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31375352540(Preprint) AAS 20-15300(Preprint) AAS 20-153OSIRIS-REx shape model performance during the navigation campaignJason M. Leonard, Jeroen L. Geeraert*, Brian R. Page*, Andrew S. French*, Benjamin W. Ashman, Peter G. Antreasian*, Coralie Adam*, Erik Lessac-Chenen*, Leilah McCarthy*, Derek Nelson*, John Pelgrift*, Eric Sahr*, Andrew Liounis?, Eric Palmer, John R. Weirich?, Brian M. Kennedy, Nickolaos Mastrodemos§, Julie Bellerose§, Daniel Lubey§, Brian Rush§, Dianna Velez§, Michael C. Moreau?, Olivier Barnouin, and Dante S. LaurettaThe Navigation Campaign of the OSIRIS-REx mission began when the first image of Bennu was recorded by the PolyCam high-resolution imager on August 17, 2018. In the ensuing months, two teams began building shape models based on imagery taken during the Approach and Preliminary Survey phases to be used for the transition to landmark navigation in the Orbital A phase. The orbit determination team began analyzing and characterizing the performance and errors associated with each shape model delivery, working closely to iterate on the next shape model delivery. By the end of Orbital A, shape models produced by the Altimetry Working Group and JPL exceeded pre-launch performance requirements. This paper provides a summary of the analysis performed during operations.IntroductionThe Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS-REx) mission is NASA’s New Frontiers class mission to B-type target asteroid (101955) Bennu., It is the first asteroid sample return endeavor by NASA. Launched in September 2016, the OSIRIS-REx spacecraft was in cruise operations until August 2018., The Navigation Campaign initiated when the first image of Bennu was recorded on OSIRIS-REx’s PolyCam high-resolution imager on August 17, 2018. The Navigation Campaign was completed in late February 2019 and consisted of three phases: Approach, Preliminary Survey, and Orbital A.The Approach phase provided the first evaluation of optical navigation (OpNav) techniques utilized for the mission on Bennu. Initial optical images of Bennu allowed the Orbit Determination (OD) team to begin estimating the orbital ephemeris of Bennu. During this phase, high-resolution rotation videos were taken with the PolyCam imager, enabling the OD team to utilize landmarks from initial shape model deliveries to estimate the spin state of Bennu to determine whether the asteroid was in principal axis rotation or non-principal axis rotation. Preliminary Survey, consisting of five targeted flybys with a close approach radius of about 7.25 km, provided the first estimate of Bennu’s mass. NOTEREF _Ref27646204 \h \* MERGEFORMAT 3, NOTEREF _Ref29395302 \h 7, Each flyby was designed to obtain detailed imaging of Bennu’s surface from different observing conditions for higher-resolution shape model development used later in the campaign. Using center-finding OpNavs, the OD team estimated Bennu’s mass. NOTEREF _Ref29395302 \h \* MERGEFORMAT 7During the two-month Orbital A phase, the Navigation team gained experience with the close proximity operations dynamics and environment around Bennu and successfully transitioned from center-finding OpNavs to landmark-based navigation. Several evaluations and iterations were completed between the OD team and the Altimetry Working Group (ALTWG), who created the shape model used for landmark navigation. An independent shape model team at Jet Propulsion Laboratory (JPL) generated another model in parallel to the one developed by the ALTWG. For both models, a center-of-mass to center-of-figure (COM-COF) offset and a Bennu reference frame z-axis to spin axis offset were estimated. After the Navigation Campaign had concluded, both ALTWG and JPL produced final high-resolution shape models that were re-evaluated against the images taken during the Navigation Campaign and verified before utilization in operations for subsequent phases. In this paper, we provide a detailed summary of the OD analysis approach and performance of various shape model deliveries throughout the Navigation Campaign. The paper will touch on the OpNav concept of operations for the Navigation Campaign, focusing on the camera modeling, imager selection, and techniques used. Next, an overview will be given of the teams involved in building the operation navigation shape models, the deliveries throughout the Navigation Campaign, and describe potential issues. A short treatise will be presented on Bennu’s pole/wobble, body-fixed reference frames, and estimation techniques utilized in the OD process. Finally, a detailed comparison of shape model performance, with a focus on the final models provided by ALTWG and JPL, the outlier detection, residual structure, and pole evolution will be covered. OpNav IMAGESPrecise modeling of the Navigation Camera (NavCam 1; Reference ) is vital when navigating around a small body like Bennu. Accurate calibrations of the distortion in the camera is necessary to reduce errors in the predicted location of a landmark in the image as well as determining the inertial direction of the boresight of the camera relative to the spacecraft reference frame. The location of the pupil of the camera itself is necessary when it becomes a significant fraction of the error budget in the camera model itself. 26816055688330Figure SEQ Figure \* ARABIC 1: NavCam 1 2x1 mosaic during Orbital A.00Figure SEQ Figure \* ARABIC 1: NavCam 1 2x1 mosaic during Orbital A.The imaging sequence throughout the Navigation Campaign was designed to alleviate potential issues involving downtrack prediction and camera pointing errors. Pre-launch covariance analysis showed that the downtrack prediction error could grow to 82 m (24 degrees) which would put part of the sunlit side of Bennu out of the NavCam 1 field of view (FOV). The OpNav processing for the Navigation Campaign consisted of both center-finding OpNav and landmark-based navigation. For the center-finding algorithms to work optimally, it was deemed necessary to have at least one complete image of Bennu fully within the FOV. Due to this, a 2x1 mosaic was designed to guarantee Bennu to be completely in a single image ( REF _Ref28849253 \h Figure 1). Each of the images in the 2x1 mosaic had a corresponding long and short exposure image at an inertial hold attitude after the required spacecraft settling time. This combination of images for each OpNav epoch allowed for a stellar (long exposure) image to provide the camera pointing direction and a resolved (short exposure) image of Bennu’s surface to correlate landmarks with. This technique removed the unknown pointing error associated with the camera direction relative to the inertial reference frame.Camera ModelingReference used the OpenCV pinpoint camera parameters to model the distortion across the focal plane of the NavCam and OSIRIS-REx Camera Suite (OCAMS; Reference ) imagers used for navigation during operations. The boresight direction, temperature dependent focal length, tangential, and radial distortion parameters were fit using stellar images and known locations of stars from the UCAC4 star catalog to reduce the errors across the entire camera. The least-squares fitting procedure produced a residual noise across the camera of 0.08 pixels. For NavCam 1, the error is constant across the focal plane indicating that there should not be any regional biases when Bennu would lie in different locations in the image. This is important due to the nadir off-pointing imaging sequence used throughout the beginning of Orbital A to combat any potential issues with downtrack prediction error. Reference NOTEREF _Ref28869821 \h 11 notes that the upper left corner of the image does have larger residuals in the camera modeling that are not exhibited in the other three corners, however, this does not impact navigation as Bennu would rarely reside in that corner of an image ( REF _Ref28849253 \h Figure 1). Similarly, the JPL shape model team used their own camera distortion models described in Reference . This camera model has similar parameters as OpenCV describing the focal length, radial and tangential distortion parameters as well as the optical axis to eliminate a distinct pattern in the posterior residuals. The models also compensated for temperature dependent effects on the focal length (0.00017081 mm/°C) similar to those estimated in Reference NOTEREF _Ref28869821 \h 11. Solving for the camera distortion model, which is essential for a high level of astrometric accuracy, is necessary to reduce its error contribution to < 0.1 pixels 1-sigma.shape model deliveriesThe ALTWG was responsible for developing and delivering the asteroid shape model at various resolutions. An independent team at JPL simultaneously produced and delivered shape models. The shape model produced by JPL was developed in parallel using the same images, ancillary telemetry data and tracking data that were available to the rest of the project, but was carried out independently, using different software processes and analysts, to add robustness to the navigation process. Similarities at a certain level did remain, however, given that the underlying technique for producing the shape model, stereophotoclinometry (SPC), was the same for the ALTWG and the JPL OpNav group. Prior to the beginning of operations, several thread tests were conducted in constructing the shape model and exchanging data between the shape model builders (ALTWG and JPL) and Flight Dynamics System (FDS) team that ensured that the shape model data format was the same between the two teams and could be readily used. Through several methods of comparison discussed below, the utilization of two teams reduced mission risk by strengthening shape model assessment. The term “shape model” collectively describes the global shape in a single digital file in the ICQ format and the set of individual maplets, that make up the global topography model. NOTEREF _Ref29376294 \h \* MERGEFORMAT 15 Each of these maplets covers a small part of the surface and overlaps with adjacent maplets to create seamless surface coverage. The vector from the body center to the center of each maplet is called the landmark vector. It was essential for the navigation team to transition from stellar and center-finding OpNav to landmark-relative OpNav by the conclusion of the Navigation Campaign. The first shape models suitable for landmark OpNav were delivered before the start of Preliminary Survey. A draft 75-cm-resolution shape model from ALTWG and JPL was due to FDS by the end of Preliminary Survey for use during Orbital A, with the final 75-cm model due at the conclusion of Orbital A. The principal shape model deliveries throughout the Navigation Campaign are summarized in REF _Ref29376069 \h Table 1. The navigation team used ALTWG shape models for operations as detailed in Table 1, but simultaneously performed OD fits with JPL shape models to assess consistency. Table SEQ Table \* ARABIC 1: Shape models delivered to the OD team.DeliveryNumber of Maplets by Resolution Operational UseName150 cm75 cm35 cm15 cm5 cmALTWG11/09/183392---11/9/18-12/4/18BENNU_APPROACH_2018_11_09b12/17/181343071835--12/29/18-1/14/19spc075draft.v11/15/19134307187122-1/15/19-1/22/19spc075draft.v71/24/19134309188834-1/24/19-6/14/19spc075draft.v96/06/19135311188736-6/6/19-7/1/19spc035.v3JPL12/03/18192186----jpl_18120312/18/1881630----jpl_18121812/31/1889642----jpl_1812311/31/191967421167---jpl_1901317/01/1919674211681087974200-jpl_190701Shape Modeling IterationShape model construction was an iterative process during operations and took two paths: iteration between the ALTWG and FDS; and the JPL team internally iterating before delivering to FDS for evaluation. Reference NOTEREF _Ref29378145 \h 14 describes in detail the iterative process taken by the ALTWG for the development of their models. The shape models constructed for the Navigation Campaign used images prior to Orbital A with the final models adding image data from the Detailed Survey phase. Trajectories used by ALTWG for the initial construction of shape models prior to Orbital A were based on center-finding OpNavs only. These trajectories were used as an a priori position for the images and are ultimately estimated along with the camera pointing in the SPC process. Potential errors concerning the apparent diameter, or scale, of the model as well as an offset in the COM-COF, and pole errors were introduced at this phase of the process. Evaluation of these errors occurred during the Orbital A phase and were iterated until a final model had converged.The JPL shape model team performed a similar iteration between the shape building and evaluation internally during the building process. The detailed processes carried out by JPL with the SPC techniques to construct landmarks and optical observables for navigation have been described in detail elsewhere (Reference and Reference ). The key difference here compared to the previous missions was that there were different cameras for constructing the landmarks and shape model and for assisting in the daily navigation operations, so there are two different paths of operations carried out in parallel as follows:1. Once Bennu reaches a minimum size, > 50 pixels apparent diameter, a set of maplets is constructed. 2. After a given set of landmarks is created, several iterations are performed; first internal to OpNav the landmark vectors, camera position and pointing are estimated and the maplets are rebuilt. Next the optical data are used by OD to update the trajectory and Bennu’s rotational frame. OD solves for potential scaling of the model and a COM-COF offset. The updated trajectory and parameters are used by OpNav to perform additional iterations solving for landmarks and rebuilding the maplets. 3. Once the landmarks converged they are used for processing images in the daily OD operations. Processing involves identifying the landmark locations in the new NavCam 1 images via cross-correlation, solving for the NavCam 1 camera position and pointing and providing new optical observables to OD. 4. As the resolution of the images increases throughout the different mission phases, new sets of maplets are created, with smaller pixel scale, that allow a higher spatial resolution and height accuracy in the topography model. The scale of the various sets of maplets is chosen to approach that of the spatial scale of the highest-resolution images. Also, the reconstruction of existing landmarks with the addition of higher-resolution images, contributes to an increase in their intrinsic spatial resolution and height accuracy. Each set of maplets is constructed by tiling the illuminated part of the surface at separation intervals that were set to allow a pre-determined overlap between adjacent maplets, typically ~50%. 5. Steps 1-4 are repeated continuously until the final shape model delivery. After the completion of a shape model delivery, the OD team evaluated the JPL model in a similar manner as the ALTWG model. Feedback was provided on the quality of landmarks, OpNav residual noise, COM-COF offsets, scaling of the model, potential shape model frame offsets, as well as rotation pole estimates. Potential IssuesWith two independent teams providing shape models, care had to be taken in how the models were evaluated and compared to each other. Of particular concern to the OD team was the definition of the shape model reference frame. Each delivery made could have a different prime meridian definition and an offset between the true spin axis and the shape model +Z axis. Consistency in trajectory and parameter reconstruction between shape model deliveries from ALTWG and JPL were evaluated regularly throughout operations. bennu landmark models and estimation APPROACHBennu, prior to the arrival of the OSIRIS-REx spacecraft, had been categorized using Earth-based observations extensively over the past several decades. NOTEREF _Ref27648641 \h \* MERGEFORMAT 1, Pre-encounter observations using radar and shape inversion indicated that Bennu had an average radius of ~250 m. NOTEREF _Ref29395829 \h \* MERGEFORMAT 18 These measurements also allowed for Bennu’s rotation period to be well-known with a rotation period of 4.3 hours. The radar and lightcurve analysis estimated that Bennu had a spin rate of 2010.49 ± 0.94 deg/day. The spin axis was determined to have a right ascension of 86.6388 degrees and a declination of –65.1086 degrees relative to the International Celestial Reference Frame (ICRF) with an uncertainty of 4 degrees. NOTEREF _Ref27648641 \h \* MERGEFORMAT 1, NOTEREF _Ref27648787 \h \* MERGEFORMAT 18Typically, external torques acting on a small body may induce rotations about other principal axes. An asteroid, such as Bennu, can become rotationally excited due to external torque mechanisms such as Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP, see Reference NOTEREF _Ref27649478 \h 22) effect or changes in its principal moments of inertia due to mass loss or gain. Small celestial bodies have shown properties of non-principal axis rotation.,, The known YORP acceleration and the a-priori pole uncertainty of 4 degrees meant that the OD team needed a higher fidelity model of the spin orientation and rates of Bennu. Using measurements in 1999, 2005, and 2012, there was an indication that Bennu's rotation rate increases over time. Reference estimated a spin rate increase based on a spin rate acceleration of 2.64 ± 1.05 ×10-6 deg/day2. Utilizing Approach phase lightcurve data, Reference updated the estimated spin rate acceleration to 3.63 ± 0.52 × 10-6 deg/day2 which was subsequently used in all modeling of the spin state by the OD team. Pole Orientation and Spin ModelingThe orientation of Bennu’s body-fixed frame relative to the ICRF is typically defined by the location of the spin axis (pole) and the equator. The International Astronomical Union (IAU) defines the orientation of a small body ( REF _Ref29375984 \h Figure 2) using two angles to define the orientation of the pole: the right ascension of the pole, α0, and the declination of the pole, δ0. The location of the prime meridian is defined by the angular separation from the IAU defined vector Q (where the ICRF equator intersects Bennu's equator) and is denoted as W. The simplest IAU model for asteroids assumes principal axis rotation where only the rotation rate, W is present and the body is spinning around the maximum moment of inertia. If the body is in principal axis rotation, there will be no rate terms given for α0 and δ0. The epoch of J2000 (1 January 2000, 12:00:00 TDB) is typically used for the initial values of the right ascension and declination. Estimating the location of the prime meridian and rotation rate can be sensitive to a-priori uncertainties in the rotation model. If the uncertainty in the rotation rate is large enough that multiple rotations can exist from the epoch to the first observation, it is necessary to advance the epoch from J2000 to a date closer to the data and propagate the conditions back to a desired epoch (i.e. J2000). 2683288508000Figure SEQ Figure \* ARABIC 2: IAU small body orientation convention. NOTEREF _Ref29409771 \h \* MERGEFORMAT 23Figure SEQ Figure \* ARABIC 2: IAU small body orientation convention. NOTEREF _Ref29409771 \h \* MERGEFORMAT 23For the case of Bennu, a potential wobble of the pole cannot be excluded. A wobble of the pole exists if there is an excitation or rotation about all three body-fixed axes with the location of the instantaneous spin axis changing in the Bennu-fixed frame. The Euler equations of rigid body motion are used to model the spin state of Bennu accurately and can be integrated by the followingω=I-1RTtτt-ωt×Iωt ,where ωt is the angular velocity vector, ω is the angular acceleration vector, I is the body's inertia tensor, Rt is the rotation matrix from the inertial to the body-fixed spin-axis frame, and τt is any external body-fixed frame torque acting on the body. This equation is integrated along with a set of quaternions defining the rotation matrix from the inertial frame to the body-fixed spin-axis frame to completely define the orientation angles αt, δ(t), and Wt. Prior to the start of the Navigation Campaign, the potential for wobble to exist at Bennu was analyzed. Reference NOTEREF _Ref28938566 \h 26 investigated how accurately the commonly used principal axis rotation model could recover the rotation state if a wobble existed. If a 1-degree wobble was present, well within the pre-arrival pole uncertainty, the principal axis rotation model could recover the spin state to an error of ~1 m on the surface of Bennu. The shape model resolutions for the Navigation Campaign range from 0.35 cm to 1.5 m per pixel ( REF _Ref29376069 \h Table 1); camera resolutions having a similar range would allow for a 1-degree wobble to be observed. Using pre-arrival moments of inertia based on the shape and expected density, a wobble frequency of 42.1 hours could be expected. This frequency is a fraction of the desired orbital period for the Orbital A frozen orbit design. It is vital for the OD team to estimate the position of the spacecraft accurately and to be able to estimate the dynamics and geophysical environment of Bennu from landmark-based images. Thus, a detailed representation of the spin state of Bennu is necessary in the presence of wobble. Landmark Reference FrameTo achieve the level of accuracy necessary for trajectory and geophysical parameter estimation using a set of integrated Euler equations for orientation, the OD team must mitigate any other potential frame and orientation issues that could arise during the shape-model building. ALTWG defines the shape model reference frame coordinates using a pre-defined PCK assuming principal axis rotation to initialize the inertial orientation of the body, a reconstructed trajectory of the spacecraft and camera location, the attitude derived from star trackers, and a least-squares fit of the pointing and spacecraft location at the time of the image. This process then produces a +Z axis that attempts to align itself along the spin axis and +X and +Y axes that are defined based on the location of the prime meridian in a specific image. This procedure should generally align the shape model coordinate frame accurately, however, there will always be a slight error in this procedure as the pole and spacecraft trajectory reconstruction changes with new images. Early in the development of the shape model, when the resolution is low and the pole is not well determined, an offset may exist between the shape model reference frame and the true instantaneous spin axis of the body. Because of this offset, the OD team estimates a frame offset between the shape model reference coordinates and the true spin axis of the body. On Approach, when a significant portion of the early shape model imaging was done, the radial distance to Bennu is uncertain to 2-3 meters. This potential error, if biased over an imaging period, can produce a scaling of the diameter of the body which directly impacts navigation of the spacecraft and estimation of Bennu’s geophysical parameters. If the shape model derived from images can adequately represent the true shape and variation of terrain, a simple scaling of the landmark location vectors is sufficient to adjust the true size of the body. However, if regional errors exist in the landmark locations, then it is possible for the reconstructed trajectory to be impacted directly producing biased locations for the spacecraft in certain regions. To alleviate this, the landmark locations are estimated in the shape model frame.Finally, the origin of the shape model should coincide with the COM of the body. However, due to the nature of the shape model generation and the knowledge known of the spacecraft’s positon at the time the images were taken, a bias vector can be introduced that defines the offset of the shape model (COF) to the COM of the body. This parameter is also estimated by the OD team to determine the offset in the shape model frame relative to what the spacecraft senses as the COM. The landmark location is written asrLMP=CRSPrLMS+rCFP ,where rLMP is the location of the landmark in the principal axis frame (P), C is the landmark scale factor, RSP is the rotation from the shape model frame (S) to the principal axis frame (P), rLMS is the landmark location in the shape frame (S), and rCF is the COM-COF offset in the principal axis frame (P). The landmark vector is projected into the image frame via the rotation defined from the stellar images, and then transformed into camera coordinates of pixel and line via the OpenCV model and distortion parameters given in Reference NOTEREF _Ref28869821 \h 11. All of the parameters may be estimated, but, a scale factor, C, should not be estimated simultaneously with the landmark vectors due to observability limitations. Additionally, a constraint should be applied when estimating the rotation from one frame to another and the landmark vectors simultaneously to ensure a rotation and counter rotation is not estimated. Landmark PerformanceEvaluation of the shape models used for navigation involved residual performance assessment, residual structure due to landmark errors, Bennu pole estimate convergence and consistency in trajectory reconstructions between shape models. The residual performance assessment gives an overall evaluation of the quality of the landmarks on a global scale and the potential for detecting outliers and structure in the residuals related to certain parameters. While this provides an initial assessment of the quality of the landmark data, further analysis is necessary to understand how the locations of the landmarks themselves can impact both the residual performance and the reconstruction of the spacecraft trajectory and pole parameters of Bennu. Since two independent teams built high-resolution navigation shape models, consistency between the two models provides insight into the quality of the models themselves.The default performance of the shape model is a key evaluation when determining if the model meets the requirements of the phase. The OD team generally estimated a scale factor, pole, and COM-COF offset for each model and evaluated the residual noise for each model ( REF _Ref29380348 \h Table 2). Table SEQ Table \* ARABIC 2: Shape model estimated parameters.NameScaleRADECCOM-COF (cm)Residual std(deg)(deg)XYZ(px)ALTWGBENNU_APPROACH_2018_11_09b-81.846–59.097----spc075draft.v10.9999685.344–60.156–9.1–12.6–65.60.69spc075draft.v71.0000685.647–60.170-2.53.318.10.51spc075draft.v91.0001185.456–60.3570.0-0.331.50.50spc035.v30.9992585.455–60.364–1.72.372.10.26JPLjpl_181203--jpl_1812181.0027986.024–60.49624.083.1220.80.66jpl_1812311.0002985.880–60.45020.050.020.00.60jpl_1901310.999085.622–60.391–7.522.380.70.55jpl_1907010.999785.570–60.3900.00.332.00.30Residual PerformanceInitial evaluation of every delivered shape model began with an assessment of the quality of the OpNav landmark residuals through the noise and structure of the landmark data. For the Navigation Campaign, the requirement placed on the quality of the shape model was to have global coverage at 75 cm maplet resolution. Pre-launch landmark noise performance was based on a weighting scheme where the expected residual noise was related to the landmark-to-maplet ratio by W=Wmin2+(S/R)21/2, where the minimum weighting, Wmin was assumed to be 1.0 pixels and the shape model resolution, S, was 75 cm with the camera resolution of the landmark, R. The camera resolution is related to the angular resolution, iFOV, and the distance to the landmark from the camera, r, such that R=r × iFOV. For Orbital A, the expected landmark residual performance was to range between 1.6 and 2.1 pixels (1-sigma) for a 75-cm shape model. REF _Ref29380348 \h Table 2 shows the actual performance of the landmarks for the delivered models. The delivered shape models outperformed the expected spread in the landmark residuals by a factor of 12 producing near constant residuals over all distances and landmark resolutions of 0.17 pixels (1-sigma) when estimating landmarks and 0.26 pixels (1-sigma) when using the landmark locations as provided. When evaluating the landmark residual performance, care must be taken when identifying outliers within the global set of landmarks. Typical methods of sigma editing using the empirical covariance are useful in removing gross outliers of the data, however, they tend to not accurately depict the distribution at hand and are very sensitive to the presence of outliers. A robust covariance approach was taken during the Navigation Campaign to identify potential outliers in the global landmark residual dataset. REF _Ref29203215 \h Figure 3 shows the comparison between outlier identification with an empirical and robust covariance approach. REF _Ref29203215 \h Figure 3a compares the ratio of the Mahalanobis distance of the data and representative outlier detection percentiles. A percentile of 99.92% was chosen for outlier detection with the blue dots indicating accepted landmark residuals and the red dots indicating rejected residuals. REF _Ref29203215 \h Figure 3b and c show the distribution of the data in the pixel and line camera coordinates, respectively, with their empirical (cyan) and robust (red) Gaussian fits. The robust covariance determination accurately removes outliers as can be seen in the more representative Gaussian curve fit. A pronounced tail does exist in the distribution seen in the positive line coordinate.righttopFigure SEQ Figure \* ARABIC 3: Empirical vs robust covariance residual outlier detection. (a) Comparison of the ratio between the empirical and robust Mahalanobis distances with outlier percentages. The distribution of the landmark residuals for the pixel (b) and line (c) coordinate are given with their empirical (cyan) and robust (red) Gaussian fits.(a)(c)(b)0Figure SEQ Figure \* ARABIC 3: Empirical vs robust covariance residual outlier detection. (a) Comparison of the ratio between the empirical and robust Mahalanobis distances with outlier percentages. The distribution of the landmark residuals for the pixel (b) and line (c) coordinate are given with their empirical (cyan) and robust (red) Gaussian fits.(a)(c)(b)To verify that there are no major distortion errors across the camera, the residuals can also be compared to their distance from the center of the camera. For Orbital A, the body of Bennu resided primarily off the boresight of the camera due to the imaging mosaic seen in REF _Ref28849253 \h Figure 1. The imager calibration should have removed the residual errors based on the radial distance from the center of the imager. REF _Ref29384305 \h Figure 4 shows the distribution of landmark residual errors as a function of the radial distance from the center of the camera for both the pixel and line coordinates. Figure SEQ Figure \* ARABIC 4: Landmark residuals relative to the center of the camera.Figure SEQ Figure \* ARABIC 4: Landmark residuals relative to the center of the camera.Correlations between the residual quality and other parameters such as emission angle, illumination angle, latitude, longitude, and cross-correlation score between the maplet and image projection can exist. Due to the terminator orbit of the spacecraft throughout Orbital A, the solar phase was typically higher than 90 degrees with a majority of the visible landmarks near the terminator having large illumination angles. REF _Ref29384238 \h Figure 5 gives the residual noise relative to various parameters of concern when correlating the maplets to assess the quality of the data. The black curves represent the running mean of the data and the cyan curves represent 1-, 2-, and 3-sigma standard deviations of the data using a rolling standard deviation algorithm. Both pixel and line coordinates of the camera do not show any correlations with the landmark latitude or longitude. Both coordinates do show a slight decrease in the noise for larger cross-correlation scores, which one would expect. For the pixel coordinate there is very little structure or biasing when comparing the residuals relative to the emission angle, illumination angle and solar phase angle. However, for the line coordinate ( REF _Ref29384238 \h Figure 5) there is a strong correlation between the residual structure and the emission angle, illumination angle and solar phase angle. For both coordinates, the noise increases for larger illumination angles but the line coordinate shows a more pronounced structure in the mean. The camera is oriented such that the line coordinate is mostly perpendicular to the terminator ( REF _Ref28849253 \h Figure 1) indicating that there could be a potential biasing of the landmark data for higher illumination angle data. 278130-4621530Figure SEQ Figure \* ARABIC 5: Line coordinate residual trends compared to potential correlated sources.0Figure SEQ Figure \* ARABIC 5: Line coordinate residual trends compared to potential correlated sources.Landmark EstimationFor each shape model delivery, the OD team re-estimated all the landmark locations and compared the shifts estimated relative to the initial locations given as the origin of the maplet. The shifts were compared on a global scale to determine any regional variations in the shape that could be impacting the trajectory reconstruction. REF _Ref29384812 \h Figure 6 gives the estimated landmark shifts with the mean shift (the COM-COF offset) removed. The COM-COF offset for this model was estimated to be -1.9 cm, -2.4 cm and 41.5 cm (body-fixed X, Y, and Z). The corrections are presented in a Bennu body-fixed altitude, East/West (positive Eastward) and North/South (positive Northward) corrections in cm. The altitude correction shows a bias of -12.6 cm across the surface, indicative of a scaling discrepancy in the shape model. There is also a noticeable degree 2 zonal error in the model where the poles are too short and the equator is too large. REF _Ref29384812 \h Figure 6e shows that there is a positive Eastward shift in the northern hemisphere of the landmarks and a negative Eastward shift in the in the southern hemisphere of the model. A considerable positive Northern shift was also estimated for the south pole of Bennu ( REF _Ref29384812 \h Figure 6e). With the corrected landmarks, the residual standard deviation was reduced from 0.26 pixels ( REF _Ref29380348 \h Table 2; spc035.v3 residual std) to 0.17 pixels. REF _Ref29385444 \h Figure 7 shows the variation of the standard deviation of the NavCam 1 OpNav measurements over the surface of Bennu after correcting the landmark locations. There does not appear to be any large regional variation in the residual noise across the surface but rather variations in localized areas due to individual landmarks. The JPL shape model team evaluated their final model (jpl_190701) in a similar fashion before delivery to the FDS OD team for evaluation. A subset of 400 landmarks distributed across the surface were chosen from the model and estimated. REF _Ref29384812 \h Figure 6b, d, and f give the estimated landmark shifts for this model with the mean shift (the COM-COF offset) removed. The COM-COF offset for this model was estimated to be 0.1 cm, 0.2 cm and 0.1 cm (body-fixed X, Y, and Z). The corrections are presented in a Bennu body-fixed altitude, East/West (positive Eastward) and North/South (positive Northward) corrections in cm. The altitude correction does not have the significant bias as seen in the spc035.v3 model from ALTWG. The final estimated shifts in jpl_190701 are significantly less than spc035.v3.Figure SEQ Figure \* ARABIC 6: Shape model landmark shifts estimated in the OD process for the ALTWG spc035.v3 model (left) and the JPL jpl_190701 model (right).Figure SEQ Figure \* ARABIC 6: Shape model landmark shifts estimated in the OD process for the ALTWG spc035.v3 model (left) and the JPL jpl_190701 model (right). Figure SEQ Figure \* ARABIC 7: Final landmark residual noise over the surface for ALTWG spc035.v3.Figure SEQ Figure \* ARABIC 7: Final landmark residual noise over the surface for ALTWG spc035.v3.Pole EvolutionThe OD team consistently estimated the spin axis of Bennu, prime meridian and rotation rate throughout the Navigation Campaign. Early landmark OpNavs from the Approach phase showed the potential for non-principal axis rotation or a shape model to principal axis frame offset. Refinement of the ALTWG and JPL models removed any indication of this as the +Z axis of the shape model began to align itself with the true spin axis. A significant shape model to principal axis frame offset (over 0.1 degree) was estimated for a single unofficial delivery from ALTWG prior to Preliminary Survey and an intermediate JPL shape model delivery at the completion of Orbital A. After another iteration of the shape model, the frame offset disappeared and the coordinate frame of the shape model aligned itself with the instantaneous spin axis.One indication that the shapes were converging between ALTWG and JPL was the convergence of the Bennu spin axis estimate (RA and DEC). REF _Ref29380348 \h Table 2 gives the estimated pole for each of the official deliveries that were used during operations. Variations on the order of 0.1 degrees were common between deliveries as the landmarks shifted regionally on the surface due to updated imagery and iterations on the shape model building itself (when using the landmark locations as provided). When estimating the landmark locations, consistent pole estimates were achieved, pointing to the fact that there were regional errors in the landmarks on the surface and slight misalignment of the +Z axis of the shape frame. The final estimated RA and DEC values Bennu’s pole at the completion of the Navigation Campaign were 85.4567 and –60.3574 degrees. Conclusion Throughout the Navigation Campaign, multiple shape model deliveries were made and evaluated based on OD trajectory solutions. The proper calibration of the NavCam 1 imager prior to Orbital A and the use of long- and short-exposure OpNavs allowed the OD team to successfully characterize shape model errors early in the mission. Techniques and modeling of the Bennu spin state, shape model frame, COM offsets, and scaling produced consistent trajectory estimates necessary for a successful completion of the Navigation Campaign. Characterization of the OpNav residuals showed a slight dependence on the illumination angle of the landmark. OpNav landmark performance exceeded all pre-arrival expectations, as demonstrated by the reduction of landmark residual noise from 2.1 pixels (pre-arrival) to 0.17 pixels (when estimating landmark locations). Landmark estimation provided more consistent parameter estimates when comparing the ALTWG and JPL shape model deliveries, giving confidence in the models. AcknowledgmentsThe authors wish to acknowledge other members of the OSIRIS-REx team who have contributed to accomplishments described in this paper: the Lockheed Martin flight operations; the Altimetry Working Group for shape model deliveries used in OpNav processing; and members of the Science Planning and Science Operations teams at the University of Arizona who have supported OpNav observation planning.This material is based upon work supported by NASA under Contracts NNM10AA11C and NNG13FC02C. OSIRIS-REx is the third mission in NASA's New Frontiers Program. Dante Lauretta of the University of Arizona, Tucson, is the mission's Principal Investigator, and the University of Arizona also leads the Science Team and the science observation planning and data processing. Lockheed Martin Space Systems in Denver built the spacecraft and is providing flight operations. Goddard Space Flight Center and KinetX Aerospace are responsible for navigating the OSIRIS-REx spacecraft. A portion of this work was conducted at the Jet Propulsion Laboratory, California Institute of Technology under contract 80NM0018D0004 with the National Aeronautics and Space Administration. ................
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