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

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{40}K,

^{238}U,

^{232}Th) and artificial (e.g.,

^{137}Cs) 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 [2,3,4], 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.

## 2. Instruments and Methods

#### 2.1. The Inertial Measurement Unit

#### 2.2. The Radar Altimeter

^{®}Micro Radar Altimeter (ALT), placed under the Radgyro fuselage (Figure 3), measures the flight altitude at ~60 Hz by using a radar sensor operating at a frequency of 24 GHz. The estimate of the minimum distance is declared reliable within a cone having 20° opening angle and the declared accuracy on altimetric measurements is 3%, with a minimum value of 0.5 m. Although the flight altitude range declared by the seller is (0.5–500) m, our data analysis on the ALT dataset revealed a significative presence of outliers at heights above 340 m (Figure 5). Neglecting effects related to wave motions and tidal variations, which are typically <0.4 m in the surveyed area [18], we performed our study considering two different datasets named α and β, corresponding respectively to H < 340 m and H > 340 m respectively. The α database is populated by data acquired in 4803 s by all 7 sensors, while the β database refers to the remaining 6892 s in which the ALT sensor is excluded (Table 2).

#### 2.3. The Three GNSS Receivers

- -
- code-only stand-alone solution (1 Hz), using a Kalman filter with constant-velocity dynamics;
- -
- code and phase double differences solution (0.2 Hz) with respect to the permanent station Madonna Dell’Acqua (Pisa) (43.7475° N, 10.3660° E, 2 a.s.l), using a Kalman filter with constant-velocity dynamics.

_{GPSAB}, d

_{GPSAC}, d

_{GPSBC}with respect to reference values (Figure 3). Following [21], an outlier is a data point that lies out of the ranges (Q

_{1}− 1.5 IQR) and (Q

_{3}+ 1.5 IQR), where Q

_{1,}Q

_{3}and IQR are first quartile, third quartile and interquartile range respectively. Outlier data have been typically recognized when flying close to the sea (Figure 6) and at an altitude range of (35–900) m (Figure 7 and Figure 8). The analysis of outlier highlights that their percentage generally decreases with increasing altitude and that the median d

_{GPSBC,}d

_{GPSAC}and d

_{GPSAB}approach the reference distances.

_{GPSAB}erraticity decreases drastically crossing the border between sea and land (Figure 6). The average reconstructed d

_{GPSAB}varies from (5.86 ± 7.18) m (over water) to (3.77 ± 0.28) m (over land), to be compared with the (3.83 ± 0.01) m reference distance. In F15, characterized by a (35–66) m flight altitude range, it is possible to observe a noise amplification due to the multipath effect over the sea. This phenomenon is well known in literature and has been studied in different environmental scenarios [22], investigating also applications like the monitoring of coastal sea levels and of the periodicity of ocean tides [23,24,25].

#### 2.4. The two Pressure and Temperature Sensors

_{PT}and H

_{PTIMU}on the basis of the decreasing exponential trend of the atmospheric pressure with respect to the altitude and accounting for the tiny variations of the temperature in the lower atmosphere:

^{2}is calculated over the flight area at ground level according to the GOCE-based geopotential model described in [26], R = 287.053 J/(kg·K) (gas constant for air), T

_{0}is the temperature at sea level (K), P

_{0}is the pressure at the sea level (Pa) and L= ΔT/ΔH = −6.5 × 10

^{−3}K/m (temperature lapse rate), constant below 11 km orthometric height [27].

_{0}. A calibration of the pressure at sea level P

_{0}is necessary in order to take into account the variation of air fluxes related to the Radgyro dynamics as well as possible variations of the atmospheric conditions during the flight [28]. The calibration of PT and PTIMU has been performed applying the inverse hypsometric formula (Equation (1)), where H

_{PT}is obtained by averaging the heights measured by GNSS receivers and ALT (at altitude less than 340 m) during 120 s of flight. This interval is chosen on the base of general agreement among sensor data, minimizing the standard deviations during the flight. Since F11 and F14 are characterized by longer acquisition times, this process has been applied during the flight in two different separated intervals.

_{GPSABC}and H

_{PT}data (Figure 10).

## 3. Results and Discussion

^{J}) of the discrepancy between H

^{J}measured by the J-th sensor and the averaged height obtained from all the sensors:

^{J}) with the mean of the residuals of the J-th sensor:

#### 3.1. Analysis of DATASET 1

#### 3.2. Analysis of DATASET 2

#### 3.3. Effect of the Accuracy of the Flight Altitude on AGRS Measurements

^{−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

^{40}K,

^{238}U,

^{232}Th ground abundances are determined by dividing the estimated ground level count rates $N\left(E,0\right)$ 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 $N\left(E,0\right)$, assuming that the uncertainty on the sensitivity constants is negligible.

^{40}K,

^{238}U,

^{232}Th 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

^{40}K,

^{238}U,

^{232}Th ground abundances are equal to 1.3%, 1.2% and 1.1% respectively.

^{40}K,

^{238}U,

^{232}Th 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.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

^{2}(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.

F11 | |||||||
---|---|---|---|---|---|---|---|

GPSB | GPSA | GPSIMU | ALT | PT | PTIMU | ||

GPSC | 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 |

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 | |

r^{2} | 0.998 | 0.997 | 0.996 | 0.998 | 0.997 | 0.996 | |

GPSB | m | 0.998 ± 0.003 | 0.987 ± 0.003 | 0.993 ± 0.002 | 1.001 ± 0.003 | 1.007 ± 0.003 | |

q | 1.46 ± 0.44 | 2.49 ± 0.51 | 1.63 ± 0.33 | −0.43 ± 0.52 | 0.00 ± 0.56 | ||

r^{2} | 0.998 | 0.997 | 0.999 | 0.997 | 0.996 | ||

GPSA | m | 0.988 ± 0.003 | 0.993 ± 0.002 | 1.001 ± 0.003 | 1.008 ± 0.003 | ||

q | 1.28 ± 0.545 | 0.40 ± 0.36 | −0.85 ± 0.49 | −1.31 ± 0.51 | |||

r^{2} | 0.996 | 0.998 | 0.997 | 0.997 | |||

GPSIMU | m | 1.003 ± 0.003 | 1.012 ± 0.002 | 1.019 ± 0.002 | |||

q | −0.48 ± 0.46 | −1.95 ± 0.37 | −2.42 ± 0.38 | ||||

r^{2} | 0.997 | 0.998 | 0.998 | ||||

ALT | m | 1.008 ± 0.002 | 1.014 ± 0.003 | ||||

q | −1.20 ± 0.40 | −1.63 ± 0.46 | |||||

r^{2} | 0.998 | 0.997 | |||||

PT | m | 1.007 ± 0.001 | |||||

q | 0.44 ± 0.19 | ||||||

r^{2} | 1.000 |

F12 | |||||||
---|---|---|---|---|---|---|---|

GPSB | GPSA | GPSIMU | ALT | PT | PTIMU | ||

GPSC | 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 |

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 | |

r^{2} | 0.997 | 0.995 | 0.995 | 0.993 | 0.993 | 0.993 | |

GPSB | m | 0.980 ± 0.004 | 0.998 ± 0.005 | 1.037 ± 0.008 | 0.997 ± 0.007 | 0.981 ± 0.007 | |

q | 3.80 ± 0.70 | −0.77 ± 0.90 | −6.08 ± 1.36 | 1.25 ± 1.25 | 3.18 ± 1.19 | ||

r^{2} | 0.998 | 0.996 | 0.992 | 0.993 | 0.993 | ||

GPSA | m | 1.017 ± 0.005 | 1.057 ± 0.007 | 1.016 ± 0.008 | 1.000 ± 0.007 | ||

q | −4.43 ± 0.95 | −9.93 ± 1.33 | −2.27 ± 1.38 | −0.35 ± 1.28 | |||

r^{2} | 0.996 | 0.993 | 0.991 | 0.992 | |||

GPSIMU | m | 1.036 ± 0.008 | 1.000 ± 0.004 | 0.983 ± 0.003 | |||

q | −4.90 ± 1.42 | 1.93 ± 0.75 | 3.85 ± 0.63 | ||||

r^{2} | 0.991 | 0.997 | 0.998 | ||||

ALT | m | 0.957 ± 0.008 | 0.941 ± 0.008 | ||||

q | 7.96 ± 1.38 | 9.92 ± 1.41 | |||||

r^{2} | 0.99 | 0.99 | |||||

PT | m | 0.983 ± 0.002 | |||||

q | 2.07 ± 0.44 | ||||||

r^{2} | 0.999 |

F15 | |||||||
---|---|---|---|---|---|---|---|

GPSB | GPSA | GPSIMU | ALT | PT | PTIMU | ||

GPSC | 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 |

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 | |

r^{2} | 0.958 | 0.992 | 0.978 | 0.994 | 0.928 | 0.962 | |

GPSB | m | 1.027 ± 0.019 | 1.108 ± 0.016 | 1.057 ± 0.019 | 1.079 ± 0.031 | 1.113 ± 0.030 | |

q | −3.47 ± 1.05 | −13.05 ± 0.95 | −0.34 ± 0.92 | −0.63 ± 1.50 | −1.51 ± 1.41 | ||

r^{2} | 0.958 | 0.975 | 0.964 | 0.968 | 0.921 | ||

GPSA | m | 1.054 ± 0.017 | 1.022 ± 0.008 | 1.032 ± 0.028 | 1.061 ± 0.028 | ||

q | −7.89 ± 0.97 | 3.37 ± 0.40 | 3.36 ± 1.38 | 2.97 ± 1.35 | |||

r^{2} | 0.971 | 0.993 | 0.916 | 0.922 | |||

GPSIMU | m | 0.952 ± 0.11 | 0.970 ± 0.025 | 1.001 ± 0.023 | |||

q | 11.57 ± 0.54 | 11.38 ± 1.21 | 10.57 ± 1.11 | ||||

r^{2} | 0.984 | 0.927 | 0.939 | ||||

ALT | m | 1.009 ± 0.027 | 1.040 ± 0.026 | ||||

q | 0.33 ± 1.31 | −0.45 ± 1.24 | |||||

r^{2} | 0.921 | 0.931 | |||||

PT | m | 1.020 ± 0.009 | |||||

q | −0.28 ± 0.45 | ||||||

r^{2} | 0.99 |

## Appendix B

^{2}(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.

F11 | ||||||
---|---|---|---|---|---|---|

GPSB | GPSA | GPSIMU | PT | PTIMU | ||

GPSC | m | 0.9996 ± 0.0001 | 1.0007 ± 0.0001 | 1.0009 ± 0.0002 | 0.9994 ± 0.0002 | 0.9987 ± 0.0002 |

q | 0.75 ± 0.11 | 0.11 ± 0.14 | 0.15 ± 0.21 | 1.57 ± 0.24 | 3.50 ± 0.26 | |

r^{2} | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | |

GPSB | m | 1.0011 ± 0.0002 | 1.0013 ± 0.0001 | 0.9998 ± 0.0002 | 0.9992 ± 0.0002 | |

q | −0.64 ± 0.18 | −0.60 ± 0.16 | 0.82 ± 0.21 | 2.75 ± 0.23 | ||

r^{2} | 1.000 | 1.000 | 1.000 | 1.000 | ||

GPSA | m | 1.0002 ± 0.0002 | 0.9987 ± 0.0003 | 0.9980 ± 0.0003 | ||

q | 0.05 ± 0.28 | 1.48 ± 0.30 | 3.40 ± 0.33 | |||

r^{2} | 1.000 | 1.000 | 1.000 | |||

GPSIMU | m | 0.9985 ± 0.0001 | 0.9979 ± 0.0001 | |||

q | 1.41 ± 0.12 | 3.34 ± 0.11 | ||||

r^{2} | 1.000 | 1.000 | ||||

PT | m | 0.9994 ± 0.0001 | ||||

q | 1.93 ± 0.11 | |||||

r^{2} | 1.000 |

F14 | ||||||
---|---|---|---|---|---|---|

GPSB | GPSA | GPSIMU | PT | PTIMU | ||

GPSC | m | 0.99997 ± 0.00005 | 0.9996 ± 0.0001 | 0.9977 ± 0.0001 | 0.9975 ± 0.0002 | 0.9982 ± 0.0002 |

q | 0.18 ± 0.08 | 0.62 ± 0.10 | 5.64 ± 0.20 | 4.25 ± 0.26 | 3.37 ± 0.24 | |

r^{2} | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | |

GPSB | m | 99960 ± 0.00004 | 0.9977 ± 0.0001 | 0.9976 ± 0.0002 | 0.9982 ± 0.0002 | |

q | 0.44 ± 0.06 | 5.47 ± 0.22 | 4.07 ± 0.28 | 3.19 ± 0.25 | ||

r^{2} | 1 | 1.000 | 1.000 | 1.000 | ||

GPSA | m | 0.9981 ± 0.0001 | 0.9980 ± 0.0002 | 0.9986 ± 0.0002 | ||

q | 5.03 ± 0.21 | 3.63 ± 0.29 | 2.75 ± 0.25 | |||

r^{2} | 1.000 | 1.000 | 1.000 | |||

GPSIMU | m | 0.9998 ± 0.0001 | 1.0005 ± 0.0001 | |||

q | −1.40 ± 0.21 | −2.28 ± 0.18 | ||||

r^{2} | 1 | 1 | ||||

PT | m | 1.0007 ± 0.0001 | ||||

q | −0.87 ± 0.17 | |||||

r^{2} | 1.000 |

## Appendix C

^{3}], $S$ is the detector cross-sectional area [m

^{2}], ${\mu}_{s}\left(E\right)$ [m

^{−1}] and $\mu \left(E\right)$ [m

^{−1}] 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 $N\left(E,z\right)$ and the count rate that one would have measured by placing the detector on the ground $N\left(E,0\right)$:

^{40}K,

^{238}U,

^{232}Th ground abundances are therefore predicted by dividing the estimated ground level count rate $N\left(E,0\right)$ 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 $N\left(E,0\right)$, inferred from the measured $N\left(E,z\right)$ according to Equation (A2).

^{40}K (1460 keV),

^{214}Bi (1765 keV) and

^{208}Tl (2614 keV), where

^{214}Bi and

^{208}Tl are the major gamma emitting radionuclides respectively belonging to the

^{238}U and

^{232}Th decay series. The adopted values for the $\mu \left(E\right)$ 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/m

^{3}and gamma mass attenuation coefficients taken from the National Institute of Standard and Technology website [27], where an air composition of 78% N

_{2}, 21% O

_{2}and 1% Ar by weight has been given for the description of the composite traversed material.

**Figure A1.**Plot of the $\mathsf{\beta}\left(\mathsf{\mu}\left(\mathrm{E}\right),\mathrm{z}\right)$ factor as function of the survey altitude z: the red, green and blue line refer respectively to the

^{40}K,

^{214}Bi (

^{238}U) and

^{208}Tl (

^{232}Th) gamma emission energies.

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**Figure 1.**The left panel shows a map of the paths flown during the four surveys over the sea between Forte dei Marmi (LU) and Marina di Pisa (PI) in Italy. The four panels on the right show the mean altitude profiles measured by GPSABC of each flight.

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

**Figure 3.**Scheme of the placement of the different devices on the Radgyro: (A) GNSS antenna (GPSA), (B) GNSS antenna (GPSB), (C) GNSS antenna (GPSC), (D) GNSS antenna connected to IMU (GPSIMU), (E) pressure and temperature sensors of IMU (PTIMU), (F) pressure and temperature sensors (PT), (G) radar altimeter (ALT), (H) gamma spectrometer NaI(Tl). GPSA, GPSB and GPSC are placed at the following relative distances: dGPSAB = dGPSAC = (3.83 ± 0.01) m and dGPSBC = (1.96 ± 0.01) m.

**Figure 5.**Percentage of outliers in the ALT dataset as a function of the orthometric height. The altitude of 340 m has been identified has a threshold above which the ALT dataset has been excluded from the global analysis.

**Figure 6.**(

**a**) Reconstructed distance between GPSA and GPSB as a function of time during a portion of F15. The dashed red line represents the (3.83 ± 0.01) m reference distance and the brown line represents the average reconstructed d

_{GPSAB}during the flight. The large fluctuations observed in the reconstructed distance when flying over the sea are strongly reduced when flying over land, in particular when flying more than 3 km far from the coast (point A). (

**b**) Mean height above the ground level z(m) (digital elevation model is subtracted) measured by GPSABC. (

**c**) Flight path of F15.

**Figure 7.**Boxplot of the distribution of d

_{GPSBC}as a function of the orthometric height H for entire 0.2 Hz dataset. The blue line represents the (1.96 ± 0.01) m reference distance between GPSB and GPSC. Black points represent outlier data.

**Figure 8.**In the upper panel are shown the percentages of outliers identified in the d

_{GPSAB}, d

_{GPSAC}and d

_{GPSBC}datasets as function of the orthometric height H. In the bottom panel the acquisition statistics is as function of the orthometric height.

**Figure 9.**Temporal profile of the pressure measured by PT (in blue) and PTIMU (in red) not calibrated, and of the Radgyro horizontal velocity (in black) before the take-off. When the back screw is turned on, the PT sensor, which is significantly exposed to the air flux, measures a depression (point A). The pressure variation registered by both sensors in B is due to the rapid increase of velocity during the taxiing. The accelerating run along a runway starts in C and in D the aircraft takes off.

**Figure 10.**Linear regression between H

_{GPSABC}and H

_{PT}data for F11. In blue and red are reported the calibrated and not-calibrated barometric data respectively. The black straight lines are the linear fits to data: in both cases r

^{2}= 0.999.

**Figure 11.**Distribution of σ(H) (standard deviations of heights) in the range (35–66) m (red solid line), (79–340) m (blue solid line) and (340–2194) m (green solid line) measured at 1 Hz.

**Figure 12.**Distribution of the residuals $\mathsf{\delta}{\mathrm{H}}_{{}^{\mathrm{i}}}^{\mathrm{J}}$ in the (464–2194) m range of altitude: GPSIMU dataset in solid green line, PTIMU and PT dataset is reported in solid blue line, and GPSABC dataset in solid red line.

**Figure 13.**Distribution of σ(H) (standard deviations of heights) calculated for GPSABC built-in solution (red solid line) and with double-difference post-processing (blue solid line), in the altitude ranges (35–66) m (

**panel a**) and (79–2194) m (

**panel b**).

**Figure 14.**Distribution of σ(H) (standard deviations of heights) in the altitude ranges (35–66) m (red solid line), (79–340) m (blue solid line) and (340–2194) m (green solid line) measured at 0.2 Hz.

**Table 1.**Main parameters of the four flights. H

_{min}and H

_{max}(minimum and maximum height) refer to the flight height above sea level calculated by averaging the measurements of the different sensors. Average horizontal and vertical speeds are calculated using the data from GPSABC.

Flight ID | Date | Time (CEST) | H_{min} (m) | H_{max} (m) | Acquisition Time (s) | Average Horizontal Speed (m/s) | Average Vertical Speed (m/s) |
---|---|---|---|---|---|---|---|

F11 | 30/03/16 | 17:42:11–19:29:38 | 79 | 2018 | 6447 | 18.9 | 0.8 |

F12 | 31/03/16 | 18:13:55–18:33:12 | 129 | 237 | 1158 | 15.5 | 0.5 |

F14 | 05/04/16 | 16:37:15–17:33:04 | 464 | 2194 | 3350 | 21.1 | 0.8 |

F15 | 05/04/16 | 19:15:19–19:27:39 | 35 | 66 | 740 | 34.4 | 0.6 |

**Table 2.**Number of entries of the datasets used in the analysis of the orthometric height values from GNSS, altimetric and barometric measurements. The 340 m height cutoff has been identified on the base of altimeter outlier data (see Figure 5), while the 0.2 Hz frequency is related to the availability of the Madonna Dell’Acqua master station data for the GNSS post-processing.

Datasets | Frequency | α H < 340 m | β H > 340 m |
---|---|---|---|

DATASET 1 | 1.0 Hz (stand-alone) | 4803 | 6892 |

DATASET 2 | 0.2 Hz (double-difference) | 960 | 1378 |

**Table 3.**Average residuals ${\overline{\mathsf{\delta}\mathrm{H}}}^{\mathrm{J}}$ and $\mathrm{R}\mathrm{M}\mathrm{S}(\mathsf{\delta}{\mathrm{H}}^{\mathrm{J}})$ 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] | ||||||||

$\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | 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] | ||||||||

$\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | 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 |

**Table 4.**Average residuals ${\overline{\mathsf{\delta}\mathrm{H}}}^{\mathrm{J}}$ and $\mathrm{R}\mathrm{M}\mathrm{S}(\mathsf{\delta}{\mathrm{H}}^{\mathrm{J}})$ for DATASET 2. Linear regression data for each couple of sensors in the five cases are reported in Table A1, Table A2, Table A3, Table A4 and Table A5.

DATASET 2α | ||||||||||||||

GPSA [m] | GPSB [m] | GPSC [m] | GPSIMU[m] | ALT[m] | PTIMU [m] | PT [m] | ||||||||

$\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | |

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 | 1.6 | 1.1 | 1.5 | −0.5 | 2.5 | 0.2 | 1.6 | −0.8 | 1.8 |

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 |

DATASET 2β | ||||||||||||||

GPSA [m] | GPSB [m] | GPSC [m] | GPSIMU[m] | ALT [m] | PTIMU [m] | PT [m] | ||||||||

$\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | $\overline{\mathsf{\delta}\mathbf{H}}$ | RMS | |

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 |

F14 | 0.6 | 1.3 | 0.4 | 1.3 | 0.6 | 1.3 | −1.6 | 2.0 | / | / | −0.1 | 1.3 | 0.1 | 1.7 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Albéri, M.; Baldoncini, M.; Bottardi, C.; Chiarelli, E.; Fiorentini, G.; Raptis, K.G.C.; Realini, E.; Reguzzoni, M.; Rossi, L.; Sampietro, D.;
et al. Accuracy of Flight Altitude Measured with Low-Cost GNSS, Radar and Barometer Sensors: Implications for Airborne Radiometric Surveys. *Sensors* **2017**, *17*, 1889.
https://doi.org/10.3390/s17081889

**AMA Style**

Albéri M, Baldoncini M, Bottardi C, Chiarelli E, Fiorentini G, Raptis KGC, Realini E, Reguzzoni M, Rossi L, Sampietro D,
et al. Accuracy of Flight Altitude Measured with Low-Cost GNSS, Radar and Barometer Sensors: Implications for Airborne Radiometric Surveys. *Sensors*. 2017; 17(8):1889.
https://doi.org/10.3390/s17081889

**Chicago/Turabian Style**

Albéri, Matteo, Marica Baldoncini, Carlo Bottardi, Enrico Chiarelli, Giovanni Fiorentini, Kassandra Giulia Cristina Raptis, Eugenio Realini, Mirko Reguzzoni, Lorenzo Rossi, Daniele Sampietro,
and et al. 2017. "Accuracy of Flight Altitude Measured with Low-Cost GNSS, Radar and Barometer Sensors: Implications for Airborne Radiometric Surveys" *Sensors* 17, no. 8: 1889.
https://doi.org/10.3390/s17081889