Accuracy of Flight Altitude Measured with Low-Cost GNSS, Radar and Barometer Sensors: Implications for Airborne Radiometric Surveys

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Article Accuracy of Flight Altitude Measured with Low-Cost GNSS, Radar and Barometer Sensors: Implications for Airborne Radiometric Surveys

Matteo Albéri 1,2,* ID , Marica Baldoncini 1,2, Carlo Bottardi 1,2 ID , Enrico Chiarelli 3, Giovanni Fiorentini 1,2, Kassandra Giulia Cristina Raptis 3, Eugenio Realini 4, Mirko Reguzzoni 5, Lorenzo Rossi 5, Daniele Sampietro 4, Virginia Strati 3 and Fabio Mantovani 1,2 ID 1 Department of Physics and Earth Sciences, University of Ferrara, Via Saragat, 1, 44122 Ferrara, Italy; [email protected] (M.B.); [email protected] (C.B.); ﬁ[email protected] (G.F.); [email protected] (F.M.) 2 Ferrara Section of the National Institute of Nuclear Physics, Via Saragat, 1, 44122 Ferrara, Italy 3 Legnaro National Laboratory, National Institute of Nuclear Physics, Via dell’Università 2, 35020 Legnaro (Padova), Italy; [email protected] (E.C.); [email protected] (K.G.C.R.); [email protected] (V.S.) 4 Geomatics Research & Development (GReD) srl, Via Cavour 2, 22074 Lomazzo (Como), Italy; [email protected] (E.R.); [email protected] (D.S.) 5 Department of Civil and Environmental Engineering (DICA), Polytechnic of Milan, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; [email protected] (M.R.); [email protected] (L.R.) * Correspondence: [email protected]; Tel.: +39-329-0715328

Received: 7 July 2017; Accepted: 13 August 2017; Published: 16 August 2017

Abstract: Flight height is a fundamental parameter for correcting the gamma signal produced by terrestrial radionuclides measured during airborne surveys. The frontiers of radiometric measurements with UAV require light and accurate altimeters flying at some 10 m from the ground. We equipped an aircraft with seven altimetric sensors (three low-cost GNSS receivers, one inertial measurement unit, one radar altimeter and two barometers) and analyzed ~3 h of data collected over the sea in the (35–2194) m altitude range. At low altitudes (H < 70 m) radar and barometric altimeters provide the best performances, while GNSS data are used only for barometer calibration as they are affected by a large noise due to the multipath from the sea. The ~1 m median standard deviation at 50 m altitude affects the estimation of the ground radioisotope abundances with an uncertainty less than 1.3%. The GNSS double-difference post-processing enhanced significantly the data quality for H > 80 m in terms of both altitude median standard deviation and agreement between the reconstructed and measured GPS antennas distances. Flying at 100 m the estimated uncertainty on the ground total activity due to the uncertainty on the flight height is of the order of 2%.

Keywords: airborne gamma-ray spectrometry; low-cost GNSS; barometric sensors; radar altimeter; IMU

1. Introduction Airborne Gamma-Ray Spectroscopy (AGRS) is a proximal remote sensing method that allows quantifying the abundances of natural (40K, 238U, 232Th) and artiﬁcial (e.g., 137Cs) radionuclides present in the topsoil (~30 cm depth) over relatively large scales. Studying the spatial distribution of these radionuclides is strategic for monitoring environmental radioactivity [1], producing thematic maps of geochemical interest [2–4], identifying radioactive orphan sources [5] or investigating areas potentially contaminated by nuclear fallout [6]. Sodium iodide scintillation detectors (NaI(Tl)) are widely employed in AGRS measurements thanks to the high portability and high detection efﬁciency which allow performing surveys over extended areas in reasonable times and minimizing costs.

Sensors 2017, 17, 1889; doi:10.3390/s17081889 www.mdpi.com/journal/sensors Sensors 2017, 17, 1889 2 of 21 Sensors 2017, 17, 1889 2 of 21 in AGRS measurements thanks to the high portability and high detection efficiency which allow performing surveys over extended areas in reasonable times and minimizing costs. InIn the last last decade decade there there has has been been a strong a strong effort effort in improving in improving spectral spectral analysis analysis techniques techniques which whichled not led only not to only high-accuracy to high-accuracy identification identification of radionuclides of radionuclides present presentin the environment in the environment [7], but also [7], butto the also possibility to the possibility of performing of performing real time real surveys, timesurveys, especially especially in the framework in the framework of homeland of homeland security securityapplications applications [8]. The [ 8].spread The spread of Unmanned of Unmanned Aerial Aerial Vehicles Vehicles (UAVs) (UAVs) is isboosting boosting research research andand developmentdevelopment inin the the field field of AGRSof AGRS applied applied to innovative to innovative sectors, sectors, such as precisionsuch as farmingprecision or farming emergency or responseemergency in response case of nuclear in case accidents, of nuclear both accidents, in terms bo ofth thein terms technologies of the technologies employed (e.g., employed prototypes (e.g., equippedprototypes with equipped CdZnTe with detectors CdZnTe [9]) detectors and of spectral [9]) and analysis of spectral methods analysis [10]. UAVs methods equipped [10]. withUAVs a lightweightequipped with gamma a lightweight spectrometer gamma typically spectrometer fly at altitudes typically and fly speeds at altitudes lower than and aspeeds helicopter, lower with than the a objectivehelicopter, of with enhancing the objective the terrestrial of enhancing gamma the signal terrestrial intensity gamma [11]. signal intensity [11]. InIn thesethese newnew technologicaltechnological scenariosscenarios aa preciseprecise evaluationevaluation ofof flightflight altitudealtitude isis mandatorymandatory forfor avoidingavoiding systematicsystematic effects effects in thein gammathe gamma signal signal corrections. corrections. In the lastIn decadethe last sophisticated decade sophisticated analytical techniquesanalytical techniques based on inverse based problemon inverse methods problem [12 ]methods as well as [12] Monte as well Carlo as simulations Monte Carlo [13 simulations] have been proposed[13] have forbeen studying proposed Digital for Elevationstudying ModelDigital (DEM) Elevation effect Model corrections (DEM) together effect corrections with corresponding together uncertaintieswith corresponding in airborne uncertainties gamma-ray in airborne spectrometry. gamma-ray This spectrometry. work addresses This these work topics addresses improving these thetopics analysis improving of data the collected analysis from of data seven collected altimeters from and seven reducing altimeters a source and of uncertaintyreducing a likesource DEM. of Inuncertainty particular like altitude DEM. measurements In particular altitude have been meas performedurements have with fourbeen low-costperformed GNSS with receivers, four low-cost one radarGNSS altimeter receivers, and one two radar low-cost altimeter barometric and two sensors low-cost in a barometric series of flights sensors over in the a series sea exploring of flights a wideover rangethe sea of exploring altitudes (froma wide 35 range to 2194 of altitudes m; Table1 (from and Figure 35 to 21941). The m; goalTable of 1 this and paper Figure was 1). toThe estimate goal of the this accuraciespaper was ofto flightestimate altitude, the accuracies investigating of flight statistical altitude, and investigating systematic effects statistical due to and calibration systematic methods, effects post-processingdue to calibration analysis methods, and post-processing sensor performances. analysis and sensor performances.

Figure 1. The left panel shows a map of the paths flown during the four surveys over the sea between Figure 1. The left panel shows a map of the paths flown during the four surveys over the sea between ForteForte deidei MarmiMarmi (LU)(LU) andand MarinaMarina didi PisaPisa (PI)(PI) inin Italy.Italy. TheThe fourfour panelspanels onon thethe rightright showshow thethe meanmean altitudealtitude profilesprofiles measuredmeasured byby GPSABCGPSABC ofof eacheach flight.flight.

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Table 1. Main parameters of the four flights. Hmin and Hmax (minimum and maximum height) refer to Tablethe flight 1. Main height parameters above sea of level the four calculated flights. by Hmin averagingand Hmax the(minimum measurements and maximum of the different height) sensors. refer to Averagethe flight horizontal height above and seavertical level speeds calculated are calculated by averaging using the the measurements data from GPSABC. of the different sensors. Average horizontal and vertical speeds are calculated using the data from GPSABC. Flight Hmin Hmax Acquisition Average Horizontal Average Vertical Date Time (CEST) ID (m) (m) Time (s) Speed (m/s) Speed (m/s) Acquisition Average Horizontal Average Vertical Flight ID Date Time (CEST) H (m) H (m) F11 30/03/16 17:42:11–19:29:38 79 min 2018 max 6447 Time (s) Speed 18.9 (m/s) Speed 0.8 (m/s) F12 31/03/16 18:13:55–18:33:12 129 237 1158 15.5 0.5 F11 30/03/16 17:42:11–19:29:38 79 2018 6447 18.9 0.8 F14 F1205/04/16 31/03/16 16:37:15–17:33:0418:13:55–18:33:12 464 129 2194 237 3350 1158 21.1 15.5 0.5 0.8 F15 F1405/04/16 05/04/16 19:15:19–19:27:3916:37:15–17:33:04 35 464 66 2194 740 3350 34.4 21.1 0.8 0.6 F15 05/04/16 19:15:19–19:27:39 35 66 740 34.4 0.6 2. Instruments and Methods 2. Instruments and Methods The aircraft used for the surveys is the Radgyro (Figure 2–4), an experimental autogyro devoted to airborneThe aircraft multiparametric used for the measurements, surveys is the Radgyro specifically (Figures designed2–4), anfor experimental radiometric autogyrosurveying devoted [14,15]. toThe airborne Radgyro multiparametric is 5.20 m long measurements, and 2.8 m high, specifically and has designed an 83-liter for radiometricfuel tank placed surveying above [14 ,15the]. Theinstrumentation Radgyro is to 5.20 avoid m longthe attenuation and 2.8 m of high, gamma and signals has an coming 83-liter from fuel tankthe ground placed due above to the instrumentationinteraction with the to avoidfuel material. the attenuation The fuselage of gamma has been signals modified coming to house from the experimental ground due tosetup the interactionfor an overall with instrumental the fuel material. payload The capacity fuselage of has120 beenkg which modified corresponds to house to the a experimentalflight autonomy setup of forapproximately an overall instrumental3 h. Moreover, payload the Radgyro capacity has of 120 two kg lateral which aerodynamic corresponds tocompartments a flight autonomy hosting of approximatelyinfrared, thermal 3 h. and Moreover, visible thecameras Radgyro and has an twoInertial lateral Measurement aerodynamic Unit compartments (IMU). Thehosting Radgyro infrared, needs thermalair through and its visible rotor cameras to generate and lift an Inertialso it cannot Measurement hover or take Unit off (IMU). vertically. The Radgyro needs air through its rotorThe todetector generate used lift sofor it gamma cannot hoverspectroscopy or take offme vertically.asurements is accommodated inside the main compartmentThe detector of the used Radgyro. for gamma It consists spectroscopy of four 10 measurements × 10 × 40 cm sodium is accommodated iodide scintillation inside detectors the main compartment(NaI(Tl)) for a of total the Radgyro.detection Itvolume consists of of about four 1016× liters10 × [16].40 cm The sodium high payload iodide scintillation and autonomy, detectors the (NaI(Tl))modularity for of a the total acquisition detection system, volume along of about with 16 the liters possibility [16]. The of highsynchronizing payload andmeasurements autonomy, thecoming modularity from different of the acquisition sensors with system, respect along to withthe reference the possibility computer of synchronizing time, make the measurements Radgyro a comingpromising from prototype different aircraft sensors for withexploring respect new to applic the referenceations in computerthe field of time, proximal make remote the Radgyro sensing. a promisingThe Radgyro prototype is aircraft equipped for exploring with seven new applicationsaltimetric sensors, in the field belonging of proximal to remotethree sensing.different instrumentalThe Radgyro classes: is equipped four GNSS with antennas seven altimetric (GPSABC, sensors, GPSIMU), belonging two to threepressure different and instrumentaltemperature classes:sensors four(PT and GNSS PTIMU) antennas and (GPSABC, one radar GPSIMU), altimeter two(ALT) pressure (Figure and 3). temperature In this study sensors the height (PT and of PTIMU)Radgyro andis referred one radar to altimeterthe GNSS (ALT) antenna (Figure locations,3). In this which study are the located height at of the Radgyro same isvertical referred position to the GNSSwith respect antenna to the locations, ground which (1.08 ± are 0.01 located m). Taking at the in sameto account vertical that position the radar with altimeter respect toaccuracy the ground is of (1.08the order± 0.01 of 3% m). of Taking the measured into account altitude that (see the Sectio radarn altimeter2.2), the difference accuracy in is distance of the order from of the 3% ground of the measuredbetween ALT altitude and (seeGNSS Section antennas 2.2), the(0.71 difference m) is negligible. in distance The from pressure the ground sensors between are calibrated ALT and GNSSusing antennasthe GNSS (0.71 (see m) Section is negligible. 2.4) and The therefore pressure the sensors barometric are calibrated altitude using is referred the GNSS to (seeGNSS Section antenna 2.4) andposition. therefore the barometric altitude is referred to GNSS antenna position.

Figure 2. Radgyro, the autogyro used for all the surveys described in Table 1. Figure 2. Radgyro, the autogyro used for all the surveys described in Table1.

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Figure 3. Scheme of the placement of the different devices on the Radgyro: (A) GNSS antenna (GPSA),Figure 3.3. (B)Scheme Scheme GNSS of antennaof the the placement placement (GPSB), of (C) theof GNSS differentthe different antenna devices (GPSC),devices on the (D)on Radgyro: theGNSS Radgyro: antenna (A) GNSS (A) connected antenna GNSS antenna (GPSA),to IMU (GPSIMU),(B)(GPSA), GNSS (B) antenna (E) GNSS pressure (GPSB), antenna and (C) (GPSB), temperature GNSS (C) antenna GNSS sensors (GPSC), antenna of (D)IMU (GPSC), GNSS (PTIMU), antenna(D) GNSS (F) connected pressureantenna toconnectedand IMU temperature (GPSIMU), to IMU sensors(E)(GPSIMU), pressure (PT), (E) and(G) pressure temperatureradar altimeter and temperature sensors (ALT), of (H) IMU sensors gamma (PTIMU), of spectrometer IMU (F) (PTIMU), pressure NaI(Tl). and(F) pressure temperature GPSA, GPSBand sensorstemperature and GPSC (PT), are(G)sensors radarplaced (PT), altimeter at the(G) followingradar (ALT), altimeter (H) relative gamma (ALT), distances: spectrometer (H) gamma dGPSAB NaI(Tl). spectrometer = dGPSAC GPSA, GPSBNaI(Tl).= (3.83 and ± GPSA,0.01) GPSC m GPSB are and placed dGPSBCand GPSC at the = (1.96followingare placed ± 0.01) relative at m. the following distances: relative dGPSAB distances: = dGPSAC dGPSAB = (3.83 =± dGPSAC0.01) m and = (3.83 dGPSBC ± 0.01) = (1.96m and± 0.01)dGPSBC m. = (1.96 ± 0.01) m.

Figure 4. AA typical typical situation of flight flight over the sea with the Radgyro. Figure 4. A typical situation of flight over the sea with the Radgyro. 2.1. The Inertial Measurement Unit 2.1. The Inertial Measurement Unit 2.1. The Inertial Measurement Unit The right lateral compartment of the Radgyro houses the MTi-G-700 GPS/INS Inertial The right lateral compartment of the Radgyro houses the MTi-G-700 GPS/INS Inertial MeasurementThe right Unit lateral (IMU, compartment Figure 3), which of the is Radgyroequipped houseswith a GNSSthe MTi-G-700 receiver acquiring GPS/INS theInertial GPS Measurement Unit (IMU, Figure3), which is equipped with a GNSS receiver acquiring the GPS signalMeasurement with a maximum Unit (IMU, frequency Figure 3),of 4which Hz, a barometeris equipped providing with a GNSS the atmospheric receiver acquiring pressure thereadout GPS signal with a maximum frequency of 4 Hz, a barometer providing the atmospheric pressure readout withsignal a withmaximum a maximum frequency frequency of 50 Hzof 4 (PTIMU) Hz, a barometer (see Section providing 2.4) and the inertialatmospheric sensors pressure retrieving readout the with a maximum frequency of 50 Hz (PTIMU) (see Section 2.4) and inertial sensors retrieving the roll, roll,with pitch a maximum and yaw frequency angles with of a 50 maximum Hz (PTIMU) frequency (see Section of 400 Hz.2.4) The and IMU inertial provides sensors height retrieving values theby pitch and yaw angles with a maximum frequency of 400 Hz. The IMU provides height values by combiningroll, pitch and the yaw data angles from with the aGNSS, maximum the frequencybarometer of and 400 Hz.the Theaccelerometers IMU provides with height a maximum values by combining the data from the GNSS, the barometer and the accelerometers with a maximum frequency frequencycombining of the 400 dataHz (GPSIMU). from the DynamicGNSS, the and barome barometricter and measurements the accelerometers allow for with height a estimationmaximum of 400 Hz (GPSIMU). Dynamic and barometric measurements allow for height estimation even with evenfrequency with weakof 400 GNSS Hz (GPSIMU). signal and Dynamic the nominal and accuracybarometric on measurements the vertical position allow foris 2 heightm (1σ) estimation [17]. weak GNSS signal and the nominal accuracy on the vertical position is 2 m (1σ)[17]. even with weak GNSS signal and the nominal accuracy on the vertical position is 2 m (1σ) [17]. 2.2. The Radar Altimeter 2.2. The Radar Altimeter ® The Smartmicro ® MicroMicro Radar Radar Altimeter Altimeter (ALT), (ALT), placed placed under under the the Radgyro Radgyro fuselage fuselage (Figure (Figure 33),), ® measuresThe Smartmicrothe flight flight altitude Micro at Radar ~60 Hz HzAltimeter by by using using (ALT), a a radar radar placed sensor sensor under operating operating the Radgyro at at a a frequency frequency fuselage of of(Figure 24 24 GHz. GHz. 3), Themeasures estimateestimate the of offlight thethe minimum minimumaltitude at distance distance~60 Hz is byis declared declaredusing a reliable radar reliable sensor within within operating a cone a cone having havingat a 20frequency◦ 20°opening opening of angle 24 angleGHz. and andtheThe declared estimatethe declared accuracy of the accuracy minimum on altimetric on distancealtimetric measurements is declaredmeasurements is 3%,reliable with is within a3%, minimum with a cone a valueminimum having of 0.5 20° m.value opening Although of 0.5 angle them. Althoughflightand the altitude declared the flight range accuracy altitude declared rangeon by thealtimetric declared seller is measurements (0.5–500)by the seller m, ouris is(0.5–500) data 3%, analysis with m, oura onminimum data the ALTanalysis datasetvalue on of revealedthe 0.5 ALT m. datasetaAlthough significative revealed the presenceflight a significative altitude of outliers range pr at esencedeclared heights of abovebyoutliers the 340se llerat m heights (Figureis (0.5–500) 5ab).ove Neglecting m, 340 our mdata (Figure effects analysis related 5). onNeglecting tothe wave ALT effectsmotionsdataset related revealed and tidal to wavea variations, significative motions which andpresence aretidal typically variationsof outliers <0.4, whichat m heights in theare surveyedtypically above 340 area<0.4 m m [18(Figure in], wethe performedsurveyed5). Neglecting area our [18],studyeffects we considering related performed to wave two our differentmotions study datasetsconsideringand tidal named variations twoα differentand, whichβ, corresponding datasets are typically named respectively <0.4 α mand in theβ to, corresponding Hsurveyed < 340 m area and respectivelyH[18], >340 we mperformed respectively. to H < 340 our m The studyandα databaseH considering > 340 m is respectively. populated two different by The data αdatasets acquireddatabase namedin is 4803populated α s and by all βby, 7 corresponding sensors,data acquired while intherespectively 4803β database s by all to 7 refersH sensors, < 340 to m the while and remaining H the > 340β database 6892m respectively. s in refers which to theThethe ALTremaining α database sensor 6892 isis excludedpopulated s in which (Table by the data2 ALT). acquired sensor isin excluded 4803 s by (Tableall 7 sensors, 2). while the β database refers to the remaining 6892 s in which the ALT sensor is excluded (Table 2).

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Table 2.2. Number of entries of the datasetsdatasets used in the analysis of the orthometric height values from GNSS, altimetric and barometric measurements. The The 340 340 m height cutoff has been identified identiﬁed on the base of altimeter outlier data (see Figure 55),), whilewhile thethe 0.20.2 HzHz frequencyfrequency isis relatedrelated toto thethe availabilityavailability ofof the Madonna Dell’Acqua master station data for the GNSSGNSS post-processing.post-processing. α β DatasetsDatasets FrequencyFrequency α H < 340 m β H > 340 m H < 340 m H > 340 m DATASETDATASET 1 1 1.0 1.0 Hz Hz (stand-alone) (stand-alone) 4803 4803 6892 6892 DATASETDATASET 2 2 0.2 0.2 Hz Hz (double-difference) (double-difference) 960 960 1378 1378

Figure 5.5. PercentagePercentage of of outliers outliers in in the the ALT ALT dataset dataset as a functionas a function of the of orthometric the orthometric height. Theheight. altitude The altitudeof 340 m of has 340 been m has identiﬁed been identified has a threshold has a thresh aboveold which above the which ALT datasetthe ALT has dataset been has excluded been excluded from the fromglobal the analysis. global analysis

2.3. The Three GNSS Receivers The Radgyro is equipped with three single frequency u-blox EVK-6T receivers, each of them coupled with a a GPS GPS ANN-MS ANN-MS active active antenna antenna having having ~100 ~100 g gweight weight and and dimensions dimensions of of48 48 mm mm × 40× mm40 mm × 13× mm,13 mm, one onelocated located on the on aircraft the aircraft cockpit cockpit (GPSA) (GPSA) and andthe others the others on the on tail the wings tail wings (GPSB (GPSB and GPSC)and GPSC) (Figure (Figure 3). 3A). low A low noise noise amplifier amplifier is isimplem implementedented on on each each receiver receiver which which is intendedintended toto compensate the loss of signal due toto cablescables andand connectors.connectors. The u-blox EVK-6T receivers contain LEA-6T modules, that can provide raw GPS data as output, allowing for advanced post-processing. post-processing. The cost of an EVK-6T receiver and ANN-MSANN-MS antennaantenna isis ofof fewfew hundredhundred Euros.Euros. Each GPS receiver is able to directly deliver a real-time solution, using NMEA GGA GGA sentences, sentences, and raw datadata toto bebe post-processedpost-processed in in standard standard RINEX RINEX format, format, both both with with a sampling a sampling frequency frequency of 1 of Hz. 1 Hz.Moreover, Moreover, the logging the logging software software records records the GPS the acquisition GPS acquisition time coupled time withcoupled the absolutewith the computerabsolute computertime in order time to correctlyin order synchronizeto correctly GPSsynchronize with the otherGPS with sensors the present other sensors onboard. present GPS raw onboard. observations GPS wereraw observations post-processed were following post-processed two different following analyses two with different the open analyses source with goGPS the open software source [19 ]:goGPS software [19]: - code-only stand-alone solution (1 Hz), using a Kalman filter with constant-velocity dynamics; -- code-onlycode and stand-alone phase double solution differences (1 Hz), solution using a Kalman (0.2 Hz) filter with with respect constant-velocity to the permanent dynamics; station - codeMadonna and phase Dell’Acqua double (Pisa) differences (43.7475 solution◦ N, 10.3660 (0.2 Hz)◦ E, with 2 a.s.l), respect using to the a Kalmanpermanent filter station with Madonnaconstant-velocity Dell’Acqua dynamics. (Pisa) (43.7475° N, 10.3660° E, 2 a.s.l), using a Kalman filter with constant-velocity dynamics. These different methods produce two datasets that we define as DATASET 1 and DATASET 2 at 1 HzThese and 0.2 different Hz respectively methods (Table produce2). Regarding two datasets GNSS-derived that we define heights, as DATASET the EGM2008 1 and model DATASET [ 20] was 2 atused 1 Hz to and convert 0.2 Hz ellipsoidal respectively heights (Table to orthometric 2). Regarding ones, GNSS-derived since it is the heights, modelcurrently the EGM2008 implemented model [20] in wasthe goGPS used software.to convert ellipsoidal heights to orthometric ones, since it is the model currently implemented in the goGPS software.

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The identification identification of of GNSS GNSS data data outliers outliers has has been been performed performed by bystudying studying the thedistribution distribution of the of the distances reconstructed between the three GPS antennas d , d , d with respect to distances reconstructed between the three GPS antennas dGPSABGPSAB, dGPSAC, dGPSBCGPSBC with respect to reference values (Figure3). Following [ 21], an outlier is a data point that lies out of the ranges (Q − 1.5 reference values (Figure 3). Following [21], an outlier is a data point that lies out of the ranges1 (Q1 − IQR) and (Q + 1.5 IQR), where Q Q and IQR are first quartile, third quartile and interquartile range 1.5 IQR) and3 (Q3 + 1.5 IQR), where1, Q31, Q3 and IQR are first quartile, third quartile and interquartile rangerespectively. respectively. Outlier Outlier data have data been have typically been typicall recognizedy recognized when flying when close flying to theclose sea to (Figure the sea6) (Figure and at 6)an and altitude at an range altitude of (35–900) range of m (35–900) (Figures7 m and (Figure8). The 7 analysisand Figure of outlier 8). The highlights analysis thatof outlier their percentage highlights generally decreases with increasing altitude and that the median d d and d approach that their percentage generally decreases with increasing altitudeGPSBC, and thatGPSAC the medianGPSAB dGPSBC, dGPSAC the reference distances. and dGPSAB approach the reference distances. We note that in F15 the d erraticity decreases drastically crossing the border between sea We note that in F15 the dGPSABGPSAB erraticity decreases drastically crossing the border between sea and land (Figure6). The average reconstructed d varies from (5.86 ± 7.18) m (over water) and land (Figure 6). The average reconstructed dGPSABGPSAB varies from (5.86 ± 7.18) m (over water) to (3.77 ±to 0.28) (3.77 ±m0.28 (over) m land), (over land),to be tocompared be compared with with the the(3.83 (3.83 ± 0.01)± 0.01) m mreference reference distance. distance. In In F15, characterized byby aa (35–66)(35–66) mm flightflight altitude altitude range, range, it it is is possible possible to to observe observe a noisea noise amplification amplification due due to tothe the multipath multipath effect effect over over the sea.the Thissea. phenomenonThis phenomenon is well is knownwell known in literature in literature and has and been has studied been studiedin different in different environmental environmental scenarios scenarios [22], investigating [22], investigating also applications also applications like the monitoring like the monitoring of coastal ofsea coastal levels sea and levels of the and periodicity of the periodicity of ocean tides of ocean [23–25 tides]. [23–25].

Figure 6. (a) Reconstructed distance between GPSA and GPSB as a function of time during a portion Figure 6. (a) Reconstructed distance between GPSA and GPSB as a function of time during a portion of of F15. The dashed red line represents the (3.83 ± 0.01) m reference distance and the brown line F15. The dashed red line represents the (3.83 ± 0.01) m reference distance and the brown line represents represents the average reconstructed dGPSAB during the flight. The large fluctuations observed in the the average reconstructed dGPSAB during the flight. The large fluctuations observed in the reconstructed reconstructed distance when flying over the sea are strongly reduced when flying over land, in distance when flying over the sea are strongly reduced when flying over land, in particular when flying particular when flying more than 3 km far from the coast (point A). (b) Mean height above the more than 3 km far from the coast (point A). (b) Mean height above the ground level z(m) (digital ground level z(m) (digital elevation model is subtracted) measured by GPSABC. elevation model is subtracted) measured by GPSABC. (c) Flight path of F15.

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GPSBC FigureFigure 7. 7. BoxplotBoxplot ofof of thethe the distributiondistribution distribution ofof of dd dGPSBCGPSBC asas asaa functionfunction a function ofof the ofthethe orthomorthom orthometricetricetric heightheight height HH forfor H entireforentire entire 0.20.2 Hz0.2Hz Hzdataset.dataset. dataset. TheThe The blueblue blue lineline line representsrepresents represents thethe the (1.96(1.96 (1.96 ±± 0.01)±0.01)0.01) mm mreferencereference reference distancedistance distance betweenbetween between GPSBGPSB GPSB andand and GPSC.GPSC. GPSC. BlackBlack points points represent represent outlieroutlier data.data.

GPSAB GPSAC FigureFigure 8.8. InIn thethe upperupper panelpanel areare shownshown thethe percentapercentagesges ofof outliersoutliers identifiedidentified inin thethe ddGPSAB,, ddGPSAC andand Figure 8. In the upper panel are shown the percentages of outliers identiﬁed in the dGPSAB, dGPSAC and GPSBC ddGPSBC datasetsdatasets as as functionfunction ofof thethe orthometricorthometric height height H.H. In In thethe bottombottom panelpanel the the acquisitionacquisition statistics statistics is is d datasets as function of the orthometric height H. In the bottom panel the acquisition statistics is asGPSBC function of the orthometric height. asas functionfunction ofof thethe orthometricorthometric height.height.

2.4.2.4. TheThe twotwo PressurePressure andand TemperatureTemperature SensorsSensors 2.4. The two Pressure and Temperature Sensors TheThe ToradexToradex OakOak USBUSB AtmosphericAtmospheric PressurePressure (PT)(PT) sensor,sensor, hostedhosted insideinside thethe RadgyroRadgyro fuselagefuselage The Toradex Oak USB Atmospheric Pressure (PT) sensor, hosted inside the Radgyro fuselage (Figure(Figure 3),3), acquiresacquires pressurepressure andand temperaturetemperature datadata withwith aa samplingsampling frequencyfrequency ofof 22 HzHz andand aa 1010 PaPa (Figure3), acquires pressure and temperature data with a sampling frequency of 2 Hz and a 10 Pa resolutionresolution (corresponding(corresponding toto approximatelyapproximately 0.80.8 mm inin height)height) andand aa ±2±2 °C°C accuracy,accuracy, respectively.respectively. resolution (corresponding to approximately 0.8 m in height) and a ±2 ◦C accuracy, respectively. TheThe pressurepressure andand temperaturetemperature datasetsdatasets providedprovided byby bothboth thethe PTPT andand thethe PTIMUPTIMU devicesdevices havehave The pressure and temperature datasets provided by both the PT and the PTIMU devices have been beenbeen processedprocessed byby applyingapplying thethe hypsometrichypsometric formformula,ula, whichwhich allowsallows estimatingestimating thethe orthometricorthometric processedPT by applyingPTIMU the hypsometric formula, which allows estimating the orthometric heights HPT heightsheights HHPT andand HHPTIMU onon thethe basisbasis ofof thethe decreasingdecreasing exponentialexponential trendtrend ofof thethe atmosphericatmospheric pressurepressure and H on the basis of the decreasing exponential trend of the atmospheric pressure with respect withwith respectrespectPTIMU toto thethe altitudealtitude andand accountingaccounting forfor ththee tinytiny variationsvariations ofof thethe temperaturetemperature inin thethe lowerlower to the altitude and accounting for the tiny variations of the temperature in the lower atmosphere: atmosphere:atmosphere:

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−LR " gLR # TPH()− g H T=−0 0 P(H) 1 HPT =PT − 1 (1)(1) L LPP 0 0 wherewhere gg == 9.8230 m/sm/s22 isis calculated calculated over over the the flight flight area area at at ground ground level according to thethe GOCE-basedGOCE-based geopotential modelmodel describeddescribed inin [[26],26], R R= = 287.053287.053 J/(kgJ/(kg·K)·K) (gas constant for air), TT00 is the temperature −3 at seasea levellevel (K),(K),P P0 0is is the the pressure pressure at at the the sea sea level level (Pa) (Pa) and andL= L∆=T Δ/∆T/HΔH= −= 6.5−6.5× ×10 10−3 K/mK/m (temperature lapselapse rate),rate), constantconstant belowbelow 1111 kmkm orthometricorthometric heightheight [[27].27]. Thanks to the the fact fact that that PT PT and and PTIMU PTIMU are are locate locatedd respectively respectively inside inside the theRadgyro Radgyro fuselage fuselage and andinside inside one onelateral lateral compartment compartment (Figure (Figure 3),3 ),it ithas has been been possible possible to to investigate howhow thethe RadgyroRadgyro dynamics affectsaffects thethe pressurepressure readout readout of of both both devices, devices, which which can can be be influenced influenced by by variations variations in thein the air fluxes,air fluxes, by theby aircraftthe aircraft velocity velocity as well as aswell by as depressions by depressions caused caused by the by rotor the motion, rotor motion, especially especially during theduring take the off take stage off (Figure stage9 (Figure). 9). Barometric altimeters are not ableable toto provideprovide absoluteabsolute heightheight withoutwithout priorprior knowledgeknowledge of thethe locallocal sea level level pressure pressure PP00. .A Acalibration calibration of ofthe the pressure pressure at sea at sea level level P0 isP 0necessaryis necessary in order in order to take to takeinto account into account the variation the variation of air fluxes of air related fluxes relatedto the Radgyro to the Radgyro dynamics dynamics as well as as possible well as variations possible variationsof the atmospheric of the atmospheric conditions conditions during the during flight the [28]. flight The [28 calibration]. The calibration of PT and of PT PTIMU and PTIMU has been has beenperformed performed applying applying the theinverse inverse hypsom hypsometricetric formula formula (Equation (Equation (1)), (1)), where where H HPTPT isis obtained obtained byby averaging thethe heightsheights measuredmeasured byby GNSSGNSS receivers receivers and and ALT ALT (at (at altitude altitude less less than than 340 340 m) m) during during 120 120 s ofs of flight. flight. This This interval interval is chosenis chosen on on the the base base of generalof general agreement agreement among among sensor sensor data, data, minimizing minimizing the standardthe standard deviations deviations during during the flight. the flight. Since Since F11 and F11 F14and are F14 characterized are characterized by longer by longer acquisition acquisition times, thistimes, process this process has been has applied been applied during during the flight the in flight two differentin two different separated separated intervals. intervals. After these calibrations an internalinternal consistencyconsistency check shows that allall systematicsystematic discrepancies ofof altitude measured by PTPT andand PTIMUPTIMU havehave beenbeen removed.removed. The successful correction is confirmedconfirmed by thethe excellentexcellent agreementagreement betweenbetween HHGPSABCGPSABC andand HHPTPT datadata (Figure (Figure 10). 10 ).

Figure 9.9.Temporal Temporal profile profile of theof the pressure pressure measured measured by PT by (in PT blue) (in and blue) PTIMU and (inPTIMU red) not (in calibrated, red) not andcalibrated, of the Radgyroand of the horizontal Radgyro horizontal velocity (in velocity black) (in before black) the before take-off. the take-off. When the When back the screw back is screw turned is on,turned the on, PT the sensor, PT sensor, which which is significantly is significantly exposed expose tod theto the air air flux, flux, measures measures a a depression depression (point(point A). TheThe pressure variation registered registered by by both both sensors sensors in inB Bis isdue due to tothe the rapid rapid increase increase of velocity of velocity during during the thetaxiing. taxiing. The Theaccelerating accelerating run along run along a runway a runway starts startsin C and in Cin andD the in aircraft D the aircrafttakes off. takes off.

Sensors 2017, 17, 1889 9 of 21 Sensors 2017, 17, 1889 9 of 21

Figure 10. Linear regressionregression betweenbetween HHGPSABCGPSABC andand H HPTPT datadata for for F11. F11. In In blue blue and and red red are are reported the calibrated andand not-calibratednot-calibrated barometricbarometric data data respectively. respectively. The The black black straight straight lines lines are are the the linear linear ﬁts fits to data:to data: in in both both cases cases r2 =r2 0.999.= 0.999.

3. Results and Discussion This section discusses the comparison and the accuracy of the orthometric heights derived by GNSS, radarradar altimeter altimeter and and barometers. barometers. The The metric metric adopted adopted is based is onbased the rooton the mean root square mean RMS( squareδHJ) ofRMS( theδ discrepancyHJ) of the discrepancy between HJ measuredbetween H byJ themeasuredJ-th sensor by the and J the-th averagedsensor and height the obtainedaveraged from height all theobtained sensors: from all the sensors: v u N 2 u N J δHJ 2 u ∑()δ H i J ti=1 i RMS δH J = = (2)(2) RMS()δ H = i 1 N N where N is the total numbers of data. For each i-th measurement obtained by J-th sensor, the residual where N is the total numbersJ of data. For each i-th measurement obtained by J-th sensor, the residual around the mean δHi is given by: around the mean δH J is given by: J J i δHi = Hi − Hi (3) δ JJ=− where Hi is the average height measured byHHH Miii sensors (For H < 340 m, M = 7, while H > 340 m, M(3) = 6, due to the fact the number of outliers of radar altimeter exceeds 30%.): where H i is the average height measured by M sensors (For H < 340 m, M = 7, while H > 340 m, M = M 6, due to the fact the number of outliers of radar altimeterJ exceeds 30%.): ∑ Hi J=1 Hi = M (4) M J  Hi J=1 (4) Since we have shown that the nominalH= accuracyi of each sensor is often underestimated and M we can’t hypothesize a priori a quality ranking, we don’t introduce any weights in Equation (4). The correlationsSince we have among shown the that uncertainties the nominal of accuracy three classes of each of sensor sensors is often (GNNS, underestimated radar altimeter and and we barometriccan’t hypothesize sensors) a priori are negligible, a qualitywhile ranking, we can’twe don’t exclude introduce any possible any weights correlations in Equation between (4). dataThe acquiredcorrelations by GNNSamong sensorsthe uncertainties or barometers. of three The analysisclasses of thesensors latter (GNNS, correlations radar goes altimeter beyond and the purposebarometric of thissensors) study, are which negligible, investigates while the we main can’t sources exclude of systematicany possible errors. correlations Moreover, between Comparing data RMS(acquiredδHJ )by with GNNS the mean sensors of theor barometers. residuals of theTheJ -thanal sensor:ysis of the latter correlations goes beyond the purpose of this study, which investigates the main sources of systematic errors. Moreover, N Comparing RMS(δHJ) with the mean of the residuals of theJ J-th sensor: ∑ δHi J i=1 δH = N (5) Nδ J Hi J  (5) δ H = i=1 N

Sensors 2017, 17, 1889 10 of 21 it is possible to highlight potential systematic biases related to the J-th sensor dataset, which can be distinguished from the variance of the residuals σ2 HJ on the base of the following relationship:

r J2 RMS δHJ = σ2(HJ) + δH (6)

where σ2 HJ is deﬁned as: N J J2 ∑ δHi − δH = σ2 HJ = i 1 (7) N − 1 This metric allows emphasizing the systematic height shift related to a speciﬁc sensor dataset with respect to the dispersion of values around the average height (see Tables3 and4). In other words from J J J J Equation (6) we learn that when the RMS(δH ) ≈ δH then σ H << δH i.e., the measurement is affected by a systematic bias which dominates the dispersion of data σ HJ . With the perspective of evaluating an overall uncertainty on the height measurement for airborne gamma ray applications, we also calculate the distribution of standard deviations σi(H) for each i-th entry of the dataset: v u M 2 u J u ∑ Hi − Hi t J=1 σ (H) = (8) i M − 1

The analysis has been performed on four different datasets (Table2), which have been distinguished according to a spatial selection cut and a GPS processing method cut, corresponding respectively to the 340 m altimeter outlier cutoff and to the 0.2 Hz frequency double-differences dataset of GPSA, GPSB and GPSC post-processing, as described in Sections 2.2 and 2.3.

J Table 3. Average residuals δH and RMS(δHJ) for data acquired at 1 Hz in the range (35–340) m (DATASET 1α) and in the range (340–2194) m (DATASET 1β).

DATASET 1α GPSA [m] GPSB [m] GPSC [m] GPSIMU [m] ALT [m] PTIMU [m] PT [m] δH RMS δH RMS δH RMS δH RMS δH RMS δH RMS δH RMS F11 −0.1 1.8 0.7 2.7 0.4 1.9 0.0 1.7 0.0 1.5 −0.8 1.7 −0.2 1.4 F12 −0.2 1.8 −0.1 2.1 0.2 2.3 0.8 1.4 −0.7 2.9 0.0 1.9 0.1 2.0 F15 1.9 2.3 0.5 2.1 1.7 2.5 5.8 5.9 −3.2 3.3 −4.1 4.3 −2.7 3.0 DATASET 1β GPSA [m] GPSB [m] GPSC [m] GPSIMU[m] ALT [m] PTIMU [m] PT [m] δH RMS δH RMS δH RMS δH RMS δH RMS δH RMS δH RMS F11 0.4 2.5 0.6 2.1 1.3 2.1 −1.4 2.3 / / −0.8 2.0 −0.1 1.6 F14 0.7 1.7 1.0 2.0 1.5 2.2 −3.1 3.4 / / −0.2 1.5 −0.1 1.7 SensorsSensors2017 2017,,17 17,, 1889 1889 1111 ofof 2121

J δ J Table 4. AverageJ residuals H and RMS(δ H ) for DATASET 2. Table 4. Average residuals δH and RMS(δHJ) for DATASET 2. Linear regression data for each couple of sensors in the ﬁve cases are reported in TablesDATASET A1–A5 2.α GPSA [m] GPSB [m] GPSC [m] GPSIMU[m] ALT[m] PTIMU [m] PT [m] DATASET 2α δH RMS δH RMS δH RMS δH RMS δH RMS δH RMS δH RMS F11 −GPSA0.5 [m]1.9 0.6 GPSB [m] 1.8 −0.2 GPSC [m]1.9 GPSIMU[m]0.2 1.9 0.2 ALT[m] 1.3 PTIMU−0.5 [m]1.8 PT0.1 [m] 1.4 F12 −δ0.2H RMS1.7 δ0.0H RMS1.4 δ0.2H RMS1.6 δ1.1H RMS1.5 −δ0.5H RMS2.5 δH0.2 RMS1.6 δH−0.8 RMS1.8 F15 2.1 2.4 0.0 1.7 0.4 1.1 6.8 6.9 −2.4 2.5 −3.8 4.1 −3.1 3.6 F11 −0.5 1.9 0.6 1.8 −0.2 1.9 0.2 1.9 0.2 1.3 −0.5 1.8 0.1 1.4 F12 −0.2 1.7 0.0 1.4 0.2 1.6DATASET 1.1 2β 1.5 −0.5 2.5 0.2 1.6 −0.8 1.8 F15 2.1 GPSA [m] 2.4 0.0 GPSB [m] 1.7 0.4 GPSC [m] 1.1 GPSIMU[m] 6.8 6.9 −2.4 ALT [m]2.5 −3.8 PTIMU4.1 [m] −3.1 PT [m]3.6

δH RMS δH RMS δH RMSDATASET δH 2βRMS δH RMS δH RMS δH RMS F11 0.1GPSA [m]2.3 0.6 GPSB [m]1.3 0.9 GPSC [m]1.7 GPSIMU[m]−0.1 1.3 ALT / [m] / PTIMU−1.4 [m]2.4 − PT0.1 [m] 1.6 F14 δ0.6H RMS1.3 δ0.4H RMS1.3 δ0.6H RMS1.3 −δ1.6H RMS2.0 δ /H RMS / δH−0.1 RMS1.3 δH0.1 RMS1.7 F11 0.1 2.3 0.6 1.3 0.9 1.7 −0.1 1.3 / / −1.4 2.4 −0.1 1.6 3.1.F14 Analysis0.6 of DATASET 1.3 0.4 1 1.3 0.6 1.3 −1.6 2.0 / / −0.1 1.3 0.1 1.7 The main results of the analysis of the 1 Hz stand-alone DATASET 1α and 1β (Table 2) are 3.1. Analysis of DATASET 1 J summarized for each sensor in Table 3 in terms of average of the residuals δH and of the root meanThe square main of results the residuals of the analysis RMS(δ HofJ ) the. The 1 Hzpoor stand-alone accuracy of DATASET data from 1α GNSSand 1 βat (Tablelow altitude2) are J summarizedmentioned in for Section each sensor2.3 is confirmed in Table3 in in termsthis analysis. of average In particular, of the residuals for H δ

FigureFigure 11.11.Distribution Distribution of ofσ (H)σ(H) (standard (standard deviations deviations of heights)of heights) in the in rangethe range (35–66) (35–66) m (red m solid(red line),solid (79–340)line), (79–340) m (blue m solid(blue line) solid and line) (340–2194) and (340–2194) m (green m (green solid line) solid measured line) measured at 1 Hz. at 1 Hz.

Sensors 2017, 17, 1889 12 of 21 Sensors 2017, 17, 1889 12 of 21

δ J J Figure 12.12. Distribution of thethe residualsresiduals δHHi ini inthe the (464–2194) (464–2194) m rangem range of altitude:of altitude: GPSIMU GPSIMU dataset dataset in solidin solid green green line, line, PTIMU PTIMU and and PT PT dataset dataset is is reported reported in in solid solid blue blue line, line, and and GPSABC GPSABC datasetdataset inin solidsolid red line.line.

3.2. Analysis of DATASET 22 In thisthis sectionsection the analysis of the 0.2 Hz double-difference DATASET 2α and DATASET 22ββ isis presented, in which the GPSA,GPSA, GPSBGPSB andand GPSCGPSC acquisitionsacquisitions havehave beenbeen post-processedpost-processed using the double differences method with respect to thethe mastermaster stationstation observationobservation data.data. PT and PTIMU are calibrated withwith thethe criteriacriteria describeddescribed inin SectionSection 2.42.4 usingusing thethe GNSSGNSS double-differencedouble-difference data.data. The doubledouble differences differences post-processing post-processing increases increase thes the quality quality of GPSA, of GPSA, GPSB GPSB and GPSC and GPSC data which data reflects in a shrinking of the σi(H) distributionσ () towards low standard deviation values at altitude which reflects in a shrinking of the i H distribution towards low standard deviation values at (79–2194) m (Figure 13 Panel b), making the median value of the distribution decrease from 1.5 m altitude (79–2194) m (Figure 13 Panel b), making the median value of the distribution decrease from (stand-alone) to 0.8 m (double-differences). We note that the major benefit of the data treatment affects 1.5 m (stand-alone) to 0.8 m (double-differences). We note that the majorJ benefit of the data the GPSABC accuracy at high altitude (340–2194) m, where the values of δH are comparable to thoseJ treatment affects the GPSABC accuracyJ at high altitude [340–2194] m, where the values of δH are obtained for (79–340) m (i.e., δH < 1 m) (Table4). J J comparableOn the basisto those of δobtainedH and RMS for (79–340)(δHJ) calculated m (i.e., δ inH Table < 1 m)4 we (Table can 4). assert that double differences J post-processingOn the basis does of δ notH produceand RMS( anyδ HJ evident ) calculated improvement in Table 4of we the can altitude assert that accuracy double at differences H < 66 m (Figure 13 Panel a). The severe multipath noise which affects the calculation of relative distances post-processing does not produce any evident improvement of the altitude accuracy at H < 66 m between the three GPS antennas and the altitude measured at 1 Hz, is not healed by double-differences (Figure 13 Panel a). The severe multipath noise which affects the calculation of relative distances post processing at heights lower than 66 m. On the other hand, the non-GNSS sensors give excellent between the three GPS antennas and the altitude measured at 1 Hz, is not healed by results in terms of linear correlation and negligible systematic effects. Observing linear regression double-differences post processing at heights lower than 66 m. On the other hand, the non-GNSS data in Table A3 for PT, PTIMU, and ALT the slope and the intercept are compatible with 1 and 0 at sensors give excellent results in terms of linear correlation and negligible systematic effects. 2σ-level respectively. Observing linear regression data in Table A3 for PT, PTIMU, and ALT the slope and the intercept are The performance of all sensors in the altitude range (79–2194) m is essentially similar: compatible with 1 and 0 at 2σ-level respectively. J J the RMSThe( δperformanceH ) varies from of all 1.3 msensors to 2.5 min andthe thealtitude maximum rangeδ H(79–2194)= 1.6 m m (Table is essentially4). The distribution similar: the of standard deviation of heights reported in Figure 14 does not showJ any peculiar feature: for altitude RMS(δ HJ ) varies from 1.3 m to 2.5 m and the maximum δH = 1.6 m (Table 4). The distribution of ranges of (79–340) m and (340–2194) m the medians are 1.6 m and 1.5 m, respectively. In particular thestandard Pearson deviation correlation of heights coefficients reported calculated in Figure for 14 all does the couplesnot show of any sensors peculiar highlight feature: perfect for altitude linear correlationranges of (79–340) in the (340–2194) m and (340–2194) m range ofm altitudethe medians (Tables are A4 1.6 and m andA5). 1.5 m, respectively. In particular the Pearson correlation coefficients calculated for all the couples of sensors highlight perfect linear correlation in the (340–2194) m range of altitude (Tables A4 and A5).

Sensors 2017, 17, 1889 13 of 21 SensorsSensors 2017 2017, ,17 17, ,1889 1889 1313 of of 21 21

FigureFigure 13. 13.13.Distribution DistributionDistribution of ofσof(H) σσ(H)(H) (standard (standard(standard deviations deviationsdeviations of heights) ofof heights)heights) calculated calculatedcalculated for GPSABC forfor GPSABCGPSABC built-in solution built-inbuilt-in (redsolutionsolution solid (red (red line) solid solid and line) line) with and and double-difference with with double-difference double-difference post-processing post-processing post-processing (blue solid (blue (blue line), solid solid in line), theline), altitude in in the the altitude altitude ranges (35–66)rangesranges (35–66) m(35–66) (panel m m a( panel)(panel and (79–2194)a a) )and and (79–2194) (79–2194) m (panel m m b( panel().panel b b).).

FigureFigure 14. 14. Distribution Distribution of of of σ σ(H)σ(H)(H) (standard (standard (standard deviations deviations deviations of of ofheights) heights) heights) in in the inthe thealtitude altitude altitude ranges ranges ranges (35–66) (35–66) (35–66) m m (red (red m (redsolidsolid solid line), line), line), (79–340) (79–340) (79–340) m m (blue (blue m (blue so solidlid solid line) line) line)and and and(340–2194) (340–2194) (340–2194) m m (green (green m (green so solidlid solid line) line) line) measured measured measured at at 0.2 0.2 at Hz. 0.2Hz. Hz.

3.3.3.3. Effect Effect of of the the Accuracy Accuracy ofof the the Flight Flight Altitude Altitude on on AGRS AGRS Measurements Measurements InIn airborneairborne gamma-raygamma-raygamma-ray spectroscopyspectroscopy measurements,measuremmeasurements,ents, knowing knowing the the surveysurvey altitudealtitude aboveabove thethe groundground is isis of ofof crucial crucialcrucial importance importanceimportance in order inin orderorder to model toto modelmodel the exponential thethe exponentialexponential attenuation attenuationattenuation photons photons havingphotons different havinghaving characteristicdifferentdifferent characteristic characteristic energies energies sufferenergies when suffer suffer traversing when when traversi traversi the airngng material. the the air air material. material. This aspect This This hasaspect aspect implications has has implications implications on the determinationonon thethe determinationdetermination of the height ofof thethe correction heightheight factorscorrectioncorrection which fafactors arectors separately whichwhich areare calculated separatelyseparately for eachcalculatedcalculated radionuclide forfor eacheach in radionuclide in order to reconstruct the counting statistics at ground level in case of flat orderradionuclide to reconstruct in order the countingto reconstruct statistics the at groundcounting level statistics in case ofat ﬂatground morphology. level in case of flat morphology. morphology.In fact, neglecting possible systematic uncertainties originating from the calibration of the In fact, neglecting possible systematic uncertainties originating from the calibration of the instrumentalIn fact, neglecting setup, the mainpossible source systematic of uncertainty uncertainties in AGRS originating measurements from is relatedthe calibration to the counting of the instrumental setup, the main source of uncertainty in AGRS measurements is related to the counting statistics,instrumental which setup, result the from main the source statistical of uncertainty nature of bothin AGRS radioactive measurements decay and is related photon to attenuation the counting in statistics, which result from the statistical nature of both radioactive decay and photon attenuation in traversingstatistics, which materials. result Considering from the statistical a NaI(Tl) nature detector of both having radioactive a volume decay of 16 and L and photon ﬂying attenuation at a height ofin traversing materials. Considering a NaI(Tl) detector having a volume of 16 L and flying at a height of 100traversing m over materials. a terrain characterized Considering bya NaI(Tl) K, U and detector Th abundances having a volume respectively of 16 equal L and to flying 0.02 g/g,at a height 2.5 µg/g of 100 m over a terrain characterized by K, U and Th abundances respectively equal to 0.02 g/g, 2.5 μg/g and100 m 9.0 overµg/g, a terrain the statistics characterized in counts by per K, U second and Th (cps), abundances recorded respectively in the three energyequal to windows 0.02 g/g, typically2.5 μg/g and 9.0 μg/g, the statistics in counts per second (cps), recorded in the three energy windows usedand 9.0 to quantifyμg/g, the the statistics content in of thecounts three per radionuclides second (cps), (1370–1570 recorded keVin the for K,three 1660–1860 energy keVwindows for U typically used to quantify the content of the three radionuclides (1370–1570 keV for K, 1660–1860 andtypically 2410–2810 used to keV quantify for Th), the are content respectively of the (103.2 three ±radionuclides10.2) cps, (12.4 (1370–1570± 3.5) cps keV and for (26.5 K, ±1660–18605.1) cps, keV for U and 2410–2810 keV for Th), are respectively (103.2 ± 10.2) cps, (12.4 ± 3.5) cps and (26.5 ± wherekeV for the U uncertaintyand 2410–2810 is estimated keV for Th), according are respectively to the Poisson (103.2 distribution ± 10.2) cps, describing (12.4 ± 3.5) the cps nature and (26.5 of the ± 5.1) cps, where the uncertainty is estimated according to the Poisson distribution describing the radioactive5.1) cps, where decay. the uncertainty is estimated according to the Poisson distribution describing the naturenature of of the the radioactive radioactive decay. decay. AssumingAssuming that that the the detector detector receives receives the the signal signal produced produced by by a a homogeneous homogeneous infinite infinite half-space half-space soilsoil volume volume source, source, the the measured measured count count ra ratete can can be be written written as as (see (see Appendix Appendix C): C):

Sensors 2017, 17, 1889 14 of 21

Assuming that the detector receives the signal produced by a homogeneous inﬁnite half-space soil volume source, the measured count rate can be written as (see AppendixC):

Z 1 − µ(E)z N(E, z) = N(E, 0) dcosθe cosθ (9) 0 where N(E, z) and N(E, 0) are respectively the counting statistics in counts per second [cps] at the survey altitude z and the one that would have been measured at ground level for photons having emission energy E, and µ(E) [m−1] is the air linear attenuation coefﬁcient, corresponding to the inverse of the mean free path traveled by a photon having energy E and traversing the air material. As the 40K, 238U, 232Th ground abundances are determined by dividing the estimated ground level count rates N(E, 0) in each speciﬁc energy window by the corresponding ground sensitivity constants (i.e., the count rate per unit radioisotope concentration), the relative uncertainty on the ground abundance is the same affecting the counting statistics N(E, 0), assuming that the uncertainty on the sensitivity constants is negligible. In order to establish the effect of the height uncertainty on the radioactive content assessment, it is necessary to go through an uncertainty propagation procedure, according to which the relative σN(E,0) uncertainty on the ground counting statistics N(E,0) can be written as follows (see AppendixC):

2 2 σN(E,0) σN(E,z) = + (β(µ(E), z)µ(E)σ )2 N(E, 0) N(E, z) z where: − (E)z R 1 1 µ dcosθ e cosϑ β(µ(E), z) = 0 cosθ (10) 1 −µ(E)z R cosϑ 0 dcosθe

σN(E,z) and N(E,z) and σz are respectively the relative uncertainty on the measured counting statistics and the absolute uncertainty on the height above ground level. The adimensional β(µ(E), z) function has a lower limit value equal to 1 and has a weak dependence on the photon energy and a stronger dependence on the survey altitude, as can be seen from Figure A1. Assuming that the uncertainty on the height above ground level is exclusively given by the uncertainty on the orthometric height (i.e., neglecting any contribution that can potentially arise from the Digital Elevation Model (DEM) of the terrain) we estimate by choosing as σz the 2.1 m median value of the standard deviation distribution of DATASET 1β that the relative uncertainty on the 40K, 238U, 232Th ground abundances at 100 m are 2.2%, 2.0% and 1.7% respectively, which result only from the uncertainty on the height above the ground (i.e., neglecting the uncertainty on the counting statistics).

4. Conclusions In this study we investigate how the combination of redundant data from seven altimetric sensors can improve the quality of flight height accuracy with the perspective to estimate the uncertainties affecting airborne radiometric measurements. In flying over the sea in the range (35–66) m, the altitude measured by GNSS antennas suffers the severe noise due to the multipath effect which is clearly reduced on the land. Although the IMU sensor provides the flight altitude by combining the data from IMU the GNSS, the barometer, and the accelerometers, the values of δH and RMS(δHIMU) are greater than 5 m, highlighting how the external correction is not effective in mitigating the noise due to the multipath on the GPS signal. On the base of our study, we can conclude that the most accurate measurement of flight altitude over the sea in the (35–66) m range has been performed by two barometric altimeters together with the radar altimeter. In this altitude regime the linear regressions (Table A3) show slopes and intercepts compatible with 1 and 0 at 2σ-level, and the median of the distribution of standard deviations of Sensors 2017, 17, 1889 15 of 21 heights is 1.1 m. Adopting this altitude error at 50 m, the relative uncertainties on the 40K, 238U, 232Th ground abundances are equal to 1.3%, 1.2% and 1.1% respectively. According to our investigation the reliability of radar altimeter is in agreement with its declared accuracy (3% of the altitude value) up to 340 m: beyond this height the number of outliers increases drastically, preventing the inclusion of these data for the comparative analysis. In the (79–340) m range the median of the distribution of standard deviations of altitude acquired by all seven sensors is 1.6 m, with double differences post-processing of the signal recorded by three single frequency GNSS antennas. Adopting conservatively this uncertainty for a 100 m flight altitude, we can estimate a relative uncertainty of 1.7%, 1.5% and 1.3% associated to 40K, 238U, 232Th ground abundances respectively. At altitude higher than 79 m, the GNSS double-difference post-processing enhanced significantly the data quality obtained by the 3 low-cost and light antennas. This is proved by a reduction of the median value of the standard deviations (from 1.5 m with stand-alone analysis to 0.8 m with double-difference processing) and by an increasing precision in the reconstruction of median distance of the three antennas with increasing altitude. Since the computation of double differences does not solve the multipath problem, the use of better performing antennas with size and cost compatible with AGRS survey is strongly recommended. According to our study, the best integration of data from GNNS antennas, radar and barometric altimeters allows reaching an accuracy better than 2% at flight altitude higher than ~80 m, which affect the estimation of ground total activity measured at 100 m with an uncertainty resulting from the sole uncertainty on the flight height of the order of 2%.

Acknowledgments: This work was partially founded by the National Institute of Nuclear Physics (INFN) through the ITALian RADioactivity project (ITALRAD) and by the Theoretical Astroparticle Physics (TAsP) research network. The co-authors would like to acknowledge the support of the Geological and Seismic Survey of the Umbria Region (UMBRIARAD), of the University of Ferrara (Fondo di Ateneo per la Ricerca scientifica FAR 2016), of the Project Agroalimentare Idrointelligente CUP D92I16000030009 and of the MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca) under MIUR-PRIN-2012 project. The authors would like to thank the staff of GeoExplorer Impresa Sociale s.r.l. for their support and Mauro Antogiovanni, Claudio Pagotto, Ivan Callegari and Andrea Motti for their collaboration which made possible the realization of this study. The authors would also like to show their gratitude to Emanuele Tufarolo for useful discussions. Author Contributions: Matteo Albéri, Marica Baldoncini, Fabio Mantovani and Virginia Strati conceived and designed the work as it is. Matteo Albéri, Marica Baldoncini and Fabio Mantovani took part to data collection with Radgyro. GNSS data processing was performed by Matteo Albéri, Carlo Bottardi, Fabio Mantovani, Eugenio Realini, Mirko Reguzzoni, Lorenzo Rossi and Daniele Sampietro. The data analysis and its interpretation was performed by Matteo Albéri, Carlo Bottardi, Fabio Mantovani, Eugenio Realini, Mirko Reguzzoni, Lorenzo Rossi and Daniele Sampietro. Matteo Albéri drafted the article which has been critically revised by Carlo Bottardi, Marica Baldoncini, Enrico Chiarelli, Giovanni Fiorentini, Fabio Mantovani, Kassandra Giulia Cristina Raptis, Eugenio Realini, Mirko Reguzzoni, Lorenzo Rossi, Daniele Sampietro and Virginia Strati. All authors gave final approval of the version to be submitted and any revised version. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A For the flights with data under 340 m are shown the values of the linear regressions between each pair of sensors in the DATASET 2α: m (slope) and q (y-intercept) with their uncertainties and the r2 (correlation coefficient). The sensors on the first row of each table give us the x values and the sensors on the first column give the y values. Sensors 2017, 17, 1889 16 of 21

Table A1. Linear regression data of F11 (DATASET 2α).

F11 GPSB GPSA GPSIMU ALT PT PTIMU m 0.994 ± 0.002 0.992 ± 0.003 0.981 ± 0.003 0.987 ± 0.002 0.996 ± 0.003 1.001 ± 0.003 GPSC q 0.21 ± 0.38 −1.56 ± 0.49 2.62 ± 0.58 1.72 ± 0.39 0.48 ± 0.51 0.05 ± 0.55 r2 0.998 0.997 0.996 0.998 0.997 0.996 m 0.998 ± 0.003 0.987 ± 0.003 0.993 ± 0.002 1.001 ± 0.003 1.007 ± 0.003 GPSB q 1.46 ± 0.44 2.49 ± 0.51 1.63 ± 0.33 −0.43 ± 0.52 0.00 ± 0.56 r2 0.998 0.997 0.999 0.997 0.996 m 0.988 ± 0.003 0.993 ± 0.002 1.001 ± 0.003 1.008 ± 0.003 GPSA q 1.28 ± 0.545 0.40 ± 0.36 −0.85 ± 0.49 −1.31 ± 0.51 r2 0.996 0.998 0.997 0.997 m 1.003 ± 0.003 1.012 ± 0.002 1.019 ± 0.002 GPSIMU q −0.48 ± 0.46 −1.95 ± 0.37 −2.42 ± 0.38 r2 0.997 0.998 0.998 m 1.008 ± 0.002 1.014 ± 0.003 ALT q −1.20 ± 0.40 −1.63 ± 0.46 r2 0.998 0.997 m 1.007 ± 0.001 PT q 0.44 ± 0.19 r2 1.000

Table A2. Linear regression data of F12 (DATASET 2α).

F12 GPSB GPSA GPSIMU ALT PT PTIMU m 1.016 ± 0.005 0.996 ± 0.006 1.015 ± 0.006 1.056 ± 0.007 1.015 ± 0.007 0.998 ± 0.007 GPSC q −2.67 ± 0.81 1.15 ± 1.01 −3.65 ± 1.01 −9.25 ± 1.27 −1.70 ± 1.25 0.28 ± 1.21 r2 0.997 0.995 0.995 0.993 0.993 0.993 m 0.980 ± 0.004 0.998 ± 0.005 1.037 ± 0.008 0.997 ± 0.007 0.981 ± 0.007 GPSB q 3.80 ± 0.70 −0.77 ± 0.90 −6.08 ± 1.36 1.25 ± 1.25 3.18 ± 1.19 r2 0.998 0.996 0.992 0.993 0.993 m 1.017 ± 0.005 1.057 ± 0.007 1.016 ± 0.008 1.000 ± 0.007 GPSA q −4.43 ± 0.95 −9.93 ± 1.33 −2.27 ± 1.38 −0.35 ± 1.28 r2 0.996 0.993 0.991 0.992 m 1.036 ± 0.008 1.000 ± 0.004 0.983 ± 0.003 GPSIMU q −4.90 ± 1.42 1.93 ± 0.75 3.85 ± 0.63 r2 0.991 0.997 0.998 m 0.957 ± 0.008 0.941 ± 0.008 ALT q 7.96 ± 1.38 9.92 ± 1.41 r2 0.99 0.99 m 0.983 ± 0.002 PT q 2.07 ± 0.44 r2 0.999 Sensors 2017, 17, 1889 17 of 21

Table A3. Linear regression data of F15 (DATASET 2α).

F15 GPSB GPSA GPSIMU ALT PT PTIMU m 0.896 ± 0.017 0.956 ± 0.008 1.015 ± 0.014 0.982 ± 0.007 0.991 ± 0.027 1.022 ± 0.026 GPSC q 5.68 ± 0.89 0.65 ± 0.43 −7.34 ± 0.82 3.65 ± 0.35 3.92 ± 1.32 3.14 ± 1.25 r2 0.958 0.992 0.978 0.994 0.928 0.962 m 1.027 ± 0.019 1.108 ± 0.016 1.057 ± 0.019 1.079 ± 0.031 1.113 ± 0.030 GPSB q −3.47 ± 1.05 −13.05 ± 0.95 −0.34 ± 0.92 −0.63 ± 1.50 −1.51 ± 1.41 r2 0.958 0.975 0.964 0.968 0.921 m 1.054 ± 0.017 1.022 ± 0.008 1.032 ± 0.028 1.061 ± 0.028 GPSA q −7.89 ± 0.97 3.37 ± 0.40 3.36 ± 1.38 2.97 ± 1.35 r2 0.971 0.993 0.916 0.922 m 0.952 ± 0.11 0.970 ± 0.025 1.001 ± 0.023 GPSIMU q 11.57 ± 0.54 11.38 ± 1.21 10.57 ± 1.11 r2 0.984 0.927 0.939 m 1.009 ± 0.027 1.040 ± 0.026 ALT q 0.33 ± 1.31 −0.45 ± 1.24 r2 0.921 0.931 m 1.020 ± 0.009 PT q −0.28 ± 0.45 r2 0.99

Appendix B For the flights with data over 340 m are shown the values of the linear regressions between each pair of sensors in the DATASET 2β: m (slope) and q (y-intercept) with their uncertainties and the r2 (correlation coefficient). The sensors on the first row of each table give us the x values and the sensors on the first column give the y values.

Table A4. Linear regression data of F11 (DATASET2β).

F11 GPSB GPSA GPSIMU PT PTIMU m 0.9996 ± 0.0001 1.0007 ± 0.0001 1.0009 ± 0.0002 0.9994 ± 0.0002 0.9987 ± 0.0002 GPSC q 0.75 ± 0.11 0.11 ± 0.14 0.15 ± 0.21 1.57 ± 0.24 3.50 ± 0.26 r2 1.000 1.000 1.000 1.000 1.000 m 1.0011 ± 0.0002 1.0013 ± 0.0001 0.9998 ± 0.0002 0.9992 ± 0.0002 GPSB q −0.64 ± 0.18 −0.60 ± 0.16 0.82 ± 0.21 2.75 ± 0.23 r2 1.000 1.000 1.000 1.000 m 1.0002 ± 0.0002 0.9987 ± 0.0003 0.9980 ± 0.0003 GPSA q 0.05 ± 0.28 1.48 ± 0.30 3.40 ± 0.33 r2 1.000 1.000 1.000 m 0.9985 ± 0.0001 0.9979 ± 0.0001 GPSIMU q 1.41 ± 0.12 3.34 ± 0.11 r2 1.000 1.000 m 0.9994 ± 0.0001 PT q 1.93 ± 0.11 r2 1.000 Sensors 2017, 17, 1889 18 of 21

Table A5. Linear regression data of F14 (DATASET2β).

F14 GPSB GPSA GPSIMU PT PTIMU m 0.99997 ± 0.00005 0.9996 ± 0.0001 0.9977 ± 0.0001 0.9975 ± 0.0002 0.9982 ± 0.0002 GPSC q 0.18 ± 0.08 0.62 ± 0.10 5.64 ± 0.20 4.25 ± 0.26 3.37 ± 0.24 r2 1.000 1.000 1.000 1.000 1.000 m 99960 ± 0.00004 0.9977 ± 0.0001 0.9976 ± 0.0002 0.9982 ± 0.0002 GPSB q 0.44 ± 0.06 5.47 ± 0.22 4.07 ± 0.28 3.19 ± 0.25 r2 1 1.000 1.000 1.000 m 0.9981 ± 0.0001 0.9980 ± 0.0002 0.9986 ± 0.0002 GPSA q 5.03 ± 0.21 3.63 ± 0.29 2.75 ± 0.25 r2 1.000 1.000 1.000 m 0.9998 ± 0.0001 1.0005 ± 0.0001 GPSIMU q −1.40 ± 0.21 −2.28 ± 0.18 r2 1 1 m 1.0007 ± 0.0001 PT q −0.87 ± 0.17 r2 1.000

Appendix C The count rate measured in a given energy window by a detector that is flying at altitude z above ground level and which originates from a homogenous infinite half-space soil volume source is given by the following equation: 1 AγS Z −µ(E)z N(E, z) = dcosθe cosϑ (A1) 2µs(E) 0 3 where Aγ is the density of photons isotropically emitted by the homogeneous volume source [γ/m ], 2 −1 −1 S is the detector cross-sectional area [m ], µs(E) [m ] and µ(E) [m ] are the soil and air linear attenuation coefficients, corresponding to the inverse of the mean free path traveled by a photon having energy E and traversing the soil and air materials, respectively. Starting from Equation (A1) it is possible to write the following relation between the count rate measured at altitude z N(E, z) and the count rate that one would have measured by placing the detector on the ground N(E, 0):

N(E, z) = N(E, 0)k(µ(E), z) (A2) where the function k(µ(E), z) is given by:

Z 1 − µ(E)z k(µ(E), z) = dcosθe cosθ (A3) 0

Gamma-ray spectrometers typically undergo a ground efﬁciency calibration procedure for the determination of the sensitivity constants, which allow for the conversion of measured count rates into ground radionuclide abundances. The 40K, 238U, 232Th ground abundances are therefore predicted by dividing the estimated ground level count rate N(E, 0) by the speciﬁc ground sensitivity constant, which represents the count rate per unit radioisotope concentration. In the hypothesis of negligible uncertainty on the sensitivity constants, the relative uncertainty on the ground abundance is equal to the relative uncertainty affecting the counting statistics N(E, 0), inferred from the measured N(E, z) according to Equation (A2). We therefore apply the standard propagation of uncertainty for uncorrelated variables to the quantity N(E, 0) in order to estimate the contribution given by the uncertainty on the survey altitude σz to the ground concentration estimation, which can be expressed according to the following equation: Sensors 2017, 17, 1889 19 of 21

2 2 2 = ∂N(E,0) + ∂N(E,0) σN(E,0) ∂N(E,z) σN(E,z) ∂k(µ(E),z) σk(µ(E),z) 2 2 (A4) = ∂N(E,0) + ∂N(E,0) ∂k(µ(E),z) ∂N(E,z) σN(E,z) ∂k(µ(E),z) ∂z σz Starting from the inverse of Equation (A2) it is possible to determine all the terms of Equation (A4) as follows:

∂N(E, 0) 1 = (A5) ∂N(E, z) k(µ(E), z) q σN(E,z) = N(E, z) (A6)

∂N(E, 0) N(E, z) = (A7) ∂k(µ(E), z) k(µ(E), z)2 Z 1 ∂k(µ(E), z) µ(E) − µ(E)z = dcosθ e cosθ (A8) ∂z 0 cosθ where the absolute uncertainty on the observed counting statistics given by Equation (A6) comes from the Poissonian nature of the radioactive decay process. By combining all the obtained terms into Equation (A4) it is possible to write the relative uncertainty on the inferred ground counting statistics as the sum of two terms as stated in the following equation:

σ 2 σ 2 N(E,0) = N(E,z) + ( ( ( ) ) ( ) )2 N(E,0) N(E,z) β µ E , z µ E σz µ(E)z 2 1 − ! (A9) σ 2 R 1 cosθ N(E,z) 0 dcosθ cosθ e = + µ(E)σz µ(E)z N(E,z) 1 − R cosθ 0 dcosθe

The first term in the summation corresponds to the relative uncertainty on the measured counting statistics, while the second term contains the product of the absolute height uncertainty σz times the air linear attenuation coefficient µ(E) which is in turn weighted by an adimensional factor β(µ(E), z) that depends on the linear attenuation coefficient itself and on the absolute survey height z. The β(µ(E), z) function contains an energy dependence as the attenuation suffered by photons is stronger for decreasing energy (i.e., the µ(E) linear attenuation coefficient decreases for increasing energy) and has also a z dependence according to which, for a fixed energy, the value of β(µ(E), z) decreases for increasing height asymptotically approaching 1. Figure A1 shows the profile of the β(µ(E), z) function for the characteristic emission energies of 40K (1460 keV), 214Bi (1765 keV) and 208Tl (2614 keV), where 214Bi and 208Tl are the major gamma emitting radionuclides respectively belonging to the 238U and 232Th decay series. The adopted values for the µ(E) gamma linear attenuation coefficients for 1460 keV, 1765 keV and 2614 keV photons propagating in air are respectively equal to 0.006430 m−1, 0.005829 m−1 and 0.004717 m−1. These values have been estimated using an air density of 1.225 kg/m3 and gamma mass attenuation coefficients taken from the National Institute of Standard and Technology website [27], where an air composition of 78% N2, 21% O2 and 1% Ar by weight has been given for the description of the composite traversed material. According to Equation (A9) it is possible to estimate the relative uncertainty on the K, U and Th abundances due solely to the uncertainty on the survey altitude σz, i.e., for a relative uncertainty on σ N(E,z) = the measured statistics N(E,z) 0. As in this study we are not considering the implications related to the use of the Digital Elevation Model (DEM) of the terrain, we adopt as σz value the median of the distribution of standard deviations of orthometric heights, which is in the worst case scenario (DATASET 1β for (340–2194) m) equal to 2.1 m. Referring to a standard survey height above the ground of 100 m, the estimated relative uncertainties on the K, U and Th concentrations deriving from the uncertainty on the survey height are respectively equal to 2.2%, 2.0% and 1.7%. Sensors 2017, 17, 1889 20 of 21 Sensors 2017, 17, 1889 20 of 21

Figure A1. Plot ofof thetheβ β((µμ((EE)),,z z)) factor factor as as function function of of the the survey survey altitude altitudez: thez: the red, red, green green and and blue blue line 40 214 238 208 232 linerefer refer respectively respectively to the to40 theK, 214K,Bi (Bi238 (U)U) and and208 TlTl (232 ( Th)Th) gamma gamma emission emission energies. energies.

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