The Celestial Tracker as an Astro Compass

Greene: Celestial Tracker as Astro Compass

The rms errors of the measurements at the U-, B-,and V-filter outputs are assumed to be

v-u =- cto,

aB= cbo,

(6)

(7)and

-V = CVo0, (8)

where U0, bo, and vo are the actual filter outputs (i.e.,not the magnitudes). Calculations were then made fordifferent values of c. In additioni, errors caused by thebrightness threshold were included. For those stars

whose U-B values were not known, a value wasassumed which was consistent with the average U-Bcolors for similar type stars.

AcKNOWNLEDGMENT

The author is indebted to A. H. Sonnenschein, R.Vogel, and M1. Weiss of Federal Scientific Corporation,Dr. H. Johnson of the University of Arizona, and Dr.XI. Roberts of Harvard College Observ-atory, for theircontributions to the work on star identification.Acknowledgment is also miade to D. Wille, Lt. R.

Cranos and R. Becker, of \Vright-Patterson Air ForceBase, for their encourageirient and support.

The Celestial Tracker as an Astro Compass*JOEL GREENEt, MEMBER, IEEE

Summary-This paper describes a navigational system whichaccurately determines aircraft true heading and an altitude interceptfrom which position is determined.

This is accomplished by automatically and continuously trackingthe light from a celestial body with a stabilized telescope utilizing aphotomultiplier tube as the sensor. The line-of-sight to the body isaccurately measured with respect to the local vertical and used tocorrect computed pointing commands. The computed information isdetermined from aircraft position, celestial data, and time.

INTRODUCTION

\ N AVIGATION is an art, and the practice of thisart has become increasingly complex in today'senvironment.

The first explorers instinctively were their own com-puters. They felt their way from place to place usingtheir natural instincts of time and motion and directedthemselves with respect to landmarks on the earth andin the heavens.

Today, the navigational concepts remain the same.We still direct or pilot ourselves with respect to known"fix" points. We still use the stars, and we still computeour relative progress by dead reckoning techniques.However, in each of these methods, man has developedby necessity a multitude of highly accurate and auto-matic navigational aids to meet his ever mounting com-plex requirements. These aids have been developed frompractically every scientific field.There are many navigational systems established on

active electronic principles utilizing ground reference

* Received June 11, 1963.t Kollsman Instrument Corporation, Elmhurst, N. Y.

stations. There are also Doppler navigational systemsusiIng the principles of radar and inertial guidance sys-tems using the gyroscopic principles.

It is the purpose of this paper to discuss a celestialnavigational system using the heavens as a referenceand an astro tracker as the sensor. This system isappropriately defined as an astro compass.

Although the system described is for aircraft use,adaptation to ships, submarines and land-based vehiclesis easily accomplished.

Let us define the conditions and problems that existin today's high speed aircraft. Speeds are as high asMach 2, and the altitude is now well above 30,000 feet.Accurate true heading and position are required to con-fine the aircraft within its prescribed corridor and atdiscrete intervals to insure flight safety and effecteconomy by reducing fuel consumption and increasingpayload.

Before establishing this celestial navigation system,careful consideration was given to the relative advan-tages and disadvantages of magnetic, electronic, inertialand celestial devices. Magnetic devices, because of theirreliance on magnetic properties and problems of driftin the free gyro or inertial mode, were not sufficientlyaccurate.

Electronic systems which use ground stations, al-though accurate, have limitations due to extended rangeand weather anid jamming or interference.

In addition, military aircraft would be required tonavigate with a minimum use of electronic equipmentin times of emergency. Under these conditions, the

1963 221

222 IEEE TRANSACTIONS ON AEROSPACE AND NAVIGATIONAL ELECTRONICS September

navigator must rely on dead reckoning, inertial andcelestial navigational methods.

Inertial systems, although indepenident, had problemsof drift, alignment, complexity and cost.

Celestial techniques, on the other hand, are precise,for at aiNxT instant of time the location of a body isknown. From the measurement of the altitude andbearing of the body, one can compute true heading andposition to a precision previously unattainable with adesign using presenit-day state-of-the-art conmpoinenits.It is not susceptible to electronic inteferenice and usesno nmagnetic properties or materials.The marriage of this system to a Doppler system for

positional inputs, anid an inertial quality platfornm forvertical information and initial heading, will then resultin a major guidance system with a high degree of ac-curacy and versatility. The addition of accurate trueheading, when properly obtained, to the Doppler dead-reckoning comnputer, will improve the positional in1-puts, and thus inmprove the astro compass true headinig.

Accurate true heading may also be used to monitorthe azimuth gimbal of the platform.

CELESTIAL NAVIGATIONThe desigin of an astro compass requires the solutioni

of several equations derived from the systems of co-ordinates defiining a body in space relative to onie'sposition on earth at any mnoment of time.

In order to establish these equations, a brief descrip-tion of celestial navigationi is a prerequisite.

Celestial navigationi is the determinatioin of positionand heading by the aid of celestial bodies, i.e., the suIn,planets, mooin and stars.

There are two systems of coordiniates generally usedin locating celestial bodies.

Oine is the equinloctial or celestial system which desig-nates the positioin of the celestial body without respectto any point oIn the earth (Fig. 1).The other is the horizon sx stemn which locates a body

oni the celestial sphere in relation to the horizoni of theobserver (Fig. 2).A direct relationship exists between the earth's co-

ordinate systemn anid that of the celestial sphere.In the celestial system of coordinates the axis of the

earth extenided cuts the celestial sphere in two poinitscalled the celestial poles. These poles designated northanid south corresponid to the North a.nd South Poles ofthe earth.The planie of the equator of the earth extended cuts

the celestial sphere in a great circle which is called theequinoctial or celestial equator.

Celestial bodies for all practical purposes are fixed inspace. The coordiniates wAhich vary slightly over theyear are declination (DEC) and sidereal hour anigle(SHA). DEC is the angular distance north or south ofthe celestial equator and called declination north or

celestial equator or angle at the celestial pole betweenthe hour circle of the verinal equinox of the constella-tioii Aries (T) and the hour circle of the star. Hourcircles are great circles of the celestial sphere passinigthrough the pole anid bodies. AIn hour circle is a func-tioIn of time because it mioves wxTith the body as it makesits daily trip arounid the earth. SHA anid DEC of allnavigationial stars are in the Air Alnmanac.The observer has latitude anid longitude as his set of

coordinates on the earth's sphere.As Aries is imuovinlg relative to Greenwich, a rela-

tionship involvinig time is required. The civil mean

timle at Greeniwich (GMNIT) is used as a reference anidfor each dav, hour anid minlute a corresponding GHAof Aries is tabulated in the Air Almanac.

In the horizon svstemi of coordinates, the observer'shorizoni extenided, cuts the celestial sphere in the celes-tial horizon. Angular distanice of the body above thehorizon is called altitude.The horizon systemn coordinate which nmeasures the

angle at the horizon between the vertical circles of thestar and north is called azimuth (Zn).

Fig. 3 combines both the horizon and celestial s7s-tems of coordinates, and from it anl interesting and well-known trianigle materializes. This is the navigationjaltriangle.The componenit sides anid inicluded aingle of this

spherical triangle are codecliniatioin, colatitude aind thelocal hour angle of the body (L,HA*).The solution of the navigationial triangle for true

azimuth and star altitude is a prime requiremernt for thedeterminationi of positioIn and headinlg.

Determination of Tru e Hfeading

The mneasuremenit of the relative bearinig of a bodyrelative to the lonigitudinial axis of anl aircraft and thesolutioni of the inavigationial trianigle theni leads to thecomputationi of true headinig of the aircraft.

Znz + Rb - THYwhere

Zn is the true azimnuth of the body mieasured fromnorth,

Rb is the relative bearinig of the body,TH is the true headinig of the aircraft.

Determination of Position

Every celestial body has a poinlt, called a substellaror grounid poinit (GP) oni the earth, which moves as theearth rotates.

Ani observer canii measure the sanme altitude of thebody from a circle of equal altitudes. Thus, this nmeas-ured altitude angle defines a locus of our positioni onearth relative to the body.The difference betweenL comrnputed and observed alti-

south. Declination is analogous to latitude on the earth'ssphere. SHA of the body is measured as the arc of the

tude is defiiied as altitude iiitercept and the error inpositioii.


LXX *

VERN-t EQUI.

1 ig. I Celestial system of coordiiiates.

Fig. 4-(A) P'ower stipply. (B) Erection amplifier. (C) Correctioncomiputer. (I)) Astro tracker signal amplifier. (E) Junction box.(F) Correction computer servo amlplifier. (G) Altittide aziiiltthcomputer servo amliplifier. (H) Astro tracker servo amplifier. (I)Accessory servo aniplifier. (J) Altitude aziiirth computer.

Fig. 2--llorizontal system of coordinates.

Fig. 3-I lorizontal and celestial system of coorcliiiates.

A

B

C

D

E

Altitude intercept antd true azimuth define a line ofposition. The use of three lines of position, commonlycalled a three-star fix, determines ani accurate position.

TIIE ASTRO COMPASS SYSTEm DESIGN RE.QuLREMtL NTSAND FUNCTIONAL DESCRIPTION

The Kolisman Instrumenit Corporation AutomaticAstro Compass KS-50-06 (MD-1) developed for the AirForce had the following specific requirements (Figs.4, 5 and 12).

Fig. 5-(A) Manual present position display panel. (B) Star datadisplay panel No. 3 (C) Star data display panel No. 2. (D) Stardata displav panel No. 1. (E) Indicator display panel. (F) Manualset panel. (G) Heading display panel. (H) Line of position displaypanel. (I) Master control panel.

CELESTIAL N-RIC

F

H

I

1963 223

-ECt


Accuracy shall be within 0.1 degree rms in altitudeand true heading.

Sensitivity shall be a 24 hour tracking capability fortrue heading.True heading information shall be obtained con-

tinuously and automatically.System shall be remotely operated, and with a

minimum of the navigator's time.Weight shall be 150 pounds and with a minimum of

panel space.Design shall be of modular construction, with much

of the system to operate in an unpressurized environ-ment.

Cost shall be minimum.System shall be unaffected by magnetic effects, and

electronic counter measures. It shall be fully operatingwithin a few minutes. It shall work at any latitude.

Figs. 6 and 7 are functional block diagrams of theKollsman KS-50-06 Automatic Astro Compass System.

Basically the system consists of several computers,an astro tracker and a Correction Computer.

iCHA 75LJV

AlT ONE'

AL 7- CORP r"-D"p j-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A. T._ A > A

TPACC<

lE1EfEL71A~

/TVEA LPLATEO

At

EAL'E f E.E:/XC,x

Fig. 6 Azimuth alignment using astro compass true heading.

The computer is required to compute the star's posi-tion at any instanit relative to the present position ofthe aircraft. From the celestial system of coordinates,Fig. 1 and the navigational triangle, the true azimuthangle (true north to the body) and altitude of the bodyare computed.The computed true azimuth when added to a coarse

true heading establishes relative bearing. This anglewith computed altitude is transm-itted to the astrotracker where it directs the line-of-sight to the area ofthe sky about the star. An instituted search patterndirects the line-of-sight until the star is detected withinthe field of view at which time tracking begins. Errorsignals from the astro tracker are then fed back asheading correction and altitude correction through cor-rection loops to the computed inputs. During tracking,the line of sight is maintained upon the star within 15seconds of arc, so that altitude and bearinig of the astrotracker are observed correct angles. Heading correctionand altitude correction are the differences between thecompulted and observed angles which are used to correctthe computed infornmation.

THE COMPUTERS

Computatioin of star pointing commands from inlputsof present position anid star coordinate information re-quires several computations, which in the KS-50-06 areaccomplished by several computers and displays.From Fig. 1 (celestial system of coordinates) and

Fig. 2 (horizontal system of coordiniates), the followingequations are obtained.LHA* = GHA*+ East Longitude or- West Longitude.GHA* = GHAT +SHA*.GHAT is obtainied from the Air or Nautical Almanac

for any day, hour and minute.

* ONLY MANUAL INPUTS AtE AALAALC

Fig. 7-KS-50-06 astro compass system block diagram.

'1- ,rcsl,FC-

TO EXTERNALEQUIPMET


SHA* is obtained from the Air or Nautical Almanac.Longitude is an exterinal input (from Doppler, dead

reckoning).Therefore, LHA* = GHAT-+SHA*+E. Long. or-W.

Long.GHAT is a function of time. Therefore, time must

be a part of these calculationis.LHA of * now establishes one input to the naviga-

tional triangle.The other two inputs to the navigational trianigle are

declination of the star (from the Air or NauticalAlmanac) and latitude from the external source (Dop-pler dead reckoning).From Fig. 3 it is seen that the navigational triangle

is solved for true azimuth and altitude from thesethree inputs.From the law of sines and cosines the following can

be proven.

Sin Az cos A - cos D sin LHA

Sin A = sin D sin L + cos D Cos L cos LHA

Cos Az cos A = sin D cos Lat - cos D sin L cos LHA,

where

LHA=Local Hour Angle of starD = DeclinationL = LatitudeA = AltitudeAz= True Azimuth.

The inputs required for the navigational triangle aresolved by several modules of the KS-50-06 (Fig. 8).

Longitude in two-speed analog form is added to GHAof Aries in a pair of differential generators, the outputof which is then added to the SHA of the celestial bodyin another pair of DG's. The output is then LHA*which is transmitted to the Navigational Triangle Com-puter.

Longitude is obtained in the primary mode from theexternal Dead Reckoning Computer, or from a self-contained manual present position paniel counter in asecondary mode.The GHA synchros are counter set in the indicator

display panel with time (GMT). Time is available as asolar or sidereal rate from a precision frequency supply.The difference between these two rates is four min-

utes per day which can result in a one degree error inLHA.SHA is counter set in the star data display unit

along with the declination of the body. These are fixedvalues and obtained from the Air Almanac.

Latitude, like longitude, is obtained from an externalsource or internally.These modules are all hermetically sealed, with high

speed counters accurate and settable to 2 minute ofarc. All primary counters are remotely set from onebasic master control panel which is the only unit re-quired to be within arm's length of the navigator.

The design of the Navigational Triangle Computerrequired serious considerations before adopting themechanical analog approach. The requirements for thiscomputer were as follows:

1) Solve navigational triangle for true azimuth andaltitude.

2) Receive 2x analog latitude, declination and LHIA.3) Transmit analog true azimuth and altitude.4) Rates consistent with a Mach 1 aircraft crossing

close to the pole.5) Light weight.6) Low cost.7) High reliability.8) Ease of maintenance.9) Accuracy of 3.0 miinutes rms to be consistent with

Air Force systems requirements.

Several methods were considered:

1) Resolver techniques (electrical).2) Digital computations.3) Mechanical analog.

The Resolver Computer requires six resolvers. Eachresolver would require compensated windings and abuffer amplifier for maximum accuracy. As each wind-ing is temperature and frequency sensitive, extremes oftemperatuire and frequenicy would be a limiting factor,although it is possible to obtain some resolvers withtemperature compensation.

Fig. 9 depicts the resolver solution.It is possible to eliminate one resolver and of course

an extra buffer amplifier. However this system of sixresolvers allows for a transverse coordinate system.

:XrEPNA.L

Fig. 8 Star and position computer.

$ SAM LONVG L Z

_GV~~~Z O- EC.A ALr/TLJOAI ---- = LAT-

AZ = 7-4,L/E A ZI/IL/rA.

Fig. 9-Star and position computer.

1963 225


For transverse coordinates the Greenwich Meridianintersection with the celestial equator is considered thetransverse celestial North Pole.

Solution of the transverse coordinates is similar to thenavigational triangle.The errors for such a system using resolvers within

0.05 per cent accuracy is in the order of 2' rims in alti-tude and azimuth.

This computer was compatible with our require-ments, except that it would have required a consider-able number of additional amplifiers. The frequencyrange was too broad and would have required a pre-cision frequency supply with some power. It wouldnot have fitted into the navigator's compartment, andit had no provisions for star storage.The next method considered was a computer based

on digital techniques.Weighing the pros and cons of analog computing

techniques vs. digital, the following tabulation re-sulted.

finally adopted was an electromechanical methodwhereby a mechanical analog could be built to simulatethe celestial sphere in miniature.

In this case, past performance of a similar type designused with a sextant established that the design in asmall package was feasible. An accuracy evaluationproved that a miniature celestial sphere with a radiusless than 3 inches could be built in production with anaccuracy of 2' rms. It would be highly reliable, insensi-tive to extremes of temperature by virtue of properchoice of materials, and insensitive to frequency varia-tions. It would be sniall in size, require only three servosand easily fit into an analog system of synchro trans-mission and computation.The spherical Triangle Computer of the Alt-Az

mechanical analog is a miniature of half of the celestialsphere. The radius of this sphere is 28 inches. North orSouth hemisphere calculations are done by appropriateswitching (Figs. 10 and 11).

Analog

Medium accuracyHigh reliabilityNo converters required

Lends self to special purposeLow cost as special purposeWide bandwidth

Digital

High accuracyMedium reliabilityRequires analog to digital and digi-

tal to analog convertersBest useful for general purposeHigh cost as general purpose

Narrow bandwidth, tied to costs andreliability

On the basis of accuracy, reliability, its special appli-cation, and cost, digital computationi was ruled out.However, this method is still a veryfeasible one if sucha system were to be included in a larger weapon system.The last computer technique to be considere(d and

LAr AX15

DeC AX /S

Fig. 10-Analog computer.

Fig. 11.

L/-,A A//S C

L/~'A -LA7r1o0,A4


In operation, the latitude input rotates the cradleabout the latitude axis, which is normal to the presentpositioni meridian. This displaces the LHA axis (P.)from the zenith (Z) by the colatitude angle. LHA anddeclination inputs rotate the star arm anywhere uponthe hemispheric surface bounded by the cradle plane(celestial equator) and with the LHA axis as the poleaxis. The true azimuth axis contains a bail and curvedrack into which the star arm slides, pulling with it thecurved rack. The bail is part of the great circle whichruns from the.star to the zenith. The movement of thestar arm along the surface of the celestial sphere causesthe bail to rotate and thus compute true azimuth, anddisplacements of the rack as measured from the stararm to the zenith along the bail is a measure of co-altitude. All the inputs are two speed servo drives andthe outputs are transmitted through two speed synchros.

Limits

Latitude: -1 degree to +91 degrees in one directioni,N or S latitude changed by switching.

Declination: 90 degrees N to 80 degrees S with thestar above the horizon.

LHA: No limits, with the star above the horizon.Altitude: -5 degrees to 80 degrees.True Azimuth: 0 degrees to 360 degrees (no limit).

Accuracies are 2-minutes rms in altitude with somedegradation in azimuth at altitudes over 75 degrees.The degradation in high altitude tracking is not

serious because good true heading is best obtained intracking low altitude stars.The servo designs are straightforward. Rates of

declination and latitude are slow except for slewing frompoint to point. In normal operation, latitude, at most,will vary at maximum aircraft rates and declinationi willremain constant.The only servo requiring high rates is LHA which

varies with longitude and time. At high latitudes,longitude will change rapidly due to meridian conver-gence and aircraft speed. However, the system is adapt-able to grid coordinates.

4) Conversion of light energy to electrical energy.5) An accurate angle positioninlg and measuring sys-

tem.

6) A means of determininig line-of-sight angles to thebody from a horizontal plane unaffected by air-craft dynamics.

Accordingly, the tracker for the M\ D-1 was developedwith several distinct units, as follows:

1) A telescope, consisting of the the optics, discrimi-nating mechanisms, a sensor, and positioning andmeasuring servos.

2) A two-gimbal structure containinig pitch and rollservos. The telescope fits into the inner gimbal(Fig. 13).

3) A housing, containinig a dome, which incidentallyis the only portion protruding from the astrotracker, and an hermetically sealed container.

Separated from the astro tracker is its associatedelectronics package which containis those elemenits re-quired to receive the sensor voltage of signal and noise,discriminate between them, and convert this signal intoappropriate error voltages.

Fig. 12.THE ASTRO TRACKER

The astro tracker is the device which collects thelight from a celestial body, detects this energy from thebackground, and measures the tracker line-of-sightangles relative to the body from a particular set of air-craft coordinates. These angles, transmitted to a com-puter, may then be used in several ways to computeaccurate true heading and altitude intercept (Fig. 12).The design of such a unit is predicated upon

1) Operational consideration, i.e., a knowledge of thespectral response of celestial bodies and back-ground light.

2) A suitable optics system to collect the light energy.3) Discrimination of signal from noise.

VMUjED /\(TO -QrE

Fig. 13-Stabilized platform with motor and synchro gear boxesshown in exploded view.

1963 227

228 IEEE TRANSACTIONS ON AEROSPACE AND NAVIGATIONAL ELECTRONICS Septembez

Operational ConsiderationsThe design of the system is predicated upon aircraft

environment and atmospheric conditions which affectlight transmission.Any effect which will bend, distort, veil or obscure

the light from a body must be considered in the design.Haze, cloud cover, refraction, Aurora effects, and shockwaves are important examples.

Aircraft flying at high speeds and altitudes are unl-affected by haze and cloud cover. At low altitudes, cloudcover can prevent tracking.The solution is to use an inertial quality compass with

a drift rate which will maintain a desired heading ac-curacy between successive star observations. Theseobservations may be made from low altitudes dependentupon percentage of sky covered in a particular geo-graphical location and the type of mission. On occasionit might be necessary to go to a high altitude to makethe observation. However, once corrected heading isestablished, this information is then used to updatethe inertial compass.Haze at high altitudes is generally no problem for

nighttime and sun observations. It can be bothersomeat low altitudes when tracking weak stars at night.However, there are generally so many brighter bodiesavailable that tracking may be maintained. Daytimestar tracking, although not a requirement for this sys-tem, is inmpaired by haze at low altitudes by obscuringlight and increasing the background noise content.

Refraction of a light ray occurs as the ray passesthrough media of different densities. Amount of refrac-tion is a function of rays incident to direction of densitygradient, temperature, water vapor content and pres-sure. Sights are nmost affected at low altitude observa-tions where the incident angle is greatest, thus causingerrors in altitude intercept. This can be compensatedfor in the system design.The Aurora Borealis (northern lights) are transient

radiation displays which illuminate portions of the skyin streamer and drapery fashion. While some relation-ship between sun spots and the Auroras are acknowl-edged, the occurrence of the latter must still be con-sidered of a random nature. Their effects on operationof the astro tracker are not considered to be serious. Ingeneral, the displays are localized, and many of theboundaries are sharply defined. For high elevations,where atmospheric density, water contenit and dust isless, reflection, or sky background illumination causedby the displays should be low, and therefore observa-tions in other portions of the sky should be unimpaired.An additional favorable condition is that the phenome-non is normally encountered at high latitudes, and herethe selection of alternative stars is much greater.While it appears that, at worst, the Aurora might

require a little more selective use of the equipment,provisions for filtering the predominant spectral lineshave been included in the design.

A system with too much sensitivity leads to ambigu-itities. That is, two or more stars within the sensivitityrange of the system, and within the search area of theline-of-sight may lead to an ambiguous solution.

Confiniing search areas and sensitivity control aremethods for decreasing ambiguous relationships.

Stars and planets vary in intensity and spectral re-sponse. Stellar magnitude ll is a logarithmic scale forindicating the relative radiant flux density received atthe earth from a star and is defined as

M = - 2.5 logf/fo or flfo = 10-0.44,

where Ao is the reference flux density for a zero magni-tude star andf is the flux density of the star in question.Thus 5 magnitudes is an intensity ratio of 100, and eachmagnitude is 2.5 times as bright as the one below it.Stars and planets brighter than a 0 magnitude star areassigned negative numbers (Sirius -1.58, Canopus-0.86) while stars and planets weaker, are assignedpositive numbers (Vega +0.14, Spica +1.21, Polaris+2.12). These magnitudes are the apparenit visualbrightness of stars. However, we measure the radianceof the stars by photoelectric detectors with cathodes ofmaterials which have a peak response in a region otherthan that of the star. Stars vary in visual color fromblue to dark red (1300°K to 100,000°K). Their spectraapproximates a black body radiator at some representa-tive temperature as modified by stellar and earth atmos-pheres. This spectra has been divided into 10 groups andeach star is designated within a group or a percentageof a group by its color temperature.

This color temperature stipulates that band of wave-lengths at which the star delivers the most energy. Acomparison of this energy spectrum to that of the re-ceptor establishes sensitivity of the system. The differ-ence between the visual and photoelectric magnitude ofa star is known as its color index. There is a class ofstars whose color index is zero. These are called classAo type stars (white) with a color temperature of11,000°K. Thus, it is possible to correct apparent visualmagnitude to magniitude as seen by the phototube whichis then used to determine its sensitivity.The Kollsman Instrument Corporation uses photo-

tubes with S-4 and S-17 cathodes. These have peak re-sponses in the blue region at about 4000 to 5000 Ang-strom units (0.4-0.5 p). Approximately 60 per cent ofthe navigational bodies fall in this region with abouta 0.5 magnitude difference between visual and phototubevalues.

Optical SystemIn establishing the design of the optics and choice of

phototube, considerations were given to track approxi-mately 58 navigational stars and the planets at night,and the sun, planets and brighter stars during the dayunder specific conditions of background light. Duringthe day, the sun and at least one other body should be


trackable anywhere on earth. As the aircraft altitudeincreases, more bodies beconme visible to the system asbackground light decreases.The economy of the design was predicated upon the

most economical optics system and a means of measuringbearing and altitude angles relative to a horizontalplane. The choice of a telescope is limited to two basictypes: refractive (lens control of the image) or reflectingwhich uses large mirrors. A reflecting telescope requires alarge dome, in order to see bodies from below the hori-zontal plane to the zenith. Stabilization of this telescopewould also require a large gimbal system, most of whichwould also have to be within the dome. We, therefore,chose for this application, a refracting type system util-izing a small 2-inch radius dome with a prism which col-lects star light and bends it down through the lenssystem to the phototube. An inverted tvpe gimbal sys-tem (Fig. 14), which holds the telescope, maintains thecenter of the prism within the center of the dome duringmaneUvers of the aircraft which do not exceed + 150in pitch and roll. The prism rests on the telescope barrelwhich is servo controlled in bearing. An altitude servo,which is mounted in a gear box external to the telescopebarrel, rotates the prism in altitude by differentialswhich remove the bearing motion.The optics system used is considered a telephoto

svstem, consisting of a dome, prism, positive and nega-tive objective lenses, and a condenser with a focallength of 7.5 inches.

Naturally, care must be maintained in alignment ofthe various optic components. The mounting of theprism and its own pyramidal errors can add sufficientlyto the bearing and altitude errors of the system. Inbearing, these errors vary as the tangent of the staraltitude and can contribute a large percentage of theerror.

Objective lens alignment can also conitribute to theover-all error in altitude and bearing. TIhese errors, al-though small, are part of the over-all accuracy. As theseelements are mounted in a tube which rotates in bearing,the optical and mechanical axes of rotation must becoincident.The choice of a hemispherical dome over a window

was a result of an analysis of system operation. Severaltypes were considered, such as the hemispherical dome,a shallow dome, and a flat plate.The flat plate is the simplest and most economiiical.

Aerodynamically it is best. However, it would seriouslylimit our operating area. Low altitude observations,especially for heading information, would be almostimpossible. If we were to go to a flat plate, the diameterof the window would reach 20-30 inches for altitudes of3 degrees. A 10-inch diameter plate would only allow usto track to 17 degrees of altitude. This would seriouslylimit the available celestial bodies and, at high latitudes,where the sunl is at low altitudes, we would have lostour most valuable body. In addition, a large diameter

STAR LIGHT

RELATIVE

EbEARfNCJS

'ObJECTIVE LENS

-FIELD LENS

- SlWOTTER

F!RA5rER

Fig. 14-Astro tracker telescope optical schematic.

would require a very rigid and thick plate because anydistortions would affect the accuracy of the system.Internal reflections would also attenuate the signal.A shallow dome, although allowing for low altitude

trackinig, introduces other problems. The imagery of thesystem would be affected by the changing slope of thedome. Special corrector lenses would be required. Thischange in imagery would also result in inaccuracies. Thehemispherical dome which was chosen can withstandspeeds of Mach 2 and its accompanying temperatures,without distortions of the image or inaccuracies. Track-ing can be accomplished to below zero degrees. Aero-dynamic tests showed no drag components.

In addition to the telephoto optics, filters are pro-vided for the sun and Aurora Borealis. Although thevoltages on the phototube can be used to control sensi-tivity, the relationship of sun to stars is so great onlya filter can be used.The fact that we are to use a pendulous tracker dic-

tates that its length shall be short in order to accom-modate it within a reasonable case diameter (13 inches)for pitch and roll inotions up to 15°. In order to discrimi-nate a 15 second displacement of the star light, a 7.5-inch focal length is required.The collecting power of the telescope is a function of

the dome, prism size and objective lens diameter. Thelargest objective useable, in the 4-inch dome, was lessthan 2 inches in diameter.The weakest star we wished to track, in order to re-

duce the effects of an ambiguous solution, was Polaris.

Signal-to-Noise ConsiderationsThe ability to track weak stars is dependent upon the

ability of the tracking system to discriminate star sig-nals from noise. Expressed as a ratio of signal currentsto noise currents, the greater this ratio, the better thetracking capability.

1963 229


In order to keep signal-to-noise ratios higher, designconsiderations are primarily concerned with reductionsin noise.

Noise emaniates from a variety of sources. The majorsources are background illuminiationi, the photomulti-plier tube as a nioise generator, and pickup.Background nioise is attributed to the reflection of

all light from particles in the air. These reflectionis, whichare functions of sunl background, city lights at low eleva-tions, moonlight, teinperature, pressure and humidity,produce randomi noise signals within the tracking sys-tem.The backgrounid light flux Fb gathered on the focal

plane of the telescope as a funiction of the sky brightnessB, objective area .Ao, anid the solid anigle a, since thebackground is not a collimated beanm.

Fb = BAoc

- do02B tan2 04

where

do= objective diameter20 =- true field of view of telescope restricted by a

circular field stop.

with this component of dark current is a shot noise re-sultiing from randonm thermionically emitted electronis,variably mutliplied by the seconidary emission gains ofninie stages. The noise current, due to thermionic emis-sion, iS appreciable and mllust be conitrolled in order toobtain maximumii signal-to-nioise ratios within our opera-tional limits.Above 110 volts/stage, a tlird regioni of dark current

begins. This current is due to regnerative ionization.However, as we do not operate in this region, this con-tribution of noise current is inonexisten-t.

Shot noise is due to currents generated by the shoteffect from thei photoelectrons in the photormultiplierdue to background light and the light fromn the starbeing tracked. The rms value of fluctuating output cur-rent originated by thermionic emission and shot nioiseis approximated by the following equation:

I" = ,-\V2qIBKI2(z\f),where A is the gaini of the phototube; q, the electroniccharge; K1, the nioise due to secondary thermionic emis-sioIn fromii the cathode; 4Af, the bandwidth of the receivinginistrument, and IB is currenit due to background.

Substituting for IB, we get

The phototube current due to background light flux isexpressed as

72IB = KB tan2 9- do SkBE,

4

where

K is a constant of conversioin,SkB sensitivity of phototube to spectrunm of back-

ground,E =efficiency of optics and attenuatioin factors.

In any applicatioins of the multiplier phototube tovery low light levels, one of the most importaint coni-siderations is the dark current of the tube. There arethree domains in each of which a different type of darkcurrent dominates: 1) ohmic leakage, 2) amplifiedthermionic emission, 3) regenerative ionization.At low voltages ohmic leakage is dominant, and it is

directly proportional to the voltage per stage. The inoisecurrenit, due to ohmic leakage, is niegligible for our ap-plicatioIl.Above 60 volts/stage the dark current caused by

thermioniic emission becomes important. This enmissioniis amplified through the tube in the same nmaniner asphotocurrent; hence, the output current caused bythermionic emission is proportional to the gain charac-teristic of the mutliplier tube. In almost any method ofusinlg the multiplier phototube, the uIltimate limitationto signal detection is thermioniic emission. Associated

I1 = -- KK,do tan 0V2q(Af)SkBeB.2

Noise is also induced in high iinpedaince circuits dueto electromaginetic and electrostatic effects. Judicioususe of low impedanice circuits and electrostatic and mag-netic shielding will reduce this noise to a minimulml.The light flux gathered by the telescope optics fromn

the star F, is a functioin of the objective area and thestar illuminiance ES.Thus

7rdo2FS EsF

4

The phototube currenit as a result of this star flux isthein

Is= K do2EsSk,E,4

where Sk& is the sensitivity of the phototube to thespectrum of light emitted by the star, aind e is efficienicyof light trainsmissioni to the phototube.

Signal-to-noise may thein be expressed as

S Is K,doE,Sk,s

-I I, K, tan 9V/ 2qAfSkBEB

It is seen that the signial-to-noise ratio varies in-versely with the field stop (0) and the square root of theband-pass.


Common methods to increase signal-to-noise are todecrease effective field of view, and the band-pass ofthe system. However, as the band-pass defines the timeconstant of the system, considerations must be givenas to how this information is to be used, and the errorswhich can be expected.The sensor, in this case a photomultiplier tube type

1P21, provides the necessary amplification and sensi-tivity of light energy conversion to electrical energy.

Amplification in this tube is 2 X 106. Tube cathodesensitivity varies over a rather wide range of 30 to 120amperes/lumen.Many factors affect sensitivity, and a limiting one is

background or "dark" current, which flows when nolight energy exists. As this "dark current" will consistof a dc and variable components, one can eliminate thedc portion and reject the variable signals by samplingtechniques.There are other types of sensors, such as photodiodes

and solid-state detectors of silicon and gallium arsenide.All these have been considered, but for this type ofamplification and sensitivity, i.e., sea level to 50,000feet, with day and night to consider, and minimumobjective size, the 1P21 photomultiplier tube was chosenas the light sensing element because it offered the high-est S/N performance of all commercially availablephotomultiplier tubes in its ability to track up to andincluding third magnitude stars.

Signal DetectionThe detection system used is a common one, generally

described as a double modulation system. The starsignal is modulated at a low frequency for nulling, andlinearity of signal, and also at a higher frequency foracquisition purposes (Fig. 14).The light from the body is focused at the focal point,

in this case the raster plane. The raster is a disk ofseveral hundred equally spaced transparent and opaquelines. The star on this plane is imaged to fall betweenany line. Therefore, rotation of this raster at a precisionfrequency will produce a carrier signal of 190 cps only ifthe starlight is upon it. Background light is not col-limated upon the raster, and its area is a function offield area and distance from field to raster. As it coversmany pairs of lines, no signal is generated of any appre-ciable magnitude.The second frequency of 30 cps is derived from a hole

of 22 minutes in diameter which is in a cylindricalopaque shutter. This device is driven by the same pre-cise frequency as the raster. The image at the shutterplane is defocused in order to obtain a linearity of signal.When the star image is at the center of the shutter,

equal areas of the image are covered by the opaque andtransparent portions of the shutter and no modulationof the carrier occurs. As the image is moved in any

direction from zero (optical and mechanical axis ofrotation), the shutter cuts unequal portions of theimage. This develops a modulation upon the carrieruntil the image is completely off the center when 100per cent modulation occurs. The light, once past theraster, is condensed upon the photo cathode surface,where the electrical energy is established.

Signal Electronics

The composite celestial signal, containing the 190-cpscarrier and the 30-cps error signal, is amplified in thetracker preamplifier (Fig. 15) with all the attendantnoise signals. A high-pass filter passes all signals over100 cps and we are left with the 190-cps carrier, and theupper and lower sideboard frequencies of 160 and 220cps, as well as noise.The output of the high-pass filter is fed simultane-

ously to the inputs of three transistorized amplifiers,namely 190- and 160-cps narrow-band amplifiers and thenoise amplifier. The noise signal (containing all signals)appears at the output of the noise amplifier as an am-

plified version of the input. The output of the 190-cpsamplifier is applied to a filter network (Twin "T"), whichpasses all frequencies except 190 cps back to the inputof the 190-cps amplifier, degenerating them. Effectively,the 190-cps amplifier is a highly selective, narrow-bandamplifier (2-cps wide), which rejects all frequencies ex-cept the 190-cps signal. The output of the 160-cpsamplifier degenerates its input in the same manner,thereby amplifying only the 160-cps signal. The outputsof the 190- and 160-cps narrow-band amplifiers areapplied simultaneously to the 30-cps error detector,where they are recombined to recover the 30-cps errorsignal content. The 30-cps error signal is then applieddirectly to the input of the 30-cps error amplifierthrough sun-star relay in the star position. It should benoted, at this point, that the error signal will not existunless the celestial body is displaced from the center ofthe field of view. For the same reason, the 160 cps wouldalso not exist. Therefore, the recovered 30-cps signalwill have the same phase and amplitude relationships asdid the original 30-cps signal generated by the shutter,with the noise component rejected by the extremelynarrow band-pass of the amplifiers.

During the sun tracking mode, a predominant 30-cpssignal appears in the tracker preamplifier. After filteringand amplification, the signal is converted into 400 cpsbearing the altitude correction signals.The error signal from an astro tracker is a function

of the image position on the shutter plane relative tothe center of rotation (mechanical and optical axis).Displacements along the line of sight are altitude errors,and across the line of sight are bearing errors.

In order to resolve the error signal into its altitudeand relative bearing components, it is necessary to

1963 231


Fig. 15.

reference them to a standard for comparison. Thisstandard is supplied by the PM reference generator. Thegenerator is driven by the shutter-raster motor at thesame 30-cps rate as the shutter. The generator containsa permanent magnet which rotates between two statorcoils placed electrically 90 degrees from each other, andgenerates an output which is two phase at a frequencyof 30 cps. After proper alignment, each phase of thegenerator references an axis of the field of view; one

phase referencing altitude, the other relative bearing.In order to rotate these two phases, so that the refer-

enced in-line axis is always along the line of sight, thePM outputs feed into a resolver which makes the neces-

sary coordinate transformation. This resolver is posi-tioned by the relative bearing gear train.The resolver outputs are amplified and used to

demodulate the 30-cps error signal into dc errors of

bearing and altitude.The output from the photomultiplier tube is main-

tained at a constant level through wide ranges in sun or

star tracking conditions and phototube variations by the

action of the automatic gain control (AGC). The AGCfunctions by providing a negative dc voltage which is

proportional to the 190-cps carrier signal. This negativedc voltage is applied to the dc input of the 800-cps highvoltage modulator which in turn generates a high volt-age output which follows the variations in AGC voltage.The higher the negative dc voltage developed, the lowerwill be the resultant high voltage applied to the photo-multiplier tube. In this manner, the sensitivity of the

photomultiplier tube is controlled, and a constant car-

rier output is maintained. During sun operation, an

AGC voltage is developed representing the sun current;and during star operation an AGC voltage is developedrepresenting the star carrier.

The Star AGC is developed from the noise amplifierand 190-cps amplifier output as a dc voltage. This isused to control the high voltage power supply and foracquisition control. The latter is used to energize thesearch-track relay.The line of sight to a body is established by the rela-

tive bearing and altitude positioning servos located inthe gear box below the telescope barrel but is still partof the telescope housing. Judicious use of accurate gear-ing and differentials in conjunction with 2-speed servosystems allows for precise bearing rotation and altitudeprism motion.The angles of bearing and altitude of the line of sight

are measured from a horizontal plane. Any errors in thishorizontal plane, or vertical, will result in heading andaltitude errors.

Several methods were considered to stabilize the astrotracker for aircraft motion. In all cases, a gyro is re-quired to produce the pitch and roll motion of the air-craft.One method was to correct bearing and altitude in an

auxiliary computer before they were transmitted to thetracker. This would permit the astro tracker telescope tobe the limiting item for the size of the tracker. The domewould have to be hyperhemispherical to accommodateadditional altitude excursions due to pitch and rollmotion. This would also require a fast tracking systemwith its attendant wide band-pass and relatively smalltime constant.A study of the computer techniques discarded the

digital type because 1) The solution rate (iteration rate)would have to be exceptionally fast, that is, in the orderof a few milliseconds, in order to keep the star signalwithin the field under all aircraft dynamics. 2) A digitalcomputer of this speed would be quite costly and, interms of its special purpose, unnecessary.The method chosen was a mechanical gimbal system.

The telescope is erected vertically in the inner or pitchgimbal, and this gimbal moved on a set of rails androllers monitored in roll. The accuracy of this system isless than 2-minute rms for + 3 degrees of pitch and roll,and increased to 2-minutes rms at + 12 degrees of pitchor roll (Fig. 13).

Correction ComputerThis computer corrects the inputs to the astro tracker

such that "tracking" errors are "nulled" or maintainedwithin a 15-second region. Each correction loop is anintegrating servo which smooths the bearing and alti-tude error information. The altitude correction loop isaltitude intercept and shown as such in conjunctionwith computed true azimuth on a display unit fromwhich the navigator may easily plot a line of position.

It was stated earlier that a crude or best availabletrue heading (BATH) was required to initially find thebody. However, once the body is acquired, heading cor-rection is added to BATH, thus establishing accurate


true heading. Heading correction is also transmitted toa display unit and has the additional functions of pro-viding true heading for acquisition, if the BATH is notfunctioning, and acting as a storage unit for the differ-ences between BATH and precise true heading.

While tracking, a heading correction builds up due tothe errors in BATH due to drift, variation, and devia-tion not accounted for. If the star is lost, due to cloudcover, or bank angles exeeding 15 degrees, we retainthe heading corrections, so that when search startsagain, we are much closer to acquisition.

Also included in this computer is the search package.Search is accomplished by an increasing voltage appliedto a resolver which then feeds the altitude and bearingservos. This can be pictured as an increasing and rotat-ing vector (00-40) at the end of which is the shutterfield. Thus a spiral scan is achieved with the field of theshutter overlapping itself at each rotation. It is impor-tant, in the sweep of the field, to keep the linear velocityconstant even though the radius of the vector increases.

Errors in this computer are small and limited by gear-ing, synchros, and servo errors.

Gyro CompensationThe spin axis of the gyro is space oriented. The verti-

cal reference attempts to keep it normal to the horizontalplane. As the earth moves at a constant rate, the voltagecorrection to erect the spin axis will be a constant andcan only be obtained by a standoff of the verticalreference. This standoff will produce a tilt error due toearth's rate in pitch and roll as a function of the trueheading of the aircraft. The equations are:

with WE=earth's rateWE cos Lat sin true heading = Pitch errorWE cos Lat cos true heading= Roll error.

An aircraft moving over the earth will create thesame effect as earth's rate. However, it is only a functionof speed and appears as a pitch error due to ship's rate.As the aircraft rotates about the surface of the earth,

radial accelerations are imparted to the vertical refer-ence. Thus a vertical standoff exists here too, whch canbe expressed as:

Coriolis error = 2WEV sin Lat (Roll error).

It is a function of the Latitude, aircraft speed andearth's rate.The gyro errors can be appreciable, unless compen-

sated for. This system has a latitude shaft, and a trueheading shaft. Resolvers on each, plus fixed normaloperational velocities of the aircraft, created circuitssufficient to compensate for 95 per cent of the errors.

System OperationThis system is remotely operated from the master

control panel (Fig. 5). The power and type of body (sunor star) is selected by the power-off filter switch. Allcounters are remotely set by the set control potentiom-

eter which rate controls and sets all counters and theclock. A star switch enables one to choose one of threestar data units. Before flight the navigator sets in theSHA and DEC of the three best bodies for the missionprofile. One body is generally at low altitude for a longperiod of time to obtain the most accurate true heading,while the remaining two units generally are two fairlyhigh bodies (450-60°), all three being approximately 120degrees apart for position fixing. GHA of Aries issimilarly set in at the beginning of the flight withGMT on the clock. The rate switch is used to establishthe solar or sidereal rate for GHA.A manual set panel enables one to set in manual

position information of latitude and longitude, if it isrequired.

In the primary mode, automatic inputs of latitudeand longitude are fed into the KS-50-06, along with theBATH. Celestial data (SHA, DEC, GMT, GHArm)have been set into the system and it is "on." The opera-tor now picks the star best suited for his needs by thestar switch. The system will now automatically and con-tinuously compute the stars pointing commands for thetelescope which is also monitored to the vertical by thevertical gyro. A spiral search scan of + 40 in bearing and±24' in altitude starts, and sweeps the field of viewwithin the above area until the star is found, acquiredand then tracked. The correction signal in bearing fromthe astro tracker now corrects the BATH to obtainaccurate true heading. Synchros on the true headingshaft are used to transmit true heading to externalequipment. The correction signal in altitude is dis-played as miles away or toward the substellar point ofthe star. Both correction signals are used to correct thecomputed star azimuth and altitude, and redirect theastro tracker automatically and continuously so thatthe astro tracker line of sight to the body is maintainedwithin 15 arc seconds.

During flight, the only effort on the part of the navi-gator is to switch from body to body to obtain lines ofposition to enable him to plot his "fix." On the otherhand, if he is only interested in true heading, he leavesthe equipment alone until the star being tracked fallsbelow the lower limit or rises over 45 degrees in altitude(as seen on the indicator display panel), at which timehe sets in the SHA and DEC of a new body from hisAir Almanac. All other settings remain.

All units, except the astro tracker, have been designedto the Air Force modular concept and specifications.These displays and controls are mounted in the naviga-tor's compartment, with only the master control panelwithin reach of his arms. The amplifiers, power sup-plies, junction box and computers are remotely installed.The astro tracker has its own unique design and mustbe located near the upper surface of the aircraft, withonly the 4-inch diameter dome protruding. All com-puters, amplifiers, display units and the astro trackerare hermetically sealed and will operate in an unpres-surized position of the aircraft.

1963 233


Installation is easily accomplished by sliding theunits into the specified racks. The astro tracker requiresits own mount, and need not be precisely aligned to theaircraft longitudinal axis. Generally the astro tracker isused to boresight all other equipments. A special bore-sight fixture is used for this purpose. However, ifalignment is to be made differently, the astro trackermay be aligned in bearing by a pair of differentialsynchros located in the junction box.

Testing of astro trackers is an art in itself. Specialsimulated stars were designed and developed so thattesting could be done from the production bench. Thesedevices approximate star size and spectral response andare calibrated to the star magnitude. These units aremounted on tracker test stands which rotate thetracker in bearing and may also tilt the tracker inpitch and roll. The star simulator is on a yoke over thetracker dome which may be moved in altitude. Thesemeasurements may be made in bearing and altitudeunder various pitch and roll excursions. A console con-taining calibrated electronics enables an operator tomake all measurements and check complete operation.All units of the KS-50-06 are checked individually totheir own specifications and with their own test equip-ment. In this manner complete interchangeability hasresulted.

Accuracy AnalysisThe dynamic accuracy of the MD-I Automatic Astro

Compass is dependent upon the degree to which theastro tracker unit measures the altitude and relativebearing of a celestial body relative to a horizontal plane.The extent to which verticality is achieved is coII-

tingent upon the ability of a vertical gyro to maintaina vertical under dynamic conditions. This gyro, whichis part of and rigidly mounted to the astro tracker unit,slaves the gimbal mounted telescope.

Errors in the indicated vertical (tilt errors) and hencethe platform attitude, which reflect in altitude (EA) andtrue heading (EH) errors, are expressed as follows:

Er, = tan A sin V sin q

EA = sin V cos k,

where

A =altitude of observed bodyV=angular error of the indicated vertical in plane

determined by the true vertical and direction oftilt

-=angle between the plane of vertical error and thevertical plane determined by the line of sight tothe observed body.

Horizontal accelerations have the effect of con-taminating the gravity sensed vertical. Since the timeconstant of the vertical gyro is less than 1 minute andthat of the aircraft greater than 2 minutes, the erectionof the vertical gyro follows the average orientationi of

the pendulous sensing element very closely. Therefore,the verticality of the vertical gyro can instanitaneouslybe in error by as much as " of arc.The net orientation assumed by the pendulous sensing

element is the vectorial sum of the gravitational ac-celeration and horizontal acceleration.

It should be appreciated that the inherent instanta-neous accuracy of the MD-1, under dynamic conditionis,exclusive of the errors developed in the vertical gyro, isbetter than 6 minutes of arc. During navigational runs,the accuracy of true heading tends to approach the 6-minute rms due to the integration of the pendulouswander from the vertical gyro.

True Heading AccuracyThe accuracy of the true heading output is given by

the following formula.

True Heading Error = (\/2V)2 + Hc2 + HT2,

where

V=error in vertical informationi supplied to theMD-1,

Hc=the computer error in azimuth,HT =the tracker error in bearing.

The specification to which the Air Force procures theKS-50-06 calls for Hc=3.2 minutes of arc rms andHT=3.5 minutes of arc rms. Assuming a 5-minute rmsvertical, the error in true heading will be 5.9-minutesrms.

Production experience, however, indicates that thecomputer and the tracker exhibit far greater accuracythan called for in the specifications. Samplings of pro-duction units indicate that the computer and trackererrors are Hc=2.0 minutes and H=2.1 minutes. Usingthese production values, and assuming a 5-miniute rmsvertical input, the accuracy of true heading is close to4.6 minutes of arc rms.

THE ASTRO COMPASS WITH OTHERNAVIGATIONAL SYSTEMS

Accurate true heading is a prime ingredient in othernavigational systems. When astro true heading is addedto systems like Doppler Dead-Reckoning Computers,and inertial platforms or directional gyros, the accuraciesof the total configuration showed remarkable increases.One of the principal sources of error in any dead-

reckoning navigation system is the heading reference.A one degree heading error can result in a positionalerror of about 2 per cent of the distance traveled fromthe last check point. Consequently, accurate headingwill considerably improve the navigational accuracy.

In practice astro true heading is added to the driftangle. Resolution of ground track velocity through thesum of these angles produces velocities N-S and E-W.These velocities, when integrated, produce present posi-

Blumhagen: Stellar Inertial Navigation

tion. As the astro compass uses present position, themore accurate the inputs, the more accurate the trueheading.

Astro true heading does not degrade with time, andis precise at any instant of time. Consequently it is usedto monitor the azimuth or true heading of inertial com-ponents such as platforms and directional gyros. Flighttests utilizing the heading correction to correct aninertial platform has resulted in an extremely accurateand stable navigational system unaffected by aircraftdynamics.The system's capability to measure altitude intercept

provides the navigator with a most useful navigationaltool. During flight any readings of altitude interceptindicate an error in position. Tracking the Pole star orany North or South star will indicate the latitude errorin miles. Tracking an East or West star will indicate alongitude error in miles provided a calculation is madefor the convergence of longitude. Much of this can bedone automatically by resolving altitude interceptthrough azimuth and thus computing the error inlatitude and longitude. By feeding this information backto the dead-reckoning computer it is possible to correctthe assumed position. 'Fhus, a relatively crude dead-reckoning system may be used because it will con-stantly be corrected. Several bodies must be tracked inorder to determine position accurately because thesolution, in order to"be convergent, is dependent upon

the number of bodies and their displacement from eachother. A system of this type is an independent and auto-matic navigational system.

It is also possible to use true heading to compute crosstrack and range miles for particular paths of flight andwhen appropriately used with desired course and driftangles one can correct the autopilot to keep the air-craft on course.Many astro compass systems are in operational use

in most large military aircraft to provide this accurateand basic navigational information.

CONCLUSIONS

The techniques for the precise photoelectric trackingof celestial bodies from aircraft have been well estab-lished. Astro compass navigational systems utilizingthese principles are now off the shelf and operational ina large number of aircraft. Although the describedsensitivities and accuracies are consistent with the re-quirements, increased accuracy (confidential) and im-provements in sensitivity to include full daylight track-ing capability of celestial bodies with relatively largefields of view have been accomplished.Although these systems may be used independently,

they lend themselves for integration into more complexguidance systems for use on aircraft, missiles, and espe-cially in space applications.

Stellar Inertial NavigationApplied to Cruise Vehicles*

VERN A. BLUMHAGENt

Summary-Basic inertial navigation systems used in cruise appli-cations will, in general, experience position errors that continue toincrease with time. A cruise vehicle is considered here to be onewhich may be expected to operate for periods of time between a fewminutes to several months, and at velocities from near zero to Mach 3near the surface of the earth. Various methods of augmenting thebasic inertial system may be applied in order to alter the effect of theerror sources by using information derived from external references.Among these are reference velocity, reference position and stellarinformation. These references may be used individually or in anycombination. This paper will deal primarily with the concepts ofutilizing stellar information in an inertial navigation system with

* Received March 4, 1963.t Inertial Navigation Division, Autonetics, a division of North

American Aviation, Inc., Anaheim, Calif.

some consideration given to the aspects of supplementing the stellarinertial system with reference velocity information.

The effect of utilizing the stellar information is to eliminate thegyro drift as a major source of error in the system. In fact, the applica-tion of proportional plus integral control will maintain the gyro biascompensation in a "tuned-up" condition so that in the event thestellar control is lost due to cloud cover or malfunction, the effect ofthe gyro contribution to system error will be minimized. The stellarinertial system will still experience unbounded errors (errors thatcontinue to increase with time) due to random inputs since theappropriate error model has undamped normal modes; however, thetheoretical ensemble rms position error is now a function of thesquare root of time instead of a linear function of time and it is possi-ble to reduce the significance of the errors for reasonable periods ofoperating time with suitable stellar monitor design. The systemerrors can be bounded with the utilization of reference velocity fordamping the system.

2351963

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The Celestial Tracker as an Astro Compass

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