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Calibration techniques for magnetometers implementing on-board de-spinning algorithms
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Advances in Space Research 41 (2008) 1571–1578 www.elsevier.com/locate/asr
Calibration techniques for magnetometers implementing on-board de-spinning algorithms P. Brown b
a,*
, M.W. Dunlop b, A. Balogh a, C. Carr a, J. Gloag a, E. Lucek a, T. Oddy
a
a The Blackett Laboratory, Imperial College London, London SW7 2AZ, UK Space Science and Technology Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, UK
Received 15 November 2006; received in revised form 2 July 2007; accepted 21 September 2007
Abstract The Fluxgate Magnetometer experiments on-board the European Space Agency’s four spacecraft Cluster Mission have the capability to store sampled magnetic field vectors in the instrument memory, either as a full resolution ‘event capture’ or as spin-resolution vectors transformed into a non-spinning co-ordinate system (de-spun). The latter capability has ensured a dataset is available which extends the partial orbital coverage achieved during nominal operations in the first years of operation. The on-board de-spin is achieved using a Walsh function with Haar coefficients and allows for up to 27 h additional data per non-coverage interval. A number of commissioning orbits were used to verify the accuracy of data collected by the de-spin mode, whereby individual spacecraft were operated separately in a number of standard normal sampling and de-spin mode combinations. Up to the present time, this data has not been available to the Cluster community. We present results here comparing the performance of the on-board de-spin algorithm versus the normal sampling modes over a number of boundary layer crossings, describe the techniques used for calibration and timeline recovery, and outline the context in which the data may be usable in future studies. Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Cluster Mission; Magnetometer; Calibration
1. Introduction Each Cluster Fluxgate Magnetometer (FGM) can deliver low resolution de-spun magnetic field vectors through the operation of the on-board MSA (Micro Structure Analyzer) memory (Balogh et al., 1997). The corresponding operating mode, called Extended Mode (FGMEXT), is designed for periods in-flight when there is no science telemetry such as during eclipse operations and spacecraft manoeuvres. Routine use of Extended Mode began on March 20th 2001 and since this date all periods outside of an AI (Acquisition Interval) have seen the instrument switch to this mode automatically. The mode was used extensively during the period 2001–2002 before the implementation of full coverage over the whole of the length *
Corresponding author. E-mail address: [email protected] (P. Brown).
of the Cluster orbits. Consequently, a reasonably large Extended Mode dataset exists, but as this mode was installed in-flight, and not tested on the ground, recovery of the de-spun vector timeline and its associated calibration is non-trivial. Consequently this dataset has up to now not been available as a routinely produced FGM data product. Since the launch of the Cluster spacecraft in 2001 there are many examples demonstrating the mission’s unique ability to facilitate multi-spacecraft studies of numerous geophysical phenomena both within and outside of the Earth’s magnetosphere (Paschmann et al., 2005; Escoubet, 2001) as well as providing special opportunities for intercalibration of the four identical suites of instruments. Such an approach has been used for the purpose of validating the Extended Mode dataset. This has been recently achieved through analysis of a number of special ‘crossmode’ intervals whereby the FGM instruments were operated in different modes on different spacecraft. The range of
0273-1177/$34.00 Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.09.028
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intervals have covered events across numerous boundary layers along the Cluster orbit and therefore give simultaneous coverage at both the on-board de-spun frequency (i.e. Extended Mode data) and the higher frequency 22.4 Hz ‘Normal Mode’ NM data, allowing for direct comparisons of the in-flight de-spun data and spin averages derived on the ground from the higher frequency NM data. Three particular examples are presented in this paper. The first interval is during a passage in the region of wave activity in the solar wind, the second is an interval where the spacecraft cross the bow shock, and the third is during a traversal from the inner magnetosphere into the sheath. The result of this analysis demonstrates that, to first order, the Extended Mode data is of usable quality for the purposes of global surveys and that generation of a fully processed Extended Mode dataset would make a worthy addition to the existing FGM datasets. 2. Mode description and de-spin algorithm: FGMEXT The early years of Cluster saw significant periods when there was no science data coverage due to resource constraints on the availability of ground stations. Fig. 1 shows a Bryant plot from the Cluster Master Science Plan showing the mode coverage of the Cluster spacecraft between January and June 2001. The dotted lines indicate periods along the orbit where there is no science data coverage. During the first year and a half of operations science data was only available for return for an average of 50% of each orbit. It became quickly apparent after launch that a large proportion of scientifically interesting events as well as survey data providing
contextual information for the purpose of analyzing captured events would be missed. Thus, the need for a magnetometer mode which could sample and store on-board the B-field for a significant proportion of these non-telemetered intervals was potentially an important development which could maximize the data return of the mission. Extending the data coverage along the orbit means the instrument data rate needs to be substantially reduced from that used in the nominal instrument modes. As the Cluster spacecraft are spin stabilized (nominal spin period is 4 s) any significant reduction in the data rate for the spin plane components requires the use of an on-board de-spin function in order to realise a spin or sub-spin vector rate – simple averaging of the sampled spinning spin plane components is not valid and would result in component mixing. Remembering that spin average time series of higher rate nominal mode data are commonly used data products the most logical and easily implemented candidate for a reduced rate sample store was spin synchronised with one averaged vector per spin being stored to memory. Each FGM contains 192Kbytes (96 K words) of MSA memory, which is normally used for capturing short periods of high time-resolution data (approximately 200 samples/s). At the time of loss of science data coverage the FGM is commanded into FGMEXT utilising the MSA to store long periods of spin averaged data (Balogh et al., 2001). The data stored by the MSA is held frozen until the next scheduled burst-memory downlink (a spacecraft telemetry mode known as ‘Burst-Mode 3’, BM3) where it is downloaded to ground. Typically there are two BM3 dumps over the course of an orbit after which the MSA is set unfrozen and is again
Fig. 1. Bryant plot showing the data and mode coverage for initial half year of Cluster operations. The dotted lines indicate periods along the orbit when there is no data coverage, i.e. the instruments are either switched off or quiescent, with no data recorded by the spacecraft. These are periods when the FGM could be switched to FGMEXT mode. (Plot courtesy of the Cluster Joint Science Operations Centre.)
P. Brown et al. / Advances in Space Research 41 (2008) 1571–1578
available for data taking from event capture or during the next scheduled FGMEXT interval. With this mode an additional 27 h of data can be recovered from non-telemetered periods which would otherwise be lost In this low resolution mode the instrument continuously measures the spacecraft spin period by calculating the elapsed time between successive sun reset pulses (SRP) and synchronising vector acquisitions to a fixed number of spin sectors. Sampled vectors are de-spun, averaged and stored to the MSA. The number of spin sectors and averaging length is fixed at 512. This value has been selected according to the underlying instrument sample rate (201.793 vectors per seconds) and the need for a power of two arising from the fact that the instrument DPU (Data processing Unit) is only capable of integer arithmetic. Although the science channel to the spacecraft bus is closed during FGMEXT operation, a reduced set of instrument Housekeeping (HK) voltages and temperatures are sent to the spacecraft bus for the purpose of health monitoring. Data is taken only by the primary sensor (Outboard sensor by default) so the secondary sensor (Inboard) is switched to a safe gain range prior to the switch to FGMEXT. Processing of the measured FGM vectors requires them to be transformed from the rotating frame of the spacecraft (or de-spun). For the MSA low resolution vectors, de-spin is achieved by implementing a Walsh Transform with Haar coefficients based on the equations shown in Table 1. These are applied in the sensor coordinate frame where Bx is nominally aligned with the spacecraft spin axis and By and Bz are the spin plane components. The transform estimates the true sinusoidal de-spin vector with a square wave approximation which is much easier to implement in assembler code and with integer arithmetic. An artificial phase delay is needed onboard in order to avoid evaluation of the function at the zero crossing points where the Haar coefficients are undefined. The scheme is similar to that implemented in hardware by the magnetometer on-board the Ulysses spacecraft (Balogh et al., 1992). Extended Mode was tested during the post-launch instrument commissioning phase but routine switching into FGMEXT was implemented only after the BM3 dumps were included in the Master Science Plan. Thus Extended Mode became operational on orbit 113 (March 2001) and
Table 1 FGMEXT de-spin and averaging equations
C H ðtÞ ¼
cosðxtÞ j cosðxtÞ j
S H ðtÞ ¼
sinðxtÞ j sinðxtÞ j
where BZ = De-spun Z component BY = De-spun Y component N = 512
PN 1 p BZ ¼
i¼0 4 ½BZSi C Hi
N PN 1 p
BY ¼
BYSi S Hi
i¼0 4 ½BZSi S Hi
þ BYSi C Hi
N
BZS = Sampled Z component BYS = Sampled Y component CHSH = Haar functions
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all periods outside of AI since this orbit have seen automatic switching of the FGM instruments into FGMEXT on all four spacecraft. The frequency of Extended Mode intervals is much higher in the early years of the mission before the implementation of full data coverage along the Cluster orbits during 2002. At the present time Extended Mode still provides magnetic field data during intervals when other Cluster payload are not taking data such as the period surrounding long eclipses, during spacecraft manoeuvres and other periods of special operations on the spacecraft. 3. Deriving the vector timeline Recovery of the Extended Mode vector timeline is significantly different to that of the in-coverage Normal and Burst Mode packets encountered during routine data processing. For these modes the UTC time in the packet header (supplied by the spacecraft) has a clearly defined relationship with the time of the first vector in each packet, recorded by the FGM internally using a spacecraft derived High Frequency (HF) 4096 Hz clock. This FGM time stamp is written to the science packet with a resolution of better than 250 ls. Subsequent vectors in the packet are time stamped by extrapolation based on the known instrument sampling rate. The method works because vectors sampled over the course of a spacecraft frame (reset period is 5.15222 s) are always packetised during the following frame and so an absolute time reference connects the FGM internal time stamp to the UTC header in the downlink packet. In this way an absolute UTC reference is availed of each and every packet (every 115 vectors in the 22.4 Hz NM mode) during processing of the FGM Normal and Burst Mode data and the time stamp of every vector can be unambiguously recovered from the contents of the FGM Science data stream alone. The Extended Mode data however, necessarily requires a more complicated time stamping scheme due to the fact that there is no relationship between the UTC header time of the downlink packet and the time stamp of any vector in the Extended Mode data, the time difference between them is completely arbitrary and is determined by the length of the Extended Mode period and also the timing of the BM3 dumps. The simplest timing scheme must have the ability to relate UTC time to the time of at least one vector from the Extended Mode packet and ideally the first vector. Given this it should be then possible to extrapolate the timeline for all subsequent vectors inside the Extended Mode packet based on an assumed spin period. By patching the FGM to ensure that the time of the first SRP is transmitted in the last valid HK packet prior to the switch into FGMEXT it has proved possible to calculate a UTC time stamp of the first de-spun vector. Subsequent vector time stamps are extrapolated based on the initial spin rate estimate. This scheme is utilised during the special processing of Extended Mode data discussed here.
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Fig. 2. Plot showing a running average of number FGM HF Clock ticks (1 tick corresponds to 240 ls) between successive SRP during 20th Feb 2001 for all four S/C. All traces have been offset to a nominal spin period of 4.0 s so that the trend on all four spacecraft is clearly visible. It can be seen that the drift in the sun pulse is minimal over typical Extended Mode interval lengths.
system to a more scientifically useful de-spun geophysical co-ordinate system such as GSE (Geocentric Solar Ecliptic) or GSM (Geocentric Solar Magnetic). The transformation includes the orthogonalisation of the three components of each vector with a calibration matrix and subtraction of an associated offset vector. The calibration matrix contains corrections to sensor parameters affecting the nominal values for the sensor gains and mis-alignments. The offset vector corrects for the presence of zero-level reading. The calibration matrix and offset vector are typically computed on a daily basis and, in the case of a spinning spacecraft such as Cluster, are related in a complex but deterministic way to the power levels of individual field component at spin and twice-spin harmonics (Kepko et al., 1996). In fact, without a secondary absolute B-field reference available on-board such as a scalar magnetometer (Dougherty et al., 2004) a complete solution to the calibration problem is extremely difficult. Nevertheless, through careful extrapolation of calibration parameters determined on ground as
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The scheme is not foolproof as it assumes that the drift in spin rate is negligible over the course of the Extended Mode sample otherwise an accumulating timing error will manifest itself. Fig. 2, for example, illustrates the drift in sun-pulse period for a typical day from February 2001. The plot graphs the change in running average of the number of ticks of the HF clock between successive sun pulses recorded by each Cluster FGM over the course of 24 h (while the spacecraft were in the solar wind and magnetosheath). For all four spacecraft the change is significantly less than 1 sun-pulse tick (<250 ls) which is within the accepted resolution used for processing normal and high resolution vectors. Thus we can see that for nominal operations during a typical period of data acquisition, the spin rate of all four spacecraft is extremely stable and so the extrapolation method proposed can be taken to be reasonable as a first order approximation. However it may well be the case that the sun-pulse drift will be much greater in periods after eclipse. It is worth noting that the timing scheme outlined above is fundamentally different from the in-coverage time stamping schemes. Instead of just a single science packet containing all information needed to produce a time series vector it is necessary to synchronise processing of HK and Science data in order to time stamp the Extended Mode data. This is a direct result of having only a HK channel data link to the spacecraft available at the instant of the switch into FGMEXT.
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Figs. 3 and 4. (Zoom of 3), Plot showing Normal Mode derived (C1) and Extended Mode (C2) field magnitude spin averages during a sequence of bow shock crossings. The traces clearly overlap overall to a high degree and features are well matched.
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well as applying some statistical techniques in-flight (e.g. Hedgecock, 1975) it is possible to closely approximate the real underlying sensor transfer function. Almost always the largest calibration errors are associated with the sensor which is most closely aligned with the spin axis (corresponding to Bz GSE on-board the Cluster spacecraft). It is not possible to apply the calibration process as described above to the Extended Mode data due to the fact the FGMEXT sample rate is equal to that of the spin rate and thus the spin frequency and twice-spin frequency are outside the FGMEXT Nyquist. Furthermore the on-board de-spin has the effect of mixing the offset and mis-alignment terms of the individual spin plane components (Bx GSE and By GSE). This situation could be addressed by up-linking offsets to the FGM on-board and including an offset subtraction instruction prior to de-spin within the Extended Mode algorithm. However due to memory constraints such a code modification in-flight was not possible. Fortunately the effect of averaging on the spin plane mixing results in cancellation of offset terms as will be seen in the
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Figs. 7 and 8. (Zoom of 7), Plots show Normal Mode derived spin averages (C2) and Extended Mode (C1, C3 and C4) as the tetrahedron traverses outbound from perigee through the magnetosphere, across the magnetopause and into the sheath. Again we see that major features are resolved and traces are consistent excluding small offset effects.
examples below. We are therefore limited to a subset of calibration parameters that can realistically be applied to despun data without the development of some new technique. As a first order correction, the calibration has been confined to spin axis offset and gain correction (applied to Bz: its situation can be taken to be unchanged from the normal calibration process as applied to higher-rate data) and an average gain applied to the de-spun Bx and By components. Errors due to mis-alignments in the spin plane data are ignored in the first instance. 5. Comparative observations
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Figs. 5 and 6. (Zoom of 5), Plot showing Normal Mode derived (C1) and Extended Mode (C2, C3) field magnitude spin averages during a solar wind passage. We can see good tracking over sharp boundaries and wave structures appear coherent and are well resolved.
A combination of operational factors resulted in a small number of unexpected intervals in early 2001 where Normal (22.4 Hz) and Extended Mode (0.25 Hz) data periods overlap on different spacecraft. This allows for limited comparisons to be made on the quality and timing of the
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Extended Mode data. Spin averages for three of these intervals are presented below which include combinations of one or more spacecraft traces. The traces follow the standard Cluster colour convention (C1 – black, C2– red, C3 – green, C4 – magenta). Given the constraints and presence of error sources with respect to the use of the Walsh transform, timing errors associated with a drifting spin rate as well as calibration errors due to offset and mis-alignment mixing from the on-board de-spin, one might expect that comparative observations between well calibrated NMderived spin averages and those produced by Extended Mode would reveal disparities in appearance of structures and associated timings. However, as the three examples presented below demonstrate there is surprisingly good matching between both types of data. The first example in Fig. 3 shows dual traces from spacecraft 1 and 2 during a sequence of bow shock crossings. The traces clearly overlap overall to a high degree and the detail shown in the expanded view in Fig. 4 confirms
that all features both in the magnetosheath levels and in the upstream region are well matched in both cases. There is an apparent small, residual offset on spacecraft 1, which is clear for the short interval around 6.6 UT. This appears to be due to a residual spin axis offset rather than arising from the different sampling positions of the spacecraft. Figs. 5 and 6 show a similar pair of plots (one expanded view) for three spacecraft traces, where spacecraft 2 and 3 are obtained from the Extended Mode data, sampling a burst of waves upstream of the bow shock. Clearly all the traces track the waves coherently in a sequence which can be shown to be consistent with the spacecraft positioning. The offset on spacecraft 1 is apparent in Fig. 6, and it is also clear the two Extended Mode traces track each other at least as well as they do spacecraft 1 and contain no significant offset. We lastly show an illustration with all four spacecraft traces for a dawn-flank, outbound magnetopause crossing in Figs. 7 and 8. The traces for spacecraft 1, 3 and 4 are
Figs. 9–12. Cluster orbit (S/C1) and tetrahedron configuration projections in the X–Y GSE and Y–Z GSE planes, together with model magnetopause. Spacecraft separation is of the order 2000 km. The derived spacecraft crossing order through the magnetopause boundary is consistent with that observed in the time series, namely C1, C4, C2 and C3 indicating that the Extended Mode timing is working correctly to a first order test.
P. Brown et al. / Advances in Space Research 41 (2008) 1571–1578
1 For interpretation of the references to colour in this text, the reader is referred to the web version of this article.
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reconstructed from the Extended Mode data. Figs. 9 and 10 show the corresponding orbit plots for the event, with an expanded view of the spacecraft configuration at the time of the magnetopause crossing. The spacecraft are located in the northern hemisphere so that the expected orientation of the magnetopause surface is as indicated by the green line, cutting through the XY plane, and is tilted into Y1. Since spacecraft 3 and 4 lie below the plane, the expectation is that spacecraft 1, 2 and 4 will exit the magnetosphere closely in sequence, and spacecraft 3 will exit a little later. The plots in Fig. 8 show just this sequence and this provides a good check on the integrity of the Extended Mode data streams. It is also true that spacecraft 3 lies inwards of the other spacecraft, relative to the tilted plane of the magnetopause, and this is reflected by the higher field magnitude measured on that spacecraft (Figs. 11 and 12). The Extended Mode dataset will be incorporated into the Cluster Science Data System as one minute averages. With this in mind it is useful to estimate the accuracy of the Extended Mode derived averages relative to a nominal dataset. Ideally we would do this by making a comparison of residual differences of data taken simultaneously in both Normal and Extended Modes on a single spacecraft. Unfortunately the operation of data acquisition in-flight precludes this possibility so that the comparisons here have been made between different spacecraft in different modes. Although the data are expected to be similar between two spacecraft, the residuals will contain differences arising from actual differences in the magnetic field at each spacecraft location in addition to any arising from the differences of mode between the two data streams. To better illustrate the comparison, Fig. 13 shows dual traces from the bow shock example discussed previously as one minute averages of the field magnitude. In the figure, the Normal Science data from spacecraft 2 have been interpolated onto the Extended Mode spacecraft 1 vector timeline and the residuals are plotted in blue. A histogram of the residuals is shown in Fig. 14. These may be compared directly to Fig. 15, which shows spacecraft 1 and 2 dual traces in the same format, as Fig. 13, but now with both sets of averages derived from Normal Mode data and Fig. 16 which displays a histogram of the residuals. The data shown in Fig. 15 are taken from a bow shock crossing during the orbit immediately following that of the Extended–Normal Mode comparison, while the spacecraft were in a similar location and configuration. The magnetic field profile encountered in both examples is fairly representative of the natural signal to be expected during a bow shock crossing. These figures together, therefore show that the Extended Mode data stream is as representative as the Normal Mode data, since the residuals remain similar in each case. A mea-
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Figs. 13 and 14. Plots showing Normal Mode derived (C1) and Extended Mode (C2) field magnitude one minute averages and C2–C1 residuals (blue) together with histograms of the residuals for the bow shock crossing on 27th April 2001. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
sure of the fidelity of the Extended Mode field recovery can be inferred from the similarity in the spread of residuals in the two histograms, i.e. if the fidelity is high then both sets of residuals should show a similar level of spread. This is exactly what is visible in the two histograms. The comparison demonstrates that the Normal Science – Extended Mode residuals are dominated by the temporal and spatial differences expected at these spacecraft separations (<1000 km) rather than by limitations in the de-spin algorithm. Thus, we may conclude that the Extended Mode derived averages can be regarded as suitable for the purpose of contextual information and provide an accuracy which is limited primarily by the errors associated with the reduced calibration applied on ground, typically of order a few nT. It therefore compares well with Normal Mode Quicklook data.
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The resultant time series compares well with spin-average data derived simultaneously from Normal Mode acquisition, in light of the limitations in the de-spin function and applied calibration. The illustrations here have provided supporting evidence of:
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Good tracking of structures between Extended Mode datasets. Good tracking of structures between Normal and Extended Mode datasets. Primary contribution to offset error is along the spin axis – calibration errors in the spin plane average towards zero. Calibration errors are not large enough to invalidate the dataset – the data quality is sufficiently good to validate its usability for the purpose of surveys. Some open issues remain regarding the time stamping of vectors. Current planning is for more detailed timing analysis of the above intervals in order to place an absolute limit on the Extended Mode vector’s time stamp accuracy. Following this it is the intention of the FGM team to incorporate this dataset into the Summary Parameter database during 2007.
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Figs. 15 and 16. Plots showing Normal Mode derived (C1) and Normal Mode derived (C2) field magnitude one minute averages and C2–C1 residuals (blue) together with histograms of the residuals for the bow shock crossing on 29th April 2001. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
6. Conclusions The FGM on-board de-spinning algorithm has been shown to successfully recover the magnetic field vector.
Balogh, A., Dunlop, M.W., Cowley, S.W.H., et al. The Cluster magnetic field investigation. Space Sci. Rev. 79, 65–91, 1997. Balogh, A., Carr, C.M., Acunˇa, M.H., et al. The Cluster magnetic field investigation: overview of in-flight performance and initial results. Ann. Geophys. 19, 1207–1217, 2001. Balogh, A., Beek, T.J., Forsyth, R.J., et al. The magnetic field investigation on the Ulysses mission: instrumentation and preliminary scientific results. Astrophys. Suppl. Ser. 92, 221–236, 1992. Dougherty, M.K., Kellock, S., Southwood, D.J., et al. The Cassini magnetic field investigation. Space Sci. Rev. 114, 331–383, 2004. Escoubet, C.P. (Ed.). Cluster special issue. Ann. Geophys. 19 (10/12), 1195–1730, 2001. Kepko, E.L., Khurana, K.K., Kivelson, M.G. Accurate determination of magnetic field gradients from four point vector measurements – Part 1: use of natural constraints on vector data obtained from a single spinning spacecraft. IEEE Trans. Mag. 32 (2), 377–385, 1996. Hedgecock, P.C. A correlation technique for magnetometer zero level determination. Space Sci. Inst. 1, 83–90, 1975. Paschmann, G., Schwartz, S.J., Escoubet, C.P., Haaland, S. (Eds.). Outer magnetospheric boundaries: Cluster results, Space Sci. Rev. 118 (1–4), 2005.
Advances in Space Research 41 (2008) 1571–1578 www.elsevier.com/locate/asr
Calibration techniques for magnetometers implementing on-board de-spinning algorithms P. Brown b
a,*
, M.W. Dunlop b, A. Balogh a, C. Carr a, J. Gloag a, E. Lucek a, T. Oddy
a
a The Blackett Laboratory, Imperial College London, London SW7 2AZ, UK Space Science and Technology Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, UK
Received 15 November 2006; received in revised form 2 July 2007; accepted 21 September 2007
Abstract The Fluxgate Magnetometer experiments on-board the European Space Agency’s four spacecraft Cluster Mission have the capability to store sampled magnetic field vectors in the instrument memory, either as a full resolution ‘event capture’ or as spin-resolution vectors transformed into a non-spinning co-ordinate system (de-spun). The latter capability has ensured a dataset is available which extends the partial orbital coverage achieved during nominal operations in the first years of operation. The on-board de-spin is achieved using a Walsh function with Haar coefficients and allows for up to 27 h additional data per non-coverage interval. A number of commissioning orbits were used to verify the accuracy of data collected by the de-spin mode, whereby individual spacecraft were operated separately in a number of standard normal sampling and de-spin mode combinations. Up to the present time, this data has not been available to the Cluster community. We present results here comparing the performance of the on-board de-spin algorithm versus the normal sampling modes over a number of boundary layer crossings, describe the techniques used for calibration and timeline recovery, and outline the context in which the data may be usable in future studies. Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Cluster Mission; Magnetometer; Calibration
1. Introduction Each Cluster Fluxgate Magnetometer (FGM) can deliver low resolution de-spun magnetic field vectors through the operation of the on-board MSA (Micro Structure Analyzer) memory (Balogh et al., 1997). The corresponding operating mode, called Extended Mode (FGMEXT), is designed for periods in-flight when there is no science telemetry such as during eclipse operations and spacecraft manoeuvres. Routine use of Extended Mode began on March 20th 2001 and since this date all periods outside of an AI (Acquisition Interval) have seen the instrument switch to this mode automatically. The mode was used extensively during the period 2001–2002 before the implementation of full coverage over the whole of the length *
Corresponding author. E-mail address: [email protected] (P. Brown).
of the Cluster orbits. Consequently, a reasonably large Extended Mode dataset exists, but as this mode was installed in-flight, and not tested on the ground, recovery of the de-spun vector timeline and its associated calibration is non-trivial. Consequently this dataset has up to now not been available as a routinely produced FGM data product. Since the launch of the Cluster spacecraft in 2001 there are many examples demonstrating the mission’s unique ability to facilitate multi-spacecraft studies of numerous geophysical phenomena both within and outside of the Earth’s magnetosphere (Paschmann et al., 2005; Escoubet, 2001) as well as providing special opportunities for intercalibration of the four identical suites of instruments. Such an approach has been used for the purpose of validating the Extended Mode dataset. This has been recently achieved through analysis of a number of special ‘crossmode’ intervals whereby the FGM instruments were operated in different modes on different spacecraft. The range of
0273-1177/$34.00 Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.09.028
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intervals have covered events across numerous boundary layers along the Cluster orbit and therefore give simultaneous coverage at both the on-board de-spun frequency (i.e. Extended Mode data) and the higher frequency 22.4 Hz ‘Normal Mode’ NM data, allowing for direct comparisons of the in-flight de-spun data and spin averages derived on the ground from the higher frequency NM data. Three particular examples are presented in this paper. The first interval is during a passage in the region of wave activity in the solar wind, the second is an interval where the spacecraft cross the bow shock, and the third is during a traversal from the inner magnetosphere into the sheath. The result of this analysis demonstrates that, to first order, the Extended Mode data is of usable quality for the purposes of global surveys and that generation of a fully processed Extended Mode dataset would make a worthy addition to the existing FGM datasets. 2. Mode description and de-spin algorithm: FGMEXT The early years of Cluster saw significant periods when there was no science data coverage due to resource constraints on the availability of ground stations. Fig. 1 shows a Bryant plot from the Cluster Master Science Plan showing the mode coverage of the Cluster spacecraft between January and June 2001. The dotted lines indicate periods along the orbit where there is no science data coverage. During the first year and a half of operations science data was only available for return for an average of 50% of each orbit. It became quickly apparent after launch that a large proportion of scientifically interesting events as well as survey data providing
contextual information for the purpose of analyzing captured events would be missed. Thus, the need for a magnetometer mode which could sample and store on-board the B-field for a significant proportion of these non-telemetered intervals was potentially an important development which could maximize the data return of the mission. Extending the data coverage along the orbit means the instrument data rate needs to be substantially reduced from that used in the nominal instrument modes. As the Cluster spacecraft are spin stabilized (nominal spin period is 4 s) any significant reduction in the data rate for the spin plane components requires the use of an on-board de-spin function in order to realise a spin or sub-spin vector rate – simple averaging of the sampled spinning spin plane components is not valid and would result in component mixing. Remembering that spin average time series of higher rate nominal mode data are commonly used data products the most logical and easily implemented candidate for a reduced rate sample store was spin synchronised with one averaged vector per spin being stored to memory. Each FGM contains 192Kbytes (96 K words) of MSA memory, which is normally used for capturing short periods of high time-resolution data (approximately 200 samples/s). At the time of loss of science data coverage the FGM is commanded into FGMEXT utilising the MSA to store long periods of spin averaged data (Balogh et al., 2001). The data stored by the MSA is held frozen until the next scheduled burst-memory downlink (a spacecraft telemetry mode known as ‘Burst-Mode 3’, BM3) where it is downloaded to ground. Typically there are two BM3 dumps over the course of an orbit after which the MSA is set unfrozen and is again
Fig. 1. Bryant plot showing the data and mode coverage for initial half year of Cluster operations. The dotted lines indicate periods along the orbit when there is no data coverage, i.e. the instruments are either switched off or quiescent, with no data recorded by the spacecraft. These are periods when the FGM could be switched to FGMEXT mode. (Plot courtesy of the Cluster Joint Science Operations Centre.)
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available for data taking from event capture or during the next scheduled FGMEXT interval. With this mode an additional 27 h of data can be recovered from non-telemetered periods which would otherwise be lost In this low resolution mode the instrument continuously measures the spacecraft spin period by calculating the elapsed time between successive sun reset pulses (SRP) and synchronising vector acquisitions to a fixed number of spin sectors. Sampled vectors are de-spun, averaged and stored to the MSA. The number of spin sectors and averaging length is fixed at 512. This value has been selected according to the underlying instrument sample rate (201.793 vectors per seconds) and the need for a power of two arising from the fact that the instrument DPU (Data processing Unit) is only capable of integer arithmetic. Although the science channel to the spacecraft bus is closed during FGMEXT operation, a reduced set of instrument Housekeeping (HK) voltages and temperatures are sent to the spacecraft bus for the purpose of health monitoring. Data is taken only by the primary sensor (Outboard sensor by default) so the secondary sensor (Inboard) is switched to a safe gain range prior to the switch to FGMEXT. Processing of the measured FGM vectors requires them to be transformed from the rotating frame of the spacecraft (or de-spun). For the MSA low resolution vectors, de-spin is achieved by implementing a Walsh Transform with Haar coefficients based on the equations shown in Table 1. These are applied in the sensor coordinate frame where Bx is nominally aligned with the spacecraft spin axis and By and Bz are the spin plane components. The transform estimates the true sinusoidal de-spin vector with a square wave approximation which is much easier to implement in assembler code and with integer arithmetic. An artificial phase delay is needed onboard in order to avoid evaluation of the function at the zero crossing points where the Haar coefficients are undefined. The scheme is similar to that implemented in hardware by the magnetometer on-board the Ulysses spacecraft (Balogh et al., 1992). Extended Mode was tested during the post-launch instrument commissioning phase but routine switching into FGMEXT was implemented only after the BM3 dumps were included in the Master Science Plan. Thus Extended Mode became operational on orbit 113 (March 2001) and
Table 1 FGMEXT de-spin and averaging equations
C H ðtÞ ¼
cosðxtÞ j cosðxtÞ j
S H ðtÞ ¼
sinðxtÞ j sinðxtÞ j
where BZ = De-spun Z component BY = De-spun Y component N = 512
PN 1 p BZ ¼
i¼0 4 ½BZSi C Hi
N PN 1 p
BY ¼
BYSi S Hi
i¼0 4 ½BZSi S Hi
þ BYSi C Hi
N
BZS = Sampled Z component BYS = Sampled Y component CHSH = Haar functions
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all periods outside of AI since this orbit have seen automatic switching of the FGM instruments into FGMEXT on all four spacecraft. The frequency of Extended Mode intervals is much higher in the early years of the mission before the implementation of full data coverage along the Cluster orbits during 2002. At the present time Extended Mode still provides magnetic field data during intervals when other Cluster payload are not taking data such as the period surrounding long eclipses, during spacecraft manoeuvres and other periods of special operations on the spacecraft. 3. Deriving the vector timeline Recovery of the Extended Mode vector timeline is significantly different to that of the in-coverage Normal and Burst Mode packets encountered during routine data processing. For these modes the UTC time in the packet header (supplied by the spacecraft) has a clearly defined relationship with the time of the first vector in each packet, recorded by the FGM internally using a spacecraft derived High Frequency (HF) 4096 Hz clock. This FGM time stamp is written to the science packet with a resolution of better than 250 ls. Subsequent vectors in the packet are time stamped by extrapolation based on the known instrument sampling rate. The method works because vectors sampled over the course of a spacecraft frame (reset period is 5.15222 s) are always packetised during the following frame and so an absolute time reference connects the FGM internal time stamp to the UTC header in the downlink packet. In this way an absolute UTC reference is availed of each and every packet (every 115 vectors in the 22.4 Hz NM mode) during processing of the FGM Normal and Burst Mode data and the time stamp of every vector can be unambiguously recovered from the contents of the FGM Science data stream alone. The Extended Mode data however, necessarily requires a more complicated time stamping scheme due to the fact that there is no relationship between the UTC header time of the downlink packet and the time stamp of any vector in the Extended Mode data, the time difference between them is completely arbitrary and is determined by the length of the Extended Mode period and also the timing of the BM3 dumps. The simplest timing scheme must have the ability to relate UTC time to the time of at least one vector from the Extended Mode packet and ideally the first vector. Given this it should be then possible to extrapolate the timeline for all subsequent vectors inside the Extended Mode packet based on an assumed spin period. By patching the FGM to ensure that the time of the first SRP is transmitted in the last valid HK packet prior to the switch into FGMEXT it has proved possible to calculate a UTC time stamp of the first de-spun vector. Subsequent vector time stamps are extrapolated based on the initial spin rate estimate. This scheme is utilised during the special processing of Extended Mode data discussed here.
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Fig. 2. Plot showing a running average of number FGM HF Clock ticks (1 tick corresponds to 240 ls) between successive SRP during 20th Feb 2001 for all four S/C. All traces have been offset to a nominal spin period of 4.0 s so that the trend on all four spacecraft is clearly visible. It can be seen that the drift in the sun pulse is minimal over typical Extended Mode interval lengths.
system to a more scientifically useful de-spun geophysical co-ordinate system such as GSE (Geocentric Solar Ecliptic) or GSM (Geocentric Solar Magnetic). The transformation includes the orthogonalisation of the three components of each vector with a calibration matrix and subtraction of an associated offset vector. The calibration matrix contains corrections to sensor parameters affecting the nominal values for the sensor gains and mis-alignments. The offset vector corrects for the presence of zero-level reading. The calibration matrix and offset vector are typically computed on a daily basis and, in the case of a spinning spacecraft such as Cluster, are related in a complex but deterministic way to the power levels of individual field component at spin and twice-spin harmonics (Kepko et al., 1996). In fact, without a secondary absolute B-field reference available on-board such as a scalar magnetometer (Dougherty et al., 2004) a complete solution to the calibration problem is extremely difficult. Nevertheless, through careful extrapolation of calibration parameters determined on ground as
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The scheme is not foolproof as it assumes that the drift in spin rate is negligible over the course of the Extended Mode sample otherwise an accumulating timing error will manifest itself. Fig. 2, for example, illustrates the drift in sun-pulse period for a typical day from February 2001. The plot graphs the change in running average of the number of ticks of the HF clock between successive sun pulses recorded by each Cluster FGM over the course of 24 h (while the spacecraft were in the solar wind and magnetosheath). For all four spacecraft the change is significantly less than 1 sun-pulse tick (<250 ls) which is within the accepted resolution used for processing normal and high resolution vectors. Thus we can see that for nominal operations during a typical period of data acquisition, the spin rate of all four spacecraft is extremely stable and so the extrapolation method proposed can be taken to be reasonable as a first order approximation. However it may well be the case that the sun-pulse drift will be much greater in periods after eclipse. It is worth noting that the timing scheme outlined above is fundamentally different from the in-coverage time stamping schemes. Instead of just a single science packet containing all information needed to produce a time series vector it is necessary to synchronise processing of HK and Science data in order to time stamp the Extended Mode data. This is a direct result of having only a HK channel data link to the spacecraft available at the instant of the switch into FGMEXT.
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Figs. 3 and 4. (Zoom of 3), Plot showing Normal Mode derived (C1) and Extended Mode (C2) field magnitude spin averages during a sequence of bow shock crossings. The traces clearly overlap overall to a high degree and features are well matched.
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well as applying some statistical techniques in-flight (e.g. Hedgecock, 1975) it is possible to closely approximate the real underlying sensor transfer function. Almost always the largest calibration errors are associated with the sensor which is most closely aligned with the spin axis (corresponding to Bz GSE on-board the Cluster spacecraft). It is not possible to apply the calibration process as described above to the Extended Mode data due to the fact the FGMEXT sample rate is equal to that of the spin rate and thus the spin frequency and twice-spin frequency are outside the FGMEXT Nyquist. Furthermore the on-board de-spin has the effect of mixing the offset and mis-alignment terms of the individual spin plane components (Bx GSE and By GSE). This situation could be addressed by up-linking offsets to the FGM on-board and including an offset subtraction instruction prior to de-spin within the Extended Mode algorithm. However due to memory constraints such a code modification in-flight was not possible. Fortunately the effect of averaging on the spin plane mixing results in cancellation of offset terms as will be seen in the
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Figs. 7 and 8. (Zoom of 7), Plots show Normal Mode derived spin averages (C2) and Extended Mode (C1, C3 and C4) as the tetrahedron traverses outbound from perigee through the magnetosphere, across the magnetopause and into the sheath. Again we see that major features are resolved and traces are consistent excluding small offset effects.
examples below. We are therefore limited to a subset of calibration parameters that can realistically be applied to despun data without the development of some new technique. As a first order correction, the calibration has been confined to spin axis offset and gain correction (applied to Bz: its situation can be taken to be unchanged from the normal calibration process as applied to higher-rate data) and an average gain applied to the de-spun Bx and By components. Errors due to mis-alignments in the spin plane data are ignored in the first instance. 5. Comparative observations
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Figs. 5 and 6. (Zoom of 5), Plot showing Normal Mode derived (C1) and Extended Mode (C2, C3) field magnitude spin averages during a solar wind passage. We can see good tracking over sharp boundaries and wave structures appear coherent and are well resolved.
A combination of operational factors resulted in a small number of unexpected intervals in early 2001 where Normal (22.4 Hz) and Extended Mode (0.25 Hz) data periods overlap on different spacecraft. This allows for limited comparisons to be made on the quality and timing of the
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Extended Mode data. Spin averages for three of these intervals are presented below which include combinations of one or more spacecraft traces. The traces follow the standard Cluster colour convention (C1 – black, C2– red, C3 – green, C4 – magenta). Given the constraints and presence of error sources with respect to the use of the Walsh transform, timing errors associated with a drifting spin rate as well as calibration errors due to offset and mis-alignment mixing from the on-board de-spin, one might expect that comparative observations between well calibrated NMderived spin averages and those produced by Extended Mode would reveal disparities in appearance of structures and associated timings. However, as the three examples presented below demonstrate there is surprisingly good matching between both types of data. The first example in Fig. 3 shows dual traces from spacecraft 1 and 2 during a sequence of bow shock crossings. The traces clearly overlap overall to a high degree and the detail shown in the expanded view in Fig. 4 confirms
that all features both in the magnetosheath levels and in the upstream region are well matched in both cases. There is an apparent small, residual offset on spacecraft 1, which is clear for the short interval around 6.6 UT. This appears to be due to a residual spin axis offset rather than arising from the different sampling positions of the spacecraft. Figs. 5 and 6 show a similar pair of plots (one expanded view) for three spacecraft traces, where spacecraft 2 and 3 are obtained from the Extended Mode data, sampling a burst of waves upstream of the bow shock. Clearly all the traces track the waves coherently in a sequence which can be shown to be consistent with the spacecraft positioning. The offset on spacecraft 1 is apparent in Fig. 6, and it is also clear the two Extended Mode traces track each other at least as well as they do spacecraft 1 and contain no significant offset. We lastly show an illustration with all four spacecraft traces for a dawn-flank, outbound magnetopause crossing in Figs. 7 and 8. The traces for spacecraft 1, 3 and 4 are
Figs. 9–12. Cluster orbit (S/C1) and tetrahedron configuration projections in the X–Y GSE and Y–Z GSE planes, together with model magnetopause. Spacecraft separation is of the order 2000 km. The derived spacecraft crossing order through the magnetopause boundary is consistent with that observed in the time series, namely C1, C4, C2 and C3 indicating that the Extended Mode timing is working correctly to a first order test.
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1 For interpretation of the references to colour in this text, the reader is referred to the web version of this article.
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reconstructed from the Extended Mode data. Figs. 9 and 10 show the corresponding orbit plots for the event, with an expanded view of the spacecraft configuration at the time of the magnetopause crossing. The spacecraft are located in the northern hemisphere so that the expected orientation of the magnetopause surface is as indicated by the green line, cutting through the XY plane, and is tilted into Y1. Since spacecraft 3 and 4 lie below the plane, the expectation is that spacecraft 1, 2 and 4 will exit the magnetosphere closely in sequence, and spacecraft 3 will exit a little later. The plots in Fig. 8 show just this sequence and this provides a good check on the integrity of the Extended Mode data streams. It is also true that spacecraft 3 lies inwards of the other spacecraft, relative to the tilted plane of the magnetopause, and this is reflected by the higher field magnitude measured on that spacecraft (Figs. 11 and 12). The Extended Mode dataset will be incorporated into the Cluster Science Data System as one minute averages. With this in mind it is useful to estimate the accuracy of the Extended Mode derived averages relative to a nominal dataset. Ideally we would do this by making a comparison of residual differences of data taken simultaneously in both Normal and Extended Modes on a single spacecraft. Unfortunately the operation of data acquisition in-flight precludes this possibility so that the comparisons here have been made between different spacecraft in different modes. Although the data are expected to be similar between two spacecraft, the residuals will contain differences arising from actual differences in the magnetic field at each spacecraft location in addition to any arising from the differences of mode between the two data streams. To better illustrate the comparison, Fig. 13 shows dual traces from the bow shock example discussed previously as one minute averages of the field magnitude. In the figure, the Normal Science data from spacecraft 2 have been interpolated onto the Extended Mode spacecraft 1 vector timeline and the residuals are plotted in blue. A histogram of the residuals is shown in Fig. 14. These may be compared directly to Fig. 15, which shows spacecraft 1 and 2 dual traces in the same format, as Fig. 13, but now with both sets of averages derived from Normal Mode data and Fig. 16 which displays a histogram of the residuals. The data shown in Fig. 15 are taken from a bow shock crossing during the orbit immediately following that of the Extended–Normal Mode comparison, while the spacecraft were in a similar location and configuration. The magnetic field profile encountered in both examples is fairly representative of the natural signal to be expected during a bow shock crossing. These figures together, therefore show that the Extended Mode data stream is as representative as the Normal Mode data, since the residuals remain similar in each case. A mea-
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Figs. 13 and 14. Plots showing Normal Mode derived (C1) and Extended Mode (C2) field magnitude one minute averages and C2–C1 residuals (blue) together with histograms of the residuals for the bow shock crossing on 27th April 2001. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
sure of the fidelity of the Extended Mode field recovery can be inferred from the similarity in the spread of residuals in the two histograms, i.e. if the fidelity is high then both sets of residuals should show a similar level of spread. This is exactly what is visible in the two histograms. The comparison demonstrates that the Normal Science – Extended Mode residuals are dominated by the temporal and spatial differences expected at these spacecraft separations (<1000 km) rather than by limitations in the de-spin algorithm. Thus, we may conclude that the Extended Mode derived averages can be regarded as suitable for the purpose of contextual information and provide an accuracy which is limited primarily by the errors associated with the reduced calibration applied on ground, typically of order a few nT. It therefore compares well with Normal Mode Quicklook data.
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The resultant time series compares well with spin-average data derived simultaneously from Normal Mode acquisition, in light of the limitations in the de-spin function and applied calibration. The illustrations here have provided supporting evidence of:
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Good tracking of structures between Extended Mode datasets. Good tracking of structures between Normal and Extended Mode datasets. Primary contribution to offset error is along the spin axis – calibration errors in the spin plane average towards zero. Calibration errors are not large enough to invalidate the dataset – the data quality is sufficiently good to validate its usability for the purpose of surveys. Some open issues remain regarding the time stamping of vectors. Current planning is for more detailed timing analysis of the above intervals in order to place an absolute limit on the Extended Mode vector’s time stamp accuracy. Following this it is the intention of the FGM team to incorporate this dataset into the Summary Parameter database during 2007.
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6. Conclusions The FGM on-board de-spinning algorithm has been shown to successfully recover the magnetic field vector.
Balogh, A., Dunlop, M.W., Cowley, S.W.H., et al. The Cluster magnetic field investigation. Space Sci. Rev. 79, 65–91, 1997. Balogh, A., Carr, C.M., Acunˇa, M.H., et al. The Cluster magnetic field investigation: overview of in-flight performance and initial results. Ann. Geophys. 19, 1207–1217, 2001. Balogh, A., Beek, T.J., Forsyth, R.J., et al. The magnetic field investigation on the Ulysses mission: instrumentation and preliminary scientific results. Astrophys. Suppl. Ser. 92, 221–236, 1992. Dougherty, M.K., Kellock, S., Southwood, D.J., et al. The Cassini magnetic field investigation. Space Sci. Rev. 114, 331–383, 2004. Escoubet, C.P. (Ed.). Cluster special issue. Ann. Geophys. 19 (10/12), 1195–1730, 2001. Kepko, E.L., Khurana, K.K., Kivelson, M.G. Accurate determination of magnetic field gradients from four point vector measurements – Part 1: use of natural constraints on vector data obtained from a single spinning spacecraft. IEEE Trans. Mag. 32 (2), 377–385, 1996. Hedgecock, P.C. A correlation technique for magnetometer zero level determination. Space Sci. Inst. 1, 83–90, 1975. Paschmann, G., Schwartz, S.J., Escoubet, C.P., Haaland, S. (Eds.). Outer magnetospheric boundaries: Cluster results, Space Sci. Rev. 118 (1–4), 2005.