.

In-orbit temperatures of GPS Block IIF are reported to show thermal variations of less than 0.5

◦C peak-to-peak [44]

GLONASS

Few bibliography is available on the satellite temperature at clock location for the different GLONASS block families. Only [13] mentions a variation of±1^◦C to be expected for GLONASS-M. As a consequence only this block family will be analysed hereafter.

Expected vs measured harmonic

Once the temperature sensitivities S for the AFS and the thermal variation T at the thermal reference point have been collected, it is possible to derive the effect in frequencyyand phase (x) of the harmonic; and the expected amplitude be computed fromST(2πf)⁻¹.

y(t) =STsin(2πf t)

x(t) =^$y(t)dt =ST(2πf)⁻¹cos(2πf t) [7.4]

In Table 7.1 the expected phase oscillation for GNSS satellites from modelled values is pared with the measured in-orbit oscillations observed by POD. Measured GPS values are com-puted from IGS final clocks, crosschecked with the values reported by [150] and GIOVE values computed from ODTS.

GPS Block-IIA presents a high dispersion with values of up to 8 ns as maximum and other satellites with values as low as 0.3 ns. There are two possibilities to explain this deviation:

a different thermal control other than reported for the satellite or different thermal sensitivity for the AFS. The answer can be found in the behaviour of different AFS activated in the same satellite. In case different activated AFS present the same improvement or degraded sensitivity in the apparent clock, the most likely reason is a satellite thermal control better than assumed

Block AFS ^◦C δf/f/^◦C Expected [ns] Measured [ns]

GPS-IIA Rb ±5.0 1E-13 ±3.44 8.0-0.3

GPS-IIR Rb+TKS ±2.5 1E-14 ±0.17 0.2-0.1

GPS-IIF Rb ±0.3 4E-14 ±0.01 0.5-0.3

GLONASS-M Cs ±1.0 2E-13 ±1.73 1.0-3.0

GIOVE-A Rb ±2.5 1E-13 ±2.01 2.0-0.8

GIOVE-B Rb ±0.5 5E-14 ±0.20 0.5-0.3

GIOVE-B PHM ±0.1 3E-14 ±0.02 0.5-0.3

Tab. 7.1: Expected versus observed harmonics

7.3 Harmonic and temperature variations

0 1 2 3 4 5 6 7 8 9 10

0 0.1 0.2 0.3 0.4 0.5

Orbit [cycles]

Amplitude [nanoseconds]

PHM RAFS

Fig. 7.5: GIOVE-B (E16) FFT with different AFS selected as nominal

(e.g.SVN-17, 29, 31). On the contrary, in case that only one of the apparent clocks presents a different behaviour with respect to the expectation, the probable reason could be a different thermal sensitivity for the particular AFS (e.g.SVN-22).

The presented values for Block-IIR are in overall in agreement with the expectation. How-ever, a major discrepancy is observed for Block IIF where only a 7 ps harmonic amplitude was expected. The expected value has been derived from the thermal sensitivity of the RAFS (2E-13/^◦C) improved by a factor of 50 due to the base temperature controller. In case the pure thermal sensitivity of the RAFS is used without this improvement factor a maximum of 0.17 ns would be expected, still below the measured values. As a consequence, either the temperature at the AFS is higher than reported, or the thermal sensitivity is still higher or there is an addi-tional contribution. As variations for the SVN62 GPS satellite carrying first L5 frequency are not expected from pure ground tests, the results reported in [88] could be due to group delay variations.

GIOVE-A also presents a good agreement between modelled and measured values. On the contrary, GIOVE-B does not present any agreement for RAFS or PHM with higher values than expected. While in the case of GPS Block-IIA the use of different AFS provided additional information this is not the case for GIOVE-B. The harmonic seems to have the same amplitude independently of the selected AFS. This point is further confirmed in Figure 7.5. The spectra of the harmonics obtained with RAFS (from 10-Jan-2011 till 10-Feb-2011) and PHM (from 01-Nov-2010 till 05-Dec-2010), using a full month of data around the AFS swap as nominal, shows little difference. From these results it can be concluded that the AFS selection has little influence on the harmonic.

Fig. 7.6: Triple carrier combinations for G25 (SVN-62) and E01 (GIOVE-B). Figure courtesy of DLR (O.Montenbruck).