electronics

Article Low Altitude Measurement Accuracy Improvement of the Airborne FMCW

Ján Labun 1, Pavol Kurdel 1, Marek Ceškoviˇcˇ 1, Alexey Nekrasov 2,3,* and Ján Gamec 4

1 Faculty of Aeronautics, Technical University of Košice, Rampová 7, 041 21 Košice, Slovakia 2 Department of Radio Engineering Systems, Saint Petersburg Electrotechnical University, Professora Popova 5, Saint Petersburg 197376, Russia 3 Higher Technical School of Computer Engineering, University of Malaga, 29071 Malaga, Spain 4 Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia * Correspondence: [email protected]; Tel.: +7-8634-360-484

 Received: 27 June 2019; Accepted: 8 August 2019; Published: 12 August 2019 

Abstract: This manuscript focuses on the analysis of a critical height of radio altimeters that can help for the development of new types of aeronautical radio altimeters with increased accuracy in measuring low altitudes. Altitude measurement accuracy is connected with a form of processing the difference signal of a radio , which carries information on the measured altitude. The definition of the altitude measurement accuracy is closely linked to the value of a critical height. Modern radio altimeters with digital processing of a difference signal could shift the limit of accuracy towards better values when the basics of the determination of critical height are thoroughly known. The theory results from the analysis and simulation of dynamic formation and the dissolution of the so-called stable and unstable height pulses, which define the range of the critical height and are presented in the paper. The theory is supported by a new method of derivation of the basic equation of a radio altimeter based on a critical height. The article supports the new theory of radio altimeters with the ultra-wide frequency deviation that lead to the increase the accuracy of a low altitude measurement. Complex mathematical analysis of the dynamic formation of critical height and a computer simulation of its course supported by the new form of the derivation of the basic equation of radio altimeter guarantee the correctness of the new findings of the systematic creation of unstable height pulses and the influence of their number on the altitude measurement accuracy. Application of the presented findings to the aviation practice will contribute to increasing the accuracy of the low altitude measurement from an during its landing and to increasing air traffic safety.

Keywords: FMCW radio altimeter; methodological error; critical height; altitude measurement accuracy; height pulses; ultra-wide frequency deviation

1. Introduction Radio altimeters are being used on board of aircrafts to measure the instant altitude of the flight. Radio altimeters are important from the point of view of flight safety, mainly when approaching landing [1,2]. Due to their specific function of measuring the low altitudes, they use the and continuous transmitted signal. This article focuses on radio altimeters of FMCW type. An FMCW radio altimeter forms information about the flight altitude through the evaluation of the difference in frequency between the transmitted and received high-frequency signals. The instant value of the difference frequency Fd (as a low-frequency information signal of the measured altitude H) is made by the time delay τ of the received signal frequency fR against the transmitted signal frequency fT. The delay of the received signal is created by overpassing the height difference on the

Electronics 2019, 8, 888; doi:10.3390/electronics8080888 www.mdpi.com/journal/electronics Electronics 2019, 8, 888 2 of 12 aircraft–ground–aircraft route [3,4]. Such a radio altimeter possesses its methodological error of height measurement ∆H, which is based on the physical fundamentals of of evaluation of the differential ± frequency. The methodological error is determined by a so-called critical height ∆H, which is the minimal height range that a radio altimeter can distinguish [4]. The value of the critical height is determined by the following equation: c ∆H = , (1) 8 ∆ f where c is the speed of light and ∆f is the frequency deviation. The range of the critical height for recent radio altimeters (corresponding with measurement accuracy) has settled on the value of 0.75 m. This manuscript deals with the principle of the formation of critical height and suggests how to decrease its value to increase the altitude measurement accuracy [5,6]. FMCW radio altimeter has a 90-year history of development and improvement for measuring aircraft altitude. At each aviation historical stage, efforts to increase the accuracy of altitude measurement have led to increasing the frequency deviation to higher values of a carrier frequency f 0. At the beginning, the altitude measurement accuracy was 2.2 m (at ∆f = 17 MHz and f = 444 MHz). ± 0 Almost 40 years ago, the accuracy of the measurement stabilized at 0.75 m (at ∆f = 50 MHz and ± f 0 = 4.4 GHz). However, attempts to increase the measurement accuracy have not stopped even after reaching this limit. Today, even advanced technologies push the limit a little forward. It is generally known that a further substantial increase of accuracy would be achieved by a significant increase of the values of the frequency deviation and carrier frequency. For instance, ∆f = 100 MHz and f 0 = 12 GHz provide an altitude measurement accuracy of 0.375 m. However, when flying over various terrains, the use of ± the very high value of the carrier frequency of 12 GHz is not so advantageous. Previously, we have proposed some methods to increase the accuracy of altitude measurement by altimeters. A new method for measuring the altitude by estimating the period of the differential frequency is presented in [4]. This method does not have a methodological error and provides better measurement accuracy, especially at low altitude, in comparison with the currently used method that is based on the classical calculation of height pulses. An innovative technique of using the for prediction of terrain collision threats has been presented in [7]. It is based on an atypical way of estimating the Doppler frequency by measuring the ratio of the number of stable and unstable height pulses between the even and odd half-periods of the modulation signal of a radio altimeter. From this point of view, [7] is close to the problem of the current manuscript. An altitude measurement accuracy improvement with a two-channel method has been considered in [8]. In the two-channel method, the deviation of the carrier frequency of the signal retains its original values. In this connection, in addition to previously published results, this manuscript supports the new theory of radio altimeters with the ultra-wide frequency deviation leading to an increase in the accuracy of a low altitude measurement, and it justifies that the measurement accuracy is fundamentally influenced by the frequency deviation and not by the carrier frequency itself. For the presented analysis, it is evident that the measurement accuracy determines a radio altimeter methodical error ∆H, which is influenced by the height range of the numbers of the formation and dissolution of unstable height pulses. Using the above mentioned historical and practical experience as well as new theoretical knowledge, the way to increase the accuracy of altitude measurement without the need to increase the carrier frequency is presented in this manuscript with the help of analysis and simulation. The method presented in this manuscript uses a classic single-channel radio altimeter like in [8], but with a doubled value for the carrier frequency deviation. Electronics 2019, 8, 888 3 of 12

2. Difference Signal of FMCW Radio Altimeter

In determining the frequency value of the radio altimeter difference frequency signal ud(t), which carries the information about the measured altitude, based on mutual immediate differences between the frequency-modulated transmitted signal uT(t) and the time-delayed frequency-modulated received signal uR(t), it can simply be presented in the following form of ud(t) = uT(t) + uR(t). Technically, this difference between the two high-frequency signals of the radio altimeter is evaluated by a balanced mixer. Since these are two near-frequency signals, mixing the procedure results in a low-frequency difference signal in which the amplitude change in time Ud(t1) carries the information about the measured altitude. By mathematical analysis of the above-mentioned mixing process, the amplitude of this difference signal is defined as [5,9,10]:

Ud(t) = UT + UR cos(ϕ0 + ϕM cosΩMt), (2) where UT is the amplitude of the frequency-modulated transmitting signal, UR is the amplitude of the received signal, φ0 and φM are the initial and variable phase of the difference signal, ΩM is the angular frequency modulation of the signal, and t is the time course of the difference signal, t = (t τ/2). 1 1 − This signal allows for the formation of some so-called unstable height pulses Nu. They alternately arise and disappear when the amplitude of the difference signal passes through zero [3,11,12]. Defining the condition of the formation and the dissolution of the unstable height pulses determines the rise HF and extinction HE heights of the individual pulses:

λ 2k 1 λ 2k 1 H = 0 − , H = 0 − , (3) F 8 1 + ξ E 8 1 ξ − where λ0 is the carrier wavelength, k is the sequence number of the height pulse, ξ is the relative value of the frequency deviation, and ξ = ∆f /f 0. Then, the two heights behind the forming pulses make it possible to define the height range of the formation of individual pulses F, and from the two heights of the following dissolution pulses, Equation (4) is used to define the height range of dissolving pulses E:

λ0 λ0 F = HF2 HF1 = , E = HE2 HE1 = . (4) − 4(1 + ξ) − 4(1 ξ) − A height range for the duration of the different unstable height pulse S is determined as the difference of height between the dissolution and formation of any height pulse:

λ0 ξ S = HE HF = (2k 1) . (5) − 4 − 1 + ξ2

Equation (4) shows us that the height range of the gradual formation of the different unstable height pulses is constant and smaller than the value of λ0/4 at any measured height. Thus, it is possible to state that F1 = F2 = F3 = ... . At the same time, it can be seen that the height range of the dissolution of unstable pulses E is also constant but bigger than the value of λ0/4 at any measured height. So, it is also possible to state that E1 = E2 = E3 = ... . Equation (5) also indicates that the height range for the duration of the different unstable height pulses constantly grows with the increase of the consequence number of the pulse k, as a result of the increase of the value of measured altitude. So, it is possible to state that S1 < S2 < S3 < ... [3,7]. Gradual increase of the height range for the duration of different unstable pulses together with the growing measured altitude cause more and more of those pulses at the same height to overlap mutually (Figures1 and2)[13]. Electronics 2019, 7, x FOR PEER REVIEW 3 of 12 between the frequency-modulated transmitted signal uT(t) and the time-delayed frequency-modulated received signal uR(t), it can simply be presented in the following form of ud(t) = uT(t) + uR(t). Technically, this difference between the two high-frequency signals of the radio altimeter is evaluated by a balanced mixer. Since these are two near-frequency signals, mixing the procedure results in a low-frequency difference signal in which the amplitude change in time Ud(t1) carries the information about the measured altitude. By mathematical analysis of the above-mentioned mixing process, the amplitude of this difference signal is defined as [5,9,10]:

𝑈𝑡 =𝑈 +𝑈 𝑐𝑜𝑠𝜑 +𝜑 𝑐𝑜𝑠𝛺𝑡, (2) where UT is the amplitude of the frequency-modulated transmitting signal, UR is the amplitude of the received signal, ϕ0 and ϕM are the initial and variable phase of the difference signal, ΩM is the angular frequency modulation of the signal, and t1 is the time course of the difference signal, t1 = (t − τ/2). This signal allows for the formation of some so-called unstable height pulses Nu. They alternately arise and disappear when the amplitude of the difference signal passes through zero [3,11,12]. Defining the condition of the formation and the dissolution of the unstable height pulses determines the rise HF and extinction HE heights of the individual pulses:

𝐻 = , 𝐻 = , (3) where λ0 is the carrier wavelength, k is the sequence number of the height pulse, ξ is the relative value of the frequency deviation, and ξ = Δf/f0. Then, the two heights behind the forming pulses make it possible to define the height range of the formation of individual pulses F, and from the two heights of the following dissolution pulses, Equation (4) is used to define the height range of dissolving pulses E:

𝐹=𝐻 − 𝐻 = , 𝐸=𝐻 − 𝐻 = . (4) A height range for the duration of the different unstable height pulse S is determined as the difference of height between the dissolution and formation of any height pulse:

𝑆=𝐻 − 𝐻 = 2𝑘 − 1 . (5) Equation (4) shows us that the height range of the gradual formation of the different unstable height pulses is constant and smaller than the value of λ0/4 at any measured height. Thus, it is possible to state that F1 = F2 = F3 = …. At the same time, it can be seen that the height range of the dissolution of unstable pulses E is also constant but bigger than the value of λ0/4 at any measured height. So, it is also possible to state that E1 = E2 = E3 = …. Equation (5) also indicates that the height range for the duration of the different unstable height pulses constantly grows with the increase of the consequence number of the pulse k, as a result of the increase of the value of measured altitude. So, it is possible to state that S1 < S2 < S3 < … [3,7]. Gradual increase of the height range for the duration of different unstable pulses together with theElectronics growing2019, 8measured, 888 altitude cause more and more of those pulses at the same height to overlap4 of 12 mutually (Figures 1 and 2) [13].

Electronics 2019, 7, x FOR PEER REVIEW 4 of 12 Electronics 2019, 7, x FOR PEER REVIEW 4 of 12 Figure 1. Height dependence of the formation and dissolution of unstable height pulses. Figure 1. Height dependence of the formation and dissolution of unstable height pulses.

Figure 2. Height ranges and windows in the area of mutual overlapping of unstable height pulses. FigureFigure 2. 2.Height Height ranges ranges and and windows windows inin thethe area of mutual overlapping overlapping of of unstable unstable height height pulses. pulses. 3. Simulation of Height Pulses Creation 3. Simulation of Height Pulses Creation Based on the above-defined theory, the simulation program for making the stable and unstable Based on the above-defined theory, the simulation program for making the stable and unstable heightheight pulses pulses of of the the radio radio altimeter altimeter has hasbeen been created.created. The The simulation simulation results results at at the the input input parameters parameters equalequal to to the the value value of of the the current current radio radio altimeters altimeters are are shown shown in in FigureFigure3 3.. The The simulationsimulation isis realized in a heighta height range range from from 0 m 0 tom 2to m, 2 m, with with a meana mean value value of of 1 1m. m. InIn Figure 33,, we can can see see that that the the first first critical critical heightheight value value ends ends at theat the 0.75 0.75 m height m height level, level, and theand second the second one ends one atends 1.5 m.at Obviously,1.5 m. Obviously, the methodic the errormethodic of the radioerror altimeterof the radio (0.75 m)altimeter is the same(0.75 asm) given is the by same the radio as given altimeter by manufacturers.the radio altimeter manufacturers.

FigureFigure 3. 3.Simulation Simulation ofof thethe formationformation of stable stable and and unstable unstable height height pulses. pulses. Figure 3. Simulation of the formation of stable and unstable height pulses. The upper part of Figure3 represents the height dependence of the creation of numbers of stable The upper part of Figure 3 represents the height dependence of the creation of numbers of (NCstable) and (N unstableC) and unstable(NU) height (NU) pulses. height pulses. By the termBy the “height term “height pulses,” pulses,” we express we express the correlation the correlation between stable (NC) and unstable (NU) height pulses. By the term “height pulses,” we express the correlation the number of pulses in the frequency area and the measured altitude expressed in the unit of length. between the number of pulses in the frequency area and the measured altitude expressed in the unit This can be partly compared to the correlation between the harmonic signal in the time domain and of length. This can be partly compared to the correlation between the harmonic signal in the time the number of periods in the frequency domain, as in Fourier transform. If we use a classical pulse domain and the number of periods in the frequency domain, as in Fourier transform. If we use a generator, then changing the frequency setting will change the number of output pulses. If we record classical pulse generator, then changing the frequency setting will change the number of output thepulses. generated If we pulsesrecord overthe generated time, there pulses will over be thetime, time there on will the be horizontal the time on axis the and horizontal amplitude axis onand the amplitude on the vertical axis. However, if the number of pulses is evaluated in some non-standard but stable time, e.g., per modulation period, then we would plot the frequency on the horizontal axis and the number of pulses per modulation period on the vertical axis. The radio altimeter is reminiscent of a quasi-pulse generator, which forms the number of pulses that correspond to the flight altitude. The peculiarity is that even with a fluent change in height, the number of pulses does not change fluently, but the formation and dissolution of the pulses are discrete, and their number creates a quantization (stairs) course when changing the altitude (Figure 3). This is due to the fact that the pulses do not occur in a separate low-frequency generator, but are formed from a differential frequency resulting from the mixing of the high frequency and frequency-modulated signals. Thus, when evaluating the number of radio altimeter pulses generated during the modulation period, where the altitude is the control parameter, then the height

Electronics 2019, 8, 888 5 of 12 vertical axis. However, if the number of pulses is evaluated in some non-standard but stable time, e.g., per modulation period, then we would plot the frequency on the horizontal axis and the number of pulses per modulation period on the vertical axis. The radio altimeter is reminiscent of a quasi-pulse generator, which forms the number of pulses that correspond to the flight altitude. The peculiarity is that even with a fluent change in height, the number of pulses does not change fluently, but the formation and dissolution of the pulses are discrete, and their number creates a quantization (stairs) course when changing the altitude (Figure3). This is due to the fact that the pulses do not occur in a separate low-frequency generator, but are formed from a differential frequency resulting from the mixing of the high frequency and frequency-modulated signals. Thus, when evaluating the number of radio altimeter pulses generated during the modulation period, where the altitude is the control parameter, then the height H is plotted on the horizontal axis, and the number of pulses N for the modulation period is plotted on the vertical axis. The stable height pulses are those of which the number increases as the altitude increases gradually and discretely with the height range ∆H, that which creates the so-called quantization (stairs) course. In each height range (which is related to the altitude measurement accuracy), the number of these pulses is stable. The frequency value of these pulses is fixed to the altitude of the aircraft, which is expressed by the basic equation of a radio altimeter presented by Equation (12). Unstable altitude pulses are those of which the number changes discreetly as the height increases, forming on every single stair ∆H a so-called comb course. In each height range ∆H, the formation and dissolution of the unstable pulse means that the total number of pulses within that range ∆H is changed by one pulse. The formation and dissolution of the unstable pulse occurs in a very small height range, so this situation is repeated in the range ∆H tens of times. The course of creation (formation and dissolution) of unstable pulses is the same in every height range ∆H (at each step). So, it is very interesting how many times the unstable pulse formation and dissolution will take place in the height range ∆H, as their number is related to the accuracy of the altitude measurement, which is the main topic of this manuscript. In the 2 m height range, three critical heights are simulated, which correspond to the two ranges of the existence of the stable pulses 2Nc. There is no stable pulse in the first range (0Nc in 1∆H in Figure3). A larger number of unstable pulses are simulated in the same 2 m height range. The bottom part of Figure3 presents the height ranges of the duration of di fferent pulses S. At the critical height of 1∆H, the height ranges of the duration of the unstable height pulses are so small that they do not overlap, and an alternation of zero and the first unstable pulses (0–1) occur at the given critical height. At all the following critical heights, the height ranges of the duration of the unstable height pulses are so big that they mutually overlap. The number of permanently existing unstable pulses is determined by the consequence number of a stable height pulse. At least one unstable pulse exists at each section of the height within the range of 2∆H. It means that one stable pulse exists at the height of alternation of the first and second unstable pulses (1–2) within the given range. Similarly, two unstable pulses exist permanently within the range of 3∆H in each section of the height. It means that there are two stable pulses. Closer analysis of this phenomenon can observe that the process of the formation and dissolution of the unstable height of pulses is not chaotic, but has regularity. The regularity of the formation and dissolution of the height pulses is related to the change in the measured height, but their number in the range of critical height corresponds to the technical parameters of the radio altimeter [11,12].

4. Number of Unstable Pulses in Range of Critical Height It is obvious from Figures1 and2, which present the height dependence of the formation of height pulses, as well as from Figure3, which shows the results of the simulation of the stable and unstable height pulses, that the higher the number of unstable pulses is in the range of critical height, the smaller the precision of height measurement. Electronics 2019, 8, 888 6 of 12

For the logical explanation of reasoning and determination of the number of unstable pulses in the range of critical height, it is necessary to move from the frequency area into the area of wavelengths. This thought is based on the generally known facts about the principle of the operation of FMCW radio Electronics 2019, 7, x FOR PEER REVIEW 6 of 12 altimeters presented in Figure4.

Figure 4. Formation of differential signal for determination of the number of unstable height pulses.Figure 4. (a Formation) frequency-modulated of differential transmitted signal for determination signal, and received of the number signal withof unstable the delayed height inpulses. time by(a) τfrequency-modulated;(b) theoretical representation transmitted of signal, the diff anderential received frequency signalover with time; the delayed (c) actual in changetime byof τ; the(b) ditheoreticalfferential representation frequency over of time; the differential (d) change frequency of the period over oftime; the (c) di actualfferential change frequency of the differential within the modulationfrequency over frequency; time; (d) (e )change temporary of the shift period of the of periods the differe of thential diff erentialfrequency frequency within the with modulation increasing thefrequency; measured (e) altitude. temporary shift of the periods of the differential frequency with increasing the measured altitude. Based on the principles that if the frequency modulation of the transmitted signal within the whole rangeBased of ∆ fonis linearthe principles (Figure4 a),that and if thatthe frequency if the time delaymodulation of received of the signal transmitted during whole signal modulation within the ± periodwhole byrange value of ±τΔisf alsois linear linear, (Figure then the4a), immediate and that if value the time of di delayfferential of received frequency signal is constant duringduring whole wholemodulation time ofperiod the modulation by value τ periodis also (Figurelinear, 4thenb). Thethe areasimmediate of the value changing of differential of the direction frequency of the is frequencyconstant during deviation whole in thetime areas of th ofe themodulation maximum period (f + ∆(Figuref )max and 4b). minimum The areas(f of the∆f )changingtransmitted of the 0 0 − min frequencydirection of are the not frequency considered. deviation in the areas of the maximum (f0 + Δf)max and minimum (f0 − Δf)min transmittedHowever, frequency the actual are situation not considered. with the formation of the differential signal is different. The difference in frequencyHowever, is notthe formedactual assituation a simple with mathematical the formation difference, of the butdifferential as interference signal ofis transmitteddifferent. TheλT anddifference received in λfrequencyR wavelengths. is not Then, formed the as wavelength a simple ofmathematical the carrying signaldifference, is minimal but asλ interference0min in the case of oftransmitted maximum λ transmittedT and received frequency λR wavelengths. (f 0 + ∆f )max Then,and, the vice wavelength versa, the of wavelength the carrying of carryingsignal is minimal signal is maximalλ0min in theλ caseat of minimum maximum transmitted transmitted frequency frequency (f (∆f0 f+) Δf.)max With and, the vice equivalent versa, the time wavelength delay τ of the of 0max 0 − min receivedcarrying signalsignal withinis maximal the whole λ0max at modulation minimum period transmitted but at frequency the different (f0 wavelengths− Δf)min. Withλ 0themin equivalentand λ0max, thetime value delay of τ di ffoference the received frequency signal (interference) within the is notwhol formede modulation by the same period way. but At at the the wavelength different ofwavelengthsλ0min, the interferenceλ0min and λ0 ismax formed, the value more of often difference and the frequency value of the(interference) higher diff iserence not formed frequency by Fthedh issame higher way. and, At vicethe wavelength versa, at the of wavelength λ0min, the interferenceλ0max, the is interference formed more is formed often and less the frequently value of and the thehigher value difference of the lower frequency difference Fdh isfrequency higher and,Fdl viceis smaller. versa, at Considering the wavelength the presented λ0max, the interference phenomenon, is theformed differential less frequently frequency and is the the value same withinof the lower the whole difference range frequency of the modulation Fdl is smaller. period Considering (Figure4c). the presentedThe above-presented phenomenon, theorythe differential is confirmed frequenc by they observation is the same of realisticwithin displaysthe whole of therange diff erenceof the signalmodulation of a radio period altimeter (Figure on 4c). an oscilloscope. In the higher frequency area f 0max and lower wavelength λ0minThe, the higherabove-presented differential theory frequency is confirmed with the lower by th wavelengthe observationλdh willof realistic be formed displays with a higherof the numberdifference of signal the height of a radio pulses altimeterN. In the on lower an oscilloscope. frequency areaIn thef 0 minhigherand frequency the higher area wavelength f0max and λlower0max, thewavelength lower diff λerence0min, the frequency higher differentialFdl with the frequency higher wavelength with theλ lowerdl will wavelength be formed with λdh awill lower be numberformed ofwith the a height higher pulses numberN (Figure of the4 d).height pulses N. In the lower frequency area f0min and the higher wavelength λ0max, the lower difference frequency Fdl with the higher wavelength λdl will be formed with a lower number of the height pulses N (Figure 4d). As a result of such unbalanced formation of differential frequency, and the fluent increase of the measured height, height pulses on the display of the oscilloscope will shift from the areas with the higher number of pulses into the area with the lower number of pulses. The presented shift of the periods of difference frequency and relevant height pulses is shown in Figure 4e. Determination of the number of unstable pulses within the range of critical height ΔH is considered for a particular case of a radio altimeter with the carrier frequency of f0 =4400 MHz, the

Electronics 2019, 8, 888 7 of 12

As a result of such unbalanced formation of differential frequency, and the fluent increase of the measured height, height pulses on the display of the oscilloscope will shift from the areas with the higher number of pulses into the area with the lower number of pulses. The presented shift of the periods of difference frequency and relevant height pulses is shown in Figure4e. Determination of the number of unstable pulses within the range of critical height ∆H is considered for a particular case of a radio altimeter with the carrier frequency of f 0 =4400 MHz, the modulation Electronics 2019, 7, x FOR PEER REVIEW 7 of 12 frequency of F = 150 Hz, and the frequency deviation of ∆f = 25 MHz. In this case, we have f = M ± 0max 4400 MHz + 25 MHz = 4425 MHz = 67.797 10 3 m, f = 4400 MHz = 68.182 10 3 m, modulation frequency of FM = 150 Hz,λ0 minand the frequency− deviation0 of ±Δf = 25 MHz.λ0 In this case, we− ⇒ × 3 ⇒ × and f = 4400 MHz 25 MHz = 4375 MHz λ = 68.571 −103 m. have0min f0max = 4400 MHz− + 25 MHz = 4425 MHz ⇒ λ0min0max = 67.797 × 10× m,− f0 = 4400 MHz  λ0 = 68.182 × 10−Then,3 m, and the f0 diminff =erence 4400 MHz of wavelengths − 25 MHz = can4375 be MHz defined  λ0maxλmax = 68.571λmin × =1068.571 −3 m. m 67.797 m = 0.774 3 − − × 10− m.Then, the difference of wavelengths can be defined λmax − λmin = 68.571 m − 67.797 m = 0.774 × 10 −3 m.The calculated value expresses the height range of the formation of an unstable height pulse. The halfThe value calculated of the numbervalue expresses of the unstablethe height height range pulsesof the withinformation half ofa an period unstable of λ height0/2 of apulse. carrier frequencyThe halff value0 presents of the the number number of ofthe unstable unstable pulses height within pulses the within critical half height a period∆H of. Thus, λ0/2 of in a the carrier case of consideredfrequency ratio f0 presents altimeter, the number the number of unstable of unstable pulses pulses within is the 44. critical height ΔH. Thus, in the case of consideredFigure5 showsratio altimeter, the results the ofnu thember simulation of unstable of pulses the formation is 44. of the number of unstable height pulses withinFigure 5 the shows critical the height results∆ ofH thefor simulation the particular of the type formation of a radio of altimeter.the number of unstable height pulses within the critical height ΔH for the particular type of a radio altimeter.

Figure 5. Simulation of number of unstable height pulses for the considering radio altimeter. Figure 5. Simulation of number of unstable height pulses for the considering radio altimeter. 5. Number of Stable Pulses in Range of Critical Height 5. Number of Stable Pulses in Range of Critical Height A recent method of increasing the accuracy of altitude measurement by the FMCW radio altimeters A recent method of increasing the accuracy of altitude measurement by the FMCW radio is based on the increase of frequency deviation with the simultaneous increase of the carrier signal altimeters is based on the increase of frequency deviation with the simultaneous increase of the frequency. However, the recent radio altimeters use the carrier frequency of 4.4 GHz with the frequency carrier signal frequency. However, the recent radio altimeters use the carrier frequency of 4.4 GHz deviation of 25 MHz (overall bandwidth of 50 MHz), and they can provide the measurement accuracy with the frequency± deviation of ±25 MHz (overall bandwidth of 50 MHz), and they can provide the of 0.75 m. ±measurement accuracy of ±0.75 m. It isIt necessaryis necessary to to increase increase the the carrier carrier frequency frequency with with the the increase increase of of the the frequencyfrequency deviationdeviation due to theto requirement the requirement for balanced for balanced frequency frequency transmission transm characteristicsission characteristics of the high-frequency of the high-frequency circuits, as wellcircuits, as active as well and as passive active elements and passive of antennas. elements of To antennas. increase theTo accuracyincrease the of theaccuracy altitude of the measurement altitude two-foldmeasurement (to the valuetwo-fold of (to0.375 the m) value by the of same±0.375 way, m) theby the value same of theway, frequency the value deviation of the frequency also should ± bedeviation increased also two-fold should (to be the increased value oftwo-fold50 MHz (to the that, value in fact, of ±50 corresponds MHz that, toin thefact, overall corresponds bandwidth to the of ± 100overall MHz), bandwidth with the simultaneous of 100 MHz), increase with of the the carriersimultaneous frequency increase approximately of the carrier to 10 GHz.frequency approximatelyBased on the to above-analyzed 10 GHz. theory, it is possible to avoid the problem of the necessity of using a higherBased carrier on frequency the above-analyzed of 10 GHz theory, through it is the possibl usee of to two avoid parallel the problem high-frequency of the necessity channels of using at the originala higher carrier carrier frequency frequency of of 4.4 10 GHz.GHz through To create the a performanceuse of two parallel signal, high-fr the frequencyequency channels multipliers at the are commonlyoriginal carrier used in frequency radio altimeters of 4.4 GHz. nowadays. To create a performance signal, the frequency multipliers are commonly used in radio altimeters nowadays. In such a way, a basic generator forms the frequency modulated signal with the center frequency of 2200 MHz and with the original frequency deviation ±Δf1 = ±25 MHz. Then, the signal is divided by two frequency band-passes into two individual high-frequency channels. Each channel forms its own frequency deviation; the first channel has +Δf1 from 2200 to 2225 MHz, and the second channel has −Δf1 from 2175 to 2200 MHz. Next, the frequency is independently multiplied two times into the value with the extreme frequency deviation of ±Δf2 = ±50 MHz in each channel; the first channel has +Δf2 from 4400 to 4450

Electronics 2019, 8, 888 8 of 12

In such a way, a basic generator forms the frequency modulated signal with the center frequency of 2200 MHz and with the original frequency deviation ∆f = 25 MHz. Then, the signal is divided ± 1 ± by two frequency band-passes into two individual high-frequency channels. Each channel forms its own frequency deviation; the first channel has +∆f 1 from 2200 to 2225 MHz, and the second channel has ∆f 1 from 2175 to 2200 MHz. Electronics− 2019, 7, x FOR PEER REVIEW 8 of 12 Next, the frequency is independently multiplied two times into the value with the extreme frequencyElectronics 2019 deviation, 7, x FOR PEER of REVIEW∆f = 50 MHz in each channel; the first channel has +∆f from 44008 of to12 MHz, and the second channel± 2 has± −Δf2 from 4350 to 4400 MHz (Figure 6). Each channel2 would only 4450 MHz, and the second channel has ∆f 2 from 4350 to 4400 MHz (Figure6). Each channel would MHz,have aand bandwidth the second that channel is commonly has −Δ fused,2 −from i.e., 4350 50 to MHz. 4400 AtMHz the (Figure same time, 6). Each each channel channel would is tuned only in only have a bandwidth that is commonly used, i.e., 50 MHz. At the same time, each channel is tuned in havefrequency a bandwidth to a different that is commonly band, but used, the overalli.e., 50 MHz.bandwidth At the issame 100 time, MHz. each The channel particular is tuned circuit in frequency to a different band, but the overall bandwidth is 100 MHz. The particular circuit connection of frequencyconnection to of a thedifferent radio band,altimeter but withthe overall extrem bandwidthe bandwidth, is 100which MHz. would The complyparticular with circuit the the radio altimeter with extreme bandwidth, which would comply with the above-presented condition, connectionabove-presented of the condition, radio altimeter can be achieved with extrem by severale bandwidth, solutions [14–17].which would comply with the can be achieved by several solutions [14–17]. above-presented condition, can be achieved by several solutions [14–17].

Figure 6. Principle of radio altimeter with extreme bandwidth. Figure 6. Principle of radio altimeter with extreme bandwidth. Figure 6. Principle of radio altimeter with extreme bandwidth. BasedBased onon thethe presentedpresented background,background, parametersparameters ofof thethe criticalcritical heightheight forfor aa radioradio altimeteraltimeter withwith extreme bandwidth have been analyzed with the help of simulation. The parameters of such a radio extremeBased bandwidth on the presented have been background, analyzed with parameters the help of of the simulation. critical height The parameters for a radio ofaltimeter such a radiowith altimeter are as the following: the carrier frequency is 4400 MHz, the modulation frequency is 150 altimeterextreme bandwidth are as the following: have been the analyzed carrier with frequency the help is 4400 of simulation. MHz, themodulation The parameters frequency of such is 150a radio Hz, Hz, and the frequency deviation is 50 MHz, which in sum gives extreme bandwidth of 100 MHz andaltimeter the frequency are as the deviation following: is 50 the MHz, carrier which frequenc in sumy givesis 4400 extreme MHz, bandwidththe modulation of 100 frequency MHz (Figure is 1507). Hz,(Figure and 7).the frequency deviation is 50 MHz, which in sum gives extreme bandwidth of 100 MHz (Figure 7).

Figure 7. Unstable height pulses of radio altimeter with extreme bandwidth. Figure 7. Unstable height pulses of radio altimeter with extreme bandwidth. From the viewpointFigure 7. Unstable of altitude height measurement pulses of radio precision, altimeter thewith results extreme for bandwidth. the radio altimeter with From the viewpoint of altitude measurement precision, the results for the radio altimeter with extreme bandwidth are: extremeFrom bandwidth the viewpoint are: of altitude measurement precision, the results for the radio altimeter with (a)extremecritical(a) criticalbandwidth height height has are: has the the value value of 0.375 of 0.375 m; m; (b) methodological(b) methodological error error of the of the radio radio altimeter altimeter is 0.375is ±0.375 m; m; (a) critical height has the value of 0.375 m; ± (c) (b)simulated(c) methodologicalsimulated values values are error are at theatof thethe height heightradio of altimeter of cca cca 5 m:5 m: is 4.5 4.5±0.375 m, m, 4.875 4.875m; m, m, and and 5.25 5.25 m, m, respectively, respectively, for for thethe bottom,(c)bottom, simulated mean, mean, and values upper and upper are values; at values;the height of cca 5 m: 4.5 m, 4.875 m, and 5.25 m, respectively, for the (d)bottom,number(d) mean,number of and simulated of uppersimulated values; unstable unstable pulses pulses subtracted subtracted within within the rangethe range of the of criticalthe critical height height is 22; is 22; (e) (d)number(e) numbernumber of calculated ofof simulatedcalculated unstable unstableunstable pulses pulsespulses within subtractedwithin range range of within critical of critical the height range height is of also isthe also22. critical 22. height is 22; (e)Based number on the of theorycalculated presented unstable in pulsesSection within 4, the rangerelation of forcritical the determinationheight is also 22. of the number of unstableBased pulses on the within theory the presented range of incritical Section height 4, the has relation been derived for the asdetermination a part of the ofresearch: the number of unstable pulses within the range of critical height has been∆ derived as a part of the research: 𝑁 = . (6) ∆ ∆ 𝑁 = . (6) From the above-presented results, it is possible ∆to conclude that by using the double value of the totalFrom frequency the above-presented deviation of results, 100 MHz it is possibleat the carrier to conclude frequency that ofby 4.4 using GHz the (a double total frequency value of thedeviation total frequency of 50 MHz deviation is recently of 100 used), MHz atit theis po carrierssible frequencyto increase of the4.4 GHzaccuracy (a total of thefrequency height deviationmeasurement of 50 two-fold. MHz is In recently this case, used), the criticalit is po heightssible isto 0.375 increase m, and the it accuracycan be obtained of the heightby the measurementformation of 22two-fold. unstable In height this case,pulses, the but critical only whenheight one is 0.375stable m, pulse and is it formed. can be Theobtained unstable by andthe formationstable pulses of 22 can unstable be supported height pulses,by the butderivation only when of a onebasic stable equation pulse ofis aformed. radio altimeter The unstable from and the stableheight pulses pulses can formation be supported [8]. by the derivation of a basic equation of a radio altimeter from the height pulses formation [8].

Electronics 2019, 8, 888 9 of 12

Based on the theory presented in Section4, the relation for the determination of the number of unstable pulses within the range of critical height has been derived as a part of the research:

2 2 f0 ∆ f NU = − . (6) 2 f0 ∆ f

From the above-presented results, it is possible to conclude that by using the double value of the total frequency deviation of 100 MHz at the carrier frequency of 4.4 GHz (a total frequency deviation of 50 MHz is recently used), it is possible to increase the accuracy of the height measurement two-fold. In this case, the critical height is 0.375 m, and it can be obtained by the formation of 22 unstable height pulses, but only when one stable pulse is formed. The unstable and stable pulses can be supported by the derivation of a basic equation of a radio altimeter from the height pulses formation [8]. The basic equation of a radio altimeter defines the relation between the value of the differential frequency and output information about the measured altitude, which is based on the basic parameters of a radio altimeter. Generally, known derivation comes out of the immediate difference of the frequencies of transmitted and received signals, proportionally to the time delay of the received signal, which depends on the measured altitude. A different method for a definition of a basic equation of a radio altimeter, based on critical height, has been derived during the research connected with the problem presented in the paper. As it has been presented in this manuscript, a certain number of stable height pulses, shaped during the time of one modulation period TM, corresponds to the measured altitude:

N H = . (7) TM

The formation of only one stable height pulse during the time of one modulation period corresponds to the height change within the range of critical height:

1 ∆H = . (8) TM

The following proportion can be obtained from Equations (7) and (8):

H N/T = M . (9) ∆H 1/TM

Replacing the modulation period by the modulation frequency in Equation (9) we have:

H NF = M . (10) ∆H FM

The product of NFM in Equation (10) presents the difference frequency, which is proportional to the altitude, so: F F = M H. (11) d ∆H Substitution of the critical height in Equation (11) from Equation (1) produces the basic equation of a radio altimeter presented in a completely different way from the generally known one, with the use of geometric similarity of triangles [18–20]:

8 ∆ f FM F = H. (12) d c This fact proves all the above-presented theoretical consideration, which allows for an increase in the accuracy of the altitude measurement by a radio altimeter. Electronics 2019, 8, 888 10 of 12

6. Software Application for Simulating the Unstable Pulses Creation For the needs of the simulation and graphical display of the formation of the unstable pulses, a software application in Qt (C++) environment has been created. The algorithm is based on a theoretical analysis of the formation and dissolution of pulses when measuring altitude by a radio Electronics 2019, 7, x FOR PEER REVIEW 10 of 12 Electronicsaltimeter 2019 (Figure, 7, x FOR8). PEER REVIEW 10 of 12

Figure 8. An example of the software application for simulating the unstable pulses creation. FigureFigure 8. 8. An An example example of of the the software software application application for for simulating simulating the the unstable unstable pulses pulses creation. creation. The individual values corresponding to the altitude of the pulse formation and dissolution depend TheThe individualindividual valuesvalues correspondingcorresponding toto thethe alaltitudetitude ofof thethe pulsepulse formationformation andand dissolutiondissolution on several parameters: the modulation frequency fm = 70 MHz, carrier frequency f 0 = 444 MHz, and depend on several parameters: the modulation frequency fm = 70 MHz, carrier frequency f0 = 444 dependfrequency on deviationseveral parameters:∆f = 8.5 MHz. the modulation One more parameterfrequency onfm = the 70 controlMHz, carrier panel isfrequency the choice f0 of= 444 the MHz, and frequency deviation Δf = 8.5 MHz. One more parameter on the control panel is the choice MHz,mean valueand frequency of the flight deviation altitude ΔHf =, around8.5 MHz. which One themore creation parameter of the on formation the control and panel dissolution is the choice of the of the mean value of the flight altitude H, around which the creation of the formation and ofunstable the mean pulses value is displayed. of the flight This isaltitude the altitude H, around that is interestingwhich the for creation us from of a certainthe formation point of view.and dissolution of the unstable pulses is displayed. This is the altitude that is interesting for us from a dissolutionThe height rangeof the is unstable limited topulses1 m is because displayed. a wider This height is the rangealtitude would that causeis interesting a graphical for ambiguity.us from a certain point of view. The height± range is limited to ±1 m because a wider height range would cause certainThe last point parameter of view. displayed The height on therange control is limited panel to represents ±1 m because the calculateda wider height number range of stablewould pulsescause a graphical ambiguity. The last parameter displayed on the control panel represents the calculated acorresponding graphical ambiguity. to the set The height last ofparameter the flight displaye altitudedH on. the control panel represents the calculated number of stable pulses corresponding to the set height of the flight altitude H. numberThese of stable parameters pulses can corresponding be changed with to the regard set height to the specificof the flight or hypothetical altitude H. type of radio altimeter These parameters can be changed with regard to the specific or hypothetical type of radio and itsThese technical parameters parameters can be using changed the application with regard control to the panel specific represented or hypothetical in Figure9 .type of radio altimeteraltimeter and and its its technical technical paramete parametersrs using using the the application application control control panel panel represented represented in in Figure Figure 9. 9.

FigureFigure 9. 9. Application ApplicationApplication control controlcontrol panel. panel.

Figure8 shows an example of the creation of unstable pulses for a set height of 4.6 m evaluated in FigureFigure 8 8 shows shows an an example example of of the the creation creation of of unst unstableable pulses pulses for for a a set set height height of of 4.6 4.6 m m evaluated evaluated the range of 3.6 m to 4.6 m. The parameters of the analyzed radio altimeter are shown in Figure9. inin the the range range of of 3.6 3.6 m m to to 4.6 4.6 m. m. The The parameters parameters of of the the analyzed analyzed radio radio altimeter altimeter are are shown shown in in Figure Figure 9. 9. The bottom part of the graph in Figure8 shows the process of gradual formation and dissolution TheThe bottombottom partpart ofof thethe graphgraph inin FigureFigure 88 showsshows thethe processprocess ofof gradualgradual formationformation andand of a large number of individual height pulses, with a change in height H. The upper part of the graph dissolutiondissolution of of a a large large number number of of individual individual height height pulses, pulses, with with a a change change in in height height H H. .The The upper upper part part presents the result of their mutual overlap by repeated formation and dissolution of one unstable ofof the the graph graph presents presents the the result result of of their their mutual mutual overlap overlap by by repeated repeated formation formation and and dissolution dissolution of of one one pulse in the ∆H range. The number of repeated formations of a single unstable pulse in the ∆H unstableunstable pulse pulse in in the the Δ ΔHH range. range. The The number number of of repeated repeated formatio formationsns of of a a single single unstable unstable pulse pulse in in the the ΔΔHH range range determines determines the the accuracy accuracy of of the the altitude altitude measurement. measurement. The The resulting resulting quantization quantization (stairs) (stairs) coursecourse of of unstable unstable pulses pulses within within the the Δ ΔHH range range shapes shapes a a number number of of stable stable pulses, pulses, which which correspond correspond toto the the measured measured altitude. altitude. The The software software application application can can be be used used to to compare compare the the height height pulse pulse creation creation andand to to simulate simulate this this process process for for different different type typess of of radio radio altimeters altimeters with with various various parameters. parameters.

7.7. Discussion Discussion and and Conclusions Conclusions

Electronics 2019, 8, 888 11 of 12 range determines the accuracy of the altitude measurement. The resulting quantization (stairs) course of unstable pulses within the ∆H range shapes a number of stable pulses, which correspond to the measured altitude. The software application can be used to compare the height pulse creation and to simulate this process for different types of radio altimeters with various parameters.

7. Discussion and Conclusions We have performed the analysis of the formation of the range of critical height of a radio altimeter methodological error when measuring the altitude. The analysis has been performed from the viewpoint of the determination of the number of unstable height pulses within the range of critical height. This manuscript focuses on the formation of unstable pulses within the range of critical height and explains the patterns between formation and dissolution of height pulses. As it is generally known, unstable pulses do not carry the information about measured altitude; they are not paid enough attention. Some works even consider the chaotic formation of the number of such pulses. Even though the unstable pulses do not determine measured altitude, and they have a critical influence on the precision of the height measurement. Precise altitude measuring relates to the method of difference signal processing. The presented analysis supported by simulation has confirmed the applicability of the basic idea for the processing of the differential signal in the form of the creation of stable and unstable pulses. The process of the determination of the number of unstable pulses within the range of critical height outlines a different view of the basic principle of a radio altimeter (shown in Figure4c). An original and exact process of the determination of the number of unstable height pulses within the range of critical height for the recent radio altimeters is also presented. This method of calculation logically follows from Equation (6), which has successfully been verified in this manuscript for a different type of a radio altimeter. The unique solution is based on the decrease of the value of the critical height by the decrease of the number of unstable pulses, which results in the doubled (extreme) increase of the frequency deviation at the original carrier frequency for the recent radio altimeters. In this way, the altitude measurement precision increases from the original value of 0.75 m to the two-times lower value of ± 0.375 m, without the need to increase the carrier frequency (two-fold). The correctness of this theory ± is highlighted by the new way of deriving the basic radio altimeter equation with the use of a critical height parameter. The results presented in the paper can be used for the design of new radio altimeters with the increased accuracy of the low altitude measurement.

Author Contributions: Conceptualization, J.L.; methodology, J.L.; software, M.C.ˇ and P.K.; validation, M.C.,ˇ A.N. and J.G.; formal analysis, J.L., A.N. and J.G.; investigation, J.L., A.N. and J.G.; resources, J.L. and P.K.; data curation, M.C.ˇ and P.K.; writing—original draft preparation, J.L.; writing—review and editing, J.L., A.N. and P.K.; visualization, M.C.ˇ and P.K.; supervision, J.L. and A.N.; project administration, J.G.; funding acquisition, J.G. Funding: Slovak authors J.L., P.K., M.C.,ˇ and J.G. has been supported by the Science Grant Agency of the Ministry of Education Science, Research, and Sport of the Slovak Republic, under contract No. 1/0772/17. Acknowledgments: A.N. wishes to express his sincere appreciation to the University of Malaga for the provided opportunities during his exchange visit. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Nebylov, A.V. Aerospace Sensors; Momentum Press: New York, NY, USA, 2013; p. 348, ISBN 1-60650-059-7. [CrossRef] 2. Kelemen, M.; Szabo, S. Pedagogical Research of Situational Management in Aviation Education and Forensic Investigation of Air Accidents: Knowledge of Aircraft Operation and Maintenance; Collegium Humanum: Warsaw, Poland, 2019; p. 144, ISBN 978-83-952951-1-9. 3. Labun, J.; Adamˇcík, F.; Pil’a, J.; Madarász, L. Effect of the measured pulses count on the methodical error of the air radio altimeter. Acta Polytech. Hung. 2010, 7, 41–49. Electronics 2019, 8, 888 12 of 12

4. Soták, M.; Labun, J. The new approach of evaluating differential signal of airborne FMCW radar-altimeter. Aerosp. Sci. Technol. 2012, 17, 1–6. [CrossRef] 5. Stove, A.G. Linear FMCW radar techniques. IEE Proc. F (Radar Signal Process.) 1992, 139, 343–350. [CrossRef] 6. Skolnik, M.I. Introduction to Radar Systems, 2nd ed.; McGraw Hill Book Company: Singapore, 1981; p. 581, ISBN 0-07-057909-1. 7. Labun, J.; Soták, M.; Kurdel, P. Technical note innovative technique of using the radar altimeter for prediction of terrain collision threats. J. Am. Helicopter Soc. 2012, 57, 85–87. [CrossRef] 8. Labun, J.; Krchˇnák, M.; Kurdel, P.; Ceškoviˇc,M.;ˇ Nekrasov, A.; Gamcová, M. Possibilities of increasing the low altitude measurement precision of airborne radio altimeters. Electronics 2018, 7, 191. [CrossRef] 9. Taylor, J. Aircraft Operation of Radio Altimeters. In Proceedings of the 24th Meeting of Working Group F, Aeronautical Communications Panel (ACP), Paris, France, 17–21 March 2011. 10. Alivizatos, E.G.; Petsios, M.N.; Uzunoglu, N.K. Architecture of a multistatic FMCW direction-finding radar. Aerosp. Sci. Technol. 2008, 12, 169–176. [CrossRef] 11. Baskakov, A.I.; Komarov, A.A.; Mikhailov, M.S.; Ruban, A.V. Modeling of the methodical errors of high-precision aircraft radar altimeter operating above the seasurface at low altitudes. In Proceedings of the 2017 Progress in Electromagnetics Research Symposium—Spring (PIERS), St. Petersburg, Russia, 22–25 May 2017; pp. 3236–3240. [CrossRef] 12. Singh, R.; Peterson, R.; Riaz, A.; Hood, C.; Bacchus, R.; Roberson, D. A method for evaluating coexistence of LTE and radar altimeters in the 4.2–4.4 GHz band. In Proceedings of the 2017 Wireless Telecommunications Symposium (WTS), Chicago, IL, USA, 26–28 April 2017; pp. 1–9. 13. Liu, J.; Shen, C.; Wu, S.; Huang, W.; Li, C.; Zhu, Y.; Wang, L. Correction method of the manned spacecraft low altitude ranging based on γ ray. Aerosp. Sci. Technol. 2016, 50, 71–76. [CrossRef] 14. Labun, J.; Grega, M.; Sopata, M.; Kmec, F. Aircraft Radio Altimeter for Small Heights with Frequency Modulation Design II. Patent 283439; Banská Bystrica, Slovak Republic, 20 June 2003. 15. Grega, M.; Labun, J. Aircraft Radar Altimeter with Frequency Modulation Design. Patent 262626; Prague, Czechoslovak Republic, 16 August 1988. 16. Kayton, M.; Fried, W.R. Systems; John Wieley & Sons: New York, NY, USA, 1997; p. 773, ISBN 0-471-54795-6. 17. Nekrasov, A. Foundations for Innovative Application of Airborne : Measuring the Water Surface Backscattering Signature and Wind; Springer: Dordrecht, The Netherlands, 2014; p. 116, ISBN 978-3-319-00620-8. [CrossRef] 18. Fasano, G.; Accardo, D.; Tirri, A.E.; Moccia, A.; Lellis, E. Radio/electro-optical data fusion for non-cooperative UAS sense and avoid. Aerosp. Sci. Technol. 2015, 46, 436–450. [CrossRef] 19. Metzger, J.; Meister, O.; Trommer, G.F.; Tumbrägel, F.; Taddiken, B. Adaptations of a comparison technique for terrain navigation. Aerosp. Sci. Technol. 2005, 9, 553–560. [CrossRef] 20. Estrada, J.; Zurek, P.; Popovi´c,Z. Harvesting of aircraft radar altimeter side lobes for low-power sensors. In Proceedings of the 2018 International Applied Computational Electromagnetics Society Symposium (ACES 2018), Denver, CO, USA, 24–29 March 2018; pp. 1–2. [CrossRef]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).