the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 01 Apr 2022
In-Situ Calibration of the Swarm-Echo Magnetometers
Abstract. CASSIOPE/e-POP, now known as Swarm-Echo, was launched in 2013 to study polar plasma outflow, neutral escape, and the effects of auroral currents on radio propagation in the ionosphere. The e-POP suite contains an array of eight instruments which include two fluxgate magnetometers on a shared boom. Until now, the two magnetometers relied on a set of prefight calibrations which limited the accuracy of the magnetic field product and their utility for some applications. Here we present the results of an in-situ calibration performed between on data from January 3, 2014, to January 30, 2021, and a case study showing the improvements the calibration has made to the data utility. Periodic vector-vector calibration using the Chaos magnetic field model results achieves an estimated RMS uncertainty of 9 nT during nominal operation. This data-product is now openly available through the ESA Swarm repository.
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RC1: 'Comment on egusphere-2022-59', Mark Moldwin, 19 Apr 2022
In-Situ Calibration of the Swarm-Echo Magnetometers
Robert M. Broadfoot, David M. Miles, Warren Holley, Andrew D. Howarth
This paper describes an in-flight calibration method for the CASSIOPE/e-POP, now known as Swarm-Echo, satellite that was launched in 2013 and included two fluxgate magnetometers on a shared boom. Several issues with the attitude determination system, failure of reaction wheels over time, and the natural drift of off-set and gains of the fluxgates contributed to the magnetometer data becoming less reliable. The paper describes applying a method to use the Earth’s model geomagnetic field during quiet times and some rules on when to trust or discard attitude determination estimates to create a new “clean” magnetometer data set.
This is a useful paper describing the new calibration methodology and will enable expanded scientific use of the SWARM-ECHO magnetic data set.
Specific and General Questions interspersed below.
- Line 11: “calibration performed on data from January 3, 2014, to January 30, 2021”
- What is the length of the boom and the distance to the two magnetometers?
- Line 20, for comparison – what is the orbital altitude of e-POP compared to the other SWARM spacecraft? Are there any “conjunctions” that can be used to calibrate magnitude (and with field-line tracing) the direction of the field between the SWARM spacecraft?
- Line 34: Suggest breaking last clause into separate sentence…” attitude. However that time interval is beyond the scope of this manuscript.”
- Line 65, 125: “data have…”
- Line 135: What is SQUAD/SLERP?
- Line 151; Is “&” used intentionally instead of “and”?
- Line 164: “metadata are…”; Line 165: “and are included”
- A lot of the work is attempting to get a good handle on the attitude of the spacecraft despite the loss of sensitivity of the star trackers and other ADS efforts. Is there housekeeping information that tells you when different subsystems are on or off to attempt to assess the magnitude of the spacecraft noise? What is the relative magnitude of the residual pointing accuracy error on the final data product compared to your estimate of the spacecraft noise?
- Line 192: “…important than the quantity” (than instead of that)
- Line 208: What is the effect of saturation of the sensor heads in terms of calibration? Was this a big effect initially (compared to the ground-calibration values), but once sensors were repeatedly permed up on orbit, minimal effect? (From Table 1 there seems to be essentially no impact on Gain.).
- Table 1: Though having a large stray field from the boom makes sense since the large X offset is seen in the outboard sensor and not the inboard, what is the boom made from that could give such a large field? It would be of interest to see the pre-flight off-set values to get a sense of the combination of the spacecraft fields and off-set drift combined.
- Line 250: “taken”
- Figure 5. Is this “all” the data or only Kp<3 and small change in Dst “quiet” data?
- Line 279: “….in in-situ…”
- Was the inboard and outboard sensor used in a “Ness”-type gradiometer way to remove any spacecraft noise? If not, why not?
- Figure 6. What are the red and blue traces in panel b?
- A wild idea not necessarily to pursue for this study (following on the “conjunction” idea in a statistical sense given above), is to use the other SWARM satellites to determine the magnetic equator (when the field is horizontal) and compare locations of Echo with the other SWARM for different 7 day intervals. The poles do shift and move over months/years, but the equator should be pretty “fixed” over multiple 7 day intervals allowing for Echo to pass over the same longitude sector. The offset in location potentially can be used to estimate “off-set” in angle using the CHAOS field line mapping.
Citation: https://doi.org/10.5194/egusphere-2022-59-RC1 -
AC1: 'Reply on RC1', Robert Broadfoot, 20 Apr 2022
Thank you for the suggested corrections, those will be implemented on the next upload.
I will attempt to answer all the questions to the best of my ability. Some of these will be vague as they involve work going on behind the scenes that I am not directly involved in (yet), and will provide more information on them when it becomes available.
I will preserve the original number of the question for easier reference.
2. What is the length of the boom and the distance to the two magnetometers?Boom length is 0.9 m. There is ~40-45 cm of separation between the two magnetometers. I am not sure of the exact number and will get back to you once it can be found.
3. Part 1: what is the orbital altitude of e-POP compared to the other SWARM spacecraft?
The main Swarm spacecraft have roughly circular orbits at ~450 km for A and C and >500 km for B. e-POP was considered to be a desirable addition to the Swarm constellation because the orbit is highly elliptical with perigee at ~330 km and apogee at ~1400 km. As such, it gets an expanded look at the magnetic field as it completes a full orbit cycle
3. Part 2: Are there any “conjunctions” that can be used to calibrate magnitude (and with field-line tracing) the direction of the field between the SWARM spacecraft?Quite a few conjunctions do exist, and there are files that detail each one. It will be interesting to find one of these conjunctions and see what we can learn from it.
6. What is SQUAD/slerp?The line in the paper can be edited to provide clarity. Essentially, they are methods of quaternion interpolation. The SQUAD/slerp refers to one or the other depending on what is needed.
More specifically: slerp stands for spherical linear interpolation and refers to interpolating between two orientations by moving at constant speed along a circular arc (as opposed to linear interpolation or lerp which idealizes the change in orientation by using linear polynomials and tends to result in very large angles of arc between each interpolation point). This is sufficient if there is a small enough change between orientations and can treat each interpolation between two points as isolated, or either you don't know or don't really care if other changes in orientation exist before or after.
SQUAD or Spherical QUADrangle interpolation is a series of slerp interpolations that assumes that other orientations exist before, during, and after the current interpolation between the two points. It smooths the connections between the interpolations as it does not treat each interpolation as an isolated event. This has roots in computer animation and is useful for smoothing movement between multiple animation frames. This of course translates well to spacecraft attitude as the craft is constantly changing orientation while moving along the orbital path.
9. Part 1: A lot of the work is attempting to get a good handle on the attitude of the spacecraft despite the loss of sensitivity of the star trackers and other ADS efforts. Is there housekeeping information that tells you when different subsystems are on or off to attempt to assess the magnitude of the spacecraft noise?
Yes there now is a publicly available housekeeping plot that shows what instruments were active and at what particular times. There is also a public BUS telemetry file that contains flags for when other various spacecraft subsystems turn on or off. Both of these are aiding us in our current quest to assess the impact of potential noise sources. Though first we need to remove the noise from the reaction wheels before we can get a good handle on other noise sources since they tend to dominate.
9. Part 2: What is the relative magnitude of the residual pointing accuracy error on the final data product compared to your estimate of the spacecraft noise?-I will need to get back to you on this one.
11. What is the effect of saturation of the sensor heads in terms of calibration?
Was this a big effect initially (compared to the ground-calibration values), but once sensors were repeatedly permed up on orbit, minimal effect? (From Table 1 there seems to be essentially no impact on Gain.).The saturation occurs in the forward analog loop of the electronics and not in the sensor head itself. As such, it should not have an impact on calibration.
12. Table 1: Though having a large stray field from the boom makes sense since the large X offset is seen in the outboard sensor and not the inboard, what is the boom made from that could give such a large field? It would be of interest to see the pre-flight off-set values to get a sense of the combination of the spacecraft fields and off-set drift combined.This one is a bit of a sore spot. Compared to the preflight zeros, the offsets found in-situ are comically large and cannot be explained by the stray fields from expected noise sources, nor can it be a product of the instrument aging as those numbers have shown up from the beginning. It is also not the boom as it is made from carbon fiber. Rather, it is likely from something not magnetically clean that was used to either secure the magnetometer or something near it on the boom and was not part of the initial design. This is especially unfortunate because it appears to magnify the effects from drift (and periodic effects). It also results in a larger RMS error post-2016 in the calibration compared to the Inboard sensor which is closer to all of the spacecraft noise.
14. Figure 5. Is this “all” the data or only Kp<3 and small change in Dst “quiet” data?This is "all" of the data (provided it was generated when one or both star trackers were providing primary attitude and the spacecraft was not undergoing a change in angular rate > 0.03 deg/sec). The Kp and Dst flags are only applied during calibration and kept separate from the final data product.
16. Was the inboard and outboard sensor used in a “Ness”-type gradiometer way to remove any spacecraft noise? If not, why not?As far as I know for the current processing chain, it has not. From the Wallis et. al 2015 paper, it appears that it was used early in the mission however it was abandoned when we began the in-situ calibration. The largest source of spacecraft noise by a considerable margin comes from the reaction wheels. This is especially prevalent prior to the first wheel failure in August 2016, but still is a considerable source after. Based on a limited understanding of Ness, I don’t know if it would be sufficient for removing the reaction wheel tone from before or after August 2016 as both contain large non-dipole terms.
We have tested different algorithms, two of which (simple differencing and a notch filter) were not magnitude persevering or had difficulty adapting to changing wheel rates. There will, however, be a paper being submitted soon by a post-doctoral researcher in the lab regarding a method that has shown success, especially in the early mission.
17. Figure 6. What are the red and blue traces in panel b?
The red and blue traces represent the cross-track measurements from Swarm-A and Swarm-C which passed through the same region of interest at a different time, which is useful from a scientific perspective . Those were not included in the recreation as the main goal was to show the change in the e-POP measurements. As a follow-up, it will be interesting to revisit the analysis done in the original paper and see what if anything has changed with the recent calibration and attitude updates.
Citation: https://doi.org/10.5194/egusphere-2022-59-AC1 - AC2: 'Reply on RC1', Robert Broadfoot, 16 Jun 2022
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RC2: 'Comment on egusphere-2022-59', Kenneth R. Bromund, 13 May 2022
General Comments
----------------This is an important paper describing the methods used to calibrate the processed CASSIOPE fluxgate magnetometer (MGF) data products that are currently available to the public.
The results are impressive. However, the style is uneven and at times there are errors, omissions or inconsistencies that must be remedied in order to make the descriptions of the methods sufficiently accurate for publication.
Specific Comments
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Section 1:Line 49: Tests were run to evaluate mutual interference of the two sensors. Was any interference identified? If so, how is this information used to aid the calibration process?
Section 3:
Although Olsen et al. (2003) is referenced for the notation used in this paper, there are many departures from this notation in this section, and it is unclear how the notation in this section relates to the results presented in Section 7.
Line 67: it would be more accurate and consistent with Olsen et al (2003) to say that the raw sensor data, E, is in engineering units that are approximately equivalent to nT.
line 71, As used in Equation (1), b is a pseudo-vector (in a non-orthogonal system), and in engineering units. specifying 1,2,3 is appropriate for the non-orthogonal system, but I note that this is inconsistent with Table 1... do the results offX, offY, offZ in Table 1 correspond to b1, b2, b3 (in which case, they might be labeled as engineering units, not nT), or are they actually nT (ie they are the offsets to be subtracted in the orthogonal, calibrated system)?Line 74: It would be appropriate to describe the dimensions of S as eu/nT, consistent with the results in your Table 1 in section 7. Subscripts 1,2,3 would be more appropriate, as S is in the non-orthogonal system...
Lines 78-79, If Equation (4) is correct, then the angles u1, u2 and u3 are not the same as the angles of the same names in Olsen et al. (2003). Please describe how u1, u2 and u3 defined, and their relation to the angles Oxy, Oxz, and Oyz reported in Table 1. Are they the angles between each pair of the slightly non-orthogonal sensors 1, 2, 3? While a figure would be helpful, it would be sufficient to define the terms clearly in the text, indicating, for example, that P represents the projections of sensors 1, 2, and 3 onto the orthogonal magnetometer reference frame, that sensors 1 and 2 are presumed to be in the X-Y plane, etc... Consider using a different notation (e.g. o12, o13, o23 ) that clarifies that these angles are not same as u1,u2,u3 in Olsen et al. (2003).
Lines 79-80. The definitions of the Euler angles (order 1-2-3) appears to differ from Olsen (2003), can you provide a reference? A more detailed description would be helpful to evaluate the physical significance of each parameter, when evaluating the results presented in Section 7.
Section 4:There is discussion of the "original" attitude system based on STK, but it is not clear what is the relevance of this system to this study. Was it relevant to previously released versions of the data? If so, please specify.
What were the methods used to verify and obtain the revised attitude solutions that "included improved alignment between different star camera modes, corrections for chromatic aberration and thermal effects in the star cameras, and corrections to frame, location, and epoch transforms"?
Is the uASC accuracy of <2arcseconds achieved only the beginning of the mission, or is this the lifetime accuracy specification? How was this verified?
Line 135: At this point, it is enough to know that "improved methods of attitude interpolation are applied to achieve robust attitude transformations", and leave the detail about SQUAD/SLERP to section 5, where you provide the reference...
The relationship between section 4 and section 5 is confusing. In some ways, section 4 appears to be intended as an introduction to section 5... It would be helpful to mention which topics will discussed further in section 5, and which topics are beyond the scope of this paper.
Section 5:I feel like I should be able to understand exactly what this section is talking about, but I'm finding it extremely difficult to follow.
Lines 138-139: This sentence is unclear. I think it's a typo. Is it intended to say:
"In-situ calibration of the MGF instruments requires rotating the reference magnetic field from its native North,
East, Center (NEC) frame into the local CRF frame of the spacecraft by convolution against the spacecraft attitude solution." ?
Line 143-145: The wording of this sentence is very confusing, and I'm pretty sure I don't understand it correctly.... "The coordinate system that defines this spacecraft (SC) coordinate system..." I'm used to thinking of SC coordinates to mean a system fixed to the spacecraft, and the reference to Figure 2, in particular, appears to re-enforce that assumption: It is the same figure that is used to illustrate the CASSIOPE spacecraft frame (CRF?) in the CASSIOPE DATA HANDBOOK online... Meanwhile, this sentence appears to describe a coordinate system defined by the spacecraft orbit: ie. one in which "+X points towards ram [and perpendicular to nadir], +Z points nadir, +Y completes the right-handed system". This is what the CASSIOPE DATA HANDBOOK calls the Orbital Reference Frame... is this what you are calling the SC coordinate system, in this paper? If so, then it does make sense to say that SC and CRF are co-aligned when YPR are all zero, as implied by this sentence....
Line 149: What is the relevance of this 'secondary-source attitude solution' if you are are using the raw star camera data to get superior revised attitude solutions? Do you have access to the raw quaternions representing the attitude of the star camera frame? Wouldn't the raw output of the star cameras be quaternions representing the star camera frame in the ECI J2000 coordinate system? How does J2000 get transformed to SC? The transformation would require the ephemeris as an input. Is this done on board, or is it re-calculated on the ground?Line 156: "the attitude solutions are then rotated into CRF": rotated nto CRF from what system? Does this mean, for example, that you apply an X-to-CRF rotation appropriate to each attitude knowledge source (X could be "star tracker A", "star tracker B", etc.) to obtain a CRF to SC attitude solution?
Line 158: SLERP is definitely to be recommended over per-element interpolation! I would be concerned about splining with SQUAD unless you are sure that the precision of each solution is much smaller than the change in attitude from one solution to the next.
Lines 158-161. Confusing sentence. Maybe SC serves as a refers to a specific coordinate system in the first instance, and as an abbreviation for 'spacecraft' in the second?In flight, one can only calibrate against the attitude determination system's idea of what CRF is, which will always contain a bias with respect to the mechanical CRF that was used to measure alignments on the ground. As you have noted, this bias will vary depending on the attitude source (star camera A, star camera B, etc.) and the solution will have varying levels of noise, depending on the source... Have you used the vector-vector calibration to evaluate the relative bias of each source, and then incorporated these bias corrections into the Swarm-Echo attitude CDF product? (That is what I assumed you meant back in section 4, when you mentioned 'improved alignment between different star camera modes'...)
Line 160: What is a Body-to-ITRF transformation? How is it derived? If Body = SC, then I would agree that a SC-to-ITRF is what is required at this point. It would be well-defined, given the ephemeris data expressed in ITRF as an input. A reference, or more details would be helpful. The documentation of the Attitude Quaternion File in the CASSIOPE PROCESSED DATA HANDBOOK seems to use the term "ITRF<-Body" to refer to the final attitude quaterion itself, rather than something used rotate the interpolated quaternions at this stage.
In any case, have you verified the accuracy of the ephemeris?
Lines 176-179: Reading this, it seems that SC and CRF are actually supposed to be the the same thing... So, either I misunderstand this paragraph, or I misunderstood everything leading up to it...
Line 180: What is SP3 format?
Section 6:The data selection methods described are all reasonable. The weighting method described in lines 220-228 seems appropriate, and is well referenced...
Section 7:
Table 1 and Figure 4: see my comments in section 3, regarding consistency of notation...
Line 256: what is meant by 'regularization'?Fig 4: Do you have an explanation for the greater variability observed on the outboard sensor, as opposed to the inboard sensor?
What mechanism is assumed to be the cause of the reaction wheel tone in the MGF data? Is it electromagnetic, or mechanical? If mechanical, it might explain why the deviations in the parameters is similar for both the inboard and outboard and outboards sensors, and that the outboard deviations appear to be slightly larger in some cases (the boom may amplify the vibrations at larger distances... ) if it is assumed to be electromagnetic, I would expect the outboard deviations to be smaller...
I note that for the outboard sensor, there is a significant correlation between variations in off_x and the e3 parameter... Perhaps only one of them is physically changing... What degree of angular error would correspond with an offset error of 15 nT?
Lines 249-250: sounds plausible... Can you show an example of the reaction wheel noise? Is it a monochromatic high frequency (whether electromagnetic or mechanical) that is aliased down into the MGF frequency range, or is it more broadband? What is the amplitude?Section 8:
I very much look forward to seeing these further developments!
For mitigating the reaction wheel tone: I would need to see examples, but I could imagine that more specific methods could be applied to identify and remove the 1 sps samples that are impacted by the reaction wheels... but indeed this might still require longer bins to make up for the lost data.
Technical Corrections
---------------------Line 59-60: typo, should be 'et al.'
Line 47: typo, should be 'stimuli'
Line 193: typo, should be 'more important than'
Line 250: typo, should be 'steps will need to be taken'Citation: https://doi.org/10.5194/egusphere-2022-59-RC2 - AC3: 'Reply on RC2', Robert Broadfoot, 16 Jun 2022
- AC4: 'Notification of correction to manuscript', Robert Broadfoot, 16 Jun 2022
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-59', Mark Moldwin, 19 Apr 2022
In-Situ Calibration of the Swarm-Echo Magnetometers
Robert M. Broadfoot, David M. Miles, Warren Holley, Andrew D. Howarth
This paper describes an in-flight calibration method for the CASSIOPE/e-POP, now known as Swarm-Echo, satellite that was launched in 2013 and included two fluxgate magnetometers on a shared boom. Several issues with the attitude determination system, failure of reaction wheels over time, and the natural drift of off-set and gains of the fluxgates contributed to the magnetometer data becoming less reliable. The paper describes applying a method to use the Earth’s model geomagnetic field during quiet times and some rules on when to trust or discard attitude determination estimates to create a new “clean” magnetometer data set.
This is a useful paper describing the new calibration methodology and will enable expanded scientific use of the SWARM-ECHO magnetic data set.
Specific and General Questions interspersed below.
- Line 11: “calibration performed on data from January 3, 2014, to January 30, 2021”
- What is the length of the boom and the distance to the two magnetometers?
- Line 20, for comparison – what is the orbital altitude of e-POP compared to the other SWARM spacecraft? Are there any “conjunctions” that can be used to calibrate magnitude (and with field-line tracing) the direction of the field between the SWARM spacecraft?
- Line 34: Suggest breaking last clause into separate sentence…” attitude. However that time interval is beyond the scope of this manuscript.”
- Line 65, 125: “data have…”
- Line 135: What is SQUAD/SLERP?
- Line 151; Is “&” used intentionally instead of “and”?
- Line 164: “metadata are…”; Line 165: “and are included”
- A lot of the work is attempting to get a good handle on the attitude of the spacecraft despite the loss of sensitivity of the star trackers and other ADS efforts. Is there housekeeping information that tells you when different subsystems are on or off to attempt to assess the magnitude of the spacecraft noise? What is the relative magnitude of the residual pointing accuracy error on the final data product compared to your estimate of the spacecraft noise?
- Line 192: “…important than the quantity” (than instead of that)
- Line 208: What is the effect of saturation of the sensor heads in terms of calibration? Was this a big effect initially (compared to the ground-calibration values), but once sensors were repeatedly permed up on orbit, minimal effect? (From Table 1 there seems to be essentially no impact on Gain.).
- Table 1: Though having a large stray field from the boom makes sense since the large X offset is seen in the outboard sensor and not the inboard, what is the boom made from that could give such a large field? It would be of interest to see the pre-flight off-set values to get a sense of the combination of the spacecraft fields and off-set drift combined.
- Line 250: “taken”
- Figure 5. Is this “all” the data or only Kp<3 and small change in Dst “quiet” data?
- Line 279: “….in in-situ…”
- Was the inboard and outboard sensor used in a “Ness”-type gradiometer way to remove any spacecraft noise? If not, why not?
- Figure 6. What are the red and blue traces in panel b?
- A wild idea not necessarily to pursue for this study (following on the “conjunction” idea in a statistical sense given above), is to use the other SWARM satellites to determine the magnetic equator (when the field is horizontal) and compare locations of Echo with the other SWARM for different 7 day intervals. The poles do shift and move over months/years, but the equator should be pretty “fixed” over multiple 7 day intervals allowing for Echo to pass over the same longitude sector. The offset in location potentially can be used to estimate “off-set” in angle using the CHAOS field line mapping.
Citation: https://doi.org/10.5194/egusphere-2022-59-RC1 -
AC1: 'Reply on RC1', Robert Broadfoot, 20 Apr 2022
Thank you for the suggested corrections, those will be implemented on the next upload.
I will attempt to answer all the questions to the best of my ability. Some of these will be vague as they involve work going on behind the scenes that I am not directly involved in (yet), and will provide more information on them when it becomes available.
I will preserve the original number of the question for easier reference.
2. What is the length of the boom and the distance to the two magnetometers?Boom length is 0.9 m. There is ~40-45 cm of separation between the two magnetometers. I am not sure of the exact number and will get back to you once it can be found.
3. Part 1: what is the orbital altitude of e-POP compared to the other SWARM spacecraft?
The main Swarm spacecraft have roughly circular orbits at ~450 km for A and C and >500 km for B. e-POP was considered to be a desirable addition to the Swarm constellation because the orbit is highly elliptical with perigee at ~330 km and apogee at ~1400 km. As such, it gets an expanded look at the magnetic field as it completes a full orbit cycle
3. Part 2: Are there any “conjunctions” that can be used to calibrate magnitude (and with field-line tracing) the direction of the field between the SWARM spacecraft?Quite a few conjunctions do exist, and there are files that detail each one. It will be interesting to find one of these conjunctions and see what we can learn from it.
6. What is SQUAD/slerp?The line in the paper can be edited to provide clarity. Essentially, they are methods of quaternion interpolation. The SQUAD/slerp refers to one or the other depending on what is needed.
More specifically: slerp stands for spherical linear interpolation and refers to interpolating between two orientations by moving at constant speed along a circular arc (as opposed to linear interpolation or lerp which idealizes the change in orientation by using linear polynomials and tends to result in very large angles of arc between each interpolation point). This is sufficient if there is a small enough change between orientations and can treat each interpolation between two points as isolated, or either you don't know or don't really care if other changes in orientation exist before or after.
SQUAD or Spherical QUADrangle interpolation is a series of slerp interpolations that assumes that other orientations exist before, during, and after the current interpolation between the two points. It smooths the connections between the interpolations as it does not treat each interpolation as an isolated event. This has roots in computer animation and is useful for smoothing movement between multiple animation frames. This of course translates well to spacecraft attitude as the craft is constantly changing orientation while moving along the orbital path.
9. Part 1: A lot of the work is attempting to get a good handle on the attitude of the spacecraft despite the loss of sensitivity of the star trackers and other ADS efforts. Is there housekeeping information that tells you when different subsystems are on or off to attempt to assess the magnitude of the spacecraft noise?
Yes there now is a publicly available housekeeping plot that shows what instruments were active and at what particular times. There is also a public BUS telemetry file that contains flags for when other various spacecraft subsystems turn on or off. Both of these are aiding us in our current quest to assess the impact of potential noise sources. Though first we need to remove the noise from the reaction wheels before we can get a good handle on other noise sources since they tend to dominate.
9. Part 2: What is the relative magnitude of the residual pointing accuracy error on the final data product compared to your estimate of the spacecraft noise?-I will need to get back to you on this one.
11. What is the effect of saturation of the sensor heads in terms of calibration?
Was this a big effect initially (compared to the ground-calibration values), but once sensors were repeatedly permed up on orbit, minimal effect? (From Table 1 there seems to be essentially no impact on Gain.).The saturation occurs in the forward analog loop of the electronics and not in the sensor head itself. As such, it should not have an impact on calibration.
12. Table 1: Though having a large stray field from the boom makes sense since the large X offset is seen in the outboard sensor and not the inboard, what is the boom made from that could give such a large field? It would be of interest to see the pre-flight off-set values to get a sense of the combination of the spacecraft fields and off-set drift combined.This one is a bit of a sore spot. Compared to the preflight zeros, the offsets found in-situ are comically large and cannot be explained by the stray fields from expected noise sources, nor can it be a product of the instrument aging as those numbers have shown up from the beginning. It is also not the boom as it is made from carbon fiber. Rather, it is likely from something not magnetically clean that was used to either secure the magnetometer or something near it on the boom and was not part of the initial design. This is especially unfortunate because it appears to magnify the effects from drift (and periodic effects). It also results in a larger RMS error post-2016 in the calibration compared to the Inboard sensor which is closer to all of the spacecraft noise.
14. Figure 5. Is this “all” the data or only Kp<3 and small change in Dst “quiet” data?This is "all" of the data (provided it was generated when one or both star trackers were providing primary attitude and the spacecraft was not undergoing a change in angular rate > 0.03 deg/sec). The Kp and Dst flags are only applied during calibration and kept separate from the final data product.
16. Was the inboard and outboard sensor used in a “Ness”-type gradiometer way to remove any spacecraft noise? If not, why not?As far as I know for the current processing chain, it has not. From the Wallis et. al 2015 paper, it appears that it was used early in the mission however it was abandoned when we began the in-situ calibration. The largest source of spacecraft noise by a considerable margin comes from the reaction wheels. This is especially prevalent prior to the first wheel failure in August 2016, but still is a considerable source after. Based on a limited understanding of Ness, I don’t know if it would be sufficient for removing the reaction wheel tone from before or after August 2016 as both contain large non-dipole terms.
We have tested different algorithms, two of which (simple differencing and a notch filter) were not magnitude persevering or had difficulty adapting to changing wheel rates. There will, however, be a paper being submitted soon by a post-doctoral researcher in the lab regarding a method that has shown success, especially in the early mission.
17. Figure 6. What are the red and blue traces in panel b?
The red and blue traces represent the cross-track measurements from Swarm-A and Swarm-C which passed through the same region of interest at a different time, which is useful from a scientific perspective . Those were not included in the recreation as the main goal was to show the change in the e-POP measurements. As a follow-up, it will be interesting to revisit the analysis done in the original paper and see what if anything has changed with the recent calibration and attitude updates.
Citation: https://doi.org/10.5194/egusphere-2022-59-AC1 - AC2: 'Reply on RC1', Robert Broadfoot, 16 Jun 2022
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RC2: 'Comment on egusphere-2022-59', Kenneth R. Bromund, 13 May 2022
General Comments
----------------This is an important paper describing the methods used to calibrate the processed CASSIOPE fluxgate magnetometer (MGF) data products that are currently available to the public.
The results are impressive. However, the style is uneven and at times there are errors, omissions or inconsistencies that must be remedied in order to make the descriptions of the methods sufficiently accurate for publication.
Specific Comments
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Section 1:Line 49: Tests were run to evaluate mutual interference of the two sensors. Was any interference identified? If so, how is this information used to aid the calibration process?
Section 3:
Although Olsen et al. (2003) is referenced for the notation used in this paper, there are many departures from this notation in this section, and it is unclear how the notation in this section relates to the results presented in Section 7.
Line 67: it would be more accurate and consistent with Olsen et al (2003) to say that the raw sensor data, E, is in engineering units that are approximately equivalent to nT.
line 71, As used in Equation (1), b is a pseudo-vector (in a non-orthogonal system), and in engineering units. specifying 1,2,3 is appropriate for the non-orthogonal system, but I note that this is inconsistent with Table 1... do the results offX, offY, offZ in Table 1 correspond to b1, b2, b3 (in which case, they might be labeled as engineering units, not nT), or are they actually nT (ie they are the offsets to be subtracted in the orthogonal, calibrated system)?Line 74: It would be appropriate to describe the dimensions of S as eu/nT, consistent with the results in your Table 1 in section 7. Subscripts 1,2,3 would be more appropriate, as S is in the non-orthogonal system...
Lines 78-79, If Equation (4) is correct, then the angles u1, u2 and u3 are not the same as the angles of the same names in Olsen et al. (2003). Please describe how u1, u2 and u3 defined, and their relation to the angles Oxy, Oxz, and Oyz reported in Table 1. Are they the angles between each pair of the slightly non-orthogonal sensors 1, 2, 3? While a figure would be helpful, it would be sufficient to define the terms clearly in the text, indicating, for example, that P represents the projections of sensors 1, 2, and 3 onto the orthogonal magnetometer reference frame, that sensors 1 and 2 are presumed to be in the X-Y plane, etc... Consider using a different notation (e.g. o12, o13, o23 ) that clarifies that these angles are not same as u1,u2,u3 in Olsen et al. (2003).
Lines 79-80. The definitions of the Euler angles (order 1-2-3) appears to differ from Olsen (2003), can you provide a reference? A more detailed description would be helpful to evaluate the physical significance of each parameter, when evaluating the results presented in Section 7.
Section 4:There is discussion of the "original" attitude system based on STK, but it is not clear what is the relevance of this system to this study. Was it relevant to previously released versions of the data? If so, please specify.
What were the methods used to verify and obtain the revised attitude solutions that "included improved alignment between different star camera modes, corrections for chromatic aberration and thermal effects in the star cameras, and corrections to frame, location, and epoch transforms"?
Is the uASC accuracy of <2arcseconds achieved only the beginning of the mission, or is this the lifetime accuracy specification? How was this verified?
Line 135: At this point, it is enough to know that "improved methods of attitude interpolation are applied to achieve robust attitude transformations", and leave the detail about SQUAD/SLERP to section 5, where you provide the reference...
The relationship between section 4 and section 5 is confusing. In some ways, section 4 appears to be intended as an introduction to section 5... It would be helpful to mention which topics will discussed further in section 5, and which topics are beyond the scope of this paper.
Section 5:I feel like I should be able to understand exactly what this section is talking about, but I'm finding it extremely difficult to follow.
Lines 138-139: This sentence is unclear. I think it's a typo. Is it intended to say:
"In-situ calibration of the MGF instruments requires rotating the reference magnetic field from its native North,
East, Center (NEC) frame into the local CRF frame of the spacecraft by convolution against the spacecraft attitude solution." ?
Line 143-145: The wording of this sentence is very confusing, and I'm pretty sure I don't understand it correctly.... "The coordinate system that defines this spacecraft (SC) coordinate system..." I'm used to thinking of SC coordinates to mean a system fixed to the spacecraft, and the reference to Figure 2, in particular, appears to re-enforce that assumption: It is the same figure that is used to illustrate the CASSIOPE spacecraft frame (CRF?) in the CASSIOPE DATA HANDBOOK online... Meanwhile, this sentence appears to describe a coordinate system defined by the spacecraft orbit: ie. one in which "+X points towards ram [and perpendicular to nadir], +Z points nadir, +Y completes the right-handed system". This is what the CASSIOPE DATA HANDBOOK calls the Orbital Reference Frame... is this what you are calling the SC coordinate system, in this paper? If so, then it does make sense to say that SC and CRF are co-aligned when YPR are all zero, as implied by this sentence....
Line 149: What is the relevance of this 'secondary-source attitude solution' if you are are using the raw star camera data to get superior revised attitude solutions? Do you have access to the raw quaternions representing the attitude of the star camera frame? Wouldn't the raw output of the star cameras be quaternions representing the star camera frame in the ECI J2000 coordinate system? How does J2000 get transformed to SC? The transformation would require the ephemeris as an input. Is this done on board, or is it re-calculated on the ground?Line 156: "the attitude solutions are then rotated into CRF": rotated nto CRF from what system? Does this mean, for example, that you apply an X-to-CRF rotation appropriate to each attitude knowledge source (X could be "star tracker A", "star tracker B", etc.) to obtain a CRF to SC attitude solution?
Line 158: SLERP is definitely to be recommended over per-element interpolation! I would be concerned about splining with SQUAD unless you are sure that the precision of each solution is much smaller than the change in attitude from one solution to the next.
Lines 158-161. Confusing sentence. Maybe SC serves as a refers to a specific coordinate system in the first instance, and as an abbreviation for 'spacecraft' in the second?In flight, one can only calibrate against the attitude determination system's idea of what CRF is, which will always contain a bias with respect to the mechanical CRF that was used to measure alignments on the ground. As you have noted, this bias will vary depending on the attitude source (star camera A, star camera B, etc.) and the solution will have varying levels of noise, depending on the source... Have you used the vector-vector calibration to evaluate the relative bias of each source, and then incorporated these bias corrections into the Swarm-Echo attitude CDF product? (That is what I assumed you meant back in section 4, when you mentioned 'improved alignment between different star camera modes'...)
Line 160: What is a Body-to-ITRF transformation? How is it derived? If Body = SC, then I would agree that a SC-to-ITRF is what is required at this point. It would be well-defined, given the ephemeris data expressed in ITRF as an input. A reference, or more details would be helpful. The documentation of the Attitude Quaternion File in the CASSIOPE PROCESSED DATA HANDBOOK seems to use the term "ITRF<-Body" to refer to the final attitude quaterion itself, rather than something used rotate the interpolated quaternions at this stage.
In any case, have you verified the accuracy of the ephemeris?
Lines 176-179: Reading this, it seems that SC and CRF are actually supposed to be the the same thing... So, either I misunderstand this paragraph, or I misunderstood everything leading up to it...
Line 180: What is SP3 format?
Section 6:The data selection methods described are all reasonable. The weighting method described in lines 220-228 seems appropriate, and is well referenced...
Section 7:
Table 1 and Figure 4: see my comments in section 3, regarding consistency of notation...
Line 256: what is meant by 'regularization'?Fig 4: Do you have an explanation for the greater variability observed on the outboard sensor, as opposed to the inboard sensor?
What mechanism is assumed to be the cause of the reaction wheel tone in the MGF data? Is it electromagnetic, or mechanical? If mechanical, it might explain why the deviations in the parameters is similar for both the inboard and outboard and outboards sensors, and that the outboard deviations appear to be slightly larger in some cases (the boom may amplify the vibrations at larger distances... ) if it is assumed to be electromagnetic, I would expect the outboard deviations to be smaller...
I note that for the outboard sensor, there is a significant correlation between variations in off_x and the e3 parameter... Perhaps only one of them is physically changing... What degree of angular error would correspond with an offset error of 15 nT?
Lines 249-250: sounds plausible... Can you show an example of the reaction wheel noise? Is it a monochromatic high frequency (whether electromagnetic or mechanical) that is aliased down into the MGF frequency range, or is it more broadband? What is the amplitude?Section 8:
I very much look forward to seeing these further developments!
For mitigating the reaction wheel tone: I would need to see examples, but I could imagine that more specific methods could be applied to identify and remove the 1 sps samples that are impacted by the reaction wheels... but indeed this might still require longer bins to make up for the lost data.
Technical Corrections
---------------------Line 59-60: typo, should be 'et al.'
Line 47: typo, should be 'stimuli'
Line 193: typo, should be 'more important than'
Line 250: typo, should be 'steps will need to be taken'Citation: https://doi.org/10.5194/egusphere-2022-59-RC2 - AC3: 'Reply on RC2', Robert Broadfoot, 16 Jun 2022
- AC4: 'Notification of correction to manuscript', Robert Broadfoot, 16 Jun 2022
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Cited
Robert M. Broadfoot
David M. Miles
Warren Holley
Andrew D. Howarth
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