electronics

Article Possibilities of Increasing the Low Altitude Measurement Precision of Airborne

Ján Labun 1 , Martin Krch ˇnák 1, Pavol Kurdel 1 , Marek Ceškoviˇcˇ 1, Alexey Nekrasov 2,3,4,* and Mária Gamcová 5

1 Faculty of Aeronautics, Technical University of Košice, Rampová 7, Košice 041 21, Slovakia; [email protected] (J.L.); [email protected] (M.K.); [email protected] (P.K.); [email protected] (M.C.)ˇ 2 Institute for Computer Technologies and Information Security, Southern Federal University, Chekhova 2, Taganrog 347922, Russia 3 Department of Radio Engineering Systems, Saint Petersburg Electrotechnical University, Professora Popova 5, Saint Petersburg 197376, Russia 4 Institute of High Frequency Technology, Hamburg University of Technology, Denickestraße 22, Hamburg 21073, Germany 5 Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, Košice 042 00, Slovakia; [email protected] * Correspondence: [email protected]; Tel.: +7-8634-360-484

 Received: 7 August 2018; Accepted: 9 September 2018; Published: 11 September 2018 

Abstract: The paper focuses on the new trend of increasing the accuracy of low altitudes measurement by frequency-modulated continuous-wave (FMCW) radio altimeters. The method of increasing the altitude measurement accuracy has been realized in a form of a frequency deviation increase with the help of the carrier frequency increase. In this way, the height measurement precision has been established at the value of ±0.75 m. Modern digital processing of a differential frequency cannot increase the accuracy limitation considerably. It can be seen that further increase of the height measurement precision is possible through the method of innovatory processing of so-called height pulses. This paper thoroughly analyzes the laws of height pulse shaping from the differential frequency presented by the number that represents the information about the measured altitude for this purpose. This paper presents the results of the laboratory experimental altitude measurement with the use of a so-called double-channel method. The application of obtained results could contribute to the increase of air traffic safety, mainly in the phase of the approaching for landing and landing itself.

Keywords: airborne radio ; methodological error; increase of measurement accuracy; height pulses; dual-channel method

1. Introduction High precision of a flight height measurement is required at low altitude, mainly in the phase of aircraft approaching for landing and landing. For this purpose, an FMCW airborne radio altimeter ( altimeter) is used for measuring the low altitudes [1]. When the flight height is measured, the principle of radiolocation with the evaluation of the time delay τ between the transmitted and received signal of a radio altimeter is used [2,3]. It can be presented that the flight altitude H directly corresponds to the delay of a received signal. The time delay is not evaluated directly for radio altimeters, but it is performed indirectly through the differential frequency Fd. The differential frequency is created between the immediate value of the

Electronics 2018, 7, 191; doi:10.3390/electronics7090191 www.mdpi.com/journal/electronics Electronics 2018, 7, x FOR PEER REVIEW 2 of 9

Electronicsand it can2018 ,be7, 191presented that the flight altitude indirectly corresponds also to the differential2 of 9 frequency. frequencyIn this of way, the transmitted the complex and measurement time-delayed receivedof the very signal. short The times dependence when measuring is linear and the it cansmall be presentedheights is thattransformed the flight altitudeinto a indirectlysimple measuremen correspondst alsoof the to thedifferential differential frequency. frequency. The relation betweenIn this the way, measured the complex altitude measurement and the differentia of thel very frequency short timesis defined when by measuring a so-called the “basic small heightsformula is of transformed radio altimeter” into a simple measurement of the differential frequency. The relation between the measured altitude and the differential frequency8Δf F is defined by a so-called “basic formula of F = M H , (1) radio altimeter” d c 8∆ f FM Fd = H, (1) where Δf is the frequency deviation, FM is the modulationc frequency c is the speed of light. whereFor∆f ais classical the frequency altitude deviation, measurementFM is method, the modulation the measurement frequency accuracyc is the speed is defined of light. by the value of so-calledFor a classical critical altitudealtitude measurementΔH of a radio method,altimeter. the The measurement critical altitude accuracy presents is defined a minimal by the altitude value ofrange so-called which critical can be altitude registered∆H byof a radio altimeter.altimeter and The displayed critical altitude for a pilot. presents The a critical minimal altitude altitude is rangealso connected which can bewith registered the radio by aaltimeter radio altimeter measurement and displayed accuracy for a pilot.±ΔH. TheIt is critical possible altitude to derive is also connectedmathematically with thethat radio the altimeter critical measurementaltitude depends accuracy on the±∆ Hfrequency. It is possible deviation to derive of mathematicallya transmitted thathigh-frequency the critical altitudesignal according depends to on the the following frequency formula deviation [3]. of a transmitted high-frequency signal according to the following formula [3]. Δ = c ∆HH= .. (2) (2) 8∆Δff The dependenceThe dependence can also can be also presen be presentedted graphically graphically [4,5] [(Figure4,5] (Figure 1). 1).

Figure 1. Dependence of the critical altitude ∆ΔH on the frequency deviation ∆Δff..

From FigureFigure1 1 we we can can see see that that at at the the low low frequency frequency deviation deviation of of 10–20 10–20 MHz MHz the the critical critical altitude altitude of 4–2of 4–2 m takesm takes place. place. This This value value is relativelyis relatively significant. significant. Therefore Therefore the the oldest oldest radio radio altimeters altimeters (ALT (ALT 1 in 1 Figurein Figure1) provided 1) provided the measurement the measurement accuracy accuracy of about of ±about2.2 m ±2.2 only. m The only. medium The frequencymedium frequency deviation ofdeviation 20–40 MHz of 20–40 provides MHz a relativelyprovides lowera relatively critical lower altitude critical of 2–1 altitude m. Some of older 2–1 typesm. Some of radio older altimeters, types of usedradio untilaltimeters, recently used (ALT until 2), providedrecently (ALT the accuracy 2), provided of about the ±accuracy1.5 m. Recent of about radio ±1.5 altimeters m. Recent use radio the ratheraltimeters high use frequency the rather deviation high frequency of about 50deviation MHz at of which about the 50 critical MHz at altitude which isthe about critical 0.75 altitude m that is ratherabout 0.75 low. m Therefore, that is rather the recent low. typesTherefore, of radio the altimetersrecent types (ALT of 3)radio provide altimeters the measurement (ALT 3) provide accuracy the ofmeasurement about ±0.75 accuracy m [6,7]. of about ±0.75 m [6,7]. From a historicalhistorical viewpoint, the accuracy is increasedincreased for approximately fiftyfifty percent at each stage of radioradio altimetersaltimeters development. Going Going the the same same way, way, to decrease the critical altitude of the ALT 33 stagestage inin twicetwice toto 0.3750.375 mm thethe frequencyfrequency deviationdeviation of 100 MHz is required to reach a new stage (ALT(ALT 4)4) forfor thethe measurementmeasurement accuracyaccuracy ofof aboutabout ±±0.30.37575 m. From this viewpoint, the paper offers a more simplesimple solutionsolution on on how how to to obtain obtain the the precision precision of theof the ALT ALT 4 stage 4 stage maintaining maintaining the recently the recently used valueused value of frequency of frequency deviation deviation of 50 MHzof 50 MHz [8,9]. [8,9].

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2. Materials and Methods Critical altitude is presentedpresented byby minimalminimal altitudealtitude differencedifference whichwhich thethe radioradio altimeteraltimeter cancan recognize.recognize. As As the the measurement measurement accuracy accuracy depends depends on on the the value value of ofthe the critical critical altitude, altitude, it should it should be beconsidered considered in more in more detail. detail. One stablestable heightheight pulsepulse NN permanently develops (at increase) or terminates (at decrease) in thethe rangerange ofof measurementmeasurement of of the the critical critical altitude. altitude A. A total total number number of permanentof permanent height height pulses pulsesN carries N carries the informationthe information about about the measured the measured altitude. altitude. It can beIt can understood be understood so that ifso we that divide if we the divide total measured the total altitudemeasuredH intoaltitude the criticalH into the altitude critical sections; altitude their sections; number thei willr number correspond will correspond to the measured to the altitudemeasured as Naltitude= H/∆ Has. TheN = presentedH/ΔH. The number presented of pulses numberN develops of pulses (or terminates)N develops within (or terminates) one modulation within period one TmodulationM and modulation period T frequencyM and modulationFM. The resulting frequency evaluated FM. The differentialresulting evaluated frequency differentialFd is proportional frequency to measuredFd is proportional altitude to and measured given by altitude the multiplication and given ofby the the number multiplication of pulses of andthe modulationnumber of pulses frequency and Fmodulationd = N × FM frequency. A discrete Fd (step-like)= N × FM. A change discrete of (step-like) the number change of permanent of the number height of pulses permanent is shown height in Figurepulses2 is by shown a thick in line. Figure Five 2 changesby a thick of theline. number Five changes of permanent of the number height pulses of permanent are shown height within pulses the presentedare shown altitude within the range presented in Figure altitude2. range in Figure 2.

Figure 2. Relation between the critical altitudealtitude and measurement accuracy.

ItIt is is possible possible to to derive derive a aharmonic harmonic course course of a of differential a differential low-frequency low-frequency signal signal [1] from [1] frommathematical mathematical analysis analysis of mutual of mutual ratios, ratios, two two high-frequency high-frequency frequency-modulated frequency-modulated signals, transmittedtransmitted andand time-delayedtime-delayed receivedreceived signalsignal ofof aa radioradio altimeter.altimeter. From thethe viewpointviewpoint of aa radioradio altimeteraltimeter operationoperation principle, the harmonic differential signal, whichwhich carriedcarried the the information information about about measured measured height height in processing in processing circuits, changescircuits, intochanges an orthogonal into an discreetorthogonal differential discreet signal.differential Height signal. pulses, Height which pulses, are the which object are of this the paper’sobject of analysis, this paper’s are shaped analysis, by thisare shaped discreet by differential this discreet signal. differential Height pulses signal. are Height shaped—alternatively pulses are shaped—alternatively creating and ceasing, creating from and the orthogonalceasing, from differential the orthogonal signal, differ each timeential the signal, time each course time of thethe differentialtime course signal of the passes differential a zero signal point. Thepasses number a zero of point. height The pulses numberk remains of height constant pulses at thek remains constant constant height. Theirat the numberconstant increases height. Their with increasingnumber increases height, andwith alternatively, increasing height, their number and altern decreasesatively, with their decreasing number decreases a height. Thewith increase decreasing of a measureda height. The height increase is considered. of a measured From theheight mathematical is considered. analysis From [1 the], the mathematical height of the analysis creation [1], pulses the H and the height of the cessation pulses H can be derived heightv of the creation pulses Hv and the heightz of the cessation pulses Hz can be derived λ k −− λ k −− = λ0 22k 1 =λ0022k 11 Hvv = ,, HHz z= ,, (3) (3) 8 1 +ξξ 88 11−−ξξ wherewhere λλ00 is the carrier wavelength, ξ isis thethe relativerelative valuevalue ofof thethe frequencyfrequency deviation,deviation, ξξ= = ∆Δff/ff0.0 . A heightheight range range of of the the duration duration of relevantof relevant height height pulse pulseS is determined S is determined as the difference as the difference between thebetween height the the height cessation the cessation and creation and pulsescreation pulses λ ξ S = H − H = λ00 ()2k −1 ξ . S = Hz z− Hv v= (2k − 1) 2 .(4) (4) 44 1 ++ξξ2

From EquationEquation (4) it cancan bebe seenseen thatthat thethe heightheight rangerange increasesincreases withwith increasingincreasing thethe numbernumber ofof height pulses.pulses. A height range of the creation of different pulses F is defined as the difference of heights between two consecutive creating pulses

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Electronics 2018, 7, x FOR PEER REVIEW 4 of 9 A height range of the creation of different pulses F is defined as the difference of heights between two consecutive creating pulses λ ()+ − λ − λ = − = 0 2 k 1 1 − 0 2k 1 = 0 F H v2 H v1 , (5) λ 82(k +11+)ξ− 1 λ8 12k+−ξ 1 4()1+λξ F = H − H = 0 − 0 = 0 , (5) v2 v1 8 1 + ξ 8 1 + ξ 4(1 + ξ) where Hv1 is the height of the creation of the first pulse, Hv2 is the height of creation of the second wherepulse. Hv1 is the height of the creation of the first pulse, Hv2 is the height of creation of the second pulse. A heightheight rangerange of of the the cessation cessation of differentof different pulses pulsesE is definedE is defined as the differenceas the difference of heights of betweenheights betweentwo consecutive two consecutive ceasing pulses ceasing pulses λ 2()k +1 −1 λ 2k −1 λ E = H − H =λ0 20(k + 1) − 1 − λ00 2k − 1= 0λ0 , E = Hz −z 2H =z1 − ξ − − ξ = ()− ξ ,(6) (6) 2 z1 8 8 11− ξ 88 11 − ξ 4 41(1 − ξ)

By defining defining the relations for the height of the creationcreation and cessation of pulses, it is possible to display the shaping of different height pulses in the general height range H (Figure3 3).). InIn thethe heightheight range 1 Δ∆H, it can be seen that with increasing the heightheight of one unstable pulse, the height range of duration continually grows, permanently creates andand ceases.ceases.

Figure 3. AA flow flow chart of the formation of permanent and non-permanent pulses.

It can also be observed from Figure 33 that that thethe heightheight sectionssections ofof creatingcreating pulsespulses havehave aa constantconstant value similarlysimilarly to to the the height height pulses pulses of cessationof cessation of the of heightthe height pulses. pulses. The height The height interval interval of the creation of the creationof pulses of is smallerpulses is than smaller the height than intervalthe height of theinterval cessation of the of pulses.cessation The of differencepulses. The produces difference the parameterproduces the±ξ parameter. ±ξ. The result of this fact is that from aa certaincertain heightheight thethe pulsespulses startstart toto mutuallymutually overlap.overlap. At the height where thethe pulsespulses startstart toto overlap,overlap, one one permanent permanent pulse pulse is is created created in in the the height height range range 2∆ 2HΔ.H But. But at atthe the same same time, time, with with further further height height growth, growth, one one (number (number twotwo inin thethe row)row) unstable pulse is is created. created. After crossingcrossing thethe heightheight range range 2 ∆2ΔHH, the, the situation situation repeats repeats in thein the range range 3∆ H3Δ. TheH. The only only difference difference is that is thatthere there are two are permanenttwo permanent pulses pulses and oneand (number one (numbe threer three in the in row) the unstablerow) unstable pulse pulse in the in range the range 3∆H. 3ΔH.In order to be able to portray two overlapping pulses in a more simple way, the height pulses in the bottomIn order part to be of able the figure to portray have two a different overlapping amplitude. pulses (The in a more size of simple the portrayed way, the amplitude height pulses is not in theconnected bottom with part theof the amplitude figure have of the a different actual height amplit impulse,ude. (The which size isof constant.) the portrayed amplitude is not connectedAt a fluent with the change amplitude of measured of the actual altitude height within impulse, the range which of critical is constant.) altitude, the creation of the permanentAt a fluent height change pulses of is measured accompanied altitude by the within development the range and of terminationcritical altitude, of unstable the creation height of pulse the permanentNV (within allheight ranges pulses of the is criticalaccompanied altitude). by Thethe unstabledevelopment height and pulse termination does not carryof unstable the measured height pulsealtitude NV but (within vice versaall ranges causes of inaccuracy the critical in thealtitude). altitude The measurement. unstable height Discreet pulse change does ofnot the carry number the measuredof unstable altitude height pulses but vice is presentedversa caus byes ainaccuracy thin line in in Figure the altitude2. There measurement. are seven changes Discreet of the change unstable of theheight number pulses of inunstable the range height of criticalpulses altitudeis presented in the bypresented a thin line altitudein Figure range. 2. There This are phenomenon seven changes is ofbased the onunstable a physical height principle pulses usedin the in range the airborne of critical FMCW altitude radio in altimeters the presen [2ted,10]. altitude range. This phenomenonBased on is a based thorough on a mathematicalphysical principle analysis used of in the thecreation airborne of FMCW permanent radio andaltimeters unstable [2,10]. height pulsesBased [2], iton is possiblea thorough to suggestmathematical and realize analysis a new of methodthe creation for increasing of permanent the altitude and unstable measurement height pulsesaccuracy. [2], it This is possible method to is suggest a so-called and realize double-channel a new method radio for altimeter increasing which the altitude uses an measurement appropriate accuracy. This method is a so-called double-channel radio altimeter which uses an appropriate procedure of assembling two differential signals mutually phase-shifted and created by the same radio altimeter. In this way, more frequent change of two unstable pulses into one permanent height

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Electronicsprocedure 2018 of, 7 assembling, x FOR PEER twoREVIEW differential signals mutually phase-shifted and created by the same radio5 of 9 altimeter. In this way, more frequent change of two unstable pulses into one permanent height pulse pulsecan be can secured. be secured. As a result, As a result, the original the original value of value the radioof the altimeter radio altimeter critical altitudecritical altitude decreases decreases in twice. inThe twice. basics The of thebasics double-channel of the double-channel method are method based ar one thebased theory on the of thetheory creation of the of creation critical altitude, of critical as altitude,a result ofas thea result alternating of the alternating creation and creation termination and termination of unstable of height unstable pulses. height pulses. TheThe presented lawlaw ofof the the unstable unstable pulses pulses creation creation in ain low a low altitude altitude range range can be can used be inused the designin the designand realization and realization of a double-channel of a double-channel radio altimeter, radio altimeter, when the when methodological the methodological error of error the altitude of the altitudemeasurement measurement decreases decreases in twice in (Figure twice4 (Figure)[11]. 4) [11].

FigureFigure 4. 4. HeightHeight pulses pulses creation creation in in a a double-channel double-channel radio radio altimeter. altimeter.

TheThe double-channel double-channel radio radio altimete altimeterr has has two two equal equal and and parallel parallel wo workingrking channels channels of of processing processing thethe differential differential signal fromfrom whichwhich oneone hashas an an artificially artificially time time delay delay of of processing processing signal signal by by the the value value of ofλ0 λ/4.0/4. Both Both channels channels must mustbe be technicallytechnically designeddesigned inin aa wayway thatthat the same signal on the input shapes shapes thethe same same height pulses on the output.output. A A ti timeme delay of the processedprocessed signalsignal byby valuevalue λλ00/8 in in the the secondsecond channel channel causes causes a a mutual mutual shif shiftt of of the the creation creation of of those those two two un unstablestable height height pulses. pulses. Alternation Alternation ofof the creation andand terminationtermination of of unstable unstable pulses pulses within within both both channels channels mutually mutually fit within.fit within. When When the theheight height within within the rangethe range of critical of critical altitude altitude∆H1 grows,ΔH1 grows, both pulsesboth pulses within within the range the range of the of first the half first of half∆H1 of/2 Δ fitH within1/2 fit within each other each and other within and thewithin range the of range the second of the half second of ∆ Hhalf1/2, of they ΔH1 start/2, they to mutually start to mutuallyoverlap. Thisoverlap. is the This result is the of increasing result of increasing the height the interval height of interval lasting of of the lasting unstable of the pulse. unstable In this pulse. way, Inthe this original way, the critical original altitude critical∆H altitude1 divides ΔH into1 divides two halves into two∆H halves1/2. The ΔH original1/2. The valueoriginal of ∆valueH1 divided of ΔH1 dividedinto two into halves two actuallyhalves actually present present two new two values new values of critical of critical altitude altitude∆H2 in Δ aH double-channel2 in a double-channel radio radioaltimeter. altimeter. The height The height pulses pulses creation creation in a double-channel in a double-channel radio altimeter radio altimeter and the and logic the of thelogic decrease of the decreaseof its methodological of its methodological error are error illustrated are illustrated in Figure 4in. Figure 4.

3. Results and Discussion 3. Results and Discussion Experimental double-channel radio altimeter has been constructed in a laboratory with the use Experimental double-channel radio altimeter has been constructed in a laboratory with the use of two classical one-channel radio altimeters operating at the carrier frequency f 0 = 444 MHz with of two classical one-channel radio altimeters operating at the carrier frequency f0 = 444 MHz with the f frequencythe frequency deviation deviation Δf =∆ 17= 17MHz. MHz. For For the the purpose purpose of of experimental experimental measurement, measurement, those those radio radio altimetersaltimeters have beenbeen disassembled disassembled mechanically mechanically and and re-configured. re-configured. A block A block diagram diagram of those of those two radio two radioaltimeters altimeters connection connection into one into double-channel one double-channel radio altimeter radio altimeter is shown is inshown Figure in5. Figure The first 5. altimeterThe first altimeter(1st channel) (1st workedchannel) asworked a complete as a complete construction construction in the original in the connection. original connection. The second The altimeter second altimeter(2nd channel) (2nd waschannel) adjusted was soadjusted that to useso that only to the use circuit only the of acircuit high-frequency of a high-frequency converter, converter, the circuit ofthe a circuitlow-frequency of a low-frequency amplifier, and amplifier, the circuit and of shapingthe circui thet of height shaping pulses the of height differential pulses frequency. of differential frequency.

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Electronics 2018Electronics, 7, x FOR PEER2018, 7REVIEW, x FOR PEER REVIEW 6 of 9 6 of 9

Figure 5. LaboratoryFigure 5.5. double-channel LaboratoryLaboratory double-channeldouble-channel radio altimeter radio block altimeter diagram block created diagram from createdtwo one-channel from twotwo one-channelone-channel radio altimeters:radio LFG altimeters: is the low-frequency LFG LFG is is the the low-frequency low-frequency generator, HFG generator, generator, is the high-frequency HFG is the high-frequency generator, PS generator, 90° is PS 9090°◦ is the 90-degreethe phase 90-degree shifter, phase At is thshifter, e attenuator, At is th the eM attenuator, is the mixer, M DSis the is themixer, signal DS divider,is the signal LFA divider, is the LFA is the low-frequencylow-frequency amplifier, ADC amplifier,amplifier, is the analog-to-digita ADCADC isis thethe analog-to-digitalanalog-to-digital converter, SSl converter,is the signal SS summator, is the signal PC summator, is the PC is the pulse counter,pulse DCA counter,counter, is the DCA DCAdirect is is thecurrent the direct direct amplifie current currentr, amplifier, TA amplifie is the TA r, istransmitti TA the transmittingis theng transmittiantenna, antenna, ngRA antenna,is RA the is the RA receiving is the , H is the altitude, are the original blocks of a one-channel radio altimeter receiving antennaantenna,receiving, H H isantenna is the the altitude, altitude, are thethe originaloriginalblocks blocks of of a a one-channel one-channel radio radio altimeter altimeter not used in the not used in thelaboratorynot laboratory used in double-channel the double-channel laboratory double-channel radio radio altimeter. altimeter. radio altimeter.

Both channelsBoth have channelschannels the have commonhave the the common transmitter common transmitter transmitterand high and high frequencyand frequency high (HF)frequency (HF) outputs, outputs, (HF) one one outputs, forfor transmitting one for transmittingandtransmitting and the the other other and for for the receiving receiving other for antennas. antennas. receiving ToTo antennas. create create a a double-channel double-channelTo create a double-channel radioradio altimeter,altimeter, radio otherother altimeter, blocks other have blocks havebeenblocks been made,made, have suchbeensuch asmade,as thethe high-frequency suchhigh-frequency as the high-frequency signalsignalattenuator attenuator signal ofof attenuatorthe the transmitter, transmitter, of the the transmitter,the delay delay line the into delay the line into thesecond linesecond into channel,channel, the second thethe channel, high-frequencyhigh-frequency the high-frequency attenuator attenuator of of attenu a a received receivedator of signal signal a received as as well well signal as as the the as merger merger well as of the an merger output of an outputlow-frequencyof low-frequency an output low-frequency differential differential signal signaldifferential [12 [12].]. signal [12]. A real altitudeA real measurement altitude measurement has not been has perf notormed beenbeen between performedperformed the between transmitting the transmitting and receiving and receiving antennas. Thatantennas. HF line That That has HF HFbeen line replaced has been by replaceda coaxial by line, a coaxialthe input line, of thewhich inputinput has of been which connected has been connectedconnected instead of theinstead transmitting of the transmitting antenna, and antenna, the output and instead the output of the instead receiving of of the the antenna. receiving receiving The antenna. antenna. attenuator, The The attenuator, attenuator, which imitatedwhich a signal imitated attenuation a a signal signal attenuationin attenuation realistic conditions, in in realistic realistic hasconditions, conditions, been connected has has been been into connected connecteda HF route. into into aThe HF a route. HF route. The change of measuredThechange change of altitude measured of measured during altitude altitudethe laboratoryduring during the themeasurements laboratory laboratory measurements measurements has been realized has has beenbeen up realizedto realized the basic up up to to the the basic altitude of 7.54altitude m by of adding 7.54 m the by co addingaxial sections the coaxialcoaxial of 0.5 sections m length. of 0.5 Six m sections length. Sixof coaxial sections lines of coaxial with the lines with the following lengthfollowing have lengthbeen realized: have been 0.5 realized:m, 1 m, 2 0.5 m, m, 4 m, 1 m,8 m, 2 m, and 4 m, 16 m.8 m, By and and their 16 16 mutualm. m. By By their their connection, mutual mutual connection, connection, it was possibleit was to create possible an toadditional createcreate anan measuring additionaladditional route measuringmeasuring of 31.5 routeroute m length ofof 31.531.5 with mm lengthlengtha 0.5 m withwith step. aa 0.50.5 mm step.step. ConsideringConsidering the shortening the coefficientshortening of coefficient coefficient 0.8 for the of line, 0.8 for and the the line, fact andthat thethe fact line that replaces the line the replaces the route of the routesignal ofof to thethe the signalsignal ground toto the andthe ground groundback, the and and 25.2 back, back, m thecoaxial the 25.2 25.2 line m m coaxial imitatedcoaxial line line measured imitated imitated measuredaltitude measured of altitude 12.6 altitude of of 12.6 12.6 m m with a 0.2withm m with step. a 0.2 a mThe0.2 step. m measuring step. The measuringThe resultsmeasuring resultswith results the with double-channel thewith double-channel the double-channel radio radio altimeter altimeter radio are altimeter shown are shown inare in shown Figure in6. Figure 6. Figure 6. From the viewpointFrom the ofviewpoint the laboratory of the experimentlaboratory s,experiment the evaluations, the ofevaluation the measured of the altitude measured altitude through thethrough differential the differentialfrequency isfrequenc more precisey is more and precise objective and than objective using thana pointer using heighta pointer height indicator. Theindicator. altitude The evaluation altitude could evaluation be done could by recordingbe done by the recording value of thethe valuedifferential of the frequencydifferential frequency on three readers:on three the readers: 1st channel, the 1st 2nd channel, channel, 2nd and channel, common and channel. common The channel. differential The differentialfrequency frequency value of the common channel was divided by two after reading. The measured altitude Hm = Fd/34 value of the common channel was divided by two after reading. The measured altitude Hm = Fd/34 could be evaluatedcould be through evaluated the throughconstant the of radioconstant altimeter of radio (K altimeter= 34) by dividing(K = 34) bythe dividing measured the value measured value of the differentialof the frequencydifferential [13]. frequency [13].

Electronics 2018, 7, 191 7 of 9 Electronics 2018, 7, x FOR PEER REVIEW 7 of 9

Figure 6. Measuring results. results.

FromFigure the 6 presents viewpoint three of curves the laboratory of measured experiments, values of the the differential evaluation frequency: of the measured the 1st channel altitude through(blue curve), the differential the 2nd channel frequency (red is curve), more precise and the and common objective channel than using(green a curve). pointer The height differential indicator. Thefrequency altitude value evaluation corresponds could with be done the byaltitude recording so that the the value number of the of differential height pulses frequency shaped onduring three readers:the time the of the 1st modulation channel, 2nd period channel, is multiplied and common by the channel. modulation The differential frequency. frequencyA discrete valueincrease of theof commonthe number channel of pulses was by divided one pulse by two within after one reading. modulation Themeasured period means altitude a discreetHm = increaseFd/34 could of the be evaluateddifferential through frequency the by constant the value of radioof modulation altimeter frequency. (K = 34) by In dividingthis way, thethe measureddifferential value frequency of the differentialincrease has frequency a discreet [ 13course]. which can be observed in the presented graphs. The step-like course of measuredFigure altitude6 presents is created. three curves of measured values of the differential frequency: the 1st channel (blueTwo curve), straight the 2nd lines channel can be (red constructed curve), and on the the common presented channel “steps” (green of each curve). graph: The one, differential which frequencyconnects tops—“tips” value corresponds of minimal with values the altitude of altitude so that on a the constant number level of heightof the differential pulses shaped frequency during the(upper time straight of the modulation line A–B); periodanother is one, multiplied which conn by theects modulation the tops—“heels” frequency. of Amaximum discrete increasevalues of of thealtitude number on a of constant pulses bylevel one of pulsethe differential within one (unmarked period bottom means astraight discreet line). increase Those of two the differentialleaning straight frequency lines byare the connected value of modulationby a horizontal frequency. line onIn a thisconstant way, thevalue differential of the differential frequency increasefrequency has of a 300 discreet Hz. course which can be observed in the presented graphs. The step-like course of measuredThe plan altitude of horizontal is created. line cross point with both full straight lines into the horizontal altitude axis Twoexpresses straight the lines critical can altitude be constructed ΔH1 measured on thepresented by a classical “steps” single-channel of each graph: radio one, altimeter. whichconnects In case tops—“tips”of the critical ofaltitude minimal of one values of the ofchannels altitude of a on double-channel a constant level radio ofaltimeter, the differential the value frequencyΔH1 = 2.7 (upperm has been straight measured. line A–B); A theoretical another one,value which of the connectscritical altitude the tops—“heels” of the experimental of maximum radio altimeters values of altitudeis 2.2 m. on aFrom constant the levelpresented of the differentialresults, it can frequency be seen (unmarked that due bottomto construction straight line). changes Those and two interconnections of the original radio altimeters, their critical altitude ΔH1 has increased from 2.2 m leaning straight lines are connected by a horizontal line on a constant value of the differential frequency to 2.7 m [14,15]. of 300 Hz. Created “steps” of the first and second channel height pulses (blue and red curves) are The plan of horizontal line cross point with both full straight lines into the horizontal altitude axis mutually shifted so that it is possible to create a sum of height pulses of both channels. The created expresses the critical altitude ∆H1 measured by a classical single-channel radio altimeter. In case of the sum of pulses of the differential frequencies of both channels has a double value and their graphic critical altitude of one of the channels of a double-channel radio altimeter, the value ∆H = 2.7 m has curve could get out of the area of single-channel dependences. Therefore, each following1 sum value been measured. A theoretical value of the critical altitude of the experimental radio altimeters is 2.2 m. of the differential frequencies pulses of both channels is divided by two. It is shown by the green From the presented results, it can be seen that due to construction changes and interconnections of the curve of the height dependence between both channels courses. original radio altimeters, their critical altitude ∆H has increased from 2.2 m to 2.7 m [14,15]. This course also has a step-like character of 1the graph on which two similar, but chain-dotted Created “steps” of the first and second channel height pulses (blue and red curves) are mutually straight lines have been constructed. At a constant value of the differential frequency of 400 Hz, shifted so that it is possible to create a sum of height pulses of both channels. The created sum of pulses there are also two inclined chain-dotted straight lines connected by a horizontal line. The plan of the of the differential frequencies of both channels has a double value and their graphic curve could get cross points of this horizontal line with both chain-dotted straight lines into the horizontal altitude out of the area of single-channel dependences. Therefore, each following sum value of the differential axis expresses the measured critical altitude ΔH2 of the double-channel radio altimeter. In case of the methodological error of a double-channel radio altimeter, a critical altitude of 1.3 m has been evaluated.

Electronics 2018, 7, 191 8 of 9 frequencies pulses of both channels is divided by two. It is shown by the green curve of the height dependence between both channels courses. This course also has a step-like character of the graph on which two similar, but chain-dotted straight lines have been constructed. At a constant value of the differential frequency of 400 Hz, there are also two inclined chain-dotted straight lines connected by a horizontal line. The plan of the cross points of this horizontal line with both chain-dotted straight lines into the horizontal altitude axis expresses the measured critical altitude ∆H2 of the double-channel radio altimeter. In case of the methodological error of a double-channel radio altimeter, a critical altitude of 1.3 m has been evaluated. The value of the critical altitude ∆H1 of each original single-channel radio altimeters was 2.7 m. So, the “new” double-channel radio altimeter should have the critical altitude of 1.35 m. However, a better value of 1.3 m has been obtained during the experiment.

4. Conclusions The paper has presented a new possibility of increasing the measurement accuracy of small altitudes by airborne radio altimeters. The new trend of the increase of the altitude measurement accuracy is based on creating the conditions for a more frequent change of the unstable pulses into permanent pulses. The results of the experimental measurements presented in the paper have proved the feasibility of the new approach to increase the altitude measuring accuracy. Application of the new method allowed to increase the altitude measuring accuracy in twice. In case of the application of this new method into recent types of radio altimeters, the accuracy of which is about ±0.75 m, the accuracy of ±0.325 m could be obtained. This solution makes it possible to increase the accuracy without having to increase the frequency deviation and to change the carrier frequency. This method can also be applied to a so-called four-channel radio altimeter, by which it could be possible to obtain the methodological error lower than ±0.2 m that is very interesting too for the further research and practical implementation. The application of obtained results could contribute to the increase of air traffic safety, mainly in the phase of the aircraft approaching for landing and landing on land as well on water [16,17].

Author Contributions: J.L. proposed the concept, methodology and wrote the manuscript; J.L., M.K., P.K., and M.C.ˇ performed experimental design and conducted experiments; A.N. and M.G. contributed to the algorithm, interpretation and validation of results and editing the manuscript. Funding: Slovak authors J.L., M.K., P.K., M.C.,ˇ and M.G. has been supported by the Science Grant Agency of the Ministry of Education Science, Research and Sport of the Slovak Republic under the contract No. 1/0772/17. Acknowledgments: A.N. wishes to express his sincere appreciation to the Technical University of Košice and Hamburg University of Technology for the provided opportunities during his exchange visits in the framework of the Erasmus+ International Mobility Program and the German Academic Exchange Service (DAAD) Program. Conflicts of Interest: The authors declare no conflict of interest.

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