Apol Lo Guidance

Apollo Onboard Navigation Techniques

Objectives j

• Review basic navigation concepts • Describe coordinate systems • Identify attitude determination techniques – Prime: PGNCS IMU Management – Backup: p CSM SCS/LM AGS Attitude Management g

• Identify state vector determination techniques – Prime: PGNCS Coasting g Flight g Navigation g – Prime: PGNCS Powered Flight Navigation – Backup: LM AGS Navigation

Review of Basic Navigation g Concepts p •

Navigation: “Where am I?”

?

Review of Basic Navigation g Concepts p • •

Navigation: “Where am I?” Vehicle maintains internal representation of where it is with respect to some external reference (coordinate system) – State vector (position and velocity vectors)

Review of Basic Navigation g Concepts p • •

Navigation: “Where am I?” Vehicle maintains internal representation of where it is with respect to some external reference (coordinate system) – State vector (position and velocity vectors) – Attitude

Review of Basic Navigation g Concepts p • •

Navigation: “Where am I?” Vehicle maintains internal representation of where it is with respect to some external reference (coordinate system) – State vector (position and velocity vectors) – Attitude

•

To maintain accuracy, this internal representation must be updated periodically using some source so rce of e external ternal “tr “truth th data” (sensor measurements)

Coordinate Systems y Planet-Fixed Coordinates Moon Fixed Coordinates Moon-Fixed Lunar ephemeris

Earth Fixed Coordinates Earth-Fixed Earth rotation

Basic Reference Coordinates REFSMMAT

Stable Member Coordinates IMU gimbal angles

Navigation Base Coordinates Nav base location

Vehicle Coordinates c.m. location

Bodyy Coordinates Vehicle-Fixed Coordinates

Basic Reference Coordinate System y

• Inertial coordinate system – All nav stars and lunar/solar ephemerides were referenced to this system – All vehicle state vectors referenced to this system except during Lunar Module (LM) powered flight

• Epoch at nearest beginning of year – Simplified inertial-to-Earth-fixed computations

Basic Reference Coordinate System y

• Origin at center of Earth or center t off moon

Basic Reference Coordinate System y

• Origin at center of Earth or center t off moon – Command and Service Module (CSM) navigation automatically transformed between Earth and moon centered when crossing the moon’s Sphere of Influence (SOI)

Lunar Sphere of Influence (r=64373.76 km, 34759 05 nmi) 34759.05 i)

Basic Reference Coordinate System y

• Origin at center of Earth or center t off moon – Command and Service Module (CSM) navigation automatically transformed between Earth and moon centered when crossing the moon’s Sphere of Influence (SOI)

Ecliptic Plane Lunar Sphere of Influence (r=64373.76 km)

• Axes: – X-axis pointed to First Point of Aries

Equatorial Plane X

Basic Reference Coordinate System y

• Origin at center of Earth or center t off moon – Command and Service Module (CSM) navigation automatically transforms between Earth and moon centered when crossing the moon’s Sphere of Influence (SOI)

Z

Ecliptic Plane Lunar Sphere of Influence (r=64373.76 km)

• Axes: – X-axis pointed to First Point of Aries – Z axis parallel to Earth mean north pole

Equatorial Plane X

Basic Reference Coordinate System y

• Origin at center of Earth or center t off moon – Command and Service Module (CSM) navigation automatically transforms between Earth and moon centered when crossing the moon’s Sphere of Influence (SOI)

Z

Ecliptic Plane Lunar Sphere of Influence (r=64373.76 km)

Y

• Axes: – X-axis pointed to First Point of Aries – Z axis parallel to Earth mean north pole – Y axis completed righthanded system

Equatorial Plane X

IMU Stable Member Coordinate System y Stable Member +X-AXIS

• Inertial coordinate system • Defined relative to BRCS b by REF REFerence to Stable Member MATrix (REFSMMAT) • Many possible alignments during a mission (discussed later)

IMU CASE (CUTAWAY)

Stable Member +Z-AXIS

STABLE MEMBER

Stable Member +Y-AXIS

CSM Vehicle Coordinate System y

• Rotating coordinate system, t fixed fi d tto CSM body • Origin along vehicle centerline, t li 25 25.4 4 m (1000 in) behind Command Module (CM) heat shield • Axes:

Egress Hatch (-Z)

Optics (+Z)

– +X “forward” along longitudinal axis 25 4 m (1000”) 25.4 (1000 )

+X

CSM Vehicle Coordinate System y

• Rotating coordinate system, t fixed fi d tto CSM body • Origin along vehicle centerline, t li 25 25.4 4 m (1000 in) behind Command Module (CM) heat shield • Axes: – +X “forward” along longitudinal axis – +Z “down” down along crew crew’s s feet when in couches

Egress Hatch (-Z)

Optics (+Z)

+Z 25 4 m (1000”) 25.4 (1000 )

+X

+Z

CSM Vehicle Coordinate System y

• Rotating coordinate system, t fixed fi d tto CSM body • Origin along vehicle centerline, t li 25 25.4 4 m (1000 in) behind Command Module (CM) heat shield • Axes: – +X “forward” along longitudinal axis – +Z “down” down along crew crew’s s feet when in couches – +Y “starboard” completed right-handed system

Egress Hatch (-Z)

+Y Y

Optics (+Z)

+Z 25 4 m (1000”) 25.4 (1000 )

+X

+Z

LM Vehicle Coordinate System y • Rotating g coordinate system, fixed to LM body • Origin along vehicle centerline, t li 5 5.08 08 m (200 in) below LM ascent stage base • Axes: – +X “up” through top hatch +X

5.08 m (200”)

LM Vehicle Coordinate System y • Rotating g coordinate system, fixed to LM body • Origin along vehicle centerline, t li 5 5.08 08 m (200 in) below LM ascent stage base • Axes: – +X “up” through top hatch – +Z “forward” through egress hatch

+X

5.08 m (200”)

+Z “out of screen”

LM Vehicle Coordinate System y • Rotating g coordinate system, fixed to LM body • Origin along vehicle centerline, t li 5 5.08 08 m (200 in) below LM ascent stage base • Axes: – +X “up” through top hatch – +Z “forward” through egress hatch – +Y “starboard” completed right handed system right-handed

+X

5.08 m (200”)

+Y +Z “out of screen”

CSM/LM / Body y Coordinate Systems y

• Axes parallel to vehicle coordinate system • Origin at vehicle center of mass +X

+Y

+Y

+X +Z

Navigation g Base Coordinate System y +XNB

• Rotating g coordinate system, fixed to navigation base

+ZNB

– IMU gimbal angles define the transformation between stable member coordinates and nav base coordinates

• Origin at center of navigation base • Axes parallel to vehicle body axes

IMU Outer Gimbal

LM +X Axis

LM +Z Axis

IMU Middle Gimbal IMU Inner Gimbal

+XNB

+ZNB

+YNB

Earth--fixed Coordinate System Earth y • Rotating coordinate system, t fixed fi d tto Earth E th – All Earth landmarks, including launch site vector referenced to this vector, system

• Origin at center of Earth • Axes: – +Z along true north pole

+Z Greenwich Meridian +X

Equator

Earth--fixed Coordinate System Earth y • Rotating coordinate system, t fixed fi d tto Earth E th – All Earth landmarks, including launch site vector referenced to this vector, system

• Origin at center of Earth • Axes: – +Z along true north pole – +X along true Greenwich meridian at equator

+Z Greenwich Meridian +X

Equator

Earth--fixed Coordinate System Earth y • Rotating coordinate system, t fixed fi d tto Earth E th – All Earth landmarks, including launch site vector referenced to this vector, system

• Origin at center of Earth • Axes: – +Z along true north pole – +X along true Greenwich meridian at equator – +Y in equatorial plane, completed right-handed system

+Z Greenwich Meridian +X +Y Y Equator

Moon--fixed Coordinate System Moon y • Rotating coordinate system, t fixed fi d tto moon

+Z

– All lunar landmarks, including landing site vector referenced to this vector, system

• Origin at center of moon • Axes: – +Z along true north pole

Moon as viewed from Earth

Moon--fixed Coordinate System Moon y • Rotating coordinate system, t fixed fi d tto moon

+Z

– All lunar landmarks, including landing site vector referenced to this vector, system

• Origin at center of moon • Axes:

+X “out of screen”

– +Z along true north pole – +X along zero longitude at equator (center of moon visible i ibl di disc)) Moon as viewed from Earth

Moon--fixed Coordinate System Moon y • Rotating coordinate system, t fixed fi d tto moon

+Z

– All lunar landmarks, including landing site vector referenced to this vector, system

• Origin at center of moon • Axes: – +Z along true north pole – +X along zero longitude at equator (center of moon visible i ibl di disc)) – +Y completed right-handed system (“trailing” moon in its orbit around the Earth))

+Y +X “out of screen”

Moon as viewed from Earth

Objectives j

• Review basic navigation concepts • Describe coordinate systems • Identify attitude determination techniques – Prime: PGNCS IMU Management – Backup: p CSM SCS/LM AGS Attitude Management g

• Identify state vector determination techniques – Prime: PGNCS Coasting g Flight g Navigation g – Prime: PGNCS Powered Flight Navigation – Backup: LM AGS Navigation

PGNCS IMU Management g •

Apollo used three-gimbal IMU –

–

•

Apollo Flight Director Attitude Indicator (FDAI) driven directly by IMU gimbal angles rather than computer – –

•

Lighter and less complex than four fourgimbal IMU, but vulnerable to gimbal lock when all three gimbals in same plane Spacecraft attitudes operationally gimbal lock constrained to avoid g

Allowed IMU to operate independently of computer Allowed gimbal lock region to be graphically depicted as red circles on FDAI ball

Periodic IMU aligns to different REFSMMATs required to: – –

Accommodate variety of mission attitudes while avoiding gimbal lock Provide meaningful FDAI attitude display to crew

Gimbal Lock Region

Common REFSMMATs

• • • • • • •

Preferred Nominal (LVLH) L Launch hP Pad d (CSM only) l ) Landing Site Liftoff Passive Thermal Control (PTC) Entry (CM only)

Preferred REFSMMAT • Used for major burns • +X aligned with ΔV vector at Time of Ignition (TIG)

ΔV +X

R

Preferred REFSMMAT • Used for major burns • +X aligned with ΔV vector at Time of Ignition (TIG) • +Y p perpendicular p to both ΔV vector and position vector at TIG – Direction could be defined to provide either “heads headsup” or “heads-down” burn attitude

ΔV +X

R

+Y into screen (“heads-up”) out of screen (“heads-down”) ( heads-down )

Preferred REFSMMAT • Used for major burns • +X aligned with ΔV vector at Time of Ignition (TIG) • +Y p perpendicular p to both ΔV vector and position vector at TIG – Direction could be defined to provide either “heads headsup” or “heads-down” burn attitude

• +Z completed p right g handed system • FDAI read 0,0,0 when in burn attitude at TIG

ΔV +X +Z (“heads-down”)

+Z (“heads-up”)

R

+Y into screen (“heads-up”) out of screen (“heads-down”) ( heads-down )

Nominal REFSMMAT • • •

Aligned with Local Vertical/Local Horizontal (LVLH) coordinates at time of alignment Used for coasting orbital flight +Z aligned with radius vector (+Rbar) at time of align

V

+Z

R

Nominal REFSMMAT • • • •

Aligned with Local Vertical/Local Horizontal (LVLH) coordinates at time of alignment Used for coasting orbital flight +Z aligned with radius vector (+Rbar) at time of align +Y aligned with negative orbital momentum vector (-Hbar) at time of align

V

+Y “out of screen”

+Z

R

Nominal REFSMMAT • • • • • • •

Aligned with Local Vertical/Local Horizontal (LVLH) coordinates at time of alignment Used for coasting orbital flight +Z aligned with radius vector (+Rbar) at time of align +Y aligned with negative orbital momentum vector (-Hbar) at time of align +X in orbit plane in direction of velocity (+Vbar) FDAI read 0,0,0 when in “airplane attitude” at time of align Note that this was an inertial orientation aligned with LVLH only at one point i t iin titime – –

Inertial pitch angle diverged from LVLH pitch angle at orbital rate Crew used Orbital Rate Display – Earth and Lunar (ORDEAL) to bias FDAI pitch angle to display LVLH attitude

V

+X +Y “out of screen”

+Z

R

Launch Pad REFSMMAT North

• CSM onlyy • +Z aligned with radius vector (+Rbar) at liftoff titime East

View of launch pad from above

+Z

Launch Pad REFSMMAT North

• CSM onlyy • +Z aligned with radius vector (+Rbar) at liftoff ti time • +X aligned with flight azimuth at liftoff time

Launch Azimuth (typ. 72° at window open)

+X X East

View of launch pad from above

+Z

Launch Pad REFSMMAT North

• CSM onlyy • +Z aligned with radius vector (+Rbar) at liftoff ti time • +X aligned with flight azimuth at liftoff time • +Y completed righthanded system • At liftoff, FDAI read pitch 90, yaw 0, roll 90 plus flight azimuth

Launch Azimuth (typ. 72° at window open)

+X X East +Y View of launch pad from above FDAI roll 162°

+Z

Landing g Site and Liftoff REFSMMATs

• +X aligned with position vector t att planned l d landing l di time

+X

R

Landing g Site and Liftoff REFSMMATs

• +X aligned with position vector t att planned l d landing l di time • +Z pointed “forward” ( (parallel ll l tto CSM orbit bit plane)

+X +Z

R

Landing g Site and Liftoff REFSMMATs

• +X aligned with position vector t att planned l d landing l di time • +Z pointed “forward” ( (parallel ll l tto CSM orbit bit plane) • +Y completed righthanded system • LM FDAI read 0,0,0 at landing • Liftoff Lift ff REFSMMAT identical except defined at planned lunar liftoff time

+X +Z +Y “out out of screen screen”

R

PTC REFSMMAT •

•

Used for passive thermal controll (“b (“barbecue b roll”) ll”) d during i translunar/transearth coast +X in ecliptic plane perpendicular to Earth-moon Earth moon line +X

PTC REFSMMAT •

•

•

Used for passive thermal controll (“b (“barbecue b roll”) ll”) d during i translunar/transearth coast +X in ecliptic plane perpendicular to Earth-moon Earth moon line +Z perpendicular to ecliptic plane directed south p

+X +Z

PTC REFSMMAT •

•

• •

Used for passive thermal controll (“b (“barbecue b roll”) ll”) d during i translunar/transearth coast +X in ecliptic plane perpendicular to Earth-moon Earth moon line +Z perpendicular to ecliptic plane directed south p +Y completed right-handed system

+X +Y +Z

PTC REFSMMAT •

•

• • •

Used for passive thermal controll (“b (“barbecue b roll”) ll”) d during i translunar/transearth coast +X in ecliptic plane perpendicular to Earth-moon Earth moon line +Z perpendicular to ecliptic plane directed south p +Y completed right-handed system PTC roll initiated from 90 deg g pitch attitude to place CSM/LM stack perpendicular to ecliptic (and hence, line of sight to sun)

+X +Y +Z

Entry y REFSMMAT • Aligned g with LVLH at predicted time of Entry Interface (EI), 122 km ((400 kft)) altitude • FDAI read pitch 180, 0, 0 in heads-down heatshield forward attitude at EI • Note that nominal EI attitude pitched 20 degrees above local horizontal

+X

+Y “into screen” +Z

IMU Alignment g Techniques q

• Two vectors required q to uniquely define orientation of one frame with respect to another – First vector fixes a line of sight (LOS) but leaves one degree of freedom (rotation ( about LOS)

IMU Alignment g Techniques q

• Two vectors required q to uniquely define orientation of one frame with respect to another – First vector fixes a line of sight (LOS) but leaves one degree of freedom (rotation ( about LOS) – Second vector fixes rotation about LOS

CSM IMU Alignment g SCT

•

•

• • •

SXT

Crew marked on two stars (or other known celestial bodies) using the sextant (SXT) or scanning telescope (SCT) Auto optics modes allowed SXT/SCT shaft and trunnion to be pointed directly at stars selected by the computer Manual optics modes allowed tweaking of SXT/SCT shaft/trunnion using optics controller Minimum Impulse Controller (MIC) could be used to tweak CSM attitude Crewman Optical Alignment Sight (COAS) could be used as backup alignment device if optics failed –

Not attached to navigation base – calibration required prior to use

O ti Optics Controller

Minimum Mi i Impulse I l Controller (MIC)

MARK and d MARK REJECT pushbuttons

LM Docked IMU Alignment g • •

Initial coarse alignment used CM gimbal i b l angles l Docking mechanism did not tightly constrain relative roll – Crew recorded docking angle (Rc) from index marks on tunnel during initial LM activation

•

Required LM gimbal angles computed manually from CM gimbal angles as follows: OGALM = 300 300° + Rc - OGACM IGALM = 180° + IGACM MGALM = 360° - MGACM

LM Orbital IMU Alignment g •

•

• • •

Crew marked on two stars (or other known celestial bodies) using the alignment optical telescope (AOT) AOT had six detent positions; however only forward position however, could be used while docked to CSM Rendezvous Radar (RR) antenna required q to be p positioned out of AOT field-of-view Crew entered detent position code and star code manually into computer COAS could be used as backup (same calibration restrictions as CSM)

LM AOT Usage g • X-line and Y-line on AOT reticle ti l used d ffor iin-flight fli ht alignment • Crew allowed star to drift across AOT field-of-view fi ld f i

X line

Y line

LM AOT Usage g • X-line and Y-line on AOT reticle ti l used d ffor iin-flight fli ht alignment • Crew allowed star to drift across AOT field-of-view fi ld f i • Crew pressed [MARK Y] when star crossed Y-line

Press [MARK Y]

LM AOT Usage g • X-line and Y-line on AOT reticle ti l used d ffor iin-flight fli ht alignment • Crew allowed star to drift across AOT field-of-view fi ld f i • Crew pressed [MARK Y] when star crossed Y-line • Crew C pressed [MARK X] when star crossed X-line • Marks could be taken in either ith order d • Crew pressed [MARK REJECT] if bad mark

Press [MARK X]

LM Lunar Surface IMU Alignment g

•

Not always possible to sight on two stars while on surface

LM Lunar Surface IMU Alignment g

• •

Not always possible to sight on two stars while on surface For first surface alignment, local gravity vector (as measured by IMU accelerometers) l t ) could ld b be substituted for one of the star sightings

g

LM Lunar Surface IMU Alignment g

• •

•

Not always possible to sight on two stars while on surface For first surface alignment, local gravity vector (as measured by IMU accelerometers) l t ) could ld b be substituted for one of the star sightings Present orientation of LM Y and Z axes stored in moonfixed coordinates at conclusion of each alignment

+Z

LM Lunar Surface IMU Alignment g

• •

•

•

Not always possible to sight on two stars while on surface For first surface alignment, local gravity vector (as measured by IMU accelerometers) l t ) could ld b be substituted for one of the star sightings Present orientation of LM Y and Z axes stored in moonfixed coordinates at conclusion of each alignment For second and subsequent alignments, could use either gravity vector and present Z axis, or present Y and Z axes

+Z

LM AOT Surface Usage g •

Stars may never cross AOT X or Y lines while on surface – LM in fixed attitude – Moon rotates very slowly – Different marking g technique q required

•

Cursor

AOT reticle had two additional markings – Radial “cursor” cursor – Archimedean “spiral” (radius increases linearly with angle)

•

AOT reticle rotated to allow cursor or spiral to be superimposed on star – Reticle angle displayed on counter, manually entered via DSKY

Archimedean Spiral

LM AOT Surface Usage g •

Stars may never cross AOT X or Y lines while on surface – LM in fixed attitude – Moon rotates very slowly – Different marking g technique q required

•

AOT reticle had two additional markings – Radial “cursor” cursor – Archimedean “spiral” (radius increases linearly with angle)

•

AOT reticle rotated to allow cursor or spiral to be superimposed on star – Reticle angle displayed on counter, manually entered via DSKY

Shaft angle (AS)

LM AOT Surface Usage g •

Stars may never cross AOT X or Y lines while on surface – LM in fixed attitude – Moon rotates very slowly – Different marking g technique q required

•

AOT reticle had two additional markings – Radial “cursor” cursor – Archimedean “spiral” (radius increases linearly with angle)

•

AOT reticle rotated to allow cursor or spiral to be superimposed on star – Angle displayed on counter, manually entered via DSKY

Reticle angle (AR)

CSM SCS Attitude Management g • Stabilization and Control System (SCS) served as b k control backup t l system t ffor the th Primary Pi G Guidance, id Navigation, and Control System (PGNCS) • Attitude reference provided by two Gyro Assemblies (GA ) each (GAs), h off which hi h contained t i d th three B Body d M Mounted t d Attitude Gyros (BMAGs) • GA2 BMAGs measure attitude rate • GA1 G BMAGs G nominally measure attitude change from f reference attitude but could be configured to measure rates as backup to GA2

CSM SCS Attitude Management g • Gyro y Display p y Coupler p (GDC) combined GA1 attitude difference with reference attitude to produce total attitude for display to crew • Reference attitude set to current IMU attitude on Attitude Set Control Panel (ASCP) then GDC (ASCP), aligned to reference • BMAGs were more drifty than IMU “drifty”

LM AGS Attitude Management g

• Abort Sensor Assemblyy (ASA) ( ) was strapdown p inertial navigation system for the Abort Guidance System (AGS) • AGS had h d access to PGNS downlist d li d data via i telemetry link • Crew had capability to command AGS to align ASA to IMU GS could cou d a also so ca calibrate b ate ASA S • AGS gyro/accelerometer biases using IMU as reference

Objectives j

• Review basic navigation g concepts p • Describe coordinate systems q • Identifyy attitude determination techniques – Prime: PGNCS IMU Management – Backup: CSM SCS/LM AGS Attitude Management

• Id Identify tif state t t vector t determination d t i ti techniques – Prime: PGNCS Coasting Flight Navigation – Prime: PGNCS Powered Flight Navigation – Backup: LM AGS Navigation

Coasting g Integration g • Encke’s Method – Use current state vector and gravity of primary body to compute p a reference conic

Coasting g Integration g • Encke’s Method – Use current state vector and gravity of primary body to compute p a reference conic – Sum all other accelerations to p propagate p g a position/velocity deviance from the reference conic

Coasting g Integration g • Encke’s Method – Use current state vector and gravity of primary body to compute p a reference conic – Sum all other accelerations to p propagate p g a position/velocity deviance from the reference conic – When deviances exceed threshold, compute new reference conic and zero the deviations (rectification)

Coasting g Integration g •

Compare to Cowell’s Method ( h l ) (shuttle): – Sum all accelerations on vehicle (including primary body gravity) and propagate directly to advance the state vector

• •

Cowell’s advantage: simpler, brute force algorithm brute-force Encke’s advantages: – Maintains more precision at larger stepsizes – More suitable for slow computers with limited precision (i.e. Apollo Guidance Computer)

Perturbing g Accelerations

• Depended on phase of mission • Earth or lunar orbit: non-spherical gravity of primary body (up to fourth order terms) • Translunar/transearth coast: Earth, lunar, and d solar l gravity it ((spherical h i l tterms only) l ) • No drag • No IMU acceleration

Measurement Incorporation p

• Several different programs available, not all on both vehicles • MCC prime for most forms of navigation; onboard capability intended as loss loss-ofof comm backup

Program

CSM

LM

Prime

Rendezvous

√

√

Onboard

Orbital

√

MCC

Cislunarmidcourse

√

MCC

Lunar Surface

√

MCC

LM Rendezvous Navigation g Navigated Actual P Passive i Vehicle V hi l Orbit O bit

Coasting IIntegration t ti

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

A ti Vehicle Active V hi l O Orbit bit + Coasting IIntegration t ti

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

• The state vectors for both vehicles are propagated to the current time

LM Rendezvous Navigation g Navigated Actual P Passive i Vehicle V hi l Orbit O bit

Coasting IIntegration t ti

RR Tracking Measurement

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

A ti Vehicle Active V hi l O Orbit bit + Coasting IIntegration t ti

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

Q

• The LM RR takes a measurement (range, range rate, shaft, or trunnion angle) of the CSM

LM Rendezvous Navigation g Navigated Actual P Passive i Vehicle V hi l Orbit O bit

Coasting IIntegration t ti

Measurement Geometry Vector RR Measurement Estimate

RR Tracking Measurement

• •

A ti Vehicle Active V hi l O Orbit bit +

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

Coasting IIntegration t ti

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

r b Qˆ -

Residual

δQ

Q

+

The navigation software computes an estimate of the RR measurement based on the current state vectors, and a measurement geometry vector The navigation software f computes the difference ff (residual) ( ) between the actual RR measurement and the estimated measurement

LM Rendezvous Navigation g Navigated Actual P Passive i Vehicle V hi l Orbit O bit

Coasting IIntegration t ti

Measurement Geometry Vector RR Measurement Estimate

RR Tracking Measurement

A ti Vehicle Active V hi l O Orbit bit +

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

Coasting IIntegration t ti

r b

α -

Residual

δQ

Q

+

+

Weighting Vector Computation

r2

Qˆ

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

r

ω

Measurement Incorporation

• The navigation software computes a weighting vector based on the current states, states the measurement geometry vector, and predefined sensor variances

LM Rendezvous Navigation g Navigated Actual P Passive i Vehicle V hi l Orbit O bit

Coasting IIntegration t ti

Measurement Geometry Vector RR Measurement Estimate

RR Tracking Measurement

A ti Vehicle Active V hi l O Orbit bit +

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

Coasting IIntegration t ti

r b

Weighting Vector Computation

r2

α

Qˆ -

δQ

Q

+

r

ω

Residual

r

ω δQ

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

r ⎡ δr ⎤ r r δx = ⎢⎢ δv ⎥⎥ r ⎣⎢δb ias ⎥⎦ SV Update

Measurement Incorporation

• The navigation software computes an update to the state vector and the estimated RR biases using the weighting vector and the measurement residual

LM Rendezvous Navigation g Navigated Actual P Passive i Vehicle V hi l Orbit O bit

Coasting IIntegration t ti

A ti Vehicle Active V hi l O Orbit bit +

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

Coasting IIntegration t ti

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

r

Measurement Geometry Vector RR Measurement Estimate

r b

• • •

Weighting Vector Computation

r2

α

Qˆ -

Q

+

r

ω

Residual

δQ

r δb ias

RR Tracking Measurement

δr r δv

r

ω δQ

Measurement Incorporation

r ⎡ δr ⎤ r r δx = ⎢⎢ δv ⎥⎥ r ⎣⎢δb ias ⎥⎦

Pass

SV Update State Vector Alarm Test Pass

Accept

Fail

Crew Action

Reject

Accept

The state vector update is tested against a predefined threshold If the test passes, the state vector and RR biases are updated Otherwise, alarm annunciated and crew either accepts or rejects the update

LM Rendezvous Navigation g Navigated

P Passive i Vehicle V hi l Orbit O bit

Coasting IIntegration t ti

+

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

A ti Vehicle Active V hi l O Orbit bit

Coasting IIntegration t ti

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+ +

+

Actual

Maneuver Δ ΔV

+

Maneuver Δ ΔV

Update Mode

r

Measurement Geometry Vector RR Measurement Estimate

r b

• •

Weighting Vector Computation

r2

α

Qˆ -

Q

+

r

ω

Residual

δQ

r δb ias

RR Tracking Measurement

δr r δv

r

ω δQ

Measurement Incorporation

r ⎡ δr ⎤ r r δx = ⎢⎢ δv ⎥⎥ r ⎣⎢δb ias ⎥⎦

Pass

SV Update State Vector Alarm Test Pass

Accept

Fail

Crew Action

Reject

Accept

State vector update can be applied to either vehicle (usually the active vehicle, LM) If CSM performs maneuver, maneuver ΔV should be externally applied to CSM vector in the LM to prevent excessive RR updates and improve state vector convergence

If it q quacks like one… • Apollo navigation software initial development by Battin was concurrentt with ith (and ( d iindependent d d t of) f) K Kalman’s l ’ work k on recursive estimators (later named Kalman filters) – Early Apollo documents didn’t use Kalman’s nomenclature – Battin B tti di discovered dK Kalman’s l ’ work kd during i d development l t

• Apollo navigation software contained several simplifications/differences from “orthodox” Kalman filter – W-matrix W matrix instead of error covariance matrix • Square root of covariance: [E] = [W][W]T • Eliminating negative numbers from matrix improved convergence

– One measurement incorporation p at a time • Reduced a lot of matrix-vector math to vector-scalar math

– Measurement edit test used state vector update rather than ratio • Ratio test incorporates covariance, becomes more stringent as state vector converges

CSM Rendezvous Navigation g

+

Coasting IIntegration t ti

+

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

A ti Vehicle Active V hi l O Orbit bit

+

Coasting IIntegration t ti

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

Maneuver Δ ΔV

+

P Passive i Vehicle V hi l Orbit O bit

Maneuver Δ ΔV

Update Mode

r

Measurement Geometry Vector VHF/SXT Measurement Estimate

VHF/SXT Measurement

δr r δv

r b

Weighting Vector Computation

r2

α

Qˆ

r

ω

-

δQ Q

+

r

ω δQ

Measurement Incorporation

r r ⎡δr ⎤ δx = ⎢ r ⎥ ⎣δv ⎦

Pass State Vector Alarm Test

Accept

Fail

Crew Action

Reject

• CSM rendezvous measurements are performed using VHF (range) and SXT (shaft and trunnion angles) • Sensor biases are not propagated

LM Lunar Surface Navigation g

+

CSM V Vehicle hi l O Orbit bit

Coasting IIntegration t ti

LM V Vehicle hi l St State t

+

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦ Planetary Inertial Orientation

r

Measurement Geometry Vector RR Measurement Estimate

RR Tracking Measurement

• • • •

δr r δv

r b

Weighting Vector Computation

r2

α

Qˆ

r

ω

-

δQ Q

+

r

ω δQ

Measurement Incorporation

r r ⎡δr ⎤ δx = ⎢ r ⎥ ⎣δv ⎦

Pass State Vector Alarm Test

Accept

Fail

Crew Action

Reject

The LM vehicle state is stored in Moon-Fixed Coordinates and updated by transforming to inertial coordinates The CSM state vector is updated using LM RR data Only RR range and range rate are incorporated, not angles RR biases are not propagated

CSM Orbital Navigation g

CSM V Vehicle hi l O Orbit bit

Coasting IIntegration t ti

Landmark Position

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

r

r rl Measurement Geometry Vector SCT Measurement Estimate

r δrl SCT Landmark Measurement

• • • • •

+

δr r δv

r b

Weighting Vector Computation

r2

α

Qˆ

r

ω

-

δQ Q

+

r

ω δQ

Measurement Incorporation

r ⎡δr ⎤ r r δx = ⎢⎢δv ⎥⎥ r ⎢⎣δrl ⎥⎦

Accept (known landmark) Crew Action

Reject

Accept (unknown landmark)

Only the CSM state vector is propagated Measurements are SCT shaft and trunnion angles on a landmark on the Earth or lunar surface All updates must be accepted or rejected by the crew Landmark may be known (update CSM state vector) or unknown (update landmark position) Sensor biases are not propagated

CSM CislunarCislunar-Midcourse Navigation g

CSM V Vehicle hi l O Orbit bit

Star Direction, Landmark Position

Coasting IIntegration t ti

+

r r ⎡r ⎤ x = ⎢ r⎥ ⎣v ⎦

+

SXT star line of sight (SLOS)

SXT landmark line of sight (LLOS)

r

Measurement Geometry Vector SXT Measurement Estimate SXT Star-Landmark/ Horizon Measurement

• • • •

δr r δv

r b

Weighting Vector Computation

r2

α

Qˆ

r

ω

-

δQ Q

+

r

ω δQ

Measurement Incorporation

r r ⎡δr ⎤ δx = ⎢ r ⎥ ⎣δv ⎦

Accept Crew Action

Reject View through SXT reticle

Only the CSM state vector is propagated Measurements are SXT marks on a star and either a landmark or Earth/moon horizon All updates d t mustt b be accepted t d or rejected j t db by th the crew Sensor biases are not propagated

Powered Flight g Navigation g •

Both CSM and LM used Average-G algorithm for state vector propagation during powered flight – Used IMU accumulated ΔV over one guidance cycle (2 seconds) – Used average gravitational acceleration over one cycle, primary body only • Earth gravity model: spherical and J2 (equatorial bulge) terms only • Lunar gravity model: spherical term only

– Estimated vehicle mass updated based on IMU sensed ΔV

• •

No measurement incorporation for CSM LM Average-G incorporated Landing Radar (LR) measurements only – – – –

•

Slant range data available starting at 12.2 12 2 km (40 kft) altitude Velocity data available starting at 10.6 km (35 kft) altitude Both range and velocity subjected to simple independent reasonableness checks All data inhibited at 15.2 m (50 ft) altitude

LM state vector propagated in Stable Member coordinates (rather than Basic Reference coordinates) during powered descent, ascent, and aborts – Since IMU aligned to landing/liftoff REFSMMAT, sometimes referred to as landing site coordinates – Average Average-G G output transformed back to BRCS for downlink

LM AGS Navigation g • AGS state vectors initialized from PGNS telemetry link upon crew command d • AGS state vectors could also be initialized via manual keyboard entries of vectors voiced up from MCC • AGS propagated CSM/LM state vectors from last initialized data using acceleration data from ASA • If LM under PGNS control, AGS acquired rendezvous radar (RR) ( ) data (range, ( range rate, and angles)) automatically from PGNS • If LM under AGS control, AGS acquired rendezvous radar d d data t via i manuall DEDA entries ti – Range and range rate only – Crew manually pointed LM +Z axis at CSM to zero RR angles

Summary y

• Review of Basic Navigation Concepts • Coordinate Systems • Attitude Determination – Prime: PGNCS IMU Management – Backup: p CSM SCS/LM AGS Attitude Management g

• State Vector Determination – Prime: PGNCS Coasting g Flight g Navigation g – Prime: PGNCS Powered Flight Navigation – Backup: LM AGS Navigation

References • • • • • • • • • • • • •

Apollo Operations Handbook, Block II Spacecraft, Volume I: Spacecraft Description. SM2A-03( ), 15 Januaryy 1970. Block II-(1), Apollo Operations Handbook, Lunar Module, LM 10 and Subsequent, Volume I: Subsystems Data. LMA790-3-LM 10, 1 April 1971. Guidance System Operations Plan for Manned LM Earth Orbital and Lunar Missions using Program Luminary 1C (LM131 rev. 1), Section 5: Guidance Equations (rev. 8). MIT Charles Stark Draper Laboratory R-567, April 1970. Guidance System Operations Plan for Manned CM Earth Orbital and Lunar Missions using Program Colossus 3, Section 5: Guidance Equations (rev. 14). MIT Charles Stark Draper Laboratory R-577, March 1971. Space Navigation Guidance and Control, Volume 1 of 2. MIT Instrumentation Laboratory R-500, June 1965. A ll 15 P Apollo Program D Description. i ti D l El Delco Electronics, t i 1971. 1971 Project Apollo Coordinate System Standards. NASA SE 008-001-1, June 1965. Apollo Training: Guidance and Control Systems - Block II S/C 101, 15 September 1967. Apollo Experience Report – Guidance and Control Systems. NASA TN D-8249, June 1976. Apollo p Experience p Report p – Onboard Navigational g and Alignment g Software. NASA TN D-6741,, March 1972. Apollo Experience Report: Very-High-Frequency Ranging System. NASA TN D-6851, June 1972. Apollo Experience Report – Guidance and Control Systems: Orbital-Rate Drive Electronics for the Apollo Command Module and Lunar Module. NASA TN D-7784, September 1974. Apollo p Guidance Computer p History y Project, j , Interview with R. Battin,, MIT,, 30 September p 2002 (http://authors.library.caltech.edu/5456/01/hrst.mit.edu/hrs/apollo/public/interviews/battin.htm).