CA1072658A - Omega-vor/dme positional data computer for aircraft - Google Patents

Omega-vor/dme positional data computer for aircraft

Info

Publication number
CA1072658A
CA1072658A CA238,746A CA238746A CA1072658A CA 1072658 A CA1072658 A CA 1072658A CA 238746 A CA238746 A CA 238746A CA 1072658 A CA1072658 A CA 1072658A
Authority
CA
Canada
Prior art keywords
omega
positional data
signal
vor
dme
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired
Application number
CA238,746A
Other languages
French (fr)
Inventor
Donald H. Baker
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Sperry Corp
Original Assignee
Sperry Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Sperry Corp filed Critical Sperry Corp
Application granted granted Critical
Publication of CA1072658A publication Critical patent/CA1072658A/en
Expired legal-status Critical Current

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Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06GANALOGUE COMPUTERS
    • G06G7/00Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/48Analogue computers for specific processes, systems or devices, e.g. simulators
    • G06G7/78Analogue computers for specific processes, systems or devices, e.g. simulators for direction-finding, locating, distance or velocity measuring, or navigation systems

Abstract

ABSTRACT OF THE DISCLOSURE

Apparatus for combining positional data from OMEGA and VOR/DME radio navigation systems to provide computed positional date corresponding thereto includes a circuit for generating an OMEGA compensation in accordance with the difference between the computed value of the positional data and the VOR/DME value thereof. The computed value is provided by algebraically adding the OMEGA compensation to the positional data from the OMEGA
system. The gain of the OMEGA compensation circuit is adjusted in an inverse relation with respect to the range of the aircraft from the VOR/DME station thus providing high accuracy positional data throughout the enroute flight of the aircraft without the attendant complexities and inaccuracies normally associated with the separate OMEGA and VOR/DME radio navigation aids.

Description

~7'~

BACKGEROU~D OF l~ElE INVENTION
lo Field of the Invention The invention relates to aircra-ft radio based area naviga-tion (RNAV) and particularly with regard to OMEGA and VOR/DME
RNAV aids.
2. Description of the Prior Art VOR/~ME radio navigation aids are utilized to provide latitude and longitude positional da~a to aircraft equipped with suitable RNAV receivers. A VOR/DME station utilizes a conven-tional VOR transmission system to provide bearing data to theaircra~t with regard to the station location as well as a standard ~ME system to provide distance data to the aircraft with regard to the station. Analog and/or digital equipment on board the aircraft converts the bearing and distance data with respect to the fixed location of the s~ation into aircraft latitude and longitude positional data in a well known manner.
The positional data provided by the VOR/~ME RNA~ aid is accurate when the aircraft is relatively close to the VOR/~ME
station but the accuracy deteriorates at substantial distances from the station. Such systems provide accuracies of several tenths of a mile within ~proximately ten miles of a station but have an error of from five to ten miles at distances of 100 to 200 miles from the facility. An error no greater than approxi-mately two miles is desired throughout the enroute flight of the aircraft to permit reduction o~ air route lane widths.
Previous attempts at enhancing enroute accuracy have in~olved the use of dual separated DME systems. Although more accurate than the VOR/DME system at significant distances from the stations, the DME/~ME system requ~es two complete ~ME receivers `~
~ DWE receiver being more complex than a VOR receiver) as well ~

~Z6~8 1 as a significantly more complex way point or leg definition ba~ed on ~he twv DME stations which provide range vectors with a signi-ficant angle with respect to each o~her as compared to the sub~
stantially simpler VOR/DME navigation system. Alternatively, inertial navigation equipment with radio update when the air-craft is close to a station has been used in navigation systems but inertial navigation equipment is extremely expensive compared to the simpler radio systems.
As is known, OM~GA is a low frequency hyperbolic navigation system providing latitude and longitude positional data through-out the worldO The OMEGA system achieves one to two mile accuracy but OMEGA receivers require elaborate equipment to corre~t for propagation effects in order to achieve this accuracy~
such propagation effects typically being of a slowl~ varying diurnal natureO
SU~MARY OF THE INVENTION
The present invention has a principal object to provide accurate positional data from a VOR/~ME radio receiver and a basic OME&A receiver without the elab~rate propagation correction equipment.
This ob~ect is achieved by an OMEGA-VOR/DME positional data computer that provides a computed positional data signal in response to corresponding OMEGA and VOR/DME positional data signals. me computer includes a cir~uit for providing an OMEGA compensation which is algebraically added to the OMEG~
positional data signal to provide the computed positional data signal. The OMEG~ compensation is ~eri~ed in accordance with the difference between the VOR/D~E positional data and the computed positional data. The gain of the OMEGA c~mpensation circuit is controlled in an in~erse relationship with regard to the range of the aircraft from the VOR/~ME station.
' ~ :
3~

- Thus, in accordance with the present invention, there is provided a computer for use in aircraft for providing a computed positional data signal in response to an OMEGA positional da~a signal from an OMEGA system, a VOR/DME
positional data signal from VOR/DME apparatus tuned ~o a stationary VOR/DME
facility and a range signal representative of the distance of said aircraft from said VOR/D~E facility, comprising first summing means responsiv~ to said VOR/DME positiollal data signal and said computed positional data signal for providing a positional data error signal representative of the difference therebetween, OMEGA compensation means responsive to said positional data error signal and said range signal for providing an OMEGA compensation signal with a dependence on said positional data error signal in accordance with an inverse function of said distance, and second summing means responsive to said OMEGA positional data signal and said OMEGA compensation signal for providing said computed positional data signal in accordance with the algebraic sum th:reof. ;~
~,..

"" ~ .
','~,: ' - 3a .~

7;~S~3 BRIEF DESCRIPTION Ol? THE DRAWINGS
Fig. 1 is a schematic block diagram of an OMEGA-VOR/DME
positional data computer instrumented in accordance with the invention;
Fig~ 2 is a schematic block diagram of an OMEGA-~OR/DME
positional data computer instr~ment~d in accordance with the invention with a digital computer;
FigO 3 is a computer program flow diagram ~or instrumenting ~he computations with regard to Fig. 2; and Fig. 4 is a ~low diagram for operating the computer of Fig.
in failure modesO
DESCRIPTIO~ OF TEIE PREFERRED EMBODIME~IT
Referring to Fig. 1, a schematic block diagram of an OMEGA-VOR/DME positional data computer is illustrated. The computer is -disclosed in terms of a latitude computation. It will be apprec~
iated that the longitude computation is pe~formed in identically the same mannerO The latitude positional data from the OMEGA -~
equipment is applied to a terminal 10 and is designated ~ O~O The data is derived ~rom a basic OMEGA ra~io receiver and is processed in a~y convenient and well known manner into the proper format for application to the computer of Fig. lo The latitude data at the terminal 10 is applied as an input to a summing circuit 11 whose output is applied through a two-position switch 12 to provide the computed latitude output ~ c of the computer.
The latitude positional data ~rom the VOR/DME system is applied to a terminal 13 and is designated ~ v~ The ~ v data is derived from the VOR/DME system in any convenient and well known m~nner to provide signals of the appropriate format to the com-puter of ~ig. 1. In a similar manner, the ~ME equipment provides an appropriate range signal R to a terminal 14 in accordance with the range of the aircraft from the VOR/DM~ facility to which the ' ~0 ,~ .

72~
aircraft equipment is tuned. The )\ v data at the terminal 13 is applied as an lnput to a summing circuit 15. The output of the summing circuit 11 is applied subtrac~ively as another input to the summing circuit 15. The output of the summing circuit 15 is applied through a gain block 16 as the input to an integrator 17.
The range signal at the terminal 14 is applied as another input to the block 16 to control the gain thereof. The gain of the block 16, designated as k, is controlled to have a~ inverse func-tional relationship wikh regard to the range from the aircra~t to the VOR/DME facility. The gain k may be inversely proportional to distance ~r may vary in ~ome other ashion than inversely propor- :
tional to distance~ For example, the gain k may vary inversely with the square or cube of the range R for reasons to be later discussed. The blocX 16 i~ in~trumented in any conventional manner to perfoxm the desired function. For example, when the gain k i3 deslgned to vary inversely proportional to R, the block 16 may be instrumented as a multiplier and a circuit for taking ~ :
the reciprocal of ~. The multiplier would then multiply the output from the summing circuit 15 by the reciprocal of R thereby 20 providing the inversely proportional relationship. 5imilar gain cir~uits are disclosed in U.S. patent 3,919,529 issued November 11, 1975 in the names of D. H~ ~aker and L. JO Bowe, entitled "Radio Navigation System", and as~igned to the assignee of the present invention.
The gain block 16 and the integrator 17 comprise an OMEGA
compensation circuit 20 for providing an OMEGA compensation signal designated as ~ . The OMEGA compensation signal ~ from the integrator 17 is applied as an input to the sum~ing circuit 11.
~ hen the OMEGA receiver is inactive or the OMEGA data is invalid a signal is applied from the OMEGA receiver ~not shown~ to .

i~,fJ~ .
.~ "
5~

- . . . '~ .`' : ' ' ' ~' '' ' 1 a terminal 21 to positi~n the switch 12 to the contact opposite that illustrated in Fig. 1. When so positioned the ~ c output is connected directly to the terminal 13 for reasons to be discussed.
The OMEGA invalid signal is also applied to a terminal 22 to clamp the integrator 17 for reasons to be discussed. In a similar manner w~en the VOR/DME equipment is inactive or the VOR/DME data is invalid the integrator 17 is again clamped via the appropriate invalid signal applied to the terminal 22, It will be appreciated from Fig. 1 that ~\C = A~o +d' and that r~
~ k(~ v ~ ~ c) (2) Substituting equation (2) into equation (1) yields ~ c ~ S k(~ v ~ c) ~ ( ) And takingthe derivativa with respect to time yields ~ c ~ o (~ v ~ c)~ ~4) Regrouping the terms yields c ~ c ~ o ~ ~ v- (5) It is therefore appreciated that if k is very large (k~
~? ~ ), then ~ c will tend to track ~ ~, the VOR/DME derived latitude. If k` is very small (k~ ~C ~), then ~ c will tend to track-~ o The ~irst condition is desirable near a VOR/DME
facility where the VOR accuracy is high. The second condition is desirable at large distances where OMEGA is significàntly more ~;
accurate than VORo Consequently, k is made to vary inversely with respect to the distance R from the aircraft to the ~OR/DME
facility, e.g., inversely proportional wl~h respect thereto as ~ollows:

k - kl/R (6 where kl is a constant.

6.

~3726~3 1 Substituting equatio~ (6) ~nto equation (3) yields ~ c = ~ o ~ kl~ ~ dt ~7) Thus it is appreciated that with the appropriate instrumentation for the block 16 as described above, equation (7) describes the implementation of the OMEG~-VoR/DME positional data computer o~
Fig~ 1.
In operation when the VOR/DME and the OMEGA data are valid, the switch 12 is positioned as illustrated in Fig. 1 and the integrator 17 is unclamped~ ~hen the aircraft is relatively near a VOR/DME facility, the gain through the block 16 is adjuste~ to be high and therefore the computer of Fig. 1 rapidly orces the output ~ rom the integrator 17 to be equal to the difference between the OMEGA derived data and the terminal 10 and the VOR/DME derived data at the terminal 13. Thus the term ~ is a compensation that is added to the OMEGA data by means of the summing circuit 11 to provide the computed data ~ c which at close proximity to a VOR/~ME acility is equal to the accurate ~ v : data~ As the aircraft départs from the vicinity of a ~OR/DME ~:
station, the gain through the blocX 16 is diminished. When the aircraft is at a substantial distance from the VOR/DME station the gain through the block k is small so that the inaccuracies of the ~ v data at the large enroute distànces from the VOR/DME
facility have a diminished e~fect on the value of the OMEGA
compensations S stored in the integrator 17. Thus it is appreciated that although the accuracy of the ~ ~ data has deteriorated, the value o the OMEGA compensation 3 that is added to the OMEGA data still retains the accuracy accumulated when the aircraft was . .
; near the VOR/D~E station because of the decoupling effect of the diminished gain through the block 16. Tt will be appreciated that a1though an inversely proportional relatmship as discussed a~ove ~.
with regard to the block 16 will provide adequate decoupling, the 7~

~72658 1 scale ~actor k utilized in determining the relative authorities of the OMEGA and the VOR/DME data may be varied in some other fas~on than inversely proportional to distance. For example, k may bevaried inversely with the square or cube of the distance to more sharply decouple the OMEGA data at long distances from the VO~/DME facility~ In the event of failure o the VOR/DME equip-ment which invalidates the associated data or in the event of momentary in~ruption of the VOR/DME data such as when tuning to a new station, a sigIlal on the lead 22 clamps the integrator 17, thus fixing the presently stored value of the OMEGA compen-sation ~ . Thus the OMEGA data ~ O at the terminal 10 continues to be properly compensated by the ixed value of ~ which is the last valid value thereof.
Similarly, when the OMEGA dat~ ~ O is invalid, a signal at the terminal 22 again clamps the integrator 17 and a signal at the terminal 21 transfers the wiper of switch 12 to the position opposite that illustrated in Fiy. 1 to connect the output ~ c directly to the VOR/DME data ~ v at the terminal 13~ Alternatively storage means tnot sho~n3 may be utilized to store the latest ; 20 value of ~ O to be utilized in the event of a failure in the ; OM~GA data. The integrator 17 is clamped when the OMEGA data fails to preserve thè last valid value of the OMEGA compensation for use when the system is again functioning properly.
When both the VOR/DME and the OMEGA dataare invalid, the output of the computer of Fig. 1 may be switched by means not shown to dead reckoning equipment such as ~hat disclosed in the aforesaid s~ .- ~ O
It will be appreciated fro~ the ~oregoing that the computer of Fig~ 1 utilizes complementary mixing of the OMEGA
and VOR/DME data to combine the d~sirable characteri~tics of ;~
each navigation source to provide high accuracy enrou~e latitudP

and longitude po~itional data while not requiring complex OMEGA

.

~LCI'7~6~3 propagation corrections. Thus a simple OMEGA receiver is utilized without the usual highly complex electronic circuitry for correct-ing the diurnal errors associated with OMEGA transmissions. It will furthermore be appreciated that the elements of Fig. 1 may be either analog or digital components with appropriately con-figured signals being applied to the terminals 10, 13 and 14, suit-able conventional signal conversion being utilized when necessary~
The computer of Fig. 1 was described in texms of discrete analog or digital components. It will be appreciated that the present invention may be embodied by a programmed digital computer for implementing the functions of the present invention repxesented, for example, by equation (7).l Referxing now to ~ig. 2, a stored ~`
program digital computer is schematically represented at 30 having the OMEGA positional data Ao~ the VOR/DME positional data v and the range of the aircraft to the VOR/VME facili*y R applied at terminals 31, 32 and 33 respectively. The computer 30 is pro-grammed in a manner to be described to provide the computed posi~
tional data ~ c as indicated by the legend~ The embodiment of Fig. 2 may operate in failure modes in a manner similar to that described above with regard to Fig. 1 in response to a VOR/DME
invalid signal at a termina~ 34 and an OMEGA invalid signal at a terminal 35. It will be appreciated that signals of appropriate formats ma~ be applied to the terminals 31-35 or suitable conven-tional conversion performed thereon by apparatus not shown or by well known programs stored within the computer 30.
Referring now to Fig. 3, the step by step computation o the computed latitude ~ c performed by the compu~er 30 is illustrated.
During each computation iteration, the computer enters the computational program flow at 40 by going to the initial address of the computational subroutine as stored in the memory o~ the computer 30. At block 41 of the flow chart the current value of the OMEGA data /~O is corrected by adding the last stored OMEGA

" ' - - :- . .. ,. , - , ~7Zti~i8 1 compensation ~to ~o~m a temporary computed la-titude ~ c~ At block 42 ~ c is subtracted ~rom the current value of the V~/DME
latitude to determine the error therebetween ~ ~ . In block 43 the gain k is computed as a function of the distance R from the VOR/DME facility where kl is a constant. In block 44 the latitude error ~ ~ is multiplied by the gain k to obtai~ the intergrand A. In block 45 the integration is performed by multiplying the intergrand ~ by ~ t, the time since the last correction, and adding the result to the previous value of the OMEGA correction ~ to form an updated ~ . In block 46 the computed latitude ~ c is obtained by adding the updated OMEGA correction ~ to the O~EGA
derived latitude ~ O. Since block 46 completes a computational iteration the program exists at 47.
It will be appreciated that the program segments associated with each o~ the blocks 40-47 are readi}y prepared by a normally skllled programmer and will not be shown herein for brevity. It will further more be appreciated that most o~ the legends within the blocks of Fig. 3 are in the format of program statements of a compiler programming lan~uage such as FORT~AN
Referring now to Fig. 4, a ~low chart for the operation of the embodiment of Fig. 2 in failure modes is illustrated. The program enter~ at 50 and at 51 tests the state of the signal applied to the terminal 34 to determine if the VOR/DME data is -~
valid. If the data is valid the program proceeds to block 52 to similarly test the validity o~ the OMEGA data in response to ; the signal at the terminal 35. If both the VOR/DME and the OMEGA
data are valid the program proceeds to the block 53 wherein the computations discussed with regard to Fig. 3 are performedO ~ -Since the computational iteration is then complete, the program e~its at 540 If, however, the VOR/DME data is found to be invalid in the block 51, the program proceeds to a block 55 ~J~ich is similar to the ~lock 52 in that the vaIidity o~ the OMEGA data -- . - . - - -. . : . :
. . ~ . . . : . . . . .

~7~S~

1 is tested. I~ the OMEGA data is valid, although the VOR/DME
data is invalid, the program proceeds to a block 56 wherein the computed latitude data ~ c is obtained by updating the current and valid OMEGA data ~ with the last computed OMEGA compensakion ~. The program then proceeds to the exit block 54. If the program reaches the block 52 and ~inds the OMEGA data invalid, although the VOR~DME data is valid, khe program proceeds to a block 57 that utilizes the VGR/DME data ~ v directly to provide the computed data ~ c whereafter the program proceeds to the exit block 54. I~, however, neither the VOR/DME nor the OMEG~
data is valid, the program proceeds through the blocks 51 and 5 to a block 60 wherein dead reckoning computations are performed ~ 75i P~ 7~e7~3~ ~q of the type discussed in the aforesaid p~-~e~ ~iea~i~n--S~ NO
4~-f -~2~ whereafter the program proceeds to the exit block 54.
It will be appreciated from the foregoing that the present invention utiliz~s the OMEGA equipment operating in a relatively simple dif~erential mode to provide hig~ enroute accuracy without the necessity for the usual complex and expensive diurnal error correction electronic circuitry. The VOR/DME positional data is given an authority which is an invers~ function of the distance from the station. Within approximately ten miles from the station the VOR/DME data is strongly used to update the OMEGA data~ At ~;~
large distances the OM~GA data displacement from the last update is utilized to provide the computed position with high accuracy and without propagation corrections7 .

Claims (5)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:
1. A computer for use in aircraft for providing a computed positional data signal in response to an OMEGA positional data signal from an OMEGA system, a VOR/DME positional data signal from VOR/DME apparatus tuned to a stationary VOR/DME facility and a range signal representative of the distance of said aircraft from said VOR/DME facility, comprising first summing means responsive to said VOR/DME positional data signal and said computed positional data signal for providing a positional data error signal representative of the difference therebetween, OMEGA
compensation means responsive to said positional data error signal and said range signal for providing an OMEGA compensation signal with a dependence on said positional data error signal in accordance with an inverse function of said distance, and second summing means responsive to said OMEGA positional data signal and said OMEGA compensation signal for providing said computed positional data signal in accordance with the algebraic sum thereof.
2. The computer of claim 1 in which said OMEGA compensation means comprises gain adjusting means responsive to said positional data error signal and said range signal for providing said positional data error signal at a gain adjusted in accordance with said inverse function of said distance, and integrator means coupled to said gain adjusting means for providing said OMEGA compensation signal in accordance with the integral of said gain adjusted positional data error signal.
3. The computer of claim 2 further including means for clamping said integrator in response to a signal indicative of invalidity of said VOR/DME positional data signal.
4. A computer of claim 2 further including means for obtaining said computed positional data signal directly from said VOR/DME
positional data signal in response to a signal indicative of invalidity of said OMEGA positional data signal.

12.
5. A computer for use in aircraft for providing a com-puted positional data signal in response to an OMEGA posi-tional data signal from an OMEGA system, a VOR/DME positional data signal from VOR/DME apparatus tuned to a stationary VOR/DME facility and a range signal representative of the distance of said aircraft from said VOR/DME facility, com-prising means for storing a previous value of an OMEGA compensa-tion signal, first means for adding the current value of said OMEGA positional data signal to said previous value of said OMEGA compensation signal to provide a temporary computed positional data signal, second means for subtracting the value of said temporary computed positional data signal from the current value of said VOR/DME positional data signal to pro-vide a positional data error signal, third means for computing a gain value in accordance with an inverse function of said distance, fourth means for multiplying the value of said positional data error signal by said gain value to provide an integrand value, fifth means for multiplying said inter-grand value by the time elapsed since the computation for said previous value of said OMEGA compensation signal and for adding the result to said previous value of said OMEGA
compensation signal to provide an updated value of said OMEGA
compensation signal, thereby performing a time integration of said positional data error signal at a gain determined by said third means, and sixth means for adding said updated value of said OMEGA compensation signal to said current value of said OMEGA positional data signal to provide said computed positional data signal.
CA238,746A 1975-01-27 1975-10-31 Omega-vor/dme positional data computer for aircraft Expired CA1072658A (en)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US05/544,105 US3941983A (en) 1975-01-27 1975-01-27 OMEGA-VOR/DME positional data computer for aircraft

Publications (1)

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CA1072658A true CA1072658A (en) 1980-02-26

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US (1) US3941983A (en)
JP (1) JPS5856835B2 (en)
CA (1) CA1072658A (en)
DE (1) DE2602817A1 (en)
FR (1) FR2298804A1 (en)
GB (1) GB1528180A (en)
IT (1) IT1062041B (en)

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* Cited by examiner, † Cited by third party
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JPS57159310A (en) * 1981-03-28 1982-10-01 Nissan Motor Co Ltd Running inductive device for car
FR2561050B1 (en) * 1984-03-07 1986-09-19 Commissariat Energie Atomique METHOD FOR MONITORING VEHICLE MOVEMENTS FROM A CENTRAL STATION
GB2270438B (en) * 1992-09-08 1996-06-26 Caterpillar Inc Apparatus and method for determining the location of a vehicle
US6999779B1 (en) 1997-02-06 2006-02-14 Fujitsu Limited Position information management system
CN105651277B (en) * 2016-01-06 2018-08-14 中国航空无线电电子研究所 A method of for continental rise navigation platform needed for selection region navigation

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US3103579A (en) * 1956-04-03 1963-09-10 Network
US3070796A (en) * 1959-12-07 1962-12-25 Gen Precision Inc Dual aerial navigation system
US3308278A (en) * 1963-02-26 1967-03-07 John H Davis Latitude-longitude computer
FR1605110A (en) * 1963-09-28 1973-03-16
GB1153847A (en) * 1967-03-27 1969-05-29 Hughes Aircraft Co Navigational Computing System
US3564222A (en) * 1968-07-01 1971-02-16 Bendix Corp Digital function generator solving the equation f(x) {32 {0 mx {30 {0 b
DE1940620A1 (en) * 1969-08-09 1971-02-11 Teldix Gmbh Navigation system for aircraft, especially for aircraft taking off and landing vertically
US3720820A (en) * 1971-03-18 1973-03-13 Tektranex Inc Calculator with a hierarchy control system
US3821523A (en) * 1973-05-07 1974-06-28 Sierra Research Corp Aircraft locating system using agile tacan vortac dme

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GB1528180A (en) 1978-10-11
US3941983A (en) 1976-03-02
IT1062041B (en) 1983-06-25
JPS5193844A (en) 1976-08-17
DE2602817C2 (en) 1987-12-17
DE2602817A1 (en) 1976-07-29
FR2298804A1 (en) 1976-08-20
FR2298804B1 (en) 1982-12-17
JPS5856835B2 (en) 1983-12-16

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