NC STATE UNIVERSITY Rafael Lugo, Robert Tolson Department of Mechanical and Aerospace Engineering North Carolina State University, Raleigh, NC and Robert Blanchard National Institute of Aerospace, Hampton, VA Entry, Descent, and Landing Trajectory and Atmosphere Reconstruction with Uncertainty Quantification using Monte Carlo Techniques 10 th International Planetary Probe Workshop San Jose State University 20 June 2013

NC STATE UNIVERSITY Introduction Trajectory reconstruction – process by which vehicle position, velocity, and orientation is determined post- flight Goals of post-flight trajectory reconstructions – Validate pre-flight models – Aid in planning of future EDL missions by identifying areas of improvement in vehicle design, e.g., reduce mass of heat shield because of overly conservative pre-flight aeroheating models Mars exploration: Missions with EDL operations – Viking 1 & 2 (20 July & 3 September 1976) – Pathfinder (4 July 1997) – Mars Exploration Rover A & B (4 & 25 January 2004) – Phoenix (25 May 2008) – Mars Science Laboratory (6 August 2012) – InSight (2016), MSL 2020 Redundant sensors (e.g., sensors other than accelerometers and rate gyroscopes) enable better trajectory estimates 2 Image courtesy of JPL

NC STATE UNIVERSITY Mars Science Laboratory Landed in Gale Crater on 6 August 2012 Largest and most sophisticated Mars vehicle – Required innovative landing technique: “Skycrane” landing used hovering platform to lower rover to surface using umbilicals – Guided entry (first for Mars) Entry vehicle equipped with two IMUs, guidance and navigation computer, and Mars EDL Instrumentation (MEDLI) suite – MEDLI included series of 7 pressure ports on heat shield that measured pressures during entry and descent – Pressure ports formed the Mars Entry Atmospheric Data System (MEADS) 3 VikingPathfinderMERPhoenixMSL Diameter (m) Entry mass (kg) m/CDAm/CDA Hypersonic L/D Hypersonic α trim (deg) Control3-axis, unguidedSpinning Uncontrolled3-axis, guided Image courtesy of JPL

NC STATE UNIVERSITY MSL Entry, Descent, and Landing 4 Flyaway Hypersonic Aero-maneuvering Begins Entry Interface Peak Deceleration Parachute Deploy Heatshield Separation Radar based solution converged Backshell Separation Powered Descent vertical flight Sky Crane (see inset) Rover Separation Mobility Deploy Touchdown Flyaway Sky Crane Detail Peak Heating Pressures & temps from MEDLI Radar Altimeter Landing Location Body accelerations & rates from IMU Initial state from radio tracking & star tracker Images courtesy of JPL & Honeywell

NC STATE UNIVERSITY Trajectory Reconstruction Generally, trajectory parameters are not measured directly and must be either estimated probabilistically or computed deterministically Two common techniques – Probabilistic/statistical approach – measurements processed in a stochastic algorithm that minimizes payoff function defined by system models (e.g., WLS, MV, EKF, UKF, etc.) – Inertial navigation – deterministic technique where acceleration and attitude rate measurements from an inertial measurement unit (IMU) are integrated given an initial state If IMU measurements and IC estimates were perfect, inertial navigation solution would be the true and unknowable trajectory in inertial space MethodAdvantagesDisadvantages Statistical methods Can blend redundant data types (pressures, altimetry, etc.) Parameter statistics readily available Requires dynamical models (atmosphere, aerodynamics, data & state noise, observation equations, etc.) Often requires filter “tuning” to assure convergence Inertial navigation Only gravity model required No convergence issues Cannot include redundant measurements Uncertainties not readily available 5

NC STATE UNIVERSITY Classical Reconstruction 6 Accelerations Inertial navigation Vehicle state R, V, q CFD force coefficient Freestream density ρ Freestream pressure P Freestream temp. T Wind angles α, β Hydrostatic equation Gravity acceleration h h axax axax V V Equation of state Angular rates Initial conditions M = molar mass R = gas constant NO redundant data NO uncertainties IMU error parameters Axial force equation

NC STATE UNIVERSITY INSTAR How can we utilize redundant data and obtain meaningful statistics from inertial navigation? Answer: Utilize Monte Carlo techniques 1.Disperse initial state conditions and IMU error parameters (acceleration & rate biases, scale factors, & misalignments) with specified uncertainties (covariance) 2.Integrate IMU data (inertial navigation) using these dispersed initial conditions to obtain set of dispersed trajectories 3.Obtain mean initial conditions and statistics (covariance) from subset of trajectories that satisfy redundant observations to within specified tolerances 4.With this new set of initial conditions and covariance, repeat steps 1-3 until convergence Inertial Navigation Statistical Trajectory and Atmosphere Reconstruction (INSTAR) – “Debuted” at 2013 AAS/AIAA Spaceflight Mechanics Conference – Demonstrated INSTAR using landing site location as redundant data Integrator INSTAR integrator is a fixed-step, three-point predictor-corrector Integrator written in Fortran95 with a MATLAB wrapper – Utilizes multi-core processing to integrate multiple trajectories simultaneously – Accelerations and rates for 1,000 trajectories (from EI-9 min to landing) can be integrated in <3 min 7

NC STATE UNIVERSITY INSTAR Overview Trajectory state can be mapped using inertial navigation into “measurement space” where redundant observations and uncertainties can be introduced Subset of trajectories that satisfy redundant data provide updated initial conditions, IMU error parameters, and covariance 8 Initial conditions IMU error parameters Statistical analysis of Landing location FADS pressures Altimetry Measurement space Representative of true and unknowable ICs, IMU parameters, and uncertainties

NC STATE UNIVERSITY INSTAR Results: IC & IMU Dispersions 9 Dispersed initial state to within given uncertainties, 10,000 cases (Gaussian distribution), 26 valid trajectories within 150 m of reference landing site (uniform distribution) Mean of ICs and full covariance computed from 26 valid trajectories, use these new initial conditions and new covariance to disperse new set of trajectories Significantly smaller distribution area Select trajectories that land within 150 m of landing site in latitude-longitude- radius space Mean of ICs and full covariance computed from valid trajectories

NC STATE UNIVERSITY INSTAR Results – Landing Location Continue to iterate, results are from 6th iteration Result: updated ICs and uncertainties, incorporating redundant data (landing site location), using only inertial navigation – Improved landing site location difference from 925 m to 19 m Nearly all uncertainties have decreased from a priori Nearly all IC Δs are under 1σ – Exceptions: Y & z-axis bias Results are used to begin next step: inclusion of FADS data 10 Initial Conditions1σ Uncertainty ParameterUnits ΔFinal ValueΔ Xm E Ym E Zm E VXVX m/s E VYVY m/s E VZVZ m/s E X deg Y deg Z deg B a,x μgμg B a,y μgμg B a,z μgμg Parameter changes from a priori

NC STATE UNIVERSITY FADS Data in INSTAR 11 Flush air data systems measure surface pressures P i at port locations defined by ( η i, ζ i ) – Statistical methods (e.g., least squares) may be used to obtain aerodynamic and atmospheric parameters Process: Given dispersed trajectories from INSTAR, compute CFD pressures & disperse using transducer scale factors and biases, and compare them to observed MEADS pressures – This method is be comparable to how INSTAR works with other redundant data – CFD errors affect solution, since model pressures and C A are obtained from CFD tables Updated uncertainties Dispersed trajectories Dispersed atmospheres INSTAR FADS observations Updated trajectory & atmosphere Transducer errors Monte Carlo distributions Atmosphere Reconstruction A priori P 0, M 0 CFD Dispersed model pressures Updated ICs, covariance, transducer errors Trajectory downselection

NC STATE UNIVERSITY MEADS Observations 12

NC STATE UNIVERSITY Atmosphere Dispersions Atmosphere reconstruction is performed for each of 1,000 dispersed trajectories For each atmosphere profile, initial pressure is taken from model that consists of two averaged mesoscale models anchored to surface pressure measurements from the Curiosity rover Behavior at 13 km corresponds to region of trajectory where altitude increases 13

NC STATE UNIVERSITY Pressure Dispersions Mach number histories are computed and used with wind angle histories to look up model pressures from pre-flight CFD database Result is a set of 7x1000 CFD-based pressure histories that are further dispersed using randomized biases and scale factors – Normal distribution, 25 Pa bias, 0.02 scale factor Dispersed model pressures are compared to the MEADS observations – Residuals from other ports display comparable behavior – Black curve: difference between nominal pressures & observations 14

NC STATE UNIVERSITY Pressure Dispersions - Downselected Dispersed trajectories are down- selected by choosing those trajectories with residuals that are within a priori MEADS measurement uncertainties Result is a subset of 33 “valid” trajectories that satisfy a priori pressure measurement uncertainties, which are a subset of original 1,000 Note decrease in magnitudes of residuals from previous slide 15

NC STATE UNIVERSITY Results – Updated Initial Conditions Compute means and standard deviations of initial conditions of 33 valid trajectories, repeat INSTAR process on to 4th iteration Nine of twelve state parameter uncertainties have further decreased (slightly) from solution obtained using only landing site location – All Δ ref are below 1σ, except for Y and B a,z – Improvements to initial state are limited because landing site already refined these New landing site is now 16.3 m away from reference (compare to 18.9 m) 16 Initial Conditions1σ Uncertainty ParameterUnitsΔ ref Δ nom ValueΔ ref Δ nom Value Xm E Ym E Zm E VXVX m/s E VYVY m/s E VZVZ m/s E X deg Y deg Z deg B a,x μgμg B a,y μgμg B a,z μgμg

NC STATE UNIVERSITY Atmo Uncertainties & Transducer Errors Transducer biases and scale factors that correspond to valid trajectories are averaged to obtain the new set of transducer biases and scale factors, as in INSTAR process – Uncertainties obtained by computing standard deviations of this subset – Uncertainties have improved from a priori values (25 Pa bias, 0.02 scale factor) 17 Bias (Pa)Scale Factor PortValue1σ1σ 1σ1σ Recall that uncertainties are due to trajectory IC dispersions, which are small –CFD errors are not considered (yet)

NC STATE UNIVERSITY Summary & Conclusions Uncertainties and updated EDL trajectory ICs can be obtained using inertial navigation and Monte Carlo dispersion techniques Demonstrated INSTAR using MSL EDL data – Redundant data: Landing site location, MEADS pressures Obtained updated pressure transducer biases and scale factors, initial conditions, and associated uncertainties – Significantly improved landing site location by adjusting initial state – Including pressures provides transducer errors but requires use of CFD models for pressures and C A Final IC & acceleration bias Δs were well under 1σ uncertainties for nearly all parameters – Exceptions: Initial Y-axis Euler angle (4.3σ) and Z-axis acceleration bias (3.2σ) Work in Progress Account for CFD errors in dispersions to get more realistic atmosphere uncertainties Compare transducer errors to those computed using FADS-based statistical solutions Acknowledgements NASA Langley: Mark Schoenenberger, Chris Karlgaard, Prasad Kutty, Jeremy Shidner, David Way, Chris Kuhl, Michelle Munk JPL MSL EDL & navigation teams 18

NC STATE UNIVERSITY References 19 1.Crassidis, J. L., and Junkins, J. L., Optimal Estimation of Dynamic Systems, Chapman & Hall/CRC, Washington, D.C., 2004, Chaps. 1, 2. 2.Grotzinger, J. P., Crisp, J., Vasavada, A. R., Anderson, R. C., Baker, C. J., Barry, R., Blake, D. F., Conrad, P., Edgett, K. S., Ferdowski, B., Gellert, R., Gilbert, J. B., Golombek, M., Gomez-Elvira, J., Hassler, D. M., Jandura, L., Litvak, M., Mahaffy, P., Maki, J., Meyer, M., Malin, M. C., Mitrofanov, I., Simmonds, J. J., Vaniman, D., Welch, R. V., and Wiens, R. C., “Mars Science Laboratory Mission and Science Investigation,” Space Science Reviews, Vol. 170, 2012, pp. 5–56. 3.Karlgaard, C. D., Kutty, P., Schoenenberger, M., Shidner, J., and Munk, M., “Mars Entry Atmospheric Data System Trajectory Reconstruction Algorithms and Flight Results,” 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, TX, January 2013, AIAA Way, D. W., Powell, R. W., Chen, A., Steltzner, A. D., San Martin, A. M., Burkhart, P. D., Mendeck, G. F., “Mars Science Laboratory: Entry, Descent, and Landing System Performance,” IEEE 2006 Aerospace Conference, March Striepe, S. A., Way, D. W., Dwyer, A. M., and Balaram, J., “Mars Science Laboratory Simulations for Entry, Descent, and Landing,” JSR, Vol. 43, No. 2 (2006), pp Blanchard, R. C., Tolson, R. H., Lugo, R. A., Huh, L., “Inertial Navigation Entry, Descent, and Landing Reconstruction using Monte Carlo Techniques,” 23rd AAS/AIAA Spaceflight Mechanics Meeting, Kauai, HI, February 2013, AAS Karlgaard, C. D., Kutty, P., Schoenenberger, M., and Shidner, J., “Mars Science Laboratory Entry, Descent, and Landing, Trajectory and Atmosphere Reconstruction,” 23rd AAS/AIAA Spaceflight Mechanics Meeting, Kauai, HI, February 2013, AAS Gazarik, M. J.,Wright, M. J., Little, A., Cheatwood, F. M., Herath, J. A., Munk, M. M., Novak, F. J., and Martinez, E. R., “Overview of the MEDLI Project,” IEEE 2008 Aerospace Conference, March Munk, M., Hutchinson, M., Mitchell, M., Parker, P., Little, A., Herath, J., Bruce, W., and Cheatwood, N., “Mars Entry Atmospheric Data System (MEADS): Requirements and Design for Mars Science Laboratory (MSL),” 6th International Planetary Probe Workshop, Atlanta, GA, June Blanchard, R.C., Desai, P.N., “Mars Phoenix Entry, Descent, and Landing Trajectory and Atmosphere Reconstruction,” Journal of Spacecraft and Rockets, Vol. 48, No. 5, 2011, pp Dyakonov, A., Schoenenberger, M., and Van Norman, J., “Hypersonic and Supersonic Static Aerodynamics of Mars Science Laboratory Entry Vehicle,” 43rd AIAA Thermophysics Conference, New Orleans, LA, June 2012, AIAA Pruett, C. D., Wolf, H., Heck, M. L., and Siemers, P. M., “Innovative Air Data System for the Space Shuttle Orbiter,” Journal of Spacecraft and Rockets, Vol. 20, No. 1, 1983, pp Siemers III, P. M., Henry, M. W., and Flanagan, P.F., “Shuttle Entry Air Data System Concepts Applied to Space Shuttle Orbiter Flight Pressure Data to Determine Air Data - STS 1-4,” 21st AIAA Aerospace Sciences Meeting, Reno, NV, January 1983, AIAA Vasavada, A. R., Chen, A., Barnes, J. R., Burkhart, P. D., Cantor, B. A., Dwyer-Cianciolo, A. M., Fergason, R. L., Hinson, D. P., Justh, H. L., Kass, D. M., Lewis, S. R., Mischna, M. A., Murphy, J. R., Rafkin, S. C. R., Tyler, D., and Withers, P. G., “Assessment of Environments for Mars Science Laboratory Entry, Descent, and Surface Operations,” Space Science Reviews, Vol. 170, 2012, pp. 793–835.

NC STATE UNIVERSITY Backup Slides 20

NC STATE UNIVERSITY Coordinate Frames Trajectory integrated in Mars-centered, Mars mean equator (MME) frame fixed at the Prime Meridian date of t 0 (“M frame”) Utilized IMU observations in descent stage (DS) frame, transformed to inertial M frame Wind angles computed from body velocity components Landing site location supplied by JPL – Assumed to be accurate to within 150 m in longitude, latitude, and radius (i.e., uniform distribution) 21 ParameterUnitsValue East longitudedeg Areocentric latitudedeg Radiusm Radius + tether length (9.4 m)m Landing site location

NC STATE UNIVERSITY INSTAR Trajectory Reconstruction 22 Initial time: t 0 – 10s – t 0 defined to be 9 min prior to entry interface Initial state (position, velocity, orientation) and covariance at t 0 – 10s provided by JPL – Solving for 12 parameters (9 initial conditions & 3 IMU errors) Gravity model: central + J 2 Used acceleration and rate data without smoothing or filtering Recall INSTAR process 1.Disperse initial conditions and IMU error parameters with specified uncertainties 2.Integrate IMU data using these initial conditions to obtain set of dispersed trajectories 3.Obtain statistics and mean initial conditions from subset of trajectories that satisfy redundant data 4.Repeat until convergence ParameterUnitsValue1σ1σ Xm E Ym E Zm E VXVX m/s E VYVY m/s E VZVZ m/s E X deg Y deg Z deg B a,x μgμg B a,y μgμg B a,z μgμg Initial Conditions, 0 frame