High-Speed Magnetic Surveying for Unexploded Ordnance Using UAV Systems

Abstract

Using Uncrewed Aerial vehicles (UAVs) to rapidly scan areas for potential unexploded ordnance (UXO) can provide an efficiency increase while minimizing detonation risks. We present a complete overview of how such mappings can be performed using scalar magnetometers, including initial sensor testing, time stamping validation, data positioning, noise removal, and source model inversion. A test survey was performed across disarmed UXO targets, during which three scalar magnetometers were towed in an airframe (“bird”) 10 m below a small (<25 kg) high speed (∼10 m/s) UAV to avoid magnetic disturbances from the UAV itself. Data were collected across ∼58 min of flight, with each sensor traversing ∼31.7 km to acquire dense data coverage across a 600 m × 100 m area. By using three individual magnetometers in the bird, UXO detection results across single-sensor data and several different multi-sensor configurations can be compared. The data obtained exhibited low apparent noise floors (on the order of tens of picoTesla) and retained a precision that enabled targeted modelling and removal of high-frequency noise with amplitudes of ±5 picoTesla. All of the different gradiometer configurations tested enabled recovery of most targets (including all major targets), although the horizontal configuration performed significantly worse in comparison.

1. Introduction

Unexploded Ordnance (UXO), such as naval and land mines, air-dropped bombs, and artillery shells, can pose considerable challenges and humanitarian risks. UXO typically persist in areas of past and current conflicts across the globe, such as sites of warfare during World Wars One and Two, and can pose risks to both commercial and military operations, as well as to the general public. Examples of particularly affected operations include coastal and offshore construction, e.g., wind farms; operations in previous and current areas of conflict, e.g., transit in areas contaminated with UXO or Improvised Explosive Devices (IEDs); post-conflict decontamination and rehabilitation; and marine traffic planning. In the aforementioned scenarios, the UXO risk is often substantial enough to warrant pre-investigation and potential removal efforts prior to primary operation commencement.

Recent developments within UAV technology have spurred the use of UAVs for magnetic surveying [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. One interesting application of UAV based magnetic surveying is UXO pre-investigations, as the approach has can provide dense coverage with high-quality raw data at low ground clearance [12,14]. The UAV approach also minimizes UXO detonation risks to on-site operators and risks to equipment and personnel associated with low altitude flights in conventional aircraft [2,12]. In this research article, we explore and document the process of acquiring such high-quality data rapidly, using a triple scalar magnetometer payload towed (via cable) 10 m below a high-speed (≥10 m/s) UAV system.

The ability to rapidly map an area for potential UXO contamination with UAV-mounted sensors is significant. Apart form the obvious efficiency increase, it also brings new possibilities previously considered impracticable, such as remote mapping of vast inter tidal zones, or recurrently mapping of area for newly introduced objects (e.g., IEDs). So far, rapid, dense aerial coverage at low altitudes have been limited to systems with sensors mounted rigidly on helicopter [15] or UAV airframes [16], which can result in lower data quality due to the proximity of sensors to the magnetic disturbance field of the airframe itself [17,18]. An alternative approach, where sensors are towed beneath the UAV (e.g., via tow cable), can produce low noise magnetic data, but may introduce swing-induced bias [19]. Such bias can be alleviated in part through dedicated sensor positioning (which provides benefits for high-fidelity processing and UXO detection efforts [12,14]), and by towing the sensors at sufficient distance to the UAV platform. Stipulation of a general tow cable length is tricky, as the region which is electromagnetically disturbed by the UAV depends on the UAV platform itself. A test with two off-the-shelf UAV systems [17] pointed to minimum tow distances of 3 m (DJI M600 hexacopter) and 5 m (DJI Wind 4 quadcopter) in order to sufficiently minimize the UAV disturbance field. As the required tow distance depends on the specific UAV system employed, longer tow distances may be suitable for heavier, more power demanding UAV systems.

This study presents the necessary requirements, considerations, and data processing steps for high-speed UAV-based UXO detection using lightweight, rapidly sampling (∼203 Hz) QuSpin QTFM total field magnetometers. The approach is demonstrated by towing three sensors beneath a UAV in a 10 m long tow cable, such that the sensors are kept between 4 and 5.5 m above an intertidal flat with 24 deliberately placed disarmed UXO and non-UXO objects, most of which had been recovered from Danish coasts or the ocean floor by the Royal Danish Navy Explosive Ordnance Disposal Services (RDN EOD Services). The data itself was collected across ∼58 min of flight, during which each sensor traversed (and measured along) a path of ∼31.7 km. Based on the acquired data, we discuss important UAV and sensor configuration requirements to enable data collection, and demonstrate critical steps required to utilize the specific QuSpin QTFM total field sensors. We present the high-fidelity data collection and processing efforts suitable to map UXO objects, including accurate positioning, sensor output pre-processing, necessary timestamping concerns and corrections, handling of noise signals from high-voltage powerlines and on-board electronics, and inversions for target objects. Our results indicate that most of the mapped targets, herein all larger targets, could be robustly detected and that the addition of extra sensors generally adds value to the captured data. However, the value gained with a horizontal configuration, is primarily due to increased efficiency. We also find that a 4 m line spacing may have been sufficient for detection purposes in the presented case. The presented workflow is, in general, suitable for any magnetometer bird, regardless of its specific sensor configuration.

2. Materials and Methods

2.1. Uncrewed Aerial Vehicle (UAV) and Supporting Systems

The UAV system used for this study was a DJI Wind 4 quadcopter fitted with a Differential Real Time Kinamatic (D-RTK) system. The RTK approach involves deploying a stationary base station to measure fluctuations (e.g., due to atmospheric signal delay) in the computed positioning estimates, obtained through the use of Global Navigational Satellite Systems (GNSS; specifically GPS L1/L2 and GLONASS G1/G2 signals), and relaying these to the UAV in real time to compensate accordingly. The resultant positioning solution has superior precision (1 cm + 1 ppm and 2 cm + 1 ppm in the horizontal and vertical directions, respectively) when compared to the UAVs standard sensor configuration. However, it should be noted that this approach does not increase accuracy per se; such improvement would require an accurately known base location to be supplied as well. As such, the D-RTK system enables the UAV to maintain a stable altitude with only minor fluctuations across multiple flights, even when conducted over extended periods (i.e., high repeatability), but retains an accuracy (i.e., potential shift relative to the external reference frame) on the order of meters. Mission planning and autonomous flight control was handled through Universal ground Control Software (UgCS), which also provides the ability to incorporate Digital Elevation Models for surveys across hilly or challenging terrain variations, where flights draped across the terrain are required.

2.2. Towed Payload System and Magnetic Sensors

The towed payload, denoted the magnetometer bird, is a completely independent system. The magnetometer bird contains a dedicated power source, three separate QuSpin QTFM total field sensors, and a custom 8-sensor compatible data logger incorporating a Novatel SPAN GNSS Inertial Navigation System (GNSS-INS), which is comprised of a GNSS receiver/antenna pair and an Inertial Measurement Unit (IMU). The antenna used was a Tallysman TW3972 (supporting triple-band GPS, GLONASS, and Galileo, among others). Apart from position and attitude determination, the data logger also timestamps the incoming sensor readings using GNSS-derived Coordinated Universal Time (UTC) for further processing, e.g., it is used to correlate the positioning solution with the magnetic sensor readings.

We selected the QuSpin Total-Field Magnetometer (QTFM) sensors due to their combination of their sensitivity, sampling rate, weight, and stability [13]. The QTFM is part of the family of optically pumped magnetometers, which are generally characterized by having high precision at the cost of heading errors and sensing deadzones [20]. Select sensor specifications of the QTFM are provided in

Table 1. Select specifications of the QuSpin Total-Field Magnetometer (QTFM). Full specifications are available from the producer [21].

Parameter	Value	Notes
Sensitivity	<1$\mathrm{pT}/\sqrt{\mathrm{Hz}}$	In 0.1–100 Hz band
Dynamic range	1000 nT to 100,000 nT
Deadzone	$\pm 7^{\circ }$	From equatorial plane
Heading error	<3 nT	When uncompensated
Sampling rate	∼203 Hz ($4.{9152}^{-1}$ kHz)	Toggleable
Atomic family	Rubidium

. Full specifications are available from the manufacturer [21].

The three QTFM sensors are mounted on the bird in a configuration that enables data collection on two vertically separated surfaces (two levels at different altitudes) simultaneously. These measurement surfaces differ in both altitude and data density, as two sensors map the upper surface, while only one maps the lower surface. For context, a mock-up overview of the sensor configuration is shown in Figure 1.

2.3. Flight Planning

Flights are carried out along a sequence of straight flight lines, with adjacent lines flown in succession. An example of a survey plan illustrating this strategy is shown in Figure 2.

In practice, the UAV flight planning can be carried out with any software that allows for flight plans consisting of a sequence of parallel flight lines. For this study, we used the Universal Ground Control Software (UGCS).

2.4. UXO Detection Survey

The UXO detection survey was carried out on the west coast of Rømø, Denmark, inside the Wadden Sea national park. The site was selected due to its wide intertidal area, typical for UXO detection scenarios along the western coast of Denmark, while providing an easily controllable area with sufficient distance to third parties.

The site was prepared by marking off a 100 m × 600 m survey area, in which a combination of 24 disarmed UXO, UXO fragments, and typical seabed debris objects were deposited. The majority of objects deposited were actual UXO, fragments, and debris/litter recovered near coasts and at sea by the RDN EOD Services. The flight lines were spaced 2 m apart, resulting in a spacing of ∼1 m and ∼2 m between lines of data at the upper and lower measurement surfaces, respectively. An overview, depicting the flown survey lines and positions of the 24 objects placed within the site, is provided in Figure 3. Additional specifications of each object are provided in

Table 2. Overview table for the UXO, UXO fragments, and debris objects placed inside the survey area.

No.	Weight	Description	Notes
1	11.8 kg	Small airdropped	L64 cm, Ø5.7 to 9 cm
2–6	$26.2\pm 1.4$ kg	155 mm shell	L57 cm; Ø5.5 to 16 cm
7	34.3 kg	Cannonball (half)	Ø33 cm. From “Slaget på Reden”
8	14.5 kg	Hinged L-beam	L93 cm, H13 cm
9	7.4 kg	Metal disc	H10 cm, Ø36 cm
10	$26.2\pm 1.4$ kg	155 mm shell	L57 cm, 5.5 to 16 cmm
11	12.3 kg	Partial metal plate	L50 cm, 43 cm, and 23 cm. H1 cm
12	19.7 kg	Square metal plate	L50 cm, H1 cm
13	?	Unknown object	L93 cm, Ø5 to 14 cm. Only tail magnetic
14	8.1 kg	Training Rocket	L95 cm, Ø7 cm. Only tip magnetic.
15	9.0 kg	Bent tail fin	L65 cm, Ø23 cm
16	6.0 kg	Airdropped	L120 cm, Ø20 cm
17	17.1 kg	Fire extinguisher	L83 cm, Ø14 cm
18	14.9 kg	Round black sphere	H42 cm, Ø45 cm
19	14.5 kg	Bouyant sea mine “316”	L60 cm, Ø25 cm
20	20.3 kg	Alu. seamine fragment	H40 cm, Ø65 cm
21	47.9 kg	Depth charge	L70 cm, Ø43 cm
22	26.3 kg	Bouyant sea mine “315”	L79 cm, Ø32 cm
23	48.3 kg	5-In training rocket	L204 cm, Ø13 cm.
24	34.4 kg	Aluminium winch	L130 cm, Ø40 cm

, while corresponding images are provided in Figure 4. Full coverage of the 600 m × 100 m area, with a 1 m data line spacing at the upper measurement surface, and a 2 m data line spacing at the lower measurement surface, was obtained in just ∼96 min, measured from the time of first take-off to the time of final landing, i.e., including intermediary landings for battery changes. The total in-air time was ∼58 min, with each sensor traversing a total of ∼31.7 km during the survey. As the surveyed area was flat, the flight altitude of the UAV was fixed at ∼15 m above the take-off location. This resulted in the altitude of the magnetic sensors (measured to the ground level) being between 4 and 5.5 m during surveying. These variations in sensor altitudes stem from altitude fluctuations, e.g., due to wind effects and gusts, of the bird system (and to a lesser degree also of the UAV), while traversing the flat intertidal area.

2.5. Position Data Processing

Positioning data from the Novatel SPAN INS system was post-processed using the Novatel inertial explorer software. The GNSS data was processed using the Precise Point Positioning (PPP) post-processing method, which incorporates precise orbit and clock bias to improve GNSS positioning solutions [22,23]. Precise clock [24] and orbit [25] files were obtained from the Crustal Dynamics Data Information System (CDDIS) [26] for the PPP method. The GNSS and IMU data were then co-processed to obtain accurate positions and attitudes of the GNSS antenna during the survey. Individual sensor positions were subsequently obtained through standard translation and rotation operations, given their positions relative to the GNSS antenna. The estimated standard deviations associated with the resultant accurate positioning solution were 2.7 cm, 3.2 cm, and 5.1 cm (average values across the survey area for the East, North, and Vertical directions, respectively). The absolute maximum estimated standard deviations exhibited at any point during surveying were 3.9 cm, 6.5 cm, and 9.9 cm (for the East, North, and Vertical directions, respectively).

2.6. Sensor Timestamping

The QTFM sensors were set up to sample at a rate of $4.{9152}^{-1}$ kHz. However, initial testing revealed significant variations in the time spans between discrete measurements. As such, it was necessary to quantify whether the timestamps in questions were accurate or affected by jitter (i.e., if there is a timestamping mismatch compared to the actual time of the sensor reading) before any subsequent data processing could take place. In order to determine whether or not this problem was associated with the custom 8-sensor data logger, we initially compared results with a proprietary data logging board available from the sensor manufacturer. In either case, the absolute time stamps are derived from the GNSS receiver equations; a non-linear system of equations where satellite pseudoranges from at least four satellites are used to simultaneously determine the 3D position of the receiver unit and its clock bias [27]. Note that although the 3D positioning accuracy of the custom unit is superior to the proprietary unit since the latter does not utilize PPP, neither unit utilizes PPP for timestamping in this application (pseudoranges are based on the speed of light, i.e., the clock accuracy improvement constituted by PPP is negligible).

The strategy used to designate the time in the data flow constitutes an important difference between the custom and proprietary logging units: While the custom logger stamps each sensor reading individually, the proprietary unit injects an absolute timestamp into the magnetometer data stream once every second, which is related to the sensor readings through a relative timestamp provided by the internal clock unit. As such, we investigated both the time spans between recorded samples (Figure 5), and the clock stability across both logging units (Figure 6).

This preliminary test suggests that the timestamps are indeed affected by some form of jitter, occurring across both data logging units. The internal clock of the QTFM showed a high apparent precision with minor oscillations. Given the disparity between the reported precision of the QTFM clock demonstrated in Figure 6a, and the apparent frequency shown in Figure 6b, a signal delay is suspected between the proprietary data logger and the external GNSS unit. The relative timestamp from the internal clock of the QTFM exhibited the smallest fluctuations over shorter timescales. As expected, the lack of GNSS-derived time stamping caused the internal clock of the QTFM to drift over longer timescales, while the time drift was found to be closer to zero when using GNSS time stamping. The consistency between the specified logging rate and the mean and median apparent frequencies (Figure 5), in addition to the low drift, suggests that the observed jitter may be correctable if averaged across a sufficiently long timescale.

Correcting the Sensor Timestamps

Having verified that the net bias in the timestamping averages out to the correct sampling rate of $4.{9152}^{-1}$ kHz, we can pose a time stamp correction as a simple linear least-squares minimization problem

$$\underset{\varphi }{min}\sum _i\left(t_i-{\tau }_i+\varphi \right)$$

(1)

where i denotes the sample number, $t_i$ is the sample time reported by the data logger, ${\tau }_i$ is the expected sample time given a fixed sampling rate of exactly $4.{9152}^{-1}$ kHz, and $\varphi$ is the (unknown) offset between the two, which provides the smallest error between the two in the least-squares sense. The new time stamps are obtained as $t_{i,new}={\tau }_i+\varphi$, in order to enforce a $4.{9152}^{-1}$ kHz sampling frequency while staying as true to the original time stamps as possible in the least-squares sense.

2.7. Reduction of External High-Frequency Noise

Due to a power line in the vicinity of the survey area, and the placement of the custom positioning and data-logging unit on the bird, high-frequency signals in the measured data were expected. The alternation frequency of common power lines in Denmark is ∼50 Hz, with slight variations due to, e.g., the varying load on the local power grid. In addition, the data logging unit produces a signal with an alternation frequency of ∼65.1 Hz. The effect of the latter signal was expected to be low, but slightly more pronounced in the lower sensor data due to it being slightly closer to the positioning and data logging unit. Using a Fast Fourier Transform, we obtain an overview of the frequency spectrum for each sensor, as compiled in Figure 7.

External disturbance signals are important to quantify for two distinct reasons: (1) For high-speed surveying, the apparent band of the external noise may be intertwined with the band of the target objects (in this case the UXO). Note that the source frequencies will vary depending on parameters such as the type, size and distance to the target objects, as well as the flight speed and direction relative to the source signature. (2) In the event of high-amplitude external noise, the external noise may contain a significant portion of the total power in the signal. In either case, the external signals will need to be addressed, and we shall here consider two primary strategies for external noise reduction: reduction by filtering and reduction by noise model fitting.

2.7.1. Reduction by Filtering

If the measured data contain a distinct noise signal, separate in the frequency domain from the source signal of interest, filtering is an obvious choice for noise removal. Based on the spectra in Figure 7, we elect to use an eighth order low-pass Butterworth filter, with a cutoff-frequency of 40 Hz, resulting in filtered signals with spectra shown in Figure 8.

2.7.2. Reduction by Noise Model Fitting

Under some circumstances, the filtering approach may not be suitable, e.g., if the source signature and disturbance bands overlap, or if the sensor sampling rates are variable.

The two disturbance signals highlighted in Figure 7 suggest that the primary disturbance stems from the 50 Hz power line signal, which has an approximately equal impact on all three sensors. With a frequency of 65.1 Hz, the secondary disturbance is expected to stem from the custom data logging unit used during the survey. Although the power contained in the secondary disturbance is significantly smaller than the 50 Hz signal, we have chosen to include it in our considerations for completeness. However, a suitable disturbance model should also consider variations to the disturbance signals during the survey. The frequency of the 50 Hz signal is expected to vary slightly on a priori grounds, as this is typical in the power grid. We allow for potential frequency variation in the 65.1 Hz signal as well, although no variation is known a priori.

Based on the available information, we propose a disturbance model $\eta$ for each of the two disturbance signals:

$$\eta (A,f,t,\varphi )=Asin(2\pi ft+\varphi )$$

(2)

where A denotes amplitude, f denotes frequency, t denotes time, and $\varphi$ is the phase offset. Note that the recovery of the unknown model parameters in Equation (2) constitutes a non-linear inverse problem. We solve the problem for all magnetometers simultaneously, under the constraint that the frequency of the two signals are assumed to be constant across magnetometers at equal times; the amplitudes are allowed to vary. We use a sequential approach, inverting for a noise signal spanning approximately one second centred at each incividual datapoint, i.e., we include the 100 prior and 100 subsequent datapoints when modelling the noise response at a given datapoint. This method is an adaptation of the approach demonstrated by [28], where a similar strategy is applied for disturbed vector magnetometers.

Before solving the non-linear inverse problem, we first band-pass filter the data to avoid instability issues caused by spectral power contained outside the target bands. The non-linear problem is then solved using a Fletcher-modified Levenberg-Marquardt solution scheme [29,30,31], yielding a set of model parameters describing the disturbance at each time stamp, and by extension, an estimate of the disturbance signal across the entire survey.

The spectra of the magnetic data, following removal of the derived noise models, are shown in Figure 9.

While the noise removed in both the filtering and model fitting approaches were largely similar (Figure 10), the 40 Hz filtered data was selected for further processing. and thus used in all inversion, since no relevant information was expected at frequencies above 40 Hz. The signal spectra presented in both Figure 8 and Figure 9, as well as the fourth difference histograms shown in Figure 11 also suggest that either approach is better than the raw data, but that the filtering approach is more prudent in the specific scenario presented here. However, we elect to include the model fitting approach as a test of the possibilities provided by the collected magnetic data, and due to its potential uses for, e.g., non-uniformly sampled signals.

2.8. Source Inversion for Unexploded Ordnance

In order to evaluate applications of the approach for UXO detection, target signatures were modelled as point-dipoles, which are known to provide close, robust fits to the scalar magnetic signatures of many UXO, given the data altitudes considered [12,14,15,32,33]. This allowed for a simpler analysis of how well-resolved the source position and moment estimates are using different sensor setups. Inversion for model parameters was performed using the probabilistic inversion framework described in [34,35], and validated against the the deterministic inversion approach documented in [12]. All inversions were carried out on the along track difference (ATD) of the sensor data, thereby circumventing the majority of the sensor heading error while enhancing smaller wavelengths [12,14].

In addition to the data and source model required for general inverse modelling, another necessary step in the probabilistic inversion process is the designation of prior distributions of the model parameters; available a priori information on the model parameters must be supplied as input for the probabilistic framework, alongside the data and forward (source) model. In the case of source inversion for UXO with the point-dipole model, suitable a priori information is typically amply available, provided that the data quality is suitable for detection purposes in the first place.

The point-dipole model depends on six model parameters, being the position in three-dimensional space $(x,y,z)$, and the components of the equivalent magnetic dipole moment $(m_x,m_y,m_z)$. Prior distributions for each model parameter were constructed as uniform distributions with excessive ranges; a conscious choice to avoid any potential biasing of the obtained solutions the (posterior probability distributions). Prior distributions for the dipole moment components were designed as uniform distributions covering the range of −8 to 8 $\mathrm{A}{\mathrm{m}}^2$ for each component. For the source position $(x,y,z)$, we specified a cube with a side length of four meters, within which the source position was expected to be located. The cube was placed such that its sides coincided with the East-North-Up reference frame of the measured data, with the horizontal span centred roughly a few metres from the actual UXO location, and spanning a vertical distance corresponding to between two and ten meters beneath the sensors (the sensor altitudes were known to be within 3–5 m from the surface and hence, the targets). The specified prior distributions thus constitute highly uncertain initial guesses, with an accuracy which is considerably less than what may readily be obtained through existing inversion methods [14] (or even through visual inspection and manual selection of a source position). Results obtained using the method of [12] are also included, for comparison purposes.

Since the triple-sensor bird provides the ability to consider both various sensors, as well as first-differences across various parings of sensors (which are sometimes inaccurately referred to as gradients, even in cases where they only constitute a coarse approximation thereto), an attempt to compare different sensor configurations for UXO detection is also made. As such, inversion was attempted on each of the 24 different targets using each of eight different data sets, each corresponding to a unique combinations of sensors, such as the along-track difference of a single sensor, the sensor-to-sensor difference across two different sensors, and various combinations of data from all three sensors. An overview of the eight different sensor configurations used to generate the data used for inversion are shown in

Table 3. Data used as input for the eight different inversions routines, each of which were performed on the full dataset (inverting independently for each of the 24 target anomalies). The estimated along track difference (ATD) was used as input for each of the inversions. The validation inversion utilized the dual slanted vertical difference ATD (dataset 8).

Data Used for Inversion	Sensors Used	Data Input
1: Lower sensor ATD	Lower	[Lower ATD]
2: Slanted vertical difference ATD	Left & Lower	[Lower ATD—Left ATD]
3: Horizontal difference ATD	Left & Right	[Left ATD—Right ATD]
4: Two individual sensor ATDs (vertical)	Left & Lower	[Left ATD, Lower Sensor ATD]
5: Two individual sensor ATDs (horizontal)	Left & Right	[Left ATD, Right ATD]
6: Double sensor & slanted ATD	Left & Lower	[Lower ATD, Left ATD, Lower ATD—Left ATD ]
7: Three individual sensor ATDs	All three	[Lower ATD, Left ATD, Right ATD]
8: Dual slanted vertical difference ATD	All three	[Lower ATD—Left ATD, lower ATD—Right ATD]

. The validation inversion was carried out on dataset 8 (in Table 3), as this was expected to provide the most information while also retaining a close resemblance to the ATD of the vertical sensor difference; a preferred approach from [12,14].

3. Results

The results obtained in this study include all data products made available by the data collection and subsequent data pre-processing, the inversion results obtained through the probabilistic inversion scheme, and the line decimation graphs.

3.1. Results from Data Pre-Processing

The results from the data pre-processing encompasses the measured magnetic data and all data products derived therefrom. Figure 12 depicts the measured magnetic data from the lower sensor, and its estimated along track difference (ATD), computed by subtracting along-track samples spaced 1 m apart. The slanted difference, computed by subtracting the lower sensor reading from one of the upper sensors, is shown in Figure 13. The exact sensor used alternates on a line-by-line basis; it is always the upper sensor with the lowest Y-coordinate in the local reference frame which is used. The horizontal difference (the difference between the two upper sensors), and its ATD, are shown in Figure 14, while the total difference, computed as the standard 2-norm across the three measured differences for each point in time, is shown in Figure 15. Due to extensive similarities between many of the data products, some have been intentionally omitted, e.g., the two different slant differences, and the raw magnetic data from the two upper sensors. Note that neither levelling nor any other filtering than the specified 40 Hz filter have been performed on any of the data.

3.2. Results from Target Inversions

An overview plot of the eight different inversions for all targets is shown in Figure 16. For each inversion, the mean value of the last 25 posterior model samples has been estimated and plotted as errorbars. The different inversion estimates are plotted in groups of each target according to the X-axis for visual comparison. Figure 16a shows the estimated height deviation (i.e., the difference between the determined target height and the estimated altitude of the beach surface). The mean estimates of object XY-positions are shown in Figure 16b. Since the target positions were only tagged with inaccurate external GNSS positions for identification purposes, any XY-position error estimates relative to the target GNSS positions have been avoided and instead, the mean of the XY-positions are subtracted and the resulting differences are shown. This mitigates the issues of inaccurate GNSS-positions and instead illustrates how well resolved the different estimates are using the different inversion setups, and how much the mean estimates may vary compared to the different inversion setups. The mean estimated magnetic moments are shown in Figure 16c. These are estimated as the vector sum over the three magnetic dipole moments that are sampled simultaneous as model parameters.

Target inversion results from the deterministic inversion method is presented in Figure 17. The data obtained from the along-track difference of the lower sensor are shown for the whole survey along with the model prediction of each anomaly, and the residual field between the model prediction and data. The survey data are visualized using two different color scales to provide a complete overview of the anomaly signal versus background signal. In Figure 17a,b the survey data are shown with a color range of ±1 nT and ±0.15 nT, respectively (the max and min range of the survey data is [−2.76, 2.10]). In Figure 17c the model predictions are plotted for inversion using the deterministic setup, and the resulting residual between survey data and model prediction is plotted in Figure 17d. It is evident from the residual plots, that the model prediction captures most of the anomaly signal for all targets. Some minor differences between model and data are seen for a few of the targets with larger anomaly signals (i.e., targets 3, 18, and 21–24). We expect these deviations to originate from shape effects, rather than data uncertainties, since no such effects are visible in the immediately neighboring anomalies. It is therefore likely that these anomalies can be modelled better with more complex models.

3.3. Results from Line Decimation Test

Using both upper sensors (left and right) in combination, a data surface with a ∼1 m data line density was achieved. The following presents this surface, as well as the results obtained by performing line decimation on it, in an effort to investigate the effect of increased line spacing on the UXO anomalies captured in the survey data. A graph of the full dataset comprising both the left and the right sensor (∼1 m line spacing) is provided alongside decimated data graphs with ∼2 m and ∼4 m line spacing in Figure 18. Decimated data graphs with ∼6 m, ∼8 m, and ∼10 m line spacing is shown in Figure 19.

4. Discussion

Several traits of interest were revealed by the processing efforts and processed data. Firstly, the sharp spectral peaks at 50 Hz and 65.1 Hz seen in Figure 7 suggest that the time-correction strategy was warranted. In general, the data exhibited low estimated noise floors regardless of sensor or noise removal strategy, and a high precision which enabled removal of even miniscule noise components (as shown in Figure 10). The exhibited differences in the noise floor estimates were as expected, with the filtering providing more suitable results, since none of the higher frequencies were expected to carry any significant information. However, in events where filtering is not an option, the noise modelling approach could potentially provide a suitable alternative to remove noise in scalar magnetic data, provided that the disturbances have a constant or near-constant frequency, such as powerline noise. Another important application of the noise modelling approach is the correction ability obtained when utilizing combinations of magnetometers, whereof some sample the disturbance signals adequately, while others sample them at a rate below the Nyquist frequency. In such cases, effects from high-frequency components can be reduced or even completely removed from the slower sampled data, if accurate disturbance models, e.g., derived with the adequately sampled data, are available.

The QTFM sensors applied in the study provided consistent results. Any heading errors were easily removed through use of ATDs computed from the data products and, to a lesser extent, through line-median removals. Regarding detection, the majority of the placed UXO targets could be recovered at the flown altitude, using any variety of different sensor configurations, although some sensor configurations were found to show more promise than others.

Upon inspection of Figure 16 it is apparent how targets with a significant anomaly signal (e.g., anomaly signal above the noise-floor and visually apparent in, e.g., the slant-difference plots) usually have well resolved mean estimates of model parameters, and a low variation between the estimated values using the different inversion setups. Results obtained by inverting the difference between the two upper sensors produced inaccurate or directly misleading results (since the distance between the target and the sensor should be between 4 and 5.5 m, any significant deviation or offset from such would suggest a bad estimation). A similar offset is seen in the estimated horizontal-position and magnetic moment, where the estimated values using the horizontal difference differs significantly. In the case of being limited to a two-sensor combination, a more vertically-aligned difference, such as the slant vertical difference, seemingly provides more information, as compared to a horizontally-aligned difference.

Targets 5, 9, 13, 14, and 20 are not considered detected for practical purposes. Although peaks in the magnetic data could be associated with these targets, it was in general not possible to determine whether these peaks stem from the target itself, from uncompensated external or background signals, or from a completely difference source (e.g., Figure 17b). As expected, and with the exception of Target 5, these are all objects with smaller mass and/or lower ferrous content, as compared to the easily detectable targets. Target 5 presents a different scenario, as two identical UXO (targets 5 and 6) were positioned 1 m apart, but target 6 seems to exhibits a significantly higher anomaly signal. Assuming that any remanent magnetization present is negligible, the orientation of the two objects may provide an explanation to this behaviour. Since target 6 was facing north/south, its long axis was largely aligned with the horizontal ambient field direction (horizontal component of the geomagnetic field), while target 5, which was oriented east-west, had a long axis perpendicular to the ambient field direction. This could explain the difference in the resultant magnetic field produced at sensor altitude, which in turn results in target 6 being detected when using a single target model inversion. It should be noted that the procedure in an actual detection scenario could differ in this circumstance. While the distinction of targets spaced only a single meter apart is irrelevant in a number of scenarios, even a rudimentary assessment or quality control of the results would pick up on the significant inversion residual of target 6 (as seen in Figure 17c), leading to a re-inversion with both different and multiple source models (given that such an assessment or effort was not performed as the standard to begin with).

While the detection capability for larger sources did not differ substantially across inversions performed on data when the lower sensor was included in the data product, we found the ATD of both slant-vertical sensor-to-sensor differences to perform best regarding object detection, and the deterministic inversion with the approach of [12] to provide both the best fit to the data and the best results overall. A distance of 16 datapoints (∼1 m) was found sufficient for the ATD to enhance shorter wavelengths while suppressing background signals, but we stress that this will generally be dependent on multiple factors, including the signal-to-noise ratio, the wavelengths of the measured anomalies (which in turn are functions of flight altitude).

When using the approach outlined in [12], reasonable (practical) detection of 20 out of the 24 targets (including both targets 5 and 6) is possible without incurring any false positives, which would leave targets 9, 13, 14, and 20 undetected. Detailed analysis of peak prominence in the targeting signal reveals that all targets can, in fact, be detected, but at the cost of a substantial amount of false positives, due to the proximity of the measured magnetic response from those four objects to the effective noise floor (noise floor when taking background signal into account as part of the noise). While this may potentially be resolved through additional processing efforts, we elect to label targets 9, 13, 14 and 20 as undetectable for practical purposes in this scenario. Note that this statement is conditioned upon all survey parameters (the setting/location, flight parameters, and measurement setup); it is expected that these targets would have been detected if the flight altitude had been lower.

The horizontal difference arguably performed the worst of all the different configurations. We consider this to be a product of weaker differences across the horizontal measurement plane, compared to, e.g., a vertical or slanted difference. It would naturally follow that the along-track differences would also suffer from this issue, however, we argue that this problem is significantly diminished in ATDs due to the option of selecting the distance across which to compute differences after data collection, while for the horizontal difference this must generally be known a priori, due to the fixed placement of sensors along the transverse axis. While problems may arise in ATDs derived from single sensors, due to uncompensated high-frequency variations present in the signal [12], the same is fundamentally also true for across-sensor differences, unless the measurement at each sensor is triggered at exactly the same time. Since the clocks are not synchronized across the different QTFM sensors, any across-sensor data products should be regarded as having the same challenges as a single QTFM sensor in this regard. Fortunately, given the rapid sampling rate, we expect that high-frequency noise sources such as powerlines can be filtered out at the ∼10 m/s flight speed employed for this study. However, some concern remains regarding noise sources with frequencies beneath 50 Hz. For a flight speed of 10 m/s, an ideal 40 Hz low-pass filtering operation will retain only spatial wavelengths longer than or equal to 0.25 m, which may be sufficient for larger targets at higher altitudes, but may not be suitable for smaller targets at lower altitudes (such as, e.g., the small UXO considered in [14]). An initial test carried out with a 20 Hz frequency cut-off in the low-pass filter (corresponding to ∼0.5 m spatial wavelength at the utilized flight speed), reveals that significant signal is lost at these spatial wavelengths. We therefore suggest considering the sampling rates of employed magnetic sensors against a priori information regarding electronic noise components when contemplating UXO surveying at high speeds. As an example hereto, 16.66 Hz AC signals from the railway system are commonplace across Scandinavia. At flight speeds around 10 m/s, and with target signatures comparable to the UXO signatures measured in this study, such a signal could potentially interfere with the target signatures. The flight speed should therefore, in general, be determined based on both external noise components and magnetometer sampling rate.

In terms of inversion consistency there is a generally well resolved estimate of target position and dipole moment, for all anomalies that are visible in the equivalent total difference plot. This is the case for six out of the seven inversion setups, with only the inversion setup concerning the horizontal difference as single data input providing a result of significantly lower quality. This implies that the horizontal difference contains less information compared to a vertical difference, which will ultimately be preferred as a sensor setup. However, inversion on the difference alone may be disadvantageous since any measurement error or positional uncertainty might be amplified when taking the sensor differences. For this reason, inversions were carried out on the ATD of multiple sensors simultaneously without computing the difference between the sensors, which have shown to be a robust way to include multiple-sensor datasets. From an inversion point of view, the triple sensor setup is optimal for target detection and characterization, but the slanted vertical configuration is preferred over the horizontal configuration.

Upon immediate inspection of the data decimation results in Figure 18 and Figure 19, the results appear somewhat similar irrespective of line spacing. Note, however, that the colorscale extent is extremely small, and recall that the background signal is nearly ideal. As such, the presented scenario is a lower limit test in an ideal background. Upon closer inspection, it is also obvious that substantial differences are in fact clearly visible. While the results across 1 m and 2 m line spacings (Figure 18a,b) are largely similar, data deterioration is already visible, albeit still at a managable level with the increase to 4 m. Consider targets 10 and 17 across the two datasets with inter-shifted line spacings of 4 m (Figure 18c,d); Target 10 cannot readily be picked out from the background in Figure 18c, but stands out clearly in Figure 18d, while the opposite is arguably true for target 17. As such, adequate information may not be guaranteed for a 4 m line spacing, but may largely be a function of the, essentially random, placement of survey lines. This effect becomes even more obvious as the survey line spacing is increased further; note the extensive differences across the two datasets with inter-shifted line spacings of 6 m, where many targets, including 8, 10, 15, 16, 17, 22, and 23, show considerable change across the survey, which could potentially result in biases of several meters or more in the recovered target positions. Across the datasets with 8 m and 10 m line spacings (Figure 19c,d), only the largest targets retain their shape. and even then only to a lesser degree. The signatures form targets 18 and 19 almost completely disappear in Figure 19d, to the point where only target 19 can be picked out, and only vaguely at that, from the background. For all purposes, however, we argue that the equivalent total difference (Figure 15) provided an excellent overview of the visible target signatures, and was simultaneously straightforward to interpret. As such, it seems promising for automated designation of inversion areas, or in the case of UXO inversions based on iterative update strategies [12,14], for determining suitable initialization locations for the inversions.

When considering these results, it should be noted that the line spacing, and axis along which the UXO are placed, generally coincide. As such, the recovered signatures may only depend on a few, or even just one line, wherefore the inversion quality must be expected to diminished with increased line spacing (and higher fidelity processing even more so, e.g., inversion for more complex source models). Based on this, it is our recommendation that for similar surveys, the line spacing does not exceed 4 m, and should ideally be around 2 m or less, for standard detection purposes. For strictly detection purposes, larger ferrous objects such as targets 21, 22, 23, and 24, may not necessarily benefit from decreasing the line spacing beneath 4 m; however, there may be substantial benefits for more complex source modelling purposes, which have not been considered in this study. Conversely, based on this data, extremely accurate positioning and wind effects which perturb towed magnetometer systems on the order a meter or less, are expected to be of little to no concern for strictly detection purposes regarding several of the larger classes of UXO considered here, when using a line spacing of 4 m or less for the altitude and other survey parameters used in this study.

5. Conclusions

The time stamps of the custom datalogger were found to exhibit severe short-timescale variations. Using a simple corrective scheme, these problems were remedied based on the long-term stability provided by GNSS-derived time stamping.

Overall, the combination of QTFM sensors and a high flight speed resulted in rapid data collection of high quality data. The 600 m × 100 m wide area was mapped simultaneously at two surfaces, resulting in acquisition of data with line spacings of 1 m (upper surface), and 2 m (lower surface), in a total of just ∼58 min of flight (∼96 min including battery changes). Each sensor traversed a ∼31.7 km long path during the survey.

The quality of the processed data enabled graphing with colorscales ranges of less than 0.15 nT when considering single sensor data, and provided the ability to specifically target and remove high-frequency external AC noise with amplitudes of ±5 picoTesla, which largely supports the sensitivity levels stated by the manufacturer. The sampling frequencies at the second-fastest sampling rate of the sensor ($4.{9152}^{-1}$ kHz) was also verified, and a simple correction strategy for data loggers with timestamps that are imprecise, but average out to be accurate over longer timescales, was presented.

Out of the 24 targets, 19 could be successfully detected when the target signatures are modelled using a dipole-model inversion, while it is argued that quality control of the initial results would additionally result in detection of target 5, bringing the total amount of targets detected for practical purposes, and without incurring any false positives to 20, given the location/setting, flight parameters, and measurement setup. The different combinations of scalar magnetic data used as input in the inversions suggests that the horizontal difference constitutes a significantly less valuable feature for target detection and characterization. Thus, for a dual sensor setup, a vertical sensor setup should be preferred over a horizontal in this survey setting, given the survey parameters and measurement setup used. The best results overall were obtained using information from all three sensors (dual slanted vertical difference ATD), with the deterministic inversion strategy. In terms of achieving the highest spatial data resolution, a triple sensor setup was also found to provide the most optimal framework of all tested systems, but the inclusion of a third sensor was not found to be strictly necessary. Since horizontally aligned sensors can provide efficiency increases of up to $100\%$ if the line spacing is comparable to the sensor spacing, our results suggest that an inverted triangular sensor configuration may prove optimal for a three-sensor bird. Such a configuration could provide the efficiency increase of horizontally aligned sensors at the lower measurement surface (which is characterized by higher signal to-noise ratios), and still retaining the ability to compute slanted vertical differences across a single upper sensor.