Hierarchical Navigation Algorithms In Support of Mars Exploration Robert H. Bishop The University of Texas at Austin May 19, 2005 Topics for Today • Navigation Algorithm Architecture Overview • Event Detection during Interplanetary Cruise • Application to Entry, Descent, and Landing
BACKGROUND • Traditional navigation algorithms use batch least-squares estimation (OD) or extended Kalman filters. – LSE optimize over long data arcs and are not easily adapted to real-time operation. – EKFs often perform poorly outside the “tuned” region • Environment changes are resolved by humans “in-the- loop” with an ad hoc and non real-time process relying heavily on: – Navigator Experience – Trial and Error Adaptation • Our investigations led us to consider adaptive estimation.
3 RD GENERATI ON “DREAM VEHI CLE”
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W HY ADAPTI VE ESTI MATI ON? • There is no systematic approach for selecting the operational navigation filter parameters. – Costly filter tuning in terms of manpower and time • There is a need for greater state estimation accuracies with less data (of potentially lower quality). – Low-cost, high-performance • There is a need to detect environmental and spacecraft changes and to take appropriate action. – Intelligent systems • Desire to increase robustness and reliability. – Mission safety and success
W HAT I S SUCCESSFUL ADAPTI VE ESTI MATI ON? • Successful adaptive navigation algorithms: – Identify the nature of changes in the spacecraft environment that cause it to deviate from the expected. – Tune the filter and model parameters corresponding to these changes to resume optimal tracking. • The adaptive algorithm must perform these tasks with a general structure based upon numerical analysis of the available data.
EVOLUTI ONARY PROCESS Mixture-of-Experts 1960 1970 1980 1990 2000 Correlation Methods Covariance Matching Methods Interactive multiple models Bayesian Methods Hierarchical Maximum Likelihood Methods Mixture-of- Adaptive filters with Experts for unknown parameters OD Hierarchical Magill’s filter bank Mixture-of- Experts for EDL UT investigations
HI ERARCHI CAL MI XTURE-OF-EXPERTS • Each module is an expert network— a Kalman filter. The function z is the input vector—the measurements. • The function y i is the ith module output—state estimate and • error covariance. The function g i is the activation of the ith output neuron of • the gating network. y 1 Expert (or Module) 1 g 1 y 2 Expert 2 g 2 z . . y . y L Expert L g L . . . Gating network
GATI NG NETW ORKS • The i th filter is associated with a GN neuron with synaptic weight a i,k • The GN calculates gating weights, g i , by mapping synaptic weights via the softmax operation T a i u i = z k • Why softmax? – Differentiable function that preserves rank order g i = e u i – Generalization of a “winner-takes-all” operation z 1,k L e u i ∑ g 1 i=1 z 1,k a i1 z 2,k 0 ≤ gi ≤ 1, g 2 a i2 u i Softmax z 2,k g i . . . ∀ i=1, 2, … L . . . . . . a im L ∑ gi = 1 z m,k g K i=1 z m,k Input layer Output layer
SYNAPTI C W EI GHT UPDATE FORMULA T W k -1 r k 1 1 - r k f( z k | α i ) = e • Conditional density 2 2 Π W k function • Distribution of the bank L f( z k ) = f( z k | α i )g i ∑ – The g ’s may be i=1 interpreted as apriori probabilities = ∑ L ( ) ( ) = lnf z ln g f z α l • Learning is achieved by k i k i = maximizing log-likelihood l i 1 with respect to g ( a ) h i = f( z k | α i )g i • Instantaneous a posteriori L f( z k | α i )g i ∑ probability injects filter performance into learning i=1 a i → a i + η (h i - g i ) z k • Synaptic weights update Learning rate
MULTI PLE LEVELS OF MODULARI TY • Filters are collected into banks to represent macromode environment changes • Within each bank, individual filter realizations represent fine, micromode, environment changes • “Best” filter in HME has the highest bank-level g ji,k in the bank with the highest top-level g i,k • Optimal filter configuration can be “masked” when containing bank does not receive highest top-level g • Method desired for identifying nominal environment without bank “masking”: Operational Control bank – The operational filter parameters and model reflect the mission nominal environment – The top-level GN identifies the nominal environment by selecting the control bank
MULTI PLE-LEVEL HME ARCHI TECTURE KF #0|0 r 0|0,k Bank-level weights g ji,k α = α 0|0 W 0|0,k regulate micromodes and r 1|0,k KF #1|0 g 0,k Bank 0 are used in top-level α = α 1|0 . Gating Network W 1|0,k . calculation. KF #K 0 |0 r K0|0,k . α = α K0 |0 A 0 W K0|0,k Top Level Macromode g k Gating Network . . zk . KF #0|L r 0|L,k Top-level weights α = α 0|L W 0|L,k g i,k regulate macromodes KF #1|L r 1|L,k g L,k Bank L α = α 1|L Gating Network . W 1|L,k . r KL|L,k KF #K L |L . A L α = α KL |L W KL|L,k Macromode g L+1,k r 0|L+1,k KF #0|L+1 g L+1,k = 1 Control bank only contains α = α 0|L+1 W 0L+1,k operational filter Control Macromode (Operational Filter)
APPLI CATI ONS • Interplanetary cruise orbit determination – Detecting small discrete disturbances – Detecting slow continuous disturbances • Mars atmospheric entry – Processing IMU as a “measurement” – Detecting atmospheric density variations
W HAT I S ORBI T DETERMI NATI ON? • Orbit Determ ination ( OD) : The process of describing the past, present, or predicted position of a satellite in terms of the orbital parameters.
THE DEEP SPACE NETW ORK • Interplanetary tracking is accomplished by 34 and 70m dishes • DSN dish time is expensive and in high demand • The primary data type is Doppler with a large number of supporting range measurements
SOLAR RADI ATI ON PRESSURE MODELI NG & SMALL FORCE DETECTI ON Mars at Launch TCM-1 • Earth at Launch Dec 4, 1996 TCM-2 • Thruster Cluster Solar Array BS shadowed Heat Rejection System (HRS) Panels Fuel Tanks Cruise Sun Stage BS in partial shadow Backshell Aeroshell TCM-3 Earth at Arrival Braking Rocket • Heatshield Lander TCM-4 • Mars at Arrival MARS PATHFINDER (MPF) July 4, 1997 15-Day Time Tics TCM=Trajectory Correction Maneuver
SRP MODEL SELECTI ON • The process of tuning the operational filter during the Mars Pathfinder mission was very time-consuming for the navigation team. • One of the main difficulties was choosing solar flux parameters. • We considered this situation using the mixture-of-experts architecture. MPF navigation team best SRP model Spacecraft Part Component Type Active Solar array Flat plate Entire cruise Launch vehicle Adapter Flat plate Entire cruise Heat rejection system Cylinder Entire cruise Backshell 1 Cylinder Before 4/16/97 Backshell 2 Flat plate After 4/16/97
GENERAL HME CONFI GURATI ON: 5 BANKS • Bank 0 : Impulsive Velocity Macromode – Filter and model parameters • Bank 1 : SRP Environment Macromode – Filter and model parameters • Bank 2 : Doppler Noise Macromode – Filter parameters • Bank 3 : Range Noise Macromode – Filter parameters • Bank 4 : Experimental Control (Nominal Operation)
PROCESSI NG DSN DATA FROM MPF MI SSI ON • MPF Cruise from TCM-2 to TCM-3 – Feb. 4 to Apr. 18, 1997 – 1612 Doppler and 3144 range observations • Unmodeled Impulsive Maneuver Identification – March 25 maneuver omitted from filter models • SRP Environment Change Identification – MPF model 4 assumed operational model
I MPULSI VE MANEUVER I DENTI FI CATI ON • The following small correction (0.7 mm/ sec) was performed on March 25, 1997 • ∆ V = [ 0.4449 0.07304 0.5301 ] mm/sec • The modeled Doppler noise = 0.2 mm/ sec • This maneuver has been omitted from all filter dynamic models to simulate an unmodeled impulsive event in the real mission data. • Successful experiment will result in Control receiving highest top-level weight until March 25 when a switch to the Impulse macromode occurs.
I MPULSE HME CONFI GURATI ON Bank # Filter # Impulse SRP R 0 (0,0) Feb. 4 * * 0 (1,0) Feb. 22 * * Impulse 0 (2,0) Mar. 12 * * 0 (3,0) Mar. 30 * * 1 (0,1) --- MPF 2 * SRP 1 (1,1) --- MPF 4 * 2 (0,2) --- * X3 Noise 2 (1,2) --- * X9 Control 3 (0,3) --- * *
I MPULSE I DENTI FI CATI ON TOP-LEVEL Hierarchy Weighting Assignments 1.0 1 Impulse SRP Control bank builds from equal 0.9 Noise synaptic initialization Control 0.8 0.8 Switch to Impulse Bank 0.7 March 25 0.6 0.6 Impulse g 0.5 Feb. 22 Mar.12 Mar. 30 0.4 Test Impulse Test Impulse Test Impulse 0.4 0.3 0.2 0.2 0.1 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 Day after 4-FEB-1997 3:1:0.0 UTC Days After 4-FEB-1997
I MPULSE I DENTI FI CATI ON BANK-LEVEL Bank 0 Weights 1 4-FEB- 22-FEB 12-MAR 30-MAR 0.5 0 0 10 20 30 40 50 60 70 Bank 1 Weights 1 MPF 2 MPF 4 0.5 0 0 10 20 30 40 50 60 70 Bank 2 Weights 1 σ R = 0.03 σ R = 0.09 0.5 0 0 10 20 30 40 50 60 70 Day after 4-FEB-1997 3:1:0.0 UTC
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