Here is information from Pat and I about the MGS Navigation Team (NAV) estimates of the spacecraft angular momentum desaturations (AMDs). This is in response to the request made to Pat at the Radio Science Team meeting to provide NAV AMD estimates. Two tables are attached giving MGS AMD information during mapping. Each AMD is modeled as an instantaneous maneuver using an epoch (AMD end time), a vector describing the position perturbation (delta-R or DR), and a vector describing the velocity perturbation (delta-V or DV). The two tables include data from March 1999 to 8 October 2001. The tables are: 1. Instantaneous maneuvers derived from Spacecraft Team (SCT) AMD files 2. Instantaneous maneuvers derived by NAV from fitting the Doppler data Some problems in the SCT AMD files were fixed before the first table was generated. Otherwise, the AMD files were those officially delivered by the SCT to the FIS. The second table contains NAV reconstructions or estimates of the AMD derived instantaneous maneuvers generated by fitting both 2-way and 1-way Doppler data. (Method 1 (epoch at AMD end time) was used in the fits and is discussed below.) The (X,Y,Z) coordinate directions in the tables are modeled close to the actual spacecraft (X,Y,Z) coordinates: Z-axis points to the center of Mars (almost nadir), and Y-axis is parallel to the spacecraft orbit angular momentum vector. The discussion below is important for a correct interpretation of the NAV table. Especially note the description of the AMD / instantaneous maneuver epochs and the derivation of the AMD position perturbations. Only spin-axis AMDs will be discussed below since the trajectory perturbation due to a yaw-axis AMD is comparatively very small. A PDF version of our paper presented at the February 2001 AAS/AIAA Space Flight Mechanics Meeting can be temporarily retrieved from the following anonymous ftp site. (There is a problem in the PDF with the plot on page 9.) Computer: navigator.jpl.nasa.gov Username: anonymous Password: e-mail address Directory: /pub/mgs/papers Filename: AAS_SFM_2001_01-100.pdf The title of the paper is "Mars Global Surveyor Mapping Orbit Determination". It also talks about some of the items mentioned below. ----------------------------------------------------------------------------- A MGS angular momentum desaturation (AMD) is composed of a series of discrete thruster pulses (typically 20-30 in number). The total time it takes for a (spin-axis) desaturation to occur is typically around three minutes. This is equivalent to the spacecraft traveling about 9 degrees around its orbit. One could try to model and estimate for each thruster firing in the AMD. However, this is inefficient and cumbersome. For this and other reasons (e.g. Doppler data frequency) this approach is not used. The AMD could also be modeled as a (constant thrust) maneuver occurring over a finite period of time. This method is also inefficient and cumbersome for our type of work and accuracies. An instantaneous maneuver model works as well and is much simpler. Therefore we use an instantaneous maneuver model in our analyses. Because of the software implementation, NAV currently treats an AMD as an instantaneous velocity perturbation (delta-V) at the _end_ of the desaturation timespan. However, the AMD has slightly perturbed the spacecraft position by this end time. Thus a small change in the Z-axis position of the spacecraft (delta-R_z) is included in the AMD model to approximately account for this perturbation. Since the MGS spacecraft orbit is almost circular, it turns out that the semi-major axis (or period) perturbation is a function of this Z component delta-R and the X component delta-V. When an orbit is fit with the Doppler data, the delta-V vector is estimated by minimizing the Doppler residuals and results in a good fit for the semi-major axis of the spacecraft orbit. Since the delta-R trajectory perturbation is not estimated, a different delta-R causes the filter estimate for the delta-V to change so that the total effect on the semi-major axis and the trajectory is the same. The NAV software will read in a SCT AMD file, convert it to a nominal delta-R and delta-V for an instantaneous maneuver model, and then estimate for the delta-V vector by fitting the Doppler data. Therefore, the estimated delta-V depends on the initial delta-R derived from the SCT AMD file. Comparing the delta-V derived from the AMD file and that estimated by NAV, it was found that the AMD files are quite inaccurate. However, most of this inaccuracy was due to a bias or offset. Therefore, NAV started applying scale factors to the SCT AMD files. (This resulted in more realistic delta-R perturbations in the trajectory, which is important since they are not estimated by NAV.) For AMD files up to "amdgen.00-242" (8/29/00), the AMD impulse bits were scaled by ~70%. Based on the NAV versus SCT AMD comparisons and SCT manuever reanalysis, the SCT revised the impulse bit computations in their AMD file generation software. This software has been used since AMD file "amdgen.00-242", at which time NAV changed the scaling factor on the SCT AMDs to 80-85%. If the AMD is defined as an instantaneous maneuver in the middle of the AMD time span, with no delta-R, then the filter estimate of the delta-V X component will be physically more realistic. Generally, this procedure does not significantly improve the Doppler fit. (A few cases exist where a significant difference can be observed, though.) So, for simplicity, NAV has kept using the model implemented in their software which puts the maneuver time at the end of the AMD time interval. Shown below is a comparison of values for DV_x from reconstructed solutions covering orbits 6971-6991 (9/28-9/30 of 2000). DV_x is derived in two ways: 1. Maneuver at end of AMD time (nominal): DR_z non-zero, DV_x estimated. 2. Maneuver at middle of AMD time: DR_z zero, DV_x estimated. X component of AMD delta-V (S/C coordinates: Nadir pointed (ISH): +Z to Mars; -X in S/C vel) Method 1 Method 2 Calendar Date DR_z (km) DV_x (km/s) DV_x (km/s) 20000928.163818180 .13034165D-2 -.65527049D-6 .493104345D-6 20000929.003318183 .11900470D-2 -.42723336D-6 .620449903D-6 20000929.072924181 .22413279D-2 -.40482961D-5 -.202281125D-5 20000929.142104182 .11900470D-2 -.48643266D-6 .554224226D-6 20000929.211320184 .23959330D-2 -.41865619D-5 -.204155120D-5 20000930.042010180 .14219405D-2 -.10842076D-5 .149011345D-6 This test was repeated again with the reconstruction analysis covering orbits 8326-8344 (1/17-1/18 of 2001), with the corresponding table given below. The "method" definitions are the same as above, with the following additions. Method 2a is the same as Method 2, except that the AMD epoch is 30 seconds later than the middle of the AMD time. Method 2b is the same as Method 2, except that the AMD epoch is 1 minute later than the middle of the AMD time. A comparison of methods 2, 2a and 2b give some idea of the sensitivity of the delta-V estimate to the epoch of the AMD derived instantaneous maneuver. X component of AMD delta-V (S/C coordinates: Nadir pointed (ISH): +Z to Mars; -X in S/C vel) Method 1 Calendar Date DR_z (km) DV_x (km/s) 20010117.113048184 .28833553D-2 -.52014172D-5 20010117.182652182 .11870326D-2 -.70904096D-6 20010118.040353182 .53200430D-2 -.81663162D-5 20010118.110322184 .28833553D-2 -.51444584D-5 20010118.170008186 .32380557D-2 -.56056351D-5 Method 2 Method 2a Method 2b Calendar Date DV_x (km/s) DV_x (km/s) DV_x (km/s) 20010117.113048184 -2.6083284D-6 -2.6538128D-6 -2.7056697D-6 20010117.182652182 3.2624072D-7 2.5427758D-7 1.9053018D-7 20010118.040353182 -3.4996187D-6 -3.5087493D-6 -3.5403569D-6 20010118.110322184 -2.5405593D-6 -2.5749957D-6 -2.6130054D-6 20010118.170008186 -2.7131155D-6 -2.7712842D-6 -2.8251564D-6 ------------------------------------------------------------------------------- Stuart Demcak | Mars Global Surveyor (MGS), Navigation Team Stuart.Demcak@jpl.nasa.gov | Jet Propulsion Laboratory -------------------------------------------------------------------------------