We present an in situ calibration process to derive the transient behavior of the offsetting fluxgate magnetometer (MGF) instruments on the Cassiope spacecraft. The dynamic behavior of the MGF changed on orbit following a software update. Characterizing the new instrument dynamics during normal spacecraft operations and then removing the transients was confounded by significant magnetic interference from the reaction wheels used to orient the spacecraft. Special operations were performed where data were taken in a safehold mode, with the reaction wheels stopped, following a single-event upset of the spacecraft bus flight computer after transiting the South Atlantic Anomaly. The slow single-axis rotation of the safehold mode was used to characterize the fluxgate's new feedback dynamics. This characterization process was then adapted for routine operation intervals with slow reaction wheel rates to allow the transient behavior to be characterized over long intervals of data spanning a wide range of temperatures. Subtracting these characterized transients from the flight data improves the instrument's noise floor and allows the instrument to accurately track rapidly changing local fields without loss of measurement fidelity. More generally, this characterization process should apply to other situations where the dynamics of an offsetting instrument must be calibrated in situ.
The Enhanced Polar Outflow Probe (e-POP) payload onboard the Cassiope
spacecraft (Yau and James, 2015) includes the
magnetic field instrument (MGF) to study small-scale field-aligned currents
(Wallis et al., 2015). The MGF
comprises two matched fluxgate magnetometers, referred to as inboard and
outboard, deployed at different distances from the spacecraft on a common
boom. The MGF uses an offsetting design, where digitally controlled magnetic
feedback extends the magnetic range of the instrument allowing it to
maintain fine (62.5 pT) resolution even in the strong ambient field at a
perigee of
Dynamic spectra of one instrument channel with
The spacecraft maneuvers around 07:05 and 07:50 UTC, resulting in the visible spectral widening of the reaction wheel tones and their harmonics as the various wheel rates change. All components of the magnetometer experience rapid change as the spacecraft rotates, requiring many rapid updates to the digital feedback and resulting in the strong interference signal observed in the uncompensated spectra in Fig. 1a. Characterizing and correcting these transients, as described herein, significantly mitigates this effect resulting in the cleaner spectra shown as Fig. 1b.
Until now, these instrument transients have been mitigated by invalidating five samples after each update in post-processing and then restoring these values by interpolation. Unfortunately, during geophysically interesting intervals the local field can vary rapidly, necessitating frequent updates to the instrument's magnetic feedback and result in a high percentage of invalidated data. This can make the data interpolation poorly constrained as unaffected measurements of the magnetic field become sparse (see the example in Fig. 9 below). Consequently, the MGF data can be significantly degraded during times of large magnetic fluctuations that are associated with its nominal science goal of characterizing intense, small-scale field-aligned currents.
It is relatively straightforward to characterize this behavior in a laboratory environment using a magnetic shield and then subtract the known transients from the measured data. However, after launch, the characterization was complicated by the magnetic interference from the reaction wheels used to three-axis stabilize the spacecraft. The attitude control system attempts to spin the reaction wheels at a common nominal speed, creating a complex superposition of similar frequency sinusoids which separate during spacecraft maneuvers (Fig. 1a). We present in situ characterization of these feedback transients in the MGF instruments and their successful compensation. These data corrections resulted in significantly improved noise floor (Fig. 1b) and a time series reconstruction which is robust even in a rapidly varying magnetic field (Figs. 1d and 9 below).
The MGF is an initial step in adapting a terrestrial fluxgate magnetometer design (Narod and Bennest, 1990) for use in a space application (Miles et al., 2013, 2017; Wallis et al., 2015). The MGF is a classic second harmonic analog fluxgate (e.g., Primdahl, 1979) with the range extended by the application of a variable magnetic offset to the sensor (Fig. 2). The output of a digital-to-analog converter (DAC) is converted into a temperature-compensated current (Acuña et al., 1978; Miles et al., 2017; Primdahl, 1970) to cancel the majority of the ambient field in the sensor. This allows the forward gain of the instrument to be increased providing 62.5 pT resolution using a 12 bit analog-to-digital converter (ADC). A proportional control loop updates every four samples (40 Hz) and varies the magnetic feedback to hold the field in the sensor near zero. Feedback on each axis is controlled independently and triggers if the residual field exceeds 32, 64, or 128 nT and is stepped in those same increments back towards zero. Most feedback updates are 32 nT – the higher levels being triggered by occasional rapid field changes such as during auroral crossings. The local magnetic field is then reconstructed as the scaled sum of the applied magnetic offset and the measured magnetic residual in the sensor.
Block diagram of the MGF instrument showing the offsetting design whereby a digital-to-analog (DAC) converter applies a digitally controlled offset current to the sensor to partially cancel the ambient magnetic field. Reproduced from Wallis et al. (2015).
This offsetting design allows the instrument to preserve its resolution even
in the near-Earth magnetic field at
This transient behavior is typically characterized and removed following each DAC update to reconstruct an accurate measurement of the local magnetic field. However, a bug in the as-launched MGF firmware caused variable timing between the updates to the DAC and the ADC sampling of the residual field in each magnetometer channel. Consequently, the ADC sampled an arbitrary phase of the settling filter response, and the transient in the reconstructed magnetic measurement varied and could not be characterized and subtracted.
This behavior was verified in the laboratory by placing the engineering spare sensor in a magnetic shield and applying a slowly varying magnetic ramp (Fig. 3a). The transients after each DAC update create the ticks visible on the ramped magnetic field. Figure 3b shows sequences of measurements adjusted to zero before a DAC update, showing the envelope of possible transients caused by sampling the settling filter after a non-constant delay. New instrument firmware (V1.3.0) was developed to make the offset between the DAC update to ADC sampling constant; this stabilized the dynamic behavior of the DAC updates (Fig. 3c). The transients did not appear to depend on the slew rate of the field used to exercise the engineering sensor and scale with the size of the feedback step. This suggests the characterized transients should be repeatable even in the more erratic environmental fields experienced on orbit, although this is difficult to verify experimentally.
The two MGF flight instruments received the new firmware in April 2014. However, processing the data generated by the new firmware was complicated by the transient behavior after a DAC update being unique to each individual sensor and electronics hardware combination. The transient behavior of the engineering spare hardware, which was simple to characterize in the laboratory, could not be directly applied to the updated flight hardware on orbit.
The challenge was to characterize the transient behavior on each axis of the inboard and outboard flight sensors sufficiently to allow for compensation of the transients in the post-processed flight data. This was further complicated by the on-orbit data being contaminated by 5 to 25 nT of local magnetic noise from the reaction wheels.
The laboratory characterization technique cannot be directly applied to
in situ data. The reaction wheels used to orient the spacecraft create a
complex
For mission reliability reasons, the wheels are not permitted to be
commanded off during normal operations as there is a stiction failure mode
that had been observed in prior missions. Serendipitously, the onboard
spacecraft computer has experienced a little over a dozen reboots since
launch, many of these occurring over the South Atlantic Anomaly. As part of
the recovery, the spacecraft enters a safehold mode where it automatically
shuts down the reaction wheels. In this mode, the magnetorquers orient the
main solar panel to the sun and trigger a
Two of these 30 min no-wheel intervals were used for an initial fit of
the transient behavior. The calibration was undertaken by looking for DAC
updates on each channel that were separated by at least 32 samples to ensure
that the analog electronics had fully settled before they were perturbed by
the subsequent DAC update. Further, the transients weakly couple between the
The sinusoidal trend created by the spacecraft spin can be approximated as linear over the 32 sample (200 ms) interval allowing the samples following a DAC update to be estimated and the transient tick to be measured. Robust linear regression was used to fit and remove any background trend during the interval (Fig. 4b). The known scaling between the feedback from the DAC (32 nT per bit) and the ADC forward loop (0.0625 nT per bit) was used to subtract the step function expected after a DAC update and reveal the transient behavior of that axis (Fig. 4c). Robust linear regression was used again to ensure that the transient starts and ends at 0 nT, and a median average was used to estimate the transient correction while ignoring outlying values (Fig. 4d).
Estimates of transient behavior of each channel of both MGF
instruments. The larger transients due to DAC
Figure 5 shows the 18 corrections fitted from
the spinning no-wheel data corresponding to the instrumental
Applying these fitted correction coefficients to several years of MGF
observations showed that the transient behavior was dependent on
temperature of the instruments' electronics package (the sensor temperatures
were recorded as well but did not have a significant effect). However, due
to technical restrictions in the spacecraft recovery process, the safe-mode
no-wheel data were only obtained after the MGF had been in the shadow of
the spacecraft for some time, which caused the instruments to be unusually cold
(
Equivalent analysis to Fig. 4 but for an interval with slowed reaction wheels.
In 2016, one of Cassiope's original four reaction wheels failed. Rebalancing
the spacecraft attitude control required that the remaining three wheels be
slowed from
Transient fitting was repeated for all data taken after the wheels were
slowed (June 2016 to December 2018). The data were then sorted into
temperature bands from
Corrections for the transients in the MGF data are applied by subtracting
the characterized ADC transients from the reported ADC readings after each
DAC update. Figure 8 shows a representative
correction for DAC
Uncorrected and corrected time series following DAC updates
Figure 1 uses a dynamic spectrum to visualize the spectral content of the uncompensated (a) and compensated (b) time series. Note that the amplitude of the vertical striping, caused by the broadband content of the transients, is almost completely suppressed.
Cross-track magnetic field measurements of an ion heating event
studied by Shen et al. (2018) with
high-amplitude small-scale magnetic perturbations. The presented transient
compensation technique captures
Figure 9 shows an event studied in Shen et al. (2018) where e-POP encountered
large in situ field variations associated with ion heating and downflow that
require instrumental slew rates exceeding 3000 nT s
The described in situ characterization and compensation successfully
mitigates the transients in the MGF data following updates to the digital
magnetic feedback. The current compensation is based on 2.5 years of data
and the transients have been fit to better than 0.5 nT for most instrument
temperatures. This correction allows MGF to resolve large-amplitude and
small-scale magnetic features of
The MGF data processing software (mgftools) described herein is maintained
in the Cassiope mission Subversion repository. Release versions of this code
are available at:
Science data from the e-POP mission are available via http via an open
date-driven folder tree at:
DMM is the PI for the MGF payload on e-POP, developed the data product processing code for the MGF, performed the in situ calibration described here, and prepared the paper with contributions from all co-authors. ADH developed the ground data-product processing software infrastructure and helped test the V2.0.0 data processing code. GAE is the e-POP mission manager and coordinated the special safe-mode operations that produced the wheel-free data used in this paper.
The authors declare that they have no conflict of interest.
The authors wish to thank Don D. Wallis, B. Barry Narod, John R. Bennest, and Jonathan E. Schmidt for insight into the operation of the MGF instrument. Andrew W. Yau, Michael J. Miles, Sarah E. Miles, and Robert M. Broadfoot provided comments on an early copy of this paper.
This research has been supported by the European Space Agency (Third Party Mission Programme), the Canadian Space Agency (Cassiope/e-POP Operations), and the University of Iowa (College of Liberal Arts and Sciences New Faculty Startup).
This paper was edited by Valery Korepanov and reviewed by two anonymous referees.