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_, ii!iiii!!iii!i!i!iii_ii"11
NATIONAL AERONAUTICS AND
. . /,X__ '__v_/_ OCT2 I. 138@
IJ
SPACE ADMINISTRATION
MSC INTERNAL NOTE NO. 68-FM-256
October 11, 1968
VERIFICATION OF SUNDISK ORBITAL
NAVIGATION PROGRAM
MISSION
".'.'. ..... (NASA°T[_XQ_9716)
!:i:i:!:i:!:!:i:o __I $AL _,¢VI _A$_0°°.°°%°°°°°°°°°
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°°°°°°°°°%°°°°°.°.'.'.-o...o*o°
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"'5 , ' I _'; "_
Mathematical Physics Branch
PLANNING AND ANALYSIS DIVISION
MANNED SPACECRAFT CENTER
HOUSTON,TEXAS
VERIFICATION OF SUNDISK N7;4-70626
PI_OGHA_ (NASA) 112 p
Unclas
00/99 16149
MSC INTERNAL NOTE NO. 68-FM-256
PROJECT APOLLO
VERIFICATION OF SUNDISK ORBITAL NAVIGATION PROGRAM
By Richard Eo EckelkampMathematical Physics Branch
October ii, 1968
MISSION PLANNING AND ANALYSIS DIVISION
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MANNED SPACECRAFT CENTER
HOUSTON, TEXAS
'W
llar_es C. Mcl:rSerson, Chief - -1_tthematical Physics Branch
Approved: _"_. 0 (_"1_( _--_.,_,
John P_ayer, Chief -'--=r"
Missio_=:qanning and Analysis Division
_J
.i
CONTENTS
Section Page
SUMMARY ............................. I
INTRODUCTION ........................... 1
The Kalman-Schmidt Filter ........ ........... 2
SUMMATION OF ORBITAL NAVIGATION EQUATIONS ............ 3
Coordinate Systems ....................... 3
Orbital Integration ...................... 4
Use of Landmark Sightings in the Kalman-Schmidt Filter ..... 6
The b-vector ......................... 7
The W matrix and a2 ..................... 9
The observation residual ................... ii
The CMC's Implementation of the Kalman Filter ......... 12
Verification of the Kalman factor .............. 13
Verification of the W updating equation ........... 14
Unknown landmarks ...................... 17
THE CMC CODING .......................... 20
Results of Coding Review .................... 37
Flow chart comparison .................... 37
Comparison of equation and astronaut procedure to coding. • 37
Illegal interfaces ...................... 37
ASTRONAUT PROCEDURES ....................... 37
BIT-BY-BIT TESTING ........................ 37
CONCLUSION ............................ 38
APPENDIX A - MIT FLOWCHARTS FOR SUNDISK REV 212 P22 ....... 39
APPENDIX B - MIT APOLLO COMPUTER LOGIC CHECKLIST INTERFACE
(GSOP IV) ........................... 61
iii
Section Page
APPENDIXC - APOLLO7 CREWCHECKLISTFORP22.......... 79
APPENDIXD - SUNDISKP22VERIFICATIONTEST- TWOKNOWNLAND-MARKSCASE.......................... 85
APPENDIXE - SUNDISKP22VERIFICATIONTEST- ONEKNOWN,ONEUNKNOWNLANDMARKCASE.................... 97
REFERENCES........................... 107
t
iv
TABLES
Table
D-I
D-II
D-Ill
D-IV
D-V
D-VI
D-VII
D-VIII
D-IX
E-I
E-II
E-III
E-IV
E-V
E-VI
E-VII
E-VIII
Page
DIFFERENCE BETWEEN THE BIT-BY-BIT AND THE
ENGINEERING-SIMULATION UNIT b-VECTOR ......... 87
THE BIT-BY-BIT UNIT b-VECTOR ............. 88
THE BIT-BY-BIT VECTOR UPDATES ............. 89
ENGINEERING-SIMULATION VECTOR UPDATES ......... 90
BIT-BY-BIT ESTIMATED LANDMARK POSITION ........ 91
ENGINEERING-SIMULATION ESTIMATED LANDMARK POSITION 92
DIFFERENCE BETWEEN THE BIT-BY-BIT AND THE
ENGINEERING-SIMULATION W-MATRIXAFTER THE SECOND
INCORPORATION .................... 93
DIFFERENCE BETWEEN THE BIT-BY-BIT AND THE
ENGINEERING-SIMULATION W-MATRIX AFTER MARK 5,.SECOND
INCORFORATION .................... 9h
BIT BY BIT W MATRIXAFTER MARK 5, SECOND
INCORPORATION ..................... 95
BIT-BY-BIT VECTOR UPDATES ............. . . 99
ENGINEERING-SIMULATION VECTOR UPDATES ......... 100
BIT-BY-BIT ESTIMATED LANDMARK POSITION ........ 101
ENGINEERING-SIMULATION ESTIMATED LANDMARK POSITION . . 102
DIFFERENCE BETWEEN THE BIT-BY-BIT AND THE ENGINEERING-
SIMULATION ESTIMATED POSITION AND VELOCITY VECTOR . . 103
DIFFERENCE IN THE RESIDUALS (ACTUAL MINUS ESTIMATED)
OF THE BIT-BY-BIT AND THE ENGINEERING-SIMULATED
POSITION AND VELOCITY VECTOR ............. 10h
DIFFERENCE IN THE DIAGONAL OF THE BIT-BY-BIT AND THE
ENGINEERING-SIMULATION W-MATRIX 105
DIAGONAL VALUES AT SPECIFIED POINTS IN THE
BIT-BY-BIT W-MATRIX .................. 106
v
VERIFICATION OF SUNDISK ORBITAL NAVIGATION PROGRAM
By Richard E. Eckelkamp
SUMMARY
This paper presents a detailed explanation and test verification
of SUNDISK 282 orbital navigation program 22 _P22). Included are a
step-by-step analysis of the coding and flow charts, a summary of the
equations utilized, an outline of astronaut procedures, and charted
results of bit-by-bit test cases.
INTRODUCTION
Orbital navigation, as contained in the roped version 282 of
SUNDISK for the command module computer_(CMC), will be exercised for
the first time on Apollo 7. This report fulfills a need of gathering
and interpreting the official documentation concerning the programunder one cover.
In orbital navigation, optical sightings on landmarks are statis-
tically weighed to correct the vehicle position and velocity in the
CMC as well as the position of the landmarks. This process can thus
determine both the orbit and the landing site.
The explanation of P22 will begin with a summation of the formula-
tion found in parts 5.1 to 5.2.8 of Section V of the GSOP (ref. 1).
A line-by-line interpretation of the coding, as presented in reference
2, will then be given. The MIT flow charts are available to aid in the
understanding of the coding. A resume of astronaut procedures and thetest results follows.
2
The Kalman-Schmidt Filter
Accurate estimates of the state vectors of bodies relative toparticular reference systems maybe computedby integration of theequations of state complementedwith processing of navigational obser-vations. Onemethod of processing observations, the Kalman-Schmidtfilter, adapted from filter theory in electrical engineering, statis-tically weighs single observations and uses them to correct statevectors while smoothing observational noise.
In orbital navigation the state vector consists of the commandmodule's position and velocity and the position of a given landmark inan inertial coordinate system. Telescope or sextant observations ofthe landmark relative to an inertial platform constitute the measurement.
Before presenting detailed information of the navigation processes,a brief outline of the Kalman-Schmidtmethod is useful.
To correct the state at time t.i
a) Make an observation Qi at t i
b) Integrate the state vectors as stored in the vehicle computer
to t.1
/Fr-v-c
r-c
v-c
i-i i
where r-c = position vector of command module
V-c = velocity vector of command module
c)
_r£ = position vector of landmark
^
Compute from this state vector the estimated observation Qi
3
^
d) Find the observation residual Qi - Qi = _Qi
e) Compute the weighting factor _. for the residual at t.-1 l
This factor is obtained by propagating the square root of the state
convariance matrix (or matrix of state uncertainty) to t..1
f) Correct the state
. . +r-C
V-C
i
i r-C
V-C
+ __iSQi
g) Also correct, or update, _ to -q_'+'where the plus denotes the
updated quantity.
This statistically weighting of single observations for vector
correctionworks well and is equivalent to the modified weighted least
square (WLS) method used for ground-based navigation. Generally, the
number of observations required to reduce initial errors to within the
system noise level and maintain this level of accuracy varies with
mission phase and navigation requirements.
SUMMATION OF ORBITAL NAVIGATION EQUATIONS
Coordinate Systems
To locate any body at a given time a coordinate system is
necessary. For the Apollo program, the basic reference system is the
nearest Besselian year (NBY) coordinate system.
The NBY system is defined in an earth-centered inertial Cartesian
system. The X-axis is along the line of intersection of the mean
equatorial plane and the mean orbit plane of the earth (equinox); Z is
along the mean north pole; and Y completes the right-handed triad - all
defined at the time of the beginning of the NBY. Vectors dated after
the Julian date of June 30 _re referenced to the following year. Forexample, the Besselian year 1968 begins on Julian day January 1.283,
1968; the Besselian year 1969, January 0.525, 1969. The center of this
system is translated to the moon's center when the vehicle is in lunar
reference.
4
As stated in reference 3, the CMC programs, including orbital navi-
gation, utilize an approximate system to locate earth fixed targets.
The transformation from this system to the NBY system for a state vector
_A in this CMC system is
io n0Z Z ~
_ANBY = 0 i i_ Az cos Az __y -A iX
where _A and _ANBY are column vectors. The onboard state vector _
first rotated about the true Z-axis by an angle -A whereZ
A = A + _(t + t )z zo ephem
is
A = angle between the X-axis and the Greenwich meridian atzo
midnight Just prior to the year preceding the reference Besselian year
tephe m = elapsed time between July i and the time that the
CMC clock was zeroed
t = time indicated in the CMC clock
= sidereal rotation rate of the earth
The transformation is completed by making small angular rotationsabout the X- and Y- axes. The values of A and A are constant for a
x y
given mission. These introduce an approximation. The resulting errors
are proportional to the elapsed time between t and the time associated
with the evaluation of A and A .x y
Orbital Integration
The state vector for the CSM is periodically integrated using
either the conic or the Encke method. In the conic mode, the perturbing
acceleration, ad(t), in the basic equation
' d 2 . "_e-- r(t) + r(t) =dt 2 -- 7-- _d(t)
is omitted. In the precision mode, an oscillating conic is defined atto, again ignoring _ad(to). The perturbing acceleration is then integratedseparately for any t + At using Nystrom's method. Whenthe perturbed
0
portion of the vector reaches a certain magnitude, currently defined as
8 kilometers, a new conic is defined, a procedure called rectification.
The time of the new conic, t ', iso
t ' = t + nat, where nAt is the elapsed time since the0 o
last rectifications at tO"
The square root of the state covariance matrix, W, is also propa-
gated forward. The covariance, or correlation matrix, is defined for
orbital navigation as
E(t) =
T T BTg g g O E
T T BTrl E q q tl
T 8Tea T 8 n a9 x9
where _, _, and _ are partial estimates of the errors in CSM position,
CSM velocity, and landmark positive, respectively. The W matrix isdefined by
E(t) = W(t)W(t) T
(T denotes transpose)and extrapolated by numerical integration of
10 i i]dw(t) = (t) 0 W(t)dt
L.O 0 0
9 x9
where_e
G(t) :r5(t)
[3_(t)[( t)T - _r2(t)I]3 x 3
I = 3 x 3 identity matrix
0 = 3 x 3 zero matrix
Despite the use of rectification, initial errors in the state and
dynamic biases neglected in the equations, for example, drag, eventuallycause the CMC vector to diverge from the actual vector. The W matrix
is subsequently affected the same. Navigation measurements are utilized
to correct both the state and the W matrix. In orbital navigation landmark
sightings are processed through the Kalman-Schmidt filter for thispurpose.
Use of Landmark Sightings in the Kalman-Schmidt Filter
CSM
u r _ landmark
Figure i.
Given that a mark relative to the navigational base coordinate
system has been made on a landmark and transmitted to the CMC,program 22will utilize this data to correct the state vector.
As outlined in the introduction, an observation is computed for the
same time as the observed data. The difference between the actual and
computed observation, _Qi' is weighted with _. and added to the statevector. -i
The b-vector.- In the computation of _., where--l
T i zTwT-_ = 2 ''_[2Z +
z = WWb
the b-vector, defined as
b = 8(COMPUTED OBSERVATION)- 8_COMPUTED STATE)
i)
_Qi (2)_X.
1
indicates how much and in which direction thestate will change for a
given change in the observation. Referring to figure 1 and following
the derivation from reference 3, let u be a unit vector pointing-S
toward an imaginary s,tar.
Assume u s × _rcA # O.
To get the b vector, take the dot product
rcACOS 8 = _c£ " _s
Take the differential:
6rcACOS 8 - rcASin e de =6Ec A . _s (3)
Now
= [r_.... E ]rcA
c£ cA
112
_rcA = ll2[_cA " r--cA]-ll2[6r--cA " r--cA+-_cA " _cA ]
[c£ " c_£
_rc£ = rc£(_)
Substituting ,(4) into (3) and rearranging,
re_ • 6rc£. - cos e - rc£ sin 8 de = 6rc£ u--S
rc£
rczCOS e ]- - us z___A____ . _rc_
68 [ rc £ rc£ sin 8
Now if we choose u perpendicular to r_--S
u-s
6e .... 5_c£rc_
This is the relation which defines b for updating the relative position
_c£" Since the CMC updates -cr and _, note
+ = [,%r_c r_c_
Then (3) becomes
6rc + 6rc_ = 6r__
-U
,se =-.-As • [6r_- 54]rc£
u
s _]=-- • [6r -
rc_ -c
The b - vector can be written compactly asm
b= l-l- I_-- rc£
Each observation point is incorporated twice, since two degrees
of freedom are available perpendicular to _c£" For the first directionof correction,
9
u (i) = unit × ×
In case the computer comoutation is difficult resulting from r c _being
parallel or near-parallel to , use
U--s
(i) = unit
For the second correction use u (2)= unitI_c × u (i_--S _ -'S '
where the plus indicates that _ has been updated by the first correction.
The W matrix and a2._ The 9-by-9 W matrix in equation (1) represents
a numerical estimate of the uncertainties associated with the mathematical
description space. These uncertainties include noises and bias on the
state vector and prediction models (lack of drag, for example) and limita-
tions of their representation for programming. For convenience, the
W matrix may be divided into nine 3-by-3 matrices:
W
Wo
W3
W6
W I W 2
w 4 w 5
w7 w8
(6)
At the beginning of a navigational sequence, this matrix must be
set to an initial value representing, among other things, an estimate
of state uncertainty. Each 3-by-B matrix is taken initially to be a
diagonal, since the initial self-correlations of vehicle position,
vehicle velocity, and landmark position, W O, W 4, W 8 respectively, cannot
be accurately determined a priori.
i0
Further, the initial correlation between W0,W4, and W8 are
simplified. The correlation betweenW0 and W4 represented by WI and
W3, are taken to be zero. For a known landmark, correlations between
W8, WO,andW4 are also taken to be zero.
For an unknownlandmark (un£), however,
W6 = K0 W0
W7 = KI WI
W8 = wun£ I + K2 W0, where K0, KI, K2, and wun£ areconstants.
These artificial correlations attempt to reflect the fact that the initialvalue of the unknownlandmarks position will be heavily affected by errorsin the vehicle state. In practice, K0 and KI are set to zero inSUNDISK. For the program COLOSSUSa more realistic approach exists forthe definition of errors associated with unknownlandmarks.
As a marking sequencing continues, the numerical size and character-istics of the Wmatrix change. Correlations between the various elementsgrow. After each state vector update from mark data, the Wmatrix isalso updated. The Wmatrix is extrapolated in time by integration, asoutlined in the introduction.
_2The term a in equation (i) is a constant representing the uncer-
tainties of the observational space. Noises and biases of the observinginstruments and the observer are included.
It should be emphasizedthat since the filter employed in orbitalnavigation is nonoptimal, i.e., all knowndynamic forces and dataerrors are not modeled, and the numerical values of _2 and the Wmatrixdo not reflect the actual estimates of instrument and state vectorerror. Further, since the filter is linear, the relative value of W
_2and a is the principle factor affecting the operation of the filter.For example, the filter will operate identically if values of W0 and_2a0 or k WQand k2 a2 are utilized, where k is any constant within thenumerical limits of the computer.
ll
The observation zesidual.- Recall from the introduction the equationfor correcting the state vector:
r-c
v-c
r_m
÷m m._
r-cl
= v + _6Q i-cm (7)
One must compute 6Qi:
Let _m be a unit vector in the NBY coordinate system pointing along
the measured line of sight. Since the optical measurement occurs in
thenavigationbase coordinate system, the transformation to NBY
coordinates is
u = [REFSMMAT] T [GIMBLE] [NAVGMBL] u
-mNB Y -m NBS
where the matrix [REFSMMAT] transforms from NBY to IMU coordinates,
[GIMBLE], from body to IMU coordinates, and [NAVGMBLE], from navigation
base to body coordinates. Superscript T denotes a transpose.
For the actual observation,
U U = COS 6)-S - m
cos • u) = eACTUAL"
For the computed observation
cos-I (us . _Um) =OCOMPUTED,
unit vector.
where the prime denotes a computed
12
Now
_Q= 8ACTUAL 8CO_UTED cos-l(_-- _ • u ) - cos-l(u • -=u')
6Q = cos-l(_ . _m ) _ _H , since -sU is perpendicular to the
estimated line of sight, _m"
The CMC's Implementation of the Kalman Filter
To utilize equation (7), up to five marks are made with the
telescope or sextant on a particular landmark. A CMC routine, auto-
optics, can aid the astronaut by aiming the observing instrument at the
estimated landmark position. (The accuracy of the aim is proportional
to the accuracy of the CMC state vector.) A residual, 6Q, is computed
with equation (8) and the b vectors are computed.
For computational purposes the W matrix is divided into 27 column
vectors within the CMC. For example, W0 in equation (6) may be written
_23
The nine dimensional quantities b, _, and _ are also divided as
zI
The Kalman computations are then performed as
2
zi:_ wi÷3j_-ji:0 l,2j=O , , (8)
13
2
j=o=-j 3i+J(9)
where 8 =1
8x. = 6Qm., where--1 ---i
(10)
Verification of the Kalman factor.- To verify that -_i' defined
in equation (9), is the Kalman weighting factor, which is normally
defined as
EM_T(MEM_T _-21-i (ii)_m= +
begin with the co.act definition given in reference i, as
i zT__= 2 __2--
z +_
which implies
_ 1 Wz (12)2 2 --
Z + I_[
To get (12) expand the Kalman equation (ii) using MIT terminology
_ = +_
(Z3)
14
From reference (i),
z = wTb
Since the basic Kalman filter in (ii) considers b as a row vector,
z = WTbT
(l_)
Substituting (14) in (13)
= W_(zz__T+ _2)-1
which is MIT's fo_ation (12)
_=
IWz
2 _2 --Z +
Verification of the W updating equation.- As noted in the
introduction, the W matrix is updated after each incorporation of
mark data. In CMC notation the update is
i = 0, i, ..., 8
_+gj = w - yzi_._i+9j --O
j = 0, i, 2
1¥ =
1+_
(15)
To verify that equation (15) follows from Kalman theory, proceed asfollows :
First equation (15) may be written (ref. i) as
T_Z
W+ =W --
i+ _+_
(16)
The Kalman update is defined as
_,+= (I - _)_,
Expanding in MIT notation,
(wwT)+ = wwT _ _bWWT
= wwT _ WWTb_T(b_WWTUT + _2)-IbWWT
15
Now following the derivation in reference 4,
(wwT)+ = w[z - _(z2 + _2)-ZzT]wT (17)
In order for equation (17) to be valid, the right side of the equation
must consist of some quantity times its transpose to update W.
Otherwise, only E could be updated and the CMC W scheme would be invalid.
Assume this quantity to be of the form
W[I- 8zz T ]-- (18)
where 6 must be found.
Equating equation (17) to equation (18) times the transpose of
equation (18):
W[I - _(z 2 + _2)-Iz_T]wT = W[I - 8_T][I - 6_T]w T
I - zzT(z 2 + N2)-I = I - 26zz T + 82zzTzz Tn--
wm n-- --w
82z 2 - 26 + (z2 + _2)-i = 0
Using the quadratic formula
2 ±_ - _z2(z2 + _2)-z6 =
2z 2
1 ±_1 _ z2(z 2 + _2)-1
2z
In order to limit the amount by which W is decreased during each
update, take the smaller 6.
Multiply by _rzz2 + ct
16
#z _22+_ _
z2 _zz2 +
Vz __2 . zII i
_2(%
_z 2 + j - _.2
2 Vz 2 _2z + c_
Since W+ = A + Bzz Tw = w+ _w=w[z- ]
AW = ,WSzz T.
Using (19)z2 +-d- - T
AW = -w _z_z
[z2 _z2 + "_2
_/iz2÷_ _ _,)(42+._2÷ _'t= -- "- P 2 + c_)
T i= -Wzz
-- 2 ._2 c_z 2 _2z + + + ol
T= -Wzz
i
-d2
(z2 + _.2) + z2 +(21)
17
Regrouping,
-Wzu
_W =2 _2
Z +
_Wz T
Tz
_z -2i+ 2+_ _2
i + z2 +7 2
Therefore, from (20) and (21)
W+= W-
which is equation (16).
Wz T
i+ 2+_ _2
UnknoSn landmarks.- The orbital navigation program can also use
optical marks made on unknown landmarks. In this mode of operation
the program uses the first mark to define the location of the landmark.
Following the derivation in reference 3, consider the plane deter-
mined by the planet center, landmark, and vehicle shown in figure 2below.
Landmark
,--e
I _u
I
ii-- CSM
Planet r--C
center Figure 2.
18
By vector addition
_£=r +z--c
To find _ and thus, [£, notice
(22)
z COS _ + r Z cos _ = r C
Z
r c - r£ cos _ rc
COS _) COS _)- -- COS
r C
Using the law of sines,
sin I sin-- = and
r r£C
rc
sin I = --sinr£
2and using the identity cos I + sin 2 i = i,
-IrqCOS I = _i- sin2 I = 1 k_/ sin 2
Now, from the figure
cos _ = cos[_ - (x + _)] = -cos(X + ,_)
cos _ = sin I sin _ - cos I cos
Combining (24), (25), and (26)
r__c 2 ,_/: _rr_£.c£')2 2cos _ = r£ sin _ + cos _ - sin
r£ 2 r£ rc 2--cos u = sin _ + cos _ -- L - l--J sinr rc C
Recall equation (23)
Z ___ w
rc
COS -- -- COSr c
(23)
(2h)
(25)
(26)
19
Z _ i - sin 2COS %)
%) -- COS _)-
r C
rc I 2COS %) COS%) cos _ L sin 2-- _ -- %)
r c
= rc[COS _ -_r_>2 - sin2 _]
So equation (22) becomes
r£ = r + r os %) - sin-c c _m
where u is the measured line of sight
(27)
o
Looking at the result for the landmark position, equation (27), onenotices the r£, the magnitude of the vector, is required. Since this is
unavailable for an unknown landmark, r£, is taken to be the mean radius of
the planet.
This approximation introduces considerable inaccuracies into the land-
mark position estimate. For the remainder of the marks, the landmark
is considered known. The resulting updates decrease the landmark error.
Having reviewed and approved the equations used in P22, this paper
will next provide an explanation of the coding of these equations.
2O
THECMCCODING
Review of the coding for the orbital navigation program has beenaccomplished chiefly through analysis of the MIT flow charts and studyof the decoding in reference 2. The Program 22 flow charts arepresented in Appendix A.
The coding analysis will follow through reference 2 line by line.
Explanation of each line will be given to the right of that line.
1. Start program
PROG 22
CODE
2. Perform R02
.
,
.
Set TARG2FLG = i
(bit 9 of FLAGWRD i)
Set TARGIFLG = 0
(bit l0 of _LAGWRD i)
Set RNDVZFLG = 0
(bit 7 of FLAGWRD 0)
6. Tdecl = Tno w
EXPLANATION
2. IMU STATUS CHECK;
if REFSM = i, IMU orientation
is known by computer and proceed.
if REFSM = 0 and IMU is on, per-
form P51 to determine alignment.
if REFSM = 0 and IMU is off, go
to POS to start up GNCS.
3. Target is a landmark.
4. Target is not L]94.
5. P20 is not running.
. Time to which integration is to
be performed is present time.
7. Perform CSM Conic 7. CSM R & V are integrated conically. •
21
8. PMGA=-i
cos [lunit (Vatt x R_att)
•
a Set RENDWFLG
(bit 1 of FLAGWRD 5)
10. TS = 0645vn
ll. Perform GOFLASHR
12. TS = 0112 Perform BLANKET
PROG. 22A
13. MARKINDX = 5
14. TS = 000118
15. Proceed to GOPERF1
16. If No R52, proceed.
If Yes R52, perform R52 and
R53 within and proceed to 18.
.
10.
ll.
16.
Assuming X of spacecraft is in
orbit plane, this checks to see
if IMU orientation is satisfactory
for P22. PMGA (displayed) is
maximum middle gimbal angle• > O .posslble. If 60 , and tlme
permits, IMU should be realigned
(P52), then key in V37E22E and
proceed. If not, proceed.
Maneuver to acquire landmark.
9. W matrix is invalid.
Machine channeling for 8. (display)
(specifies VN PATTERN for display
routine).
Display of 8; exit to realign
or continue as decided.
12. Display interface routine.
13.
14.
15.
Communication cell with R53.
Channeling to display.
Display interfacing for choice of
auto-optics (R52).
Monitor and respond to landmark
parameters. R53 is called within
R52 automatically or by selection
of manual optics.SCT trunnion or shaft and
trunnion may be driven toward
CMC's estimate of landmark posi-
tion.
22
17. Perform R53
18. NUM8NN= QPRETmk
19. NUMBKK= i
20. $22LOC= SVMRKDAT
21. SVMRKDAT+ i = EMARKSTAT+ i
i = 0, i, ...35
22. Perform 22 LMKID.
23. 22LMKIDa. LANDMARK= bits 9-4 of
22LMBD0
17.
18.
21.
Marks are made; then accepted
or rejected; up to 5 unrejected
marks may be stored.
Total number of marks taken =
total number of marks taken.
Serial no. of mark being processed.
Buffer cell location of 1st mark
data to be processed.
35 cells divided into 5 sets,
i for each mark, containing
(TIME 2:1) (TIME 1:2) (CD_),
(CDUS), (CDU z) (CDUT), (CDU x)
composing a table to avoid lossif restart occurs.
a. ID for first mark is placedin 22 LMBDO and coded as
A, B, C, D, and E where
A = i known
= 2 unknown
B = i coordinates stored
= 2 coordinates not stored
CD = landmark serial number
E = i (earth landmark)
and initialized as A = l,
B = l, CD = ID, E = 1
23
be
C.
d,
ee
f.
g.
h.
if LNDMKSTR = O,
(bit 7 of FLAGWRD 2)LANDMARK -- LANDMARK + 210
if LNDMKSTR = I,LANDMARK = LANDMARK + 29
if LNDKNOWN = 0,
(bit 8 of FLAGWRD 6)LANDMARK = LANDMARK + 21B
if LNDKNOWN = i
LANDMARK = LANDMARK + 212
_DMARK = _DMARK + I
TS = o57o w
Perform GOFLASHR
i. 22LMBDO = bit 9-4 of LANDMARK
J. Set bit 7 (LNDMKSTR) of
FLAGWRD 2 = bit l0 of LANDMARK
k. Set bit 8 (LNDKNOWN) of
FLAGWRD 6 = bit 13 of LANDMARK
Perform MKRELEAS
MKRELEAS
a. Release VAC areas assignedto marks.
b. MARKSTAT = 0
c. Inhibit interrupts
b, If landmark coordinates are
not stored, B = 2.
c. If landmark is stored, B = 1.
d. If landmark is unknown, A = 2.
e. If landmark is known, A = i.
f. Landmark is an earth landmark.
g. Machine channeling for display.
h. Displays LANDMARK, proceedor terminate and load new data.
i. Corrected ID is placed back in22LMBD0.
J. Landmark stored or not stored.
k. Landmark known or unknown.
a•
be
C.
VAC area is now available
for other use.
Mark storage cells are now
available for a future set
of marks.
Following sequence will not
be interrupted.
24
26.
27.
28.
d. Set bit 9 of OPTMODES = 0
e. OPTIND = -i
f. Set bit 2 of channel 12 = 0
g. Return
If ORBWOK (bit 6 of FLAGWORD 3)
= i, set WDIM91NC (bit 9 of
FLAGWORD 5) = i
If 0RBWOK = 0
w. = 0 (i = o, i, ..., 53)i
a. W0 = CWORBPS
W 4 = ,,
W 8 = ,,
W36 = CWORBVL
W40 = ,,
W44 = ,,
b, Set 0RBWOK = i
c. Set WDIM91NC = 0
Perform S22FLAGS
a. Perform INSTALL
b. Tdecl = ES22LOC dP
d. Optics switched from computercontrol mode.
e. Driving of optics is bypassed.
f. Disable optics CDU error
counter.
g. --_
26. If W matrix is valid for
orbital navigation, it is set
as 9 × 9 for incorporation
purposes.
27. If W matrix is invalid for
orbital navigation, ...
a. Reinitialize upper 6 × 9
to a diagonal in the
upper left 6 × 6.
b. W matrix is valid for
orbital navigation.
c. W matrix is not a 9 × 9
for incorporation purposes.
28. Preparation for integration.
a. Grabs integration packageand secures it from other
users.
b. integration will be up to
time of i mark, stored in E.
25
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
c. Set bits 5(STATEUP), c.
3(CSMINT), 2(WDIMEN 9), and
l(WMATINT) of FLAGWRD 3 = 1
CMpermanent state vector and
9 _ 9 W matrix are to be
integrated.
d. Let CONINT (bit 4 of
FLAGWRD 3) = 0
d. Encke integration.
e. Return e. --
Set WDIMEN9 (bit 2 of
FLAGWRD 3) = 0
29. W matrix is 6 × 6.
If WDIM9INC = 0, set WMATINT 30. W matrix is to be integrated.
(bit 1 of FLAGWRD 3) = 0
Perform INTEGRV 31. Integration.
CSMPOS= _Ratt
If LNDKN0WN = i, proceed to
22LMKI.
if LNDKNOWN = 0, Proceed
32. Answer.
33. If landmark is known, proceed
to 22LMKI; otherwise, proceed
[We are now treating an unknown landmark]
MARKDATA = $22LOC 34. Address of next mark data.
w. = o (i = 5h - 8o)1
W72 = Kwun
W76 = Kwun
W80 = Kwun
35. - 39. Lower right 3 x 3 ofW matrix is initialized for
unknown landmark tracking.
K2=I
[w8] = [w8] +K 2 [Wo]
X i = - MABKDATA
MARKDOWN = i = EMARKDATA + i,
(i = O-6)
h0. - 42. Mark data is shoved into
buffers for computations.
SI = MARKDATA + 2
Perform SXTNB 43. TS converted to double precision
for pointing vector computation.
25
44. Perform NBSM
45. uM = TS [_FS_T]
46. TS1 = unit CSMPOS
47. ALPHAV z = TSI, z
48. Perform GETERAD
49. oRBCOSA= -gM" TS.
50. ALPHAV = CSMPO_ = t COMPO_I
_R3C0SA '_/(i EP'ADM _ 2- co_o_l]
-(1 - ORBCOSA)J_UM
51. Delay 2 secs (via DELAYJOB)
52. Proceed to S22BIG2
S22BIG2
a. Set ERADFISC
(bit 13 of FLGWRD1) = 1
b. TS = ES22LOCdp
c. Perform LAT - LONG
d. If NUM8NN - NUM8KK _ 0,'
go to 9DWT06DW
e. NUMBKK = NUMBKK + i
f. $22LOC = $22LOC + 7
44. Computes pointing vector in IMU
coordinates.
45. Pointing vector in NBY coordinates.
46. For 50.
47. For &8.
48. Compute Fischer radius
at latitude of landmark.
49. For 50.
50. First estimate of [1.
a. Use Fischer ellipsoid radius.
b. Time of mark.
Co
do
eo
fo
rI converted to latitude,
longitude, and attitude.
If this is last mark, go
to ......
Serial nt_nber of mark date
is increased by one.
Starting address of next
mark data.
g. Proceed to S22BIGI g. --
27
[Now if we had marked on a known landmark, we would be back at 33 and
starting 22LMK1 ]
22 LMKI
a.
b.
If LNDMKSR (bit 7 of
FLAGWRD2) = 0, proceed to
22LMKDAT; otherwise, proceed.
TS = bits 14 - 4 of
22LMBO0, shifted right 3
places
c. Xl = LLATAB + 6TS
a. If landmark coordinates
are not stored, ....
c. Address of landmark
table entry.
d. LA_T-- -Xl d. Latitude, longitude, and
altitude stored.
e. Proceed to $22.16A e. mm
[If coordinates had not been stored in a above]
22LMKDAT
a. LANDALT = ALT/K2dcptl a. Scale altitude for display;store in LA_TDALT.
b. LANDLONG = 1/2 LONG b. Longitude/2 displayed for
better accuracy.
C.
d.
TS = 0689vn
Proceed to GOFLASH;
(1) If terminate proceed
to GOTOPOOH
c. Channeling for display.
d. Display of landmarkcoordinates.
(2) If proceed, proceedto $22.16
(2) if accept data, ...
(3) 0therwise, proceed. (3) if reject data, ...
e. ALT = K2dcptl LANDALT
f. LONG = 2LONDLONG
e., f. Data has been modified.
This is rescaling asabove.
28
a.
Proceed to c
w. = o (i = 5_-8o)1
b. W72 = CWmk
c. W76 = Cwm k
d. W80 = CWmk
e. If LNDMKSTR = i,
f.
S22BIGI
53.
54.
55.
56.
57.
[W8] = K3d 4 [W8]
Proceed to $22B161
Set ERADFISC
(Bit 13 of FLAGWRD i) = i
TS = ES22LOCdp
Perform LALOTORV
X789 = Krfactl ALPHAV
Perform S22FLAGS
58. Perform INTEGRV
59. CSMPOS = Rat t
6o. M_mDATA : S22LOC
61. X1 = - MARKDATA
62. MARKDOWN + i = EMARKDATA + i
_: (0-6)
63. SI = MARKDATA + 2
53.
g. Recycle from c till satisfied.
Initialize lower right
3 × 3 for known landmark
incorporation.
f.
If landmark is stored,
reduce W 8.
Use Fischer ellipsoid radius
for coordinate computations.
54. Time of mark.
55. Gets Ax, A, Az, and _.
56. Rescales r to kilometers.
57. Sets flags for and time of next
mark for integration.
58. W matrix and CSM vector are inte-
grated to specific time.
59. Answer.
60. Address of next mark data.
61-63. Mark data is shoved into
buffers for computations.
29
64. Perform SXTNB
65. Perform NBSM
66. UM = TS [REFSMMAT]
67. RCLP = X789 - Krfactl CSMPOS
64. TS converted to double precision
for pointing vector computation.
65. Computes pointing vector in IMU
coordinates.
Pointing vector in NBY coordinates.
Relative landmark vector.
68. Set FSTINCRP = i
(bit ll of FLAGWRD5)
69. TS = RCLP * UNIT Z
70. IfITsl<2-6km,USTAR=UNIT Y
68.
71. IfITsl__2-6_, usT_=UNITTS
72. Proceed to $22B164
$22B164
73. VARIANCE (RCLP) 2= _ (KscTVAR +
K )IMUVAR
First incorporation of measure-
ment data is being made.
69. TS now contains star unit vector
u- (o1.
-s [i]70. If 69 overflows, U (°) = 0--S
NBY
Perform BVECTORS
BVECTORS
a,
71. If 69 doesn't overflow, .....
72.
74. --
75. BVECTOR and other intermediate
Kalman computations.
BVECTOR 0 = unit(UNIT RCLP *- USTAR) -
b. UST__= B_CTO_Ro
DELTAQ = K2p i 1_c<PI
[cos -1 (BVECTOR_o . _UM) - 1/4],
(i/4 = 90 O)
C.
3O
d. BVECTOR, = 0
e. BVECTOR 2 = 0
f. RETURN
76. BVECTOR 2 =-USTAR_
77. Set WDIM91NC (bit 9 of
FLAGWRD5 ) = ]
78. Set CSMUPDT (bit 8 of
FLAG_DZ) = Z
79. Perform ]NCORPI
80. INCORPI
76. BVECTOR for update of landmark.
77. W matrix is 9 × 9 for incorpor-
ation purposes.
78. CSM state vector is to be
updated.
79. --
80. --
b.
= [wo] B_CTOR_0+ a-c.
[W3] B_CTO_RI + [W6] B_CTO_R2
zI = [WI] B_CTOR_o +
[W4] BVECTO_R 1 + [W7] BVECTO_R 2
c. z 2 : [W2] BVECTOR +
[W5] BVECTO_R 1 + [W8] BVECTO_R 2
d. If WDIM91NC = 0, d.
z2= 0
2 2 2e. LITLA = z + z 1 + z 2 e.-0
+ VARIANCE
TS =QLITLA VARIANCE f-h.f.
g.
h.
GAMMA = 1/(TS + LITLA)
DELQDA = DELTAQ/LITLA
Computation of z, where
z=wT b
If W matrix is not a 9 × 9
for incorporation purposes.
2 _2z +
Intermediate steps
in computing the Kalman.
31
81.
82.
i.
J ,
k,
i.
m.
n.
OMEGA 0 = z0 [W0] + zI [WI] i-n.
+ z2 [w2]
0MEG_A1 = zo [W3]
+ zI [W4] + z2 [W5]
OMEGA 2 = z0 [W6] + zI [W7]
+ z2 [w8]
DELTA X = DELQDA OMEGA-0 -0
DELTA X1 = DELQ,DA OMEGA 1
DELTA X2 = DELQDA OMEGA 2
o. RETURN
DSTEMldp = Kkmmtr 2 81,82.
IDELTA X01
DSTEM1 + 2dp = Kkmmc s 2
IDELTA Xll
TS = 0649vn 83-85.
Perform GOFLASHR
If terminate, proceed to
fourth line of S22BIG2 ;
if proceed, go to 87;
otherwise, proceed
TS = 002 and perform BLANKET
END of JOB 86. --
More intermediate steps and
state correction computa-tions.
Scaling for display.
Display routines and
incorporation decision.
87. Perform 1NCORP2 87. --
32
88. 1NCORP2
a. EGRESS = return address
b. Perform INTSTALL
88_
C, OMEGAM = GAMMA OMEGA-0 -0
_ o_o_i-- o_ O_GAI
e. OMEGa2 = OAn_A OMEG_A2
f. Set INTPHS (bit i3 of
FLAGWRD5) = i
g.
h.
i.
j ,
k,
[wo] --[wo] -zo OMEGa_o
[WI] --[Wi] - ZlO_G__0
[W3] = [W3] - Z_OO_G__I
[w_]= [w_]- zI OM_O_I
If WDIM91NC = i,
[W 2] = [W2] - Z20N[EGAM_o
[W5] = [W5] - Z 20MEGAM_ I
[w6]= [w6] - Z_oO_G__2
[W7] = [W7] - ZI OMEGA/J_2
[W8] = [W8] - Z 2 OMEGA/J_2
b. Grabs and secures
orbital package for matrix
updating procedures.
c-e. --
f. To preclude loss of
integrating package to
priority if a restart occurs.
g-j. W matrix is updated.
k. Additional W matrix updating
for a 9 x 9
i. If CSMUPDT = i
(bit 8 of FLGWRD1)
i. If the CSM state vector is
to be updated, do so.
33
(1) TSl = D_TA[cm
DELTAX-O
(2) TS2 = NUV_cm + DELTAX_ 1
(3) If there is no over-
flowing in computing
TS1 and/or TS2:
DELTAIc m = TSl_
NU__cm = TS2_
(4) If overflow has occurred
in computing TS 1 and/or
TS2:
_rectcm = RVCcm +
DELTAV + DELTAXcm -O
RCV =-cm _rectcm
V = VCV +-rectcm -cm
NUVcm + DELTAX1
VCV = V-cm -rectcm
DELTAV = 0-cm
NUV = 0cm
T --0ccm
XKEP = 0cm
(5) If WDIM91NC = 1
x 789_= x 789_+ D_._T__2
(1)-(3). For no overflow
condition add weighted
residual to perturbation
portion of vector.
(4 For overflow condition
add weighted residual to
the whole state vector,
i.e., the conic portion
plus the perturbed por-
tion, and consider this
update as a new rectifi-cation.
(5) If matrix is 9 × 9,
update the landmark
coordinates.
34
(6) Perform PTOACSM
(7) R = K- rfctr (RCV + TDELTAV)
(8) Z = Kvfct r (VCV + TNUV)
(9) Tpptm = Tet
(6) New vector is labeled
as the permanent state
vector.
(7)-(9) --
89.
90.
m. If CSMUPOT = 0 m.
n. QPRET = EGRESS
_. PROCEED TO INTWAKE
CSMPOS = Klk b 15 (RCV-cm
+ DEL AVm)
If FSTINCRP (bit ii of
FLAGWRD 5 ) = 1
RCLP = X 789 -
- Krfactl CSMPOS
n.
(9.
If LM state vector is to be
updated, perform i, but with
LM vectors.
Which returns
89. CSM position vector rescaled
90. If first incorporation of a
measurement, compute relative
landmark position and recycleto $22B164
Proceed to S22B16h
91. Proceed to $22B162.
92.
91.
ithin S22BI62. 12.d. If NUMSNN - NUMSKK < 0go to 9DWT06DW
9DWT06DW 92.
Recycle to S22BI62 to process
next mark
I_f all marks have been]
rocessed go to 9DWTO6D_
Converts upper 6 × 9 of 9 × 9
matrix to an equivalent 6 × 6
35
93. $22.1P5
a. I f LNDMKSTR _= 0
(bit 7 of FLAGWRD 2)
(1) If 22LMBO = K22mdmx '
22LMBDO = 0
93.
a, If landmark is not stored,
serial number of cell where
landmark data is stored is
kept as one, since only onelandmark can be stored in
Sundisk
(2) If 22LMBD _ K22mbmx '
22LMBD0 = 22LMBD
b. Proceed to $22EX3 b, mm
94. $22EX3 94.
a. LANDMARK = 22LMBDO a. Landmark code = number in
22LMBD0
b. Proceed to'S22EX33 b, mN
95. $22EX33 .....
a. TS = 6570vn
b. Perform GOFLASHR
95.
a. For display of landmarks ID.
(i) If terminate, proceed (i)
to 22TERM,
If proceed, go to l;(2)
(3)
If one does not wish
to see display of updated
landmark, ...
(2) If one wishes to see
them, ...
otherwise, proceed to S22EX3 (3) Otherwise, recycle ....
c. TS = 1012 and perform c. Kills displayBLANKET
d. End of Job d. --
e. LANDALT = ALT/K2dcptl e
f. LANDLONG = 1/2 LONG
e. Scaling for display
f. For display
36
96.
g. TS = 0689vn
h, Proceed to GOFLASH;
(1) if terminate, proceed to
22TERM ;
(2) if proceed, proceed;
(3) otherwise, go to i.
i, TS = bits 14-4 of 22LMBDO,
right shifted 3 places
j. XI = LLATAB + 6 TS
k. EXl--_AT
1. If LNDMKSTR (bit 7 of
flagword 2) = 0
22LMBDO = 22LMBDO + Klbll
m. Proceed to 22TERM
22TERM
a. TS = OOO178
b. Proceed to 60PERFI;
(l)
(2)
96.
If terminate, proceed
to GOTOPOOH ;
If proceed, proceed to
GOTOPOOH;
(3) Otherwise, proceed to
PROG22A
g.
h.
Verb-noun flash for display
of updated landmark coordi-
nates
(z) If one doesn't want
updated landmark coordi-
nates to be stored as the
landing site, .._.
(2), (3) --
i-k. Landmark data is stored.
i, If landmark is not tagged as
stored, indicate that one
has now been stored.
m. --
ao
b.
(i) and (2) P22 is finished.
(3) Recycle to perform
another sighting
37
Results of Coding Review
Flow chart comparison.- A comparison of the above coding and the MIT
flow charts in appendix A reveals no differences except occasional
insignificant order changing of steps and the omission of the W8 down-grade (page 9 of appendix A) for a stored landmark in the coding. In
this latter instance, as at other times during the review, reference to
the actual SUNDISK revision 282 listing was used to resolve difficulties.
The W 8 downgrade is not contained in the 282 listing.
Comparison of equation and astronaut procedure to codin6.- Besides
the comparison between coding and flow charts, checks have been made
between coding and equations, and coding and astronaut procedural inter -
faces, as outlined in reference 5 and reproduced in appendix B. In all
instances, the comparisons were satisfactory. P22's interfaces with R52,
R53, R02, CSMCONIC, P52, and P00 also appear satisfactory.
Illegal interfaces.- Not all interfaces with P22 are valid, however.
Generally, none of the P30's or P40's (P3X or P4X) should be called while
P22 is running, or vice versa, due to shared erasable cells (ref. 6).
Verb 82 cannot be used during P22 for the same reason (ref. 7).
Programs 22 and 20 cannot be operated simultaneously since P22 initializes
the W matrix to a 9-by-9 (ref. 8). Program 22 or any program cannot be
called by verb 37 if integration is in process, or in P05 until the time
specified in reference 8. Before running any program, reference 8 andits updates should be read.
ASTRONAUT PROCEDURES
Crew procedures for exercising the orbital navigation program are
presented in appendices B and C. Appendix B contains the procedures and
interfaces among the crew, CMC, and the ground, as written by MIT in
reference 5. Appendix C gives the concentrated crew procedures for P22
which are to be carried onboard the CM during Apollo 7 (ref. 9).
Comparison of appendices B and C reveals no differences save the
omission of the IMU status check (R02) in appendix C.
BIT-BY-BIT TESTING
The final "roped" version of SUNDISK 282 has been tested on the
MSC bit-by-bit simulator. This simulator contains an exact representation
of the CMC, i.e., the machine language coding is the same.
38
Results of the bit-by-bit tests for orbital navigation are contained
in appendices D and E. The tables (ref. i0) contain comparisons between
the W-matrix, b-vector, and state vectors as computed by SUNDISK 282 P22
and by a reliable onboard bench program outlined in reference 3.
Two bit-by-bit cases were run. The first case (appendix D) involved
sightings on two known landmarks. The second case (appendix E), is a rerun
of the first case with the first landmark considered unknown. In both
cases, only three marks could be taken on the second landmark due to
constraints within the environmental program associated with the bit-by-bit simulator.
For both cases the results are excellent. Differences between the
SUNDISK program and the engineering simulations are small and can be
attributed to differences between fixed and floating point machines. These
results, added to other studies of P22 with the engineering simulator,
indicate the program operates correctly and performs well in flight
configuration.
CONCLUSION
From the study of equations, coding, astronaut procedures, and
testing which has been presented, SUNDISK 282 orbital navigation program.
P22 has been verified as valid for earth orbital flight.
"39
APPENDIX A
MIT FLOWCHARTS FOR SUNDISK REV 212 P22
41
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P22
I FL VSl N89 ]MARK
LAT XX.XXX DEG (+NORTH)
LONG/2 XX.KXX DEG (+EAST)
._LT . .KX.X.XX NM
f T-MARK _ REJECT
(KNOWN - i MARX MIN)SCT
(UNKNOWN - 2 MARX MIN)SrtAfter surf marks
OPTICS [Afte-r S_ FL _0 N25 ]MODE-CMC[ MARKS El 00016 TERM MARK
ENTR [
ENT_.OPTICS MODE - CMC
_'L v05 _7oR2 ABCDE
[LDD
PRO
LMK i 2
DATA
"A KNOWN U'N_NO___
B STORED NOT STRD
CD (I.D. NUMBER___E EARTH LUNAR
LMK IDENTITY
DEG
DEG
NM--_UNSTORED _ FL N89
V06"
KNOWH LAT XX .XXX
K2-12KXI LONG/2 XX. XXX
. . _ _T , ..xxx.xx_I [[_0 LDD
1
[oKk_N V06 N49 ORB PARAMETER
$TRD FL
r UNKWN/ AR KXXX.X NM_'NSTRD AV XXXX .X FPS
PRO---_UPDATE STATE V34E---_REJECT .MARK DATA
I VECTOR (Tillall marks used)
ALTER LAST MARK US_)
I FL V05 NT0 IL_K ID
"I R2 x,xc_x....
_gQ V_d_-pITEP 15!
L
s_
P22,23
q
0
4-4
RECORD
PRO (stores in CMC)
14 FL V06 N89
LAT XX. X_X.X
LONG/2 XX, XXX
ALT XXX. XX
V34E (Don't store)
FL V5G N25 | PERFORM
R1 00017 ] ADDITIONAL SiG_TINGS
IENTR--_RET STEP 6
l
_ iIPRO
FL V50 N07 ]
,_,K IDENTITY
DEG (+NORTH)
DEC; (+EAST)
N.N
17 G/N PP_ OPTICS - OFF
_xiP23-CSM-CISLUNAR_MIDCOURSE NAV MEASURE_._ENT PROC_IM
CMC - ON(Req) pg 0/2-1
G/N PWR OPTICS - ON (up)CMC ATT - IMTJ
.05G sw - OFF
SCS LOGIC - BUS 3
OPTICS MODE - MAN
OPTICS MODE - ZERO (15 secs)
Move RHC to LEB
Select SC control
PERF STAR - L_[K ACQ
1 K_y V37E23E
_ev59 J rERFORMOPT:CSCA_IE2 !1 iCtr moon in SCT PRO----_STEP 4
ACQ LUN_ I./,IK IN SXTSUPERDIPOSE SI,OS & LLOS
MARK
l
I FL V06 N87 _ BIAS ANGLE(TRUN)R2 XX.XXX J DI';G
PRO V32E--_RI,;T STEP 2
I
I-
O"
oo r
f|
._ e- L
_3
o
85
APPEN IX D
SLTNDISK F22 VERIFICATION TEST - TWO KNOWN LANDMABES CASE
87 ¸
TABLE D-I.- DIFFERENCE BETWEEN THE BIT-BY-BIT
AND THE ENGINEERING-SIMULATION UNIT b-VECTOR
Mark no.
1
2
Incorporation
no.
First
Second
First
Second
First
Second
First
Second
First
Second
First
Second
First
Second
First
Second
bl
.00010925
-.00002955
.00625410
.00000434
.oooo187o
-.oooo1613
.oooo54oo
.00004329
.00003496
-.00021332
.00006993
.000003
-.00000597
-.00001594
.00004537
.01065872
b2
.00039536
.00012107
.O0OOO885O
-.00002697
.00008554
-.00000897
.00006314
.00035168
.00006639
.00015567
.00029096
-.00002593
-.00016595
.00004936
-.0000474
.00019926
b 3
.00002127
.000000174
.00000745
.00000037
.00001657
.00000034
.00001012
.OOOOOO38
.00000435
.00000072
.OOO129O3
.000012
.00026864
.OOOOOO18
.00001425
.0OO0523O
88
TABLE D-II.- THE BIT-BY-BIT UNIT b-VECTOR
Mark no. IncorporatiOnno. bl b2 b3
i
2
3
4
i
2
First
Second
First
Second
First
Second
First
Second
First
Second
First
Second
First
Second
First
Second
.01722365
.96760445
.01692410
.99287134
-.01325370
.99284787
-.06199400
.87520529
-.09830496
.59285168
-.02082393
.99875302
-.10489403
.97362556
-.39230337
.23289772
.06601096
-.25247107
.08906350
-.11919103
.11024054
.11938646
.11216514
.48375168
.07236639
.80531167
.41681896
.04992407
.44763405
.22815184
.09168866
.97249826
-.99767023
-.OOOOO018
-.99596855
.000OO063
-.99381657
.00000234
-.99175388.00000262
-.99252165
-.00000277
-.90875097
.00001247
-.88804336
.O0000115
-.91525475
-.00240317
89
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° 91
TABLE D-V.- BIT-BY-BIT ESTIMATED
LANDMARK POSITION
Mark no.
i Before inc. i
After inc. 2
2 After inc. 2
3 After inc. 2
4 After inc. 2
5 After inc. 2
1 Before inc. 1
After inc. 2
2 After inc. 2
3 After inc. 2
X
-ii 915 844.
-ii 920 412.
-ii 932 272.
-ii 946 187.
-ll 960 939.
-ll 974 579.
-16 71_ 688.
-16 720 517.
-16 727 617.
-16 746 h19.
r£, ft
12 998 932.
13 000 596.
12 989 420.
12 974 770.
12 959 903.
12 946 970.
7 377 763.3
7 379 7o2.1
ii 228 431.
ii 221 747.
ii 221 465.
ii 221 155.
ii 220 926.
ii 220 790.
io 167 490.
i0 163 640.
7 362 582.6 lO 161 587.
7 313 567.1 lO 158 936.
92
TABLED-VI.- ENGINEERING-SIMULATIONESTIMATED
LANDMARKPOSITION
r£, ftMark no.
X Y "Z
i
2
3
4
5
i
-11 915 826.
-ii 920 460.
-ii 932 336.
-11 946 184.
-ii 960 923.
-ii 974 566.
-16 714 671.
-16 720 415.
-16 727 508.
-16 746 321.
12 998 456.
13 000 166.000
12 988 976.
12 974 563.
12 959 814.
12 946 910.
7 377 346.9
7 379 474.1
7 362 355.6
7 313 570.4
ii 228 979.
ii 221 841.33681
ii 221 542.
ii 221 259.
ii 221 037.
ii 220 907.
i0 167 805.
i0 162 551.
lO 161 539.
i0 159 026.
95
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.97
APPENDIX E
SUNDISK P22 VERIFICATION TEST - ONE KNOWN, ONE UNKNOWN LANDMARK CASE
E_<
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i01
TABLE E-III.- BIT-BY-BIT ESTIMATED LANDMARK POSITION
Mark no.X Y Z
Unknown
2 Before Inc. i
After Inc. 2
3 After Inc. 2
4 After Inc. 2
5 After Inc. 2
-ii 931 967.
-ii 932 667.
-ii 946 634.
-ii 961 449.
[-ii 974 998.
i12 992 613.
12 992 693.
12 979 028.
12 962 645.
12 949 ll9.
ii 220 524.
ii 220 577.
ii 220 454.
ii 220 120.
ii 219 936.
Known
i Before Inc. i
After Inc. 2
2 After Inc. 2
3 After Inc. 2
-16 714 688._
-16 720 707.
-16 727 834.
-16 746 721.
7 377 776.1
7 380 254.o
7 363 162.1
7 315 078.5
10167 490.i0 161 428.
i0 160 369.
lo 158 148.
102
TABLE E-IV.- ENGINEERING-SIMULATION
ESTIMATED LANDMARK POSITION
r£, ft
Mark no.
X Y Z
Unknown
2
3
4
5
-ii 931 917.
-Ii 932 656.
-ii 946 618.
-ii 961 434.
-ii 974 969.
12 992 613.
12 992 689.
12 979 045.
12 962 673.
12 949 141.
Known
i
ii 220 566.
ii 220 609.
ii 220 501.
ll 220 168.
ii 219 999.
-16 714 671.
-16 720 716.
-16 727 763.
-16 746 629.
7 377 346.9
7 380 018.0
7 363 222.7
7 314 991.9
i0 167 805.
i0 161 313.
i0 160 388.
i0 158 136.
103
TABLEE-V.- DIFFERENCEBETWEENTHEBIT-BY-BIT ANDTHEENGINEERING-
SIMULATIONESTIMATEDPOSITIONANDVELOCITYVECTOR
Mark no.
[
2
3
5
|
Time of state vector
comput at ion
Initialization
Before incorp.
After second incorp.
After second incorp.
Before incorp.
After second incorp.
Ar , ft-C
....AX AY
0.0 0.0
Unknown
AZ
0.0
2.0 2.0 -6.O
6;o 24.0 -2.0
-44.0 26.0 -3.0
Known
ii.6 2.0 2.0
17.o 78.7 -30.
Av , fps-C
0.0 0.0
-.002 .005
-.o24 .029
.046 -.042
-.016 -.004
-.022 .005
.OO8
.024
-. 028
.0O2
.040
104
TABLE E-VI.- DIFFERENCE IN THE RESIDUALS (ACTUAL
MINUS ESTIMATED) OF THE BIT-BY-BIT AND THE
ENGINEERING-SIMULATED POSITION AND VELOCITY VECTOR
Mark no.Time of state vector
computation
Initialization
2 Before incorp.
After second incorp.
After second incorp.
Before incorp.
After second incorp.
After second incorp.
6rc, ft _ _v c, fps
-AY _ _,
O.OlO.O o.o o.oUnknown
-2.0
-4.7
-31.4
Known
-1.7
20.0
-76.
_ -.o05
-.oo5
.010
.004
.011
-.OO7
.ooo6
-.0006
105
0L'q<_ 0
4-_
<30
.,::3
0
<3 0
0_I
_£_ oI
Pq _
o_ _ >'_
,M
H_ 4._
e_
' J_ _ o
O
._ o
O o ,..-I
_ ,_--t
0
o _ _,o cO 0"_
o I I" I
,.H0", 0"_ ,-I
0 00 u x o
0 o.I t" OJ
o _0 _ _ _ r
_0 I I
OJ
I I l
0"_o oJ kO
o
I I I
,-i
o _ o
I I I
0,-I ,-4 ,-0
0 I" I
0 0 oJ
0 I I
oJ oJ aO,-I ,M o_
0 o
o I" I
OJ
_ o
_D 0OJ I._
I I I
CO OJ COOJ _0
OJ I r_I
',D
,--4 ,_
r_
I OJ
O
I I I
0e3 m ,--I
I° I
I I I
106
H
H
D_0_
CO
_q
OO
H
I
HHI--I
I
F_
I
E-4H
I
I
H
H
HO
_ 4O_ o.I OJ
0 C_ 04oJ _- _ ,-I
_ 0
.t.q
o>l
.X
o
X
O
o 0
-_ 4a
O@ o
cO
CtlO
t"q
0d
0", CO ed0", _ M3
C_ _ oOoJ .--I
8
O4
Oq Lf'X _04 .._ Lr_0 O_ O0 0
Dq I" II
Lf'X L_ Oq
0 0 r--I r--I
_ l" I I"
O_l0 0
d _ 4o_ _ co
o4 c_l
_ 4
(xl ctl
_ 40", c_l0,1 oJ
0.M4_
b_
,-t.rq4_.et
.-_ oqo C_
ox c_ 0
I I°
_ ,O
J _; 4_-- Lr, '.__q _ ,_I
I I I
4 _ 4O_ Oh o',
8 _ d_-I _-_ ,-M
I I I
_._
107
REFERENCES
i. MIT: Guidance System Operations Plan for Manned CM Earth Orbital
Missions Using Program Sundisk, Section 5, Guidance Equations
(Rev. 2). MIT Instrumentation Laboratory, March 1968.
o TRW: Programmed Guidance Equations for Sundisk Command Module Earth
Orbital Program, Revision l, based on DISK 282 Program.
TRW/Houston, NAS 9-4816, February 25, 1968.
. Clifford, J. B., Jr.: Apollo Coasting Flight Navigation Simulation -
OBSIM/NAVSIM Program Formulation. TRW note no. 67-FMT-5B1, July 25,1967.
_. Phillips, Laurel A.: Apollo Onboard Orbit Determination Equations.
MSC memorandum no. 66-FM42-228, August 4, 1966.
. Guidance System Operations Plan for Manned CM Earth Orbital Missions
Using Program SUNDISK, Section 4, GNCS Operational Modes (Rev. 2).
June 1968.
6. Kimball, Garner R.: Additional Sundisk Program Notes. MSC Draft
for Corrections to Sundisk Program Notes, July 8, 1968.
7. Fox, M.: Discrepancy Report Status (June 28, 1968).
TRW memorandum no. 68:7252.1-99, July 9, 1968.
8. Kimball, Garner R.: Updated Sundisk Program Notes and Discrepancies.
MSC memorandum, May 18, 1968.
9. Flight Crew Support Division, Spacecraft Systems Branch: Crew Check
List, Apollo 7. May l, 1968.
10. Olah, G. T.: Sundisk P22 (Orbital Navigation) Verification.
TRW memorandum draft, September 1968.