Kalman Filter and Wavelet Cross-Correlation for VHF Broadband Interferometer Lightning Mapping

applied sciences

Article Kalman Filter and Wavelet Cross-Correlation for VHF Broadband Interferometer Lightning Mapping

Ammar Alammari 1,2, Ammar A. Alkahtani 1,*, Mohd Riduan Ahmad 2, Fuad Noman 1 , Mona Riza Mohd Esa 3 , Muhammad Haziq Mohammad Sabri 1 , Sulaiman Ali Mohammad 3, Ahmed Salih Al-Khaleefa 2,4 , Zen Kawasaki 5 and Vassilios Agelidis 1,6

1 Institute of Sustainable Energy (ISE), Universiti Tenaga Nasional (UNITEN), Selangor 43000, Malaysia; [email protected] (A.A.); [email protected] (F.N.); [email protected] (M.H.M.S.); [email protected] (V.A.) 2 Atmospheric and Lightning Research Laboratory, Center for Telecommunication Research and Innovation (CeTRI), Fakulti Kejuruteraan Elektronik dan Kejuruteraan Komputer (FKEKK), Universiti Teknikal Malaysia Melaka (UTeM), Melaka 76100, Malaysia; [email protected] (M.R.A.); [email protected] (A.S.A.-K.) 3 IVAT, Sekolah Kejuruteraan Elektrik, Fakulti Kejuruteraan, Universiti Teknologi Malaysia (UTM), Johor 8300, Malaysia; [email protected] (M.R.M.E.); [email protected] (S.A.M.) 4 Network and Communication Technology (NCT) Lab, Fakulti Teknologi & Sains Maklumat (FTSM), Universiti Kebangsaan Malaysia (UKM), Bangi 43600 UKM, Selangor, Malaysia 5 Graduate School of Engineering, Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan; [email protected] 6 Department of Electrical Engineering, Technical University of Denmark, Anjer Engeluds Vej 1 Bygning 101A, 2800 Kgs. Lyngby, Denmark * Correspondence: [email protected]

Received: 9 April 2020; Accepted: 29 May 2020; Published: 20 June 2020

Abstract: Lightning mapping systems based on perpendicular crossed baseline interferometer (ITF) technology have been developed rapidly in recent years. Several processing methods have been proposed to estimate the temporal location and spatial map of lightning strikes. In this paper, a single very high frequency (VHF) ITF is used to simulate and augment the lightning maps. We perform a comparative study of using different processing techniques and procedures to enhance the localization and mapping of lightning VHF radiation. The benchmark environment involves the use of different noise reduction and cross-correlation methods. Moreover, interpolation techniques are introduced to smoothen the correlation peaks for more accurate lightning localization. A positive narrow bipolar event (NBE) lightning discharge is analyzed and the mapping procedure is confirmed using both simulated and measured lightning signals. The results indicate that a good estimation of lightning radiation sources is achieved when using wavelet denoising and cross-correlations in wavelet-domain (CCWD) with a minimal error of 3.46◦. The investigations carried out in this study confirm that the ITF mapping system could effectively map the lightning VHF radiation source.

Keywords: interferometer (ITF); lightning mapping; magnetic direction ﬁnder (MDF); time of arrival (TOA)

1. Introduction Lightning is a natural phenomenon that occurs in the atmosphere. When electrical discharges are generated, electromagnetic radiations over diﬀerent ranges of frequencies are produced, usually extending from the Ultra-Low Frequency (ULF) through the Ultra-High Frequency (UHF) [1]. Electromagnetic ﬁelds are emitted either from cloud-to-ground (CG) strikes, intra-cloud (IC) lightning,

Appl. Sci. 2020, 10, 4238; doi:10.3390/app10124238 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 4238 2 of 14 and some in-cloud processes [2–6]. The physics behind lightning initiation suggested that lightning is produced when a considerable amount of warm air is up-drafted to a height where an extremely low temperature can cause particles of frozen ice to produce electric charge disconnections [7]. Lightning strikes can cause harm to human beings and extend effects to systems operating in the surrounding environment. These effects can be minimized if reliable lightning mapping and localization systems are deployed to enable accurate prediction and detection of lightning strikes [4], [8–11]. Lightning mapping provides sufficient information on detected CG flashes at a particular range of frequencies. The very high frequency (VHF) band has been important for lightning mapping and for studying the lightning process over the past four decades [12]. The VHF lightning mapping is carried out in two different ways: time of arrival (TOA) and direction of arrival (DOA) or what is generally known as interferometry (ITF). The VHF lightning mapping has been traditionally performed using the TOA approach and narrow-band ITF systems to locate the radiation sources [13–15]. The TOA uses the time difference of arrival (TDOA) technique which requires at least four to five antennae [6]. On the other hand, the narrowband ITF system uses closely spaced multiple baseline antennae (in order of n wavelength, nλ) to resolve the radiation measurement ambiguities and obtain the desired angular resolution [9]. The use of broadband ITF for lightning localization was first introduced by [2], and has been developed rapidly during the past few decades [16–20]. Unlike the narrowband ITF, the broadband ITF uses all frequency components which are then used to produce a better resolution of lightning discharges. In the latest development of ITF systems, an array of closely spaced antennae (three perpendicular antennae) are used to capture and map the lightning radiation into the two-dimensional mapping of sources [9]. Despite the significant improvements made to map lightning using ITF systems, the mapping accuracy remains a challenge. In this paper, we exploit the effects of different parameters of well-established methods to estimate the lightning maps accurately. We propose a modified cross-correlation method to solve problems in the DOA calculation and to improve the lightning location accuracy. We examine various noise filtering to reduce the low and high noise frequency contents. Noisy lightning signals impact the cross-correlation performance and lead to incorrect estimation of phase difference. Different generalized cross-correlation techniques are used to estimate the TDOA in a segment-wise manner. These techniques include conventional time and frequency domain cross-correlation. However, these generalized cross-correlation methods are more sensitive to the embedded noise in the signal, which results in wrong TDOA estimations. Therefore, we extend the proposed framework to include the wavelet-based cross-correlation, which reduces the noise and improves the system location accuracy. We then compare the proposed technique to the conventional cross-correlation techniques. We also investigate the effect of interpolating the cross-correlation function in determining the time difference. To assess the performance of the proposed lightning mapping approach, we introduce a simulation technique to generate a broadband ITF lightning. In the simulation part, we examine the effectiveness of the proposed methods in a noisy environment, where two Gaussian noises with different SNRs (in dB) are added to the simulated lightning signals. This paper is organized as follows. In Section2, we discuss the background of the broadband ITF, the preprocessing of the original data, the related steps of lightning mapping estimation, and the simulation procedure of lightning data. Section3 presents the obtained lightning mapping from the measured VHF radiation sources and also a comparison with the simulation result. This paper is concluded in Section4.

2. Materials and Methods This section introduces the broadband ITF structure and the related methods used for two-dimensional lightning mapping. Then, we present the proposed procedure for lightning data simulations. Appl.Appl. Sci. 2020,, 1010,, 4238x FOR PEER REVIEW 33 ofof 1413

2.1. Broadband Interferometer (ITF) 2.1. Broadband Interferometer (ITF) Figure 1 shows the proposed lightning mapping general procedures consisting of three stages: (1) PreprocessingFigure1 shows to the assess proposed the VHF lightning signal quality, mapping by general removing procedures noise components consisting and of three performing stages: (1)amplitude Preprocessing normalization. to assess (2) the A VHF piecewise signal quality,procedure by removingis used to noisesegment components the lightning and performingsignals into amplitudeoverlapped normalization. sliding windows (2) Ato piecewiseperform the procedure cross-correlations is used to and segment calculate the lightning the phase signals difference into overlappedfrom overlapping sliding VHF windows signals to performtime difference the cross-correlations at each pair of and antennae. calculate Different the phase cross-correlation difference from overlappingtechniques in VHF time-domain signals time (TD), difference frequency-domain at each pair of (FD) antennae. and wavelet-domain Different cross-correlation (WD) were techniques applied. in(3) time-domain The lightning (TD), maps frequency-domain are derived by (FD) calculating and wavelet-domain the azimuth (WD)and elevation were applied. angles (3) Thefrom lightning the ITF mapsgeometry. are derived by calculating the azimuth and elevation angles from the ITF geometry.

FigureFigure 1.1. The procedure of lightning mapping.mapping.

2.1.1.2.1.1. Preprocessing PriorPrior toto capturing the lightning electric fieldfield (E-field)(E-field) signalsignal atat the VHF-ITF system, the lightning electricelectric fieldfield signalsignal travelstravels from its originorigin in thethe clouds and usually propagates through open space. TheThe signalsignal isis aaffectedffected byby reflection,reflection, refraction,refraction, absorption,absorption, andand otherother interferenceinterference means.means. To removeremove thethe unwantedunwanted noisenoise fromfrom thethe recordedrecorded lightning,lightning, signalssignals areare usuallyusually filteredfiltered usingusing bandpassbandpass filtersfilters withwith didifferentfferent cut-ocut-offff frequenciesfrequencies [[9,21,22].9,21,22]. InIn thisthis paper,paper, wewe investigateinvestigate threethree typestypes ofof noisenoise filteringfiltering approachesapproaches includingincluding bandpass filterfilter (BPF), Kalman filterfilter (KF) [[23,24],23,24], and wavelet transform (WT) denoisingdenoising [[25].25]. The key difference difference between these filt filtersers is that the BPF isis thethe simplestsimplest andand fastestfastest approachapproach ofof filteringfiltering in-bandin-band noises;noises; however,however, itit implicitlyimplicitly assumesassumes thatthat thethe noisenoise occupiesoccupies aa specificspecific frequencyfrequency bandband (e.g.,(e.g., 2020 toto 100100 MHz).MHz). Hence, the BPFBPF fails if the noisenoise occupiesoccupies didifferentfferent frequencyfrequency bands.bands. The The WT WT denoising denoising solves solves this this issue issue by bydec decomposingomposing the thesignal signal into intodifferent different frequency frequency sub- sub-bandsbands and andapply apply thresholding thresholding rules rules to eliminate to eliminate the unwanted the unwanted frequency frequency contents contents from fromdifferent different sub- sub-bands.bands. However, However, WT requires WT requires prior prior information information of the of specific the specific bands bands when when the noise the noise exists. exists. The TheKalman Kalman filter filter can canexplicitly explicitly model model the the signal signal as asa astochastic stochastic process process given given prior prior knowledge knowledge of thethe noisenoise statisticalstatistical parameters which make Kalman filterfilter superior in cases where thethe noisenoise frequencyfrequency bandband isis unknown.unknown. The The main limitation of the Kalman filter filter is that it assumes the signal has onlyonly GaussianGaussian noise.noise.

2.1.2.2.1.2. Time DiDifferenceﬀerence ofof ArrivalArrival (TDOA)(TDOA) ToTo calculate the TDOA TDOA and and determine determine the the direction direction of ofthe the lightning lightning VHF VHF radiation radiation source, source, the thecross-correlation cross-correlation has has been been traditionally traditionally used used for for estimating estimating the the similariti similaritieses between between two crossedcrossed baselinesbaselines (consisting(consisting ofof threethree antennae).antennae). This This process is achieved by usingusing slidingsliding overlappedoverlapped windows.windows. Besides, the generalized cross-correlationcross-correlation technique is one of the most classical time delay estimationestimation methods.methods. Figure 2 illustrates the basic geometry of orthogonal baselines for two-dimensional lightning mapping. From Figure 2, the given two baselines (BC and BD) separated by distance d (15 m in this study), the TDOAs at each baseline can be calculated as, Appl. Sci. 2020, 10, 4238 4 of 14

Figure2 illustrates the basic geometry of orthogonal baselines for two-dimensional lightning Appl.mapping. Sci. 2020 From, 10, x FOR Figure PEER2, REVIEW the given two baselines (BC and BD) separated by distance d (15 m in4 of this 13 study), the TDOAs at each baseline can be calculated as, 𝛥𝜙 𝜏 (1) ∆φ2𝜋𝑓1 τ = (1) d1 2π f 𝛥𝜙 𝜏 (2) ∆φ2 τ = 2𝜋𝑓 (2) d2 2π f where 𝜏 and 𝜏 are the time differences of the baselines BC and BD, respectively. 𝛥𝜙 2𝜋𝑓𝜏 iswhere the phaseτd1 and differenceτd2 are the of a time distant diﬀ erencessignal (with of the frequency baselines BC𝑓 in and Hz) BD, arriving respectively. at two antennae.∆φ = 2π f τ𝛥𝜙d is can the bephase found diﬀ implicitlyerence of a by distant performing signal (with the cross frequency‐correlationf in Hz) procedure. arriving at two antennae. ∆φ can be found implicitly by performing the cross-correlation procedure.

Radiation Source

El B D North Az C

East

Figure 2. BasicBasic interferometer interferometer geometry [9,19]. [9,19].

2.1.3. Lightning Lightning Mapping Mapping For sources locatedlocated in in two two spatial spatial dimensions, dimensions, two two angles angles are are needed needed to specifyto specify the directionthe direction and andheight height of the of radiation the radiation source, source, namely namely the azimuth the azimuth (Az) and (𝐴𝑧 elevation) and elevation (El) angles. (𝐸𝑙) From angles. the From spherical the sphericalcoordinate coordinate in Figure2 in, the FigureAz and2, theEl 𝐴𝑧angles and can 𝐸𝑙 beangles found can by, be found by,

𝜏! 𝐴𝑧 arctanτd 1 (3) Az = arctan 𝜏 (3) τd2

c 𝑐q El𝐸𝑙= arccos arccos τ2𝜏+𝜏τ2 (4) d 𝑑 d1 d2 where c is the speed of light, τ and τ are the TDOAs of the two orthogonal baselines. The TDOA where c is the speed of light, 𝜏d1 and 𝜏d2 are the TDOAs of the two orthogonal baselines. The TDOA (τ ) between every pair of antennae cannot exceed the transit time τ = c/d. This constrains the (𝜏d) between every pair of antennae cannot exceed the transit time transit𝜏 𝑐⁄ . 𝑑 This constrains instance between the brackets of Equation (4) to have values in the range of 1. However, any values the instance between the brackets of Equation (4) to have values in the range± of ±1. However, any exceed the 1 range are considered as wrong estimations due to existing noise, and the corresponding values exceed± the ±1 range are considered as wrong estimations due to existing noise, and the correspondingAz and El angles 𝐴𝑧 can and be 𝐸𝑙 neglected angles can from be the neglected cross-correlation from the calculations.cross‐correlation calculations. In this this paper, paper, we we compare compare the the performance performance of three of three filtering filtering approaches, approaches, a Butterworth a Butterworth BPF filter BPF offilter order of order4 and 4 cut and‐off cut-o frequenciesff frequencies of (20–100 of (20–100 MHz) MHz) (fdesign (fdesign MATLAB MATLAB function), function), a Kalman a Kalman filter (implementedfilter (implemented in MATLAB in MATLAB [26] as [in26 [24]),] as in and [24 a]), wavelet and a denoising wavelet denoising technique technique(wdenoise (wdenoiseMATLAB function).MATLAB The function). wavelet The filtering wavelet methods filtering are abbreviated methods are in abbreviated this study for in simplicity, this study e.g., for WT simplicity,‐Coif5‐ SUREe.g., WT-Coif5-SURE is the wavelet isdenoising the wavelet using denoising the Coiflet using wavelet the Coiflet function wavelet of functionorder 5 with of order Stein 5 withʹs unbiased Stein’s riskunbiased estimate risk estimate(SURE) (SURE)thresholding thresholding rule. Besides rule. Besides the influence the influence of ofdifferent different wavelet wavelet denoising functions, we also report the results of using two different different thresholding rules, SURE and Universal Threshold. Wavelet Wavelet denoising methods alter alter the estimated wavelet coefficients coefficients before the reversed transformation (reconstruction),(reconstruction), which which is is achieved achieved with with some some thresholding thresholding rules. rules. The The Kalman Kalman filter filter is a ispowerful a powerful tool thattool uses that the uses state the space state formulations space formulations with a set with of mathematical a set of mathematical equations toequations recursively to recursivelyestimate future estimate observations future observations minimizing minimizing the mean square the mean error square of these error estimates. of these Hence,estimates. the Hence, output the output of the Kalman filter is considered as a clean copy of the noisy signal where the filter successfully eliminates the Gaussian noises. Further details of the implemented Kalman filter in this paper can be found in [24]. Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13

Three cross-correlation methods are used; namely, cross-correlation in the time domain (CCTD), cross-correlation in the frequency domain (CCFD), and cross-correlation in the wavelet domain (CCWD). We have implemented the three cross-correlation methods in MATLAB, where a recursive sliding dot-product was used for CCTD, recursive conjugate dot-product of fft MATLAB function for CCFD, and modwtxcorr MATLAB function for CCWD. The cross-correlation is used to measure the similarity of lightning signals received at multiple antennae. In this context, a measure of similarity Appl. Sci. 2020, 10, 4238 5 of 14 is to locate the peak of cross-correlation (the highest value of correlation coefficients over time lags) which then used to calculate the time delay of arrival between the correlated signals. of the Kalman filter is considered as a clean copy of the noisy signal where the filter successfully 2.2.eliminates Hardware the Gaussian noises. Further details of the implemented Kalman filter in this paper can be foundFigure in [24 3]. shows the configuration diagram of the proposed ITF system which consists of three sets ofThree antennae, cross-correlation with two perpendicular methods are baselines used; namely, of 15 cross-correlationm in length (3λ), inband-pass the time filters, domain low (CCTD), noise amplifierscross-correlation (LNA), incoaxial the frequencycables, and domain an oscilloscope (CCFD),. Two and types cross-correlation of parallel-pla inte the antennae wavelet of domainsize A4 and(CCWD). A3 are We used have to capture implemented the VHF the E-field three cross-correlationand Fast E-field (10 methods Hz up into MATLAB,3 MHz) of wherelightning a recursive flashes, respectively.sliding dot-product For the wasVHF used E-field for antenna, CCTD, recursive the gap between conjugate the dot-product two plates ofis ffaboutt MATLAB h = 1 cm function and 3 cm for forCCFD, Fast andE-field modwtxcorr to avoid the MATLAB fringing function effects forfor CCWD.the VHF The sensor cross-correlation [27,28]. The Fast is used E-field to measure antenna the is usedsimilarity to determine of lightning the signalstype of receivedlightning at flash, multiple and antennae.the VHF E-field In this context,antenna ais measure used to ofcapture similarity the lightningis to locate radiation the peak emissions. of cross-correlation Figure 3 (theillustra highesttes the value implemented of correlation antennae coefficients B, C, over and time D were lags) arrangedwhich then in usedperpendicular to calculate baselines the time with delay two of side arrivals BC between and BD theto measure correlated the signals. phase difference. The broadband ITF system was installed in Klebang Beach, Malacca Strait, Melaka, Malaysia (2.216304° 2.2. Hardware N, 102.192288° E). TheFigure received3 shows VHF the signal configuration at each antenna diagram is of sequentially the proposed passed ITF systemthrough which preamplifier consists and of three BPF beforesets of being antennae, digitized with twoand perpendicularstored in external baselines memory. of 15 mThe in LNA length amplifie (3λ), band-passs the low-power filters, low signals noise preservingamplifiers (LNA),the signal-to-noise-ratio coaxial cables, and of anthe oscilloscope. received signal. Two The types bandwidth of parallel-plate of the BPF antennae is limited of size to the A4 rangeand A3 40–80 are usedMHz to with capture a center the VHFfrequency E-field of and 60 FastMHz E-field [17]. The (10 Hzfiltered up to analog 3 MHz) signal of lightning is then passed flashes, torespectively. the oscilloscope For the (PicoScope VHF E-field 3000 antenna, series [29] the wi gapth 100 between MHz thebandwidth) two plates through is about threeh = 1coaxial cm and cables 3 cm offor 15 Fast m length. E-field toThe avoid output the fringingof the antenna effects was for the digiti VHFzed sensor in the [27 oscilloscope,28]. The Fast at E-fielda sampling antenna frequency is used ofto 250 determine MS/s with the type a vertical of lightning resolution flash, of and 8 thebits. VHF Data E-field records antenna were isevent-triggered used to capture and the stored lightning in segmentsradiation of emissions. 200 ms length. Figure Then,3 illustrates the retrieved the implemented data from the antennaeoscilloscope B, C,are and transferred D were to arranged a personal in computerperpendicular with baselines MATLAB with software two sides for BC lightning and BD to localization measure the analysis. phase diff Aerence. summary The broadband of the ITF’s ITF attributessystem was is given installed in Table in Klebang 1. Beach, Malacca Strait, Melaka, Malaysia (2.216304◦ N, 102.192288◦ E).

FigureFigure 3. 3. VHFVHF broadband broadband digital digital interferom interferometereter data data acquisition acquisition system. system.

2.3. SimulationThe received VHF signal at each antenna is sequentially passed through preamplifier and BPF before being digitized and stored in external memory. The LNA amplifies the low-power signals In this sub-section, numerical simulations are conducted to assess the performance of the preserving the signal-to-noise-ratio of the received signal. The bandwidth of the BPF is limited to the proposed mapping methods using simulated VHF-ITF signals. An actual measured signal (from range 40–80 MHz with a center frequency of 60 MHz [17]. The filtered analog signal is then passed to antenna B is used as a reference to simulate the other perpendicular antennae (C and D). Given the the oscilloscope (PicoScope 3000 series [29] with 100 MHz bandwidth) through three coaxial cables of hand-crafted azimuth and elevation incident angles, the signals of antennae C and D are copies of 15 m length. The output of the antenna was digitized in the oscilloscope at a sampling frequency of antenna B with a phase shift for each temporal sliding window. This simulation can provide an 250 MS/s with a vertical resolution of 8 bits. Data records were event-triggered and stored in segments insight into the best methodological approach for estimating lightning mapping. Figure 4 illustrates of 200 ms length. Then, the retrieved data from the oscilloscope are transferred to a personal computer the proposed steps to simulate the lightning mapping signals and to evaluate the performance of the with MATLAB software for lightning localization analysis. A summary of the ITF’s attributes is given estimation methods. in Table1.

2.3. Simulation In this sub-section, numerical simulations are conducted to assess the performance of the proposed mapping methods using simulated VHF-ITF signals. An actual measured signal (from antenna B is used as a reference to simulate the other perpendicular antennae (C and D). Given the hand-crafted azimuth and elevation incident angles, the signals of antennae C and D are copies of antenna B with a Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 13

Table 1. The parameters for the interferometer and the lightning flash. Appl. Sci. 2020, 10, 4238 6 of 14 Parameters Description Sample interval 4 ns phase shift for each temporalSampling sliding Rate window. of VHF This simulation 250 can MS/s provide an insight into the best methodological approach forNo estimating of samples lightning mapping. Figure 52,000,0024 illustrates the proposed steps to simulate the lightning mapping signals and to evaluate the performance of the estimation methods. Number of Antennae 3

Table 1.SignalThe parameters band-limited for the interferometer 40–80 and the MHz lightning ﬂash. Centred Frequency 60 MHz Distance betweenParameters antennae Description 15 m baseline PicoscopeSample interval Picoscope 4 ns 3000 (3405D) Sampling Rate of VHF 250 MS/s No of samples 52,000,002 2.3.1. Generation of Azimuth andNumber Elevation of Antennae Angles 3 Signal band-limited 40–80 MHz This part presents some basicCentred but Frequencypowerful data augmentation 60 MHz techniques. Data augmentation is a strategy that enables practitionersDistance between to signific antennaeantly increase 15 m baseline the diversity of data available for analysis, without actually collectingPicoscope new data. Picoscope 3000 (3405D)

FigureFigure 4. 4.TheThe procedure procedure of of simulati simulatingng lightninglightning signals. signals.

2.3.1. Generation of Azimuth and Elevation Angles Various data augmentation techniques were implemented in this study, such as adding GaussianThis noise, part scaling, presents and some flipping basic but and powerful their co datambinations. augmentation Figure techniques. 5 shows Datasome augmentation examples of isthese lightninga strategy data that augmentation enables practitioners techniques. to significantly The generated increase 𝐴𝑧 the diversityand 𝐸𝑙 angles of data availablefrom the for hand-crafted analysis, lightningwithout signal actually are collectingassumed new to data.be real-positive or negative values. The Gaussian noise 𝜀 is an Various data augmentation techniques were implemented in this study, such as adding Gaussian independent and identically distributed random variable, 𝑁~0,1 , with zero-mean and unit- noise, scaling, and flipping and their combinations. Figure5 shows some examples of these lightning variance, which is added to the 𝐸𝑙 angles; the output 𝐸𝑙 = 𝐸𝑙 +𝜀,∀𝜏 𝜏 is a shifted data augmentation techniques. The generated Az and El angles from the hand-crafted lightning version of the real 𝐸𝑙 values constrained to the transit time between two antennae 𝜏 = = signal are assumed to be real-positive or negative values. The Gaussian noise ε is an independent 5 and10 identically 𝑠. distributed random variable, N (0, 1), with zero-mean and unit-variance, which is ∼ added to the El angles; the output Elˆ = El + ε , τ < τ is a shifted version of the real El values i i i ∀ di transit constrained to the transit time between two antennae τ = d = 5 10 8 s. transit c × − For scaling augmentation, since the simulated azimuth (Az) and elevation (El) angles fall in a relatively narrow range, the outward scaling is used as it expands the azimuth and elevation range, forcing the proposed methods to make assumptions about what lies beyond the simulated values boundary. The lightning representations can be flipped horizontally and vertically. However, in practice, lightning mapping is not preferred to be flipped vertically. A horizontal flip is equivalent to rotating the lightning curve by 180 degrees. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 13 Appl. Sci. 2020, 10, 4238 7 of 14

a. b.

c. d.

FigureFigure 5. 5. ExampleExample of of angles angles augmentation augmentation by by (a)( aadding) adding Gaussian Gaussian noise, noise, (b) (scaling,b) scaling, (c) flipping, (c) ﬂipping, (d) combination(d) combination of (a, of b, (a and–c). c).

2.3.2.For Derivation scaling augmentation, of Time Delay since the simulated azimuth (𝐴𝑧) and elevation (𝐸𝑙) angles fall in a relatively narrow range, the outward scaling is used as it expands the azimuth and elevation range, For calculating the time delay τ and τ , a reverse mathematical derivation of the geometrical forcing the proposed methods to maked1 assumptiond2 s about what lies beyond the simulated values equations in Section 2.1.2 is followed. τ can be derived from the spherical Equation (3) and as follows, boundary. The lightning representationsd1 can be flipped horizontally and vertically. However, in practice, lightning mapping is not preferred to be flipped vertically. A horizontal flip is equivalent to τd1 = tan(Az)τd2 (5) rotating the lightning curve by 180 degrees.

From Equations (4) and (5), the TDOA τd2 can be found by, 2.3.2. Derivation of Time Delay q (El) = c 2 + 2 For calculating the time delay 𝜏 cosand 𝜏, a dreverseτd1 mathematicalτd2 derivation of the geometrical equations in Section 2.1.2 is followed. 𝜏 can be qderived from the spherical Equation (3) and as d cos(El) = τ2 + τ2 (6) follows, c d1 d2 d2 2 2 2 2 cos (El) = τ + τ 𝜏 c= tan𝐴𝑧 𝜏 d1 d2 (5)

FromSubstituting Equations Equation (4) and (5) (5), into the Equation TDOA 𝜏 (6) we canget be found by,

2 𝑐 d coscos2𝐸𝑙(El) == (tan𝜏(Az +)τ 𝜏)2 + τ 2 c2 𝑑 d2 d2 2 d 2(El) = 2(Az) 2 + 2 c2 cos tan τd2 τd2 𝑑 2 cos𝐸𝑙 = 𝜏 + 𝜏 d 𝑐cos2(El) = τ2 ((1 + tan2(Az)) c2 d2 (7) d2 cos2(El) 𝑑 τ2 = cosd2𝐸𝑙 c=2(( 1𝜏+tan +2( Az𝜏)) 𝑐 r (6) d2 cos2(El) τ = Substituting Equation (5) into Equationd2 (6) wec2(( 1get+tan 2(Az)) 𝑑 Consequently, substitutingcos Equation𝐸𝑙 = (7) tan into𝐴𝑧 Equation(5),𝜏 + 𝜏 we can obtain the time diﬀerence 𝑐 between the two antennae: r 𝑑 d2 cos2(El) cos τ𝐸𝑙= =tan tan(Az)𝐴𝑧 𝜏 + 𝜏 𝑐 d1 c2(1+tan2(Az) (8) 𝑑 = d tan(Az) cos(El) cos𝐸𝑙τ d=1 𝜏 1q + tan𝐴𝑧 𝑐 c (1+tan2(Az)) 𝑑cos𝐸𝑙 𝜏 = 𝑐1 + tan𝐴𝑧 (7) Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 13

𝑑 cos𝐸𝑙 𝜏 = 𝑐1 + tan𝐴𝑧

Consequently, substituting Equation (7) into Equation(5), we can obtain the time difference between the two antennae:

𝑑cos𝐸𝑙 𝜏 = tan𝐴𝑧 𝑐1 + tan𝐴𝑧

𝑑 tan𝐴𝑧 cos𝐸𝑙 Appl. Sci. 2020, 10, 4238 𝜏 = 8 of 14 𝑐1 + tan𝐴𝑧 (8) 2.3.3. Simulated ITF Signals 2.3.3. Simulated ITF Signals Given a captured lightning signal of antenna B (located at Cartesian coordinate 0 of Figure2), Figure6 Givenillustrates a captured the proposed lightning simulation signal of antenna steps, includingB (located windowing,at Cartesian coor calculatingdinate 0 of the Figure amount 2), of Figure 6 illustrates the proposed simulation steps, including windowing, calculating the amount of temporal shift for each particular window, and using Equations (7) and (8) to produce corresponding temporal shift for each particular window, and using Equations (7) and (8) to produce corresponding simulated step-wise signals for antennae C and D, respectively. The simulated sliding windows are simulated step-wise signals for antennae C and D, respectively. The simulated sliding windows are then concatenated to form a full track of VHF-ITF lightning signals. then concatenated to form a full track of VHF-ITF lightning signals.

𝑊 FigureFigure 6. The 6. The general general procedure procedure of of Simulating Simulating ITF Signal. Where Where W n isis the the window window length length (i.e., (i.e., 256 256 samples), 𝑊 ,𝑖 = 1,...,𝑁 is window counter, 𝑁 is the total number of sliding windows of the samples), Wi , i = 1, ... , N is window counter, N is the total number of sliding windows of the processed ITF signal, 𝑊 +1 is the temporal shift for subsequent windows (1 sample). processed ITF signal, Wn + 1 is the temporal shift for subsequent windows (1 sample). 3. Results3. Results and and discussion discussion In thisIn this paper, paper, we we consider consider the the use use ofof thethe broadbandbroadband ITF ITF technique technique for for the the analysis analysis of VHF of VHF lightninglightning mapping. mapping. A A comparison comparison ofof variousvarious proce processingssing methods methods of of the the VHF VHF lightning lightning signals signals is is performed.performed. The The simulation simulation was was conducted conducted toto investigateinvestigate the the impact impact of of noise noise and and data data resolution resolution on on lightninglightning mapping mapping accuracy. accuracy. Di Differentfferent filtering filtering andand cross-correlation techniques techniques were were implemented implemented introducing new processing methods such as Kalman filter and wavelet-based cross-correlation. The introducing new processing methods such as Kalman filter and wavelet-based cross-correlation. best performing set of methods are validated using collected real lightning signals. Figure 7 shows The best performing set of methods are validated using collected real lightning signals. Figure7 shows an example of cross-correlation steps to determine the TDOA 𝜏 using two antennae sliding an examplewindows.Appl. Sci. of 2020 cross-correlation, 10, x FOR PEER REVIEW steps to determine the TDOA τd using two antennae sliding9 of windows. 13

Figure 7. Example of the processing steps used to determine the TDOA (τ ) at antennae B and C. Figure 7. Example of the processing steps used to determine the TDOA (𝜏) at antennaed B and C. (a) (a) NormalizedNormalized waveforms waveforms from from thethe twotwo antennae B Band and C Cfor for a 256 a 256 (1.042 (1.042 μs) sampleµs) sample window; window; (b) the (b) the cross-correlationcross-correlation of antennae of antennae B and B and C C signals signals with with two vertical vertical red red dash-lines dash-lines indicate indicate the zoomed the zoomed plot areaplot in area c; (c in) illustratingc; (c) illustrating the the interpolation interpolation ﬁtting fitting (red color) color) of ofthe the expanded expanded view view cross-correlation cross-correlation (blue color)(blue withcolor) verticalwith vertical red dash-linered dash-line showing showing the the peakpeak of of correlation. correlation.

1 𝑑𝑖𝑠𝑡 = 𝐴𝑧 𝐴𝑧 + 𝐸𝑙 𝐸𝑙 (9) 𝑊

where 𝑊 is the total number of sliding windows in the processed lightning data. To summarize the performance of the simulated dataset overall, we compute the average of Euclidean distances. Table 2 summarizes the performance comparisons of the suggested lightning mapping estimation methods. In Table 2, The Euclidean distances were calculated for each simulated ITF datum and then averaged over the entire available augmented lightning dataset to show the overall benchmarking performance of the suggested approaches. We compare three main filtering approaches listed in the first column of Table 2. It can be seen that, when using the CCTD method, the KF and BPF show the lowest Euclidean distances of 3.55° and 3.63° respectively. The linear- interpolation factor used to achieve these results was 8. The WT denoising also shows relatively low distances of 3.94° when using the Fejer-Korovkin function with cubic-interpolation of factor 8. For the CCFD method, the best performance was achieved using the Kalman filter without interpolation with a distance of 3.59°, while the BPF and wavelet denoising performed comparably to that of the CCTD method showing minimum distances of 3.76° and 3.94°, respectively. On the other hand, using CCWD, the WT denoising shows the best performance with a distance of 3.46° using the Symlet function without any interpolations. BPF and KF also provide comparable results to that of the WT with 3.76° and 3.47°. Generally, from Table 2, the filtering methods do not show significant enhancements in the performance when increasing the cross-correlation interpolation factor due to the relatively small window size adapted from Stock et al. [9]. The introduced wavelet filtering shows better performance than that of the BPF. However, the variation of wavelet functions and the thresholding methods show almost similar performances. On the other hand, the KF outperforms both the BPF and the WT in general. This is because KF can recursively estimate the noise regardless of the frequency contents. Appl. Sci. 2020, 10, 4238 9 of 14

3.1. Simulation Results The performance of the lightning mapping estimation was measured based on the number of sliding windows over the time course of the analyzed ITF lightning signals, where each pair of Az El − angles are correctly estimated relative to the ground-truth simulated lightning map. The Euclidean distance between the estimated and the actual-simulated lightning map was used to measure the estimation error, Wn r 1 X 2 2 dist = Azi Azˆ i + Eli Elˆ i (9) Wn − − i=1 where Wn is the total number of sliding windows in the processed lightning data. To summarize the performance of the simulated dataset overall, we compute the average of Euclidean distances. Table2 summarizes the performance comparisons of the suggested lightning mapping estimation methods. In Table2, The Euclidean distances were calculated for each simulated ITF datum and then averaged over the entire available augmented lightning dataset to show the overall benchmarking performance of the suggested approaches. We compare three main filtering approaches listed in the first column of Table2. It can be seen that, when using the CCTD method, the KF and BPF show the lowest Euclidean distances of 3.55◦ and 3.63◦ respectively. The linear-interpolation factor used to achieve these results was 8. The WT denoising also shows relatively low distances of 3.94◦ when using the Fejer-Korovkin function with cubic-interpolation of factor 8. For the CCFD method, the best performance was achieved using the Kalman filter without interpolation with a distance of 3.59◦, while the BPF and wavelet denoising performed comparably to that of the CCTD method showing minimum distances of 3.76◦ and 3.94◦, respectively. On the other hand, using CCWD, the WT denoising shows the best performance with a distance of 3.46◦ using the Symlet function without any interpolations. BPF and KF also provide comparable results to that of the WT with 3.76◦ and 3.47◦. Generally, from Table2, the filtering methods do not show significant enhancements in the performance when increasing the cross-correlation interpolation factor due to the relatively small window size adapted from Stock et al. [9]. The introduced wavelet filtering shows better performance than that of the BPF. However, the variation of wavelet functions and the thresholding methods show almost similar performances. On the other hand, the KF outperforms both the BPF and the WT in general. This is because KF can recursively estimate the noise regardless of the frequency contents. In comparing the cross-correlation techniques, the CCWD method outperforms the other methods in all cases. This is due to the inherent capability of wavelet transforms to enhance the signals further and reduce the noise effects, providing a better time-domain resolution and reliable estimation of lighting maps. Moreover, comparing several wavelet functions in WT denoising helps to identify the best combination of WT parameters that fits the analyzed signals. A noticeable enhancement of cross-correlation methods was found introducing cross-correlation in the wavelet domain for estimating the lightning maps.

3.2. Real Data Results The main challenge of source localization is to identify the radiation emitted by the source out of noisy signals received by the measuring ITF system. Figure8 shows an example of a positive narrow bipolar event (NBE). Figure9 shows measured VHF signals related to a lightning flash triggered by the discharge process of the NBE, as observed in Figure8. This measurement represents a time expanded window of 20 µs (5000 samples). The observed signals of antenna B and D show significant similarity with possible phase shift or a time lag. However, the signal of antenna C shows slightly different noise characteristics. Appl. Sci. 2020, 10, 4238 10 of 14

Table 2. Comparison (Euclidean distance) of lightning mapping estimation consisting of diﬀerent ﬁltering and cross-correlation approaches.

Correlation Method CCTD CCFD CCWD Interp. Method Linear Cubic Linear Cubic Linear Cubic Interp. Factor 1 2 4 8 1 2 4 8 1 2 4 8 1 2 4 8 1 2 4 8 1 2 4 8 WT-Coif5-SURE 4.08 3.99 4.04 4.10 4.08 4.16 4.10 4.08 4.08 4.35 4.53 4.60 4.08 4.16 4.10 4.08 3.65 3.90 3.86 4.76 3.65 4.80 4.78 4.75 WT-Coif-UNIVERSAL 8.54 8.23 8.24 8.29 8.54 8.40 8.37 8.35 8.54 8.65 8.85 8.95 8.54 8.40 8.37 8.35 11.22 11.51 11.84 12.65 11.22 12.67 12.62 12.59 WT-db10-SURE 4.19 4.10 4.08 4.16 4.19 4.10 4.07 4.03 4.19 4.41 4.47 4.55 4.19 4.10 4.07 4.03 3.85 3.89 3.79 4.62 3.85 4.57 4.57 4.54 WT-db10-UNIVERSAL 9.10 8.98 9.05 9.12 9.10 9.03 9.00 8.97 9.10 9.15 9.27 9.32 9.10 9.03 9.00 8.97 11.39 11.66 11.59 12.23 11.39 12.21 12.23 12.19 WT-FK14-SURE 4.06 3.96 3.95 4.02 4.06 3.99 3.96 3.94 4.06 4.30 4.37 4.44 4.06 3.99 3.96 3.94 3.98 4.10 3.92 4.80 3.98 4.80 4.68 4.65 WT-FK14-UNIVERSAL 9.30 9.24 9.35 9.44 9.30 9.26 9.24 9.22 9.30 9.34 9.47 9.53 9.30 9.26 9.24 9.22 12.40 12.47 12.30 12.96 12.40 12.85 12.95 12.92 WT-Sym4-SURE 4.06 3.97 4.00 4.07 4.06 4.11 4.07 4.03 4.06 4.36 4.50 4.62 4.06 4.11 4.07 4.03 3.46 3.74 3.71 4.59 3.46 4.62 4.57 4.51 WT-Sym4-UNIVERSAL 10.46 10.18 10.17 10.23 10.46 10.31 10.31 10.27 10.46 10.60 10.72 10.84 10.46 10.31 10.31 10.27 11.84 12.22 12.37 13.16 11.84 13.20 13.14 13.10 BPF 3.76 3.63 3.77 3.85 3.76 3.83 3.80 3.76 3.76 3.97 4.17 4.27 3.76 3.83 3.80 3.76 3.76 3.86 3.76 4.62 3.76 4.62 4.59 4.54 KF 3.59 3.55 3.65 3.84 3.59 3.71 3.80 3.61 3.59 3.89 4.07 4.25 3.59 3.71 3.80 3.61 3.47 3.78 3.68 4.55 3.47 4.53 4.51 4.48 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 13

In comparing the cross-correlation techniques, the CCWD method outperforms the other methods in all cases. This is due to the inherent capability of wavelet transforms to enhance the signals further and reduce the noise effects, providing a better time-domain resolution and reliable estimation of lighting maps. Moreover, comparing several wavelet functions in WT denoising helps to identify the best combination of WT parameters that fits the analyzed signals. A noticeable enhancement of cross-correlation methods was found introducing cross-correlation in the wavelet domain for estimating the lightning maps.

Table 2. Comparison (Euclidean distance) of lightning mapping estimation consisting of different filtering and cross-correlation approaches.

Correlation CCTD CCFD CCWD Method Interp. Method Linear Cubic Linear Cubic Linear Cubic Interp. Factor 1 2 4 8 1 2 4 8 1 2 4 8 1 2 4 8 1 2 4 8 1 2 4 8 WT-Coif5-SURE 4.08 3.99 4.04 4.10 4.08 4.16 4.10 4.08 4.08 4.35 4.53 4.60 4.08 4.16 4.10 4.08 3.65 3.90 3.86 4.76 3.65 4.80 4.78 4.75 WT-Coif- 11.2 11.5 11.8 12.6 11.2 12.6 12.6 12.5 8.54 8.23 8.24 8.29 8.54 8.40 8.37 8.35 8.54 8.65 8.85 8.95 8.54 8.40 8.37 8.35 UNIVERSAL 2 1 4 5 2 7 2 9 WT-db10-SURE 4.19 4.10 4.08 4.16 4.19 4.10 4.07 4.03 4.19 4.41 4.47 4.55 4.19 4.10 4.07 4.03 3.85 3.89 3.79 4.62 3.85 4.57 4.57 4.54 WT-db10- 11.3 11.6 11.5 12.2 11.3 12.2 12.2 12.1 9.10 8.98 9.05 9.12 9.10 9.03 9.00 8.97 9.10 9.15 9.27 9.32 9.10 9.03 9.00 8.97 UNIVERSAL 9 6 9 3 9 1 3 9 WT-FK14-SURE 4.06 3.96 3.95 4.02 4.06 3.99 3.96 3.94 4.06 4.30 4.37 4.44 4.06 3.99 3.96 3.94 3.98 4.10 3.92 4.80 3.98 4.80 4.68 4.65 WT-FK14- 12.4 12.4 12.3 12.9 12.4 12.8 12.9 12.9 9.30 9.24 9.35 9.44 9.30 9.26 9.24 9.22 9.30 9.34 9.47 9.53 9.30 9.26 9.24 9.22 UNIVERSAL 0 7 0 6 0 5 5 2 WT-Sym4-SURE 4.06 3.97 4.00 4.07 4.06 4.11 4.07 4.03 4.06 4.36 4.50 4.62 4.06 4.11 4.07 4.03 3.46 3.74 3.71 4.59 3.46 4.62 4.57 4.51 WT-Sym4- 10.4 10.1 10.1 10.2 10.4 10.3 10.3 10.2 10.4 10.6 10.7 10.8 10.4 10.3 10.3 10.2 11.8 12.2 12.3 13.1 11.8 13.2 13.1 13.1 UNIVERSAL 6 8 7 3 6 1 1 7 6 0 2 4 6 1 1 7 4 2 7 6 4 0 4 0 BPF 3.76 3.63 3.77 3.85 3.76 3.83 3.80 3.76 3.76 3.97 4.17 4.27 3.76 3.83 3.80 3.76 3.76 3.86 3.76 4.62 3.76 4.62 4.59 4.54 KF 3.59 3.55 3.65 3.84 3.59 3.71 3.80 3.61 3.59 3.89 4.07 4.25 3.59 3.71 3.80 3.61 3.47 3.78 3.68 4.55 3.47 4.53 4.51 4.48

3.2. Real Data Results The main challenge of source localization is to identify the radiation emitted by the source out of noisy signals received by the measuring ITF system. Figure 8 shows an example of a positive narrow bipolar event (NBE). Figure 9 shows measured VHF signals related to a lightning flash triggered by the discharge process of the NBE, as observed in Figure 8. This measurement represents a time expanded window of 20 μs (5000 samples). The observed signals of antenna B and D show significant similarity with possible phase shift or a time lag. However, the signal of antenna C shows slightly different noise characteristics. In the simulation results shown before, it is noted that the wavelet-based CCWD method produced the best performance of lightning mapping using the Symlet function with linear Appl.interpolation Sci. 2020, 10 of, 4238 level 8. Therefore, the same setup is implemented for real lightning data mapping.11 of 14

Appl. Sci. 2020, 10, x FOR PEERFigure REVIEW 8. Fast Electric field ﬁeld pulse relevant to a positive NBE. 11 of 13

FigureFigure 9. 9.TheThe VHF VHF radiation radiation signals signals associated associated with with positive positive NBE NBE received received by by antennae antennae B, B, C, C, and and D D..

FigInure the 10 simulation shows the results constructed shown before, map itof is the noted lightning that the source wavelet-based location CCWDfor positive method NBE. produced The startingthe best p performanceosition of radiation of lightning sources mapping was in usingthe higher the Symlet altitude function about with66° elevation. linear interpolation However, ofthese level detected8. Therefore, sources the are same isolated setup from is implemented the well-defined for real lightning lightning channel data mapping. and considered outliers. The colourFigure changes 10 inshows Figure the 10 constructeda with time map from of blue the lightningto green, correspond source locationing to for the positive lightning NBE. progression The starting timeposition in Fig ofure radiation 9. It can sources be seen was that in the the channel higher altitudefrom the about bottom 66 ◦(23°elevation. elevation) However, to the 32 these° elevation detected wassources approximately are isolated straight from the with well-defined small changes lightning in azimuth channel angles and considered range, corresponding outliers. The to colour the trajectorychanges inof Figurethe lightning 10a with flash. time Up from to bluethe 32° to green, elevation, corresponding the shape toand the the lightning height progressionof the channel time showedin Figure certain9. It can consistency be seen that with the the channel observation from the of bottom positive (23 NBE.◦ elevation) In Figure to the 10 32b, ◦ theelevation radiation was elevationapproximately angles straightand fast with electric small field changes change in azimuthobservations angles (black range, waveform) corresponding are superimposed to the trajectory on of thethe VHF lightning waveform flash. (gray), Up to theshowing 32◦ elevation, the downward the shape propagation and the height of the of VHF the channel source. showedThe negative certain electricconsistency field waveform with the observation is indicative of of positive an upward NBE.-directed In Figure current, 10b, the consistent radiation with elevation a positive angles NBE. and Overall,fast electric all three field filtering change methods observations implement (blacked waveform) in this paper are superimposed show comparable on the accu VHFracy waveform for this lightning(gray), showing mapping the with downward some propagation errors that of could the VHFresult source. from The the negative limited electric windowing field waveform approach is conductedindicative in of this an upward-directedstudy, or due to the current, existing consistent in-band hardware with a positive-interference NBE. Overall, noises when all three collecting filtering themethods data. To implemented avoid such noise in this effects, paper it show is better comparable to properly accuracy filter the for thisanalog lightning signal mappingfrom the antennae with some beforeerrors the that signal could is result digitized, from the such limited that extreme windowing noises approach contaminate conducted no portion in this ofstudy, the or bandwidth due to the whichexisting contributes in-band hardware-interferenceto the cross-correlation noises. when collecting the data. To avoid such noise effects, it is better to properly filter the analog signal from the antennae before the signal is digitized, such that extreme noises contaminate no portion of the bandwidth which contributes to the cross-correlation.

Figure 10. Interferometer data for NBE. (a) Lightning map plotted in elevation vs. azimuth. (b) Expanded view of the lightning map of a. (c) Showing the breakdown, each colored circle-marker denotes the elevation angles (altitude) vs. time.

4. Conclusion Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 13

Figure 9. The VHF radiation signals associated with positive NBE received by antennae B, C, and D.

Figure 10 shows the constructed map of the lightning source location for positive NBE. The starting position of radiation sources was in the higher altitude about 66° elevation. However, these detected sources are isolated from the well-defined lightning channel and considered outliers. The colour changes in Figure 10a with time from blue to green, corresponding to the lightning progression time in Figure 9. It can be seen that the channel from the bottom (23° elevation) to the 32° elevation was approximately straight with small changes in azimuth angles range, corresponding to the trajectory of the lightning flash. Up to the 32° elevation, the shape and the height of the channel showed certain consistency with the observation of positive NBE. In Figure 10b, the radiation elevation angles and fast electric field change observations (black waveform) are superimposed on the VHF waveform (gray), showing the downward propagation of the VHF source. The negative electric field waveform is indicative of an upward-directed current, consistent with a positive NBE. Overall, all three filtering methods implemented in this paper show comparable accuracy for this lightning mapping with some errors that could result from the limited windowing approach conducted in this study, or due to the existing in-band hardware-interference noises when collecting the data. To avoid such noise effects, it is better to properly filter the analog signal from the antennae Appl.before Sci. the2020 ,signal10, 4238 is digitized, such that extreme noises contaminate no portion of the bandwidth12 of 14 which contributes to the cross-correlation.

Figure 10. InterferometerInterferometer data data for for NBE. NBE. (a ()a )Lightning Lightning map map plotted plotted in inelevation elevation vs. vs. azimuth. azimuth. (b) (Expandedb) Expanded view view of ofthe the lightning lightning map map of of a. a. (c ()c )Showing Showing the the breakdown, breakdown, each each colored colored circle-marker denotes thethe elevationelevation anglesangles (altitude)(altitude) vs.vs. time.time.

4. Conclusion Conclusions Broadband interferometry for the two-dimensional mapping of lightning progression was used to examine the effects of different factors on the accuracy of the lightning maps. In this paper, various lightning signal proceeding approaches are compared, including different filtration methods and cross-correlation techniques, introducing interpolation to effectively estimate the fractional time of arrival delay realizing the location of VHF lightning radiation sources in two dimensions. Simulations were conducted to provide enough analysis when comparing the performance of implemented approaches for estimating lightning maps. Aggregated results show that the CCWD outperforms the other correlation methods in estimating the TDOAs regardless of the interpolations. This is because the wavelet transform not only can reduce the noise but also weakens the effects of the peak resolution of cross-correlation. The filtering methods also show comparable performance with wavelet denoising, which shows slightly better performance when using Symlet function. Several improvements of the current study could be achieved by involving other parameters, such as tuning the sliding window size, the windowing function, the amount of overlap.

Author Contributions: Conceptualization, A.A. and M.R.A.; methodology, A.A.; software, A.A. and F.N.; validation, A.A.A., M.R.A., Z.K. and M.R.M.E.; formal analysis, A.A.; investigation, M.H.M.S.; resources, M.H.M.S. and S.A.M.; data curation, M.H.M.S.; writing—original draft preparation, A.A.; writing—review and editing, A.S.A.-K.; visualization, V.A.; supervision, M.R.A. and A.A.A.; project administration, M.R.A.; funding acquisition, A.A.A. and M.R.A. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by Universiti Tenaga Nasional (UNITEN) under BOLD2025 fund, in part by the Ministry of Higher Education, Malaysia, under Fundamental Research Grant Scheme (FRGS) (FRGS/2018/FKEKK-CETRI/F00361), and in part by Universiti Teknologi Malaysia (UTM) under Q04G19 and R4F966 research grants (FRGS). Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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