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					Deep Space Navigation

         Robert Mase
    Jet Propulsion Laboratory
California Institute of Technology
       Pasadena, California         1
                   The Navigation Process
Five tasks need to be performed for successful navigation,
  whether on Earth or in deep space:

Task                    Student Example            Deep Space Example
1. Obtain a map         Log onto Mapquest          Planetary ephemerides

2. Plot a course        Find route to Spring Break Select target body, compute
                        destination                launch/arrival conditions

3. Take measurements    Speedometer, odometer,     Radiometric tracking data,
                        in-car GPS                 pictures of target & star

4. Calculate position   Read road signs, GPS       Numerical least-squares fit of
                                                   tracking data

5. Make course          Turn the wheel, hit the    Perform propulsive maneuver
   corrections          gas pedal or brakes

      Navigation Uncertainty - Analogy
If you know where you are, and where you need to get to,
   why do you need Navigation at all?
– Problem: Your friend wants to meet you in Florida at your Spring Break
   destination just as you arrive with a cold beverage

– Solution: If you start out in Atlanta, heading to Spring Break destination,
   know what time you are leaving, and the speed limit, you can calculate
   exactly when you should arrive… or can you?

– What if there is an accident, or traffic jam, or you stop for gas or food?
   What if your odometer is off by 2 miles/hour?
   What is the street signs are poor and you take a wrong turn?
    • Can you predict these things exactly ahead of time?

– How can we account for unseen events ahead of time to compensate?
    • I’ll be there at 5:00 plus or minus an hour
    • Friend complains: Cold beverage will get warm waiting one hour in the
      hot Florida sun!

    – Solution : Cellphone! - Call with an update when you get close
           Navigation Uncertainty
Previous example doesn’t really apply to deep-
  space navigation… or does it?
  True there are no traffic jams or pit-stops in space…
    But what can affect the trajectory?

  Do we know all propulsive events that will happen?
  Do we know all forces that will act on the spacecraft?
  Do we know all of our measurements are exactly right?
  Do we know exactly where our target is?
  Do we know exactly where we are?
  Does any of this matter?

• Typical trajectory to Mars is about 250 days
   • 250 days x 86,400 sec/day = 21,600,000 secs

• Typical propulsive maneuver will impart on the order of 1 to 10
  meters/sec (2 - 20 mph) of velocity change to the spacecraft
   • We can measure the velocity change to within 1 mm/sec (0.002 mph)

• If we are wrong by only 1 mm/sec:
                      (Simple linear calculation)
                      Distance = Velocity * Time
                1E-6 km/sec * 21,600,000 sec = 21.6 km

   We will arrive 21.6 km off from where we should be

• Acceleration due to solar radiation pressure
   Typical uncertainty is on the order of 1E-12 km/sec/sec

• If we are wrong by only 1E-12 km/sec/sec:

                           Distance = 1/2 *a *t2
          1/2 * (1E-12 km/sec/sec) * (21,600,000 sec)2 = 230 km

   We will arrive 230 km off from where we should be

Note: The uncertainty will decrease with time to go

   • The closer we get to the target, the number of things that can happen
     between now and arrival decreases
   • The effect of any individual perturbation decreases with time to go
                       Error Sources
So what else do we have to contend with?
• Measurement Errors:
   •   Measurement noise
   •   Earth orientation
   •   Tracking station locations
   •   Transmission media
   •   Instrumental signal delay effects
   •   Spacecraft oscillator instability

• Force Modeling Errors:
   •   Gravity
   •   Propulsive maneuver events
   •   Solar radiation pressure
   •   Outgassing

None of these things are known exactly, so we must account for our
  lack of knowledge by calculating the associated uncertainty
                Navigation Uncertainty
What strategy can we use to account for uncertainty or
• We always have the ability to adjust the trajectory - fire the thrusters
    •   In a car we can speed up or slow down, can turn left or right

• Small adjustments early in the trajectory have a bigger effect
    •   Can change travel time significantly by driving slightly faster all the way
    •   This will change the planned arrival time, but will not decrease the
        uncertainty in what time you will actually arrive

• Adjustments at the last minute more precise, but limited in scope
    •   If you wait until you are almost there, there is not much left to deter you
    •   Can’t significantly change arrival time just one mile from your destination

We schedule a series of opportunities to adjust the trajectory consistent
  with our knowledge of the trajectory and associated uncertainty

Make big adjustments early to get in the ballpark, make more precise
  adjustments later when there is more certainty in arrival conditions                8
          Navigation Measurements
What measurements do we have to work with?
• Doppler - measures the line-of-site velocity between the
  spacecraft and the tracking station
   • Typically accurate to 0.1 mm/sec (0.0002 mph !)
• Range - Measures the line-of-site distance from the
  spacecraft to the tracking station
   • Typically accurate to a couple of meters
• Can measure position and velocity quite accurately
   • But only in one direction
• On Earth we have handheld GPS which uses 4 or more
  satellites to unambiguously triangulate your location
   • For spacecraft, we can use two tracking stations at once to
     triangulate, referred to as an interferometric measurement

          Mars Odyssey Spacecraft

                                      (located inside)

Gamma Sensor
                                   High Energy Neutron
                                   Detector (HEND)

   Neutron Spectrometer
Mars Odyssey Trajectory

                                          Earth at


                                                     Mars Arrival
    TCM-1                                    TCM-4   23-Oct-2001


 Mars at                  TCM-2                                     11
           Mars Odyssey - Launch
• If the spacecraft was launched and never performed any kind of
  trajectory correction maneuver, where would it end up?

     Mars Odyssey - First Maneuver
• The first propulsive maneuver: 3.6 m/s, 46 days after launch
   • Moved arrival point 60,000 km closer to Mars
   • But still large uncertainty (> 1000 km) in expected arrival conditions

                        TCM-1 Target
                       and 3  Deliv ery

                 TCM-1 Reconstruction
   Mars Impact

                                                               TCM-1 Design

        Mars Odyssey - Final Maneuver
• The final maneuver: 0.08 m/s, 12 days prior to arrival
   • Needed to be accurate to ±25 km, ended up <5 km from the target

                                           Inc lination
                OD Know led ge             C ons traint
                   prior to                  ±0.2Þ
                TC M-4 De s ign

                                                                TC M-4 Target
                                                                and Ex pec ted
                                  TC M-4                                          Altitude
                                                                 3 De liv ery
                                                                                 C ons traint
    B¥R ( km)

                                                                                  ±25 k m
                                           R ec ons truc tion


                                                B¥T km)
           Mars Exploration Rovers
• Two rovers to be landed on the surface of Mars
   • Parameter of interest is Entry Flight Path Angle, ±0.10 degree rqmt
   • Translates to a position uncertainty at entry of a couple of kilometers

          Mars Exploration Rovers
• Goal: Land a Rover on the surface of Mars

    Cassini - In Orbit Around Saturn
• Goal: Deliver Huygens Probe into Titan atmosphere

   Cassini Probe Delivery Accuracy
• Must wait until Navigation accuracy is sufficient to meet entry
  corridor requirements to release the probe
   • Parameter of interest is Entry Flight Path Angle, ±3 degree rqmt

  • Mission: Collect Particles of Solar Wind
  • Navigation Goal: Deliver Sample Canister to Earth, “land” in Utah
                    Low Gain Antenna-Forward                SRC Backshell
  SAPY                    (LGA-FWD)                                                       SRC Heatshield
& Release                               Detachable Aft                                             Minus-Z Propellant T ank
                                       Conical Segment                                                (-ZPROPT ANK)
                Solar Array Plus-Y         (DACS)

                                                                                                           Transponder 1
                                       SAPY Hinge
                                                                                                          Single Pole Double Throw RF Switch
        2-Axis Sun Sensor A                                                                                            (SPDT)
        (2-AXIS SUNSENA)                                              Hinge
                                                                                                               Genesis Ion Monitor
            Genesis Electron Monitor                                                                                  (GIM)
                    (GEM)                                                                                  Single Pole Triple Throw RF Switch
                                                                                                                           2-Axis Sun Sensor B
                            Transponder 2                        SRC +Z Strut                       SAMY Hinges            (2-AXIS SUNSENB)

                                                            Hinge           Launch                             Solar Array Minus-Y
                                                           Retract          Vehicle
                                                                                       Power                         (SAMY)
                                                          Mechanism         Adapter
                                                                             (LVA)    Controller
                                 Plus-Z Propellant Tank                               Assembly                                                 SAMY
                                    (+ZPROPTANK)              Medium Gain Antenna      (PCA)                                                 Retention
                                                                    (MGA)                                                                    & Release
                                                                              X                           Low Gain Antenna-Aft

Genesis Trajectory

    Genesis “Landing” Zone in Utah
• Navigation to the atmosphere was perfect
• Parachute did not open, canister “landed” in safe zone

  Deep Space Missions have unique
     constraints and requirements

Even all Mars missions are not the same
      Landers vs Orbiter vs Rovers

  But all require accurate Navigation


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