Improving resolution in deep learning-based estimation of drone
position and direction using 3D maps
Masatoshi Hamanaka1
Abstract— We propose a method to improve the resolutionof drone position and direction estimation on the basis of deeplearning using three-dimensional (3D) topographic maps in nonglobal positioning system (GPS) environments. GPS is typicallyused to estimate the position of drones flying outdoors. However,it becomes difficult to estimate the position if the signal fromGPS satellites is blocked by tall mountains or buildings, or if
there are interference signals. To avoid this loss of GPS, wepreviously developed a learning-based flight area estimation
method using 3D topographic maps. With this method, theflight area could be estimated with an accuracy of 98.4% inexperiments conducted in 25 areas, each 40 meters square.
However, a resolution of 40 meters square is difficult to use fordrone control. Therefore, in this study, we will verify whether
it is possible to improve the resolution by multiplexing the area
division and the data acquisition direction. We also investigatedwhether the flight direction of the drone can be detected using a
3D map. Experimental results show that the position estimation
was 96.8% accurate at a resolution of 25 meters square, andthe direction estimation was 92.6% accurate for 12-direction
estimation.

I. INTRODUCTION
Our goal is to use drones for delivery in mountainous
areas. Drones require a lot of energy to climb, so in themountains, it is more energy efficient to fly them in thevalleys rather than along the peaks. When flying in a valley,signals from global positioning system (GPS) satellites canbecome blocked, which reduces navigational accuracy andmakes flight difficult. Furthermore, GPS signals are very
weak and subject to a variety of disturbances in general, andsuch problems increase the chances of a crash when flying
a GPS-controlled drone [1], [2].
Assisted-GPS (A-GPS) [3], [4] and quasi-zenith satellite
systems (QZSS) [5] are two approaches that have aimed tosolve these problems. A-GPS augments regular GPS with cell
tower data and Wi-Fi positioning to enhance the quality andprecision when operating in poor satellite signal conditions.
However, there are no cell towers or Wi-Fi on mountainsides
or high up in the air. As for QZSS, while it provides highly
precise and stable positioning services that are compatible
with GPS, the services are only available in the Asia-Oceania
region. Moreover, QZSS cannot be used if there are jammingwaves, as is often the case with GPS.
As a drone technology in a non-GPS environment, amethod of finding an emergency landing site using SLAM
has been proposed [6]. Another method using artificial intelligence (AI) to determine the safety of landing sites using
1 Masatoshi Hamanaka is the team leader of the Music Information
Intelligence Team at RIKEN Center for Advanced Intelligence Project,Tokyo, Japan masatoshi.hamanaka@riken.jp

ultrasonic sensors has been proposed [7]. These assume thatthe drone will move slowly when GPS signals cannot be acquired [6], [7]. Our premise is that even if the GPS cannot be
captured during high-speed movement, the proposed method
will correctly estimate the position and continue high-speed
movement.
To address these non-GPS issues, we previously proposeda method to estimate the flight area using deep learningtechniques [8] to match the ground surface vectors obtainedby a two-dimensional (2D) LiDAR [9], [10] mounted on adrone with a three-dimensional (3D) map acquired by a land
observation satellite (Fig. 1)[11]. Although deep learning
has been used to estimate the positions of persons andobjects from camera images, at the time of writing, no suchmethod has been proposed for estimating the position of an
unmanned aircraft system (UAS) [12], [13].
The main advantage of our method is that we consider
terrain undulations as unique information similar to fingerprints and solve localization as a machine-learning problem.
Our flight experiment results showed that this method could
estimate the flight area with an accuracy of 98.4%. However,
we encountered the following two problems when it came tocontrolling the drone’s flight.

LiDAR

Fig. 1.

Acquisition of surface vectors by LiDAR.

Low resolution: In the flight experiment, we estimatedwhich area was 40 meters square from the five vertical andfive horizontal areas. The resolution of 40 meters squareis insufficient when flying at a low altitude (e.g., when
landing), so it is necessary to detect the position with ahigher resolution. At this time, if the area is reduced toincrease the resolution, the learning data for each area isalso reduced, and the accuracy of area estimation by deeplearning is consequently lowered as well.
Area estimation methods based on deep learning sufferfrom low estimation accuracy near area boundaries [11]because it is difficult to learn samples that have very similar
surface vectors but different areas. When the area is sub-

divided, the average estimation accuracy decreases because
the number of samples near the area boundary increases
relatively.
Therefore, in our improved method, we do not change thesize of the area division but perform more than one estimation instead. In these multiple estimations, we constructfour area estimators with different area boundaries and form
a common area by superimposing all four estimation areas,
which is then set as the final estimation area.
Compass error: Assuming that the nose of the drone isfacing north, we used the surface vectors located 25 meters
to the left and right of the drone as data for learning andestimating the deep neural networks. However, there aremany places where compass errors occur (e.g., near powerlines), and it is difficult to always fix the nose direction to
the north. If the scanning direction of LiDAR greatly differsfrom that at the time of deep learning, it becomes difficult toestimate the area. Furthermore, to implement drone autopilot
in places where GPS is difficult to use, it is necessary tocorrectly estimate the direction in addition to the position of
the drone.
At present, it is possible to estimate the direction by
generating learning data when the drone faces various directions. However, a ground surface vector is similar toa surface vector whose LiDAR acquisition direction has
slightly changed, and it is difficult to distinguish them evenby using deep learning. Similar to area estimation, it isdifficult to learn samples with similar surface vectors but
different direction information.
To sufficiently distinguish the directions in which thedrone is facing, our improved method uses a four-direction
estimator with 90-degree increments. The common direction
formed by superimposing the estimation directions of thethree estimators is the final estimated direction.
The rest of this paper is organized as follows. In Section
2, we present the learning and evaluation data and the basic
algorithm of position estimation based on the ground surface
shape. Section 3 describes the multiplexing of area divisions,and Section 4 describes the direction estimation. We discuss
the experiments and results in Section 5 and conclude in
Section 6 with a summary and mention of future work.
II. POSITION ESTIMATION USING SURFACEVECTOR
The flight area of a drone can be estimated by using
pattern matching between the 3D topographical map and theground surface shape acquired by the drone. In this case, it
is more efficient to perform pattern matching between 3D
shapes acquired using 3D LiDAR. However, 3D LiDAR isheavy and difficult to mount on small drones. Lightweight 3D
LiDAR has also become available [14]. However, 3D LiDAR
that can be measured over long distances has a narrowvertical field of view, and the data that can be obtained is
not much different from that of 2D LiDAR. In addition,
the sensor or mirror rotation type used in many small 3D
LiDARs has the problem that the scanning point shifts by

the distance that the drone has flown during the scanning
time when it flies at high speed.
Therefore, in this work, we equipped the drone with acompact, lightweight 2D LiDAR that was originally developed for automated driving and used it to acquire a 2D
surface cross-section (Fig. 1).
The estimation of the flight area of a drone using deeplearning is performed in two steps. First, the 2D surface
vector is acquired by the 2D LiDAR mounted on the drone.
Next, the area is estimated from the 2D surface vector byusing a network learned in advance. In this section, we
describe the construction of the learning and evaluation data.
A 2D LiDAR (LD-MRS, SICK AG) is mounted on thedrone to acquire the ground cross-sectional shape (Fig. 2).
The altitude of the ground surface can be measured to an

Fig. 2.

Matrice 600 [15] equipped with LD-MRS.

accuracy of about 20 centimeters if a LiDAR with an angularresolution of 0.125 degrees is mounted facing verticallydownward and the UAS flies 30 meters above the ground[16]. In our experiments, we set 100 measurement points(one every 50 centimeters on the left and right of the flightpath) and recorded the differences in height between thesepoints as a 100-dimensional 2D surface vector. The heightof the drone was fixed at 30 meters from an average altitude(Fig. 3). The method itself is capable of handling various
altitudes, enabling the area in the height direction to be
estimated simultaneously [11]. However, we chose to set thealtitude to a constant level to prevent difficulty in verifying
the basic performance of the method due to the large amountof training data. Another reason is hardware limitations. LDMRS can measure up to 150 meters, but as the altitude
increases, it becomes more difficult for the laser to reachthe ground, which increases the number of points that are
difficult to measure. Thus, the altitude was set at 30 meters.
We divided the flight area into a lattice and assigned
different labels to its elements. The initial position of thedrone was randomly determined, and a set of the groundshape vectors calculated from the 3D map and the labels of
the area were used as learning data.
We used an AW3D global high-resolution 3D map acquired by Maxer (formerly DigitalGlobe) satellites [17].
Maxer’s imagery provides high-precision elevation models

Average altitude
30 mfour lattices with five 100-meter square areas vertically andhorizontally, we will have a 25-meter square sub-area. The
range of the identifiable sub-area is 425 meters square in
289 sub-areas (= 17 × 17), where all four lattices overlap(Fig. 5).
500 m

Identifiable sub-area

50 m, 100 measurement points

Hiddenlayer 1

Hidden Hidden
layer n-1 layer n……………...

Area 2……………...

……………...

（100 dim.）……………...

……..
Groundsurface
vector……..
Fig. 4.

Outputlayer
Area 1
Area 3
Area 4……………...

Input
layer

MLP for estimating area labels.

Supervised learning with back-propagation was used todetermine all of the network parameters, including the biasof the units and the weights of the connections between theunits.
III. MULTIPLE ESTIMATIONS OF DRONEPOSITION
The lattice that divides the area is shifted by a quarterof the size of one area, and the four lattices overlap. Then,overlaying the lattices creates a sub-area that is one-fourth
the size of the original area. For example, if we stack

425 m

at 0.5-m to 2-m resolution.
Pattern matching between the 3D map and the groundsurface vector acquired by 2D LiDAR typically requires
numerous matchings, which makes it difficult to perform
in real time. Thus, we estimated the flight area from theground surface shape in real time by using a multilayer
perceptron (MLP) [18]. It is possible to use a convolutional
neural network [19] or support vector machine [20] as adiscriminator, but since real-time performance is importantfor drone position detection, we decided to use the MLP,
which has a simple structure and fast processing speed.
The MLP for estimating the flight area is shown in Fig. 4.
The input for the experiment was 100 units corresponding to
the 100-dimensional ground surface vector. Each dimensionof the surface vector was normalized to zero mean and variance one. The output units of the MLP were area labels. The
MLP had n hidden layers; i.e., we varied n and the numberof units in the experiments. The input layer, intermediate
layers, and output layer were all fully connected.

Sub-area

25 m

100 measurement points.

500 m

Fig. 3.

25 m
Four overlapping lattices

425 m
Fig. 5.

Four overlapping lattices and sub-area.

When the area label is attached as shown on the left ofFig. 6, the sub-area indicated in black on the right of Fig. 6
with lattice 1 has the area label 6, lattice 2 is labeled with
1, lattice 3 is labeled with 2, and lattice 4 is labeled with 1.
That is, the combinations of labels on the four grids in each
sub-area are all different and identifiable.
In the figure, it appears as though one area is estimated byeach of the four lattices, but in fact, the probability of beingin each of the 25 areas is calculated. Then, the probabilities
are added to estimate which sub-area is the highest.
IV. DIRECTION ESTIMATION USING SURFACEVECTOR
It is possible to estimate the direction of the drone by
dividing the directions into twelve. However, if the 12direction estimator is made directly, the accuracy will be very
low because many learning and estimating data are near theboundary. Therefore, we make three 4-direction estimatorsthat are offset by 30 degrees. Then, we superimpose themand identify the overlapping part to construct the 12-direction
estimator.
There are 100 LiDAR scan points across 50 meters perpendicular to the drone (Fig. 7). The center point of the drone
is the center of the LiDAR scan. We rotate the LiDAR scanaround the center point of the drone with a resolution of 1
degree to create surface vectors in all directions. Labels areadded to the surface vector in accordance with the directionof the drone.
We set three of the aforementioned four-direction estimators with an angle of 30 degrees and assign a different arealabel to each. At the time of estimation, the direction inwhich the estimation results of the three estimators overlap
is set as the final estimation direction (Fig. 8). Similar to the
sub-area estimation, the figure appears to show that one ofthe directions is estimated by all three direction estimators,
but in fact, the existence probabilities of each of the four
directions are calculated. Then, we estimate the direction in(a) Area label in a lattice
１

6

11

16

21

２

７

12

17

22

３

８

13

18

23

４

９

14

19

24

５

10

15

20

25

Lattice 1: label 6(b) Sub-area on four lattices

Center point of drone

Lattice 2: label 1

100 LiDAR measurement points over 50 m

Directionlabel: A
Lattice 3: label 2

Lattice 4: label 1

Directionlabel: B

Directionlabel: D

Directionlabel: C
Fig. 6.

Area label of sub-area.

which the highest probability is calculated by adding theprobabilities.

Label: A

Direction of drone

V. IMPLEMENTATION
We constructed a deep neural network by inputting a 100dimensional surface vector and outputting position labels foreach of the four lattices and direction labels for each of thethree estimators. The first to fifth layers are fully connected
layers, and ReLU was used as the activation function (Fig. 9).

Label: B

Label: DLabel: C

The sixth to eighth layers are also fully connected layers
but are branched for each output, and ReLU was used as
the activation function. Softmax was used as the activation
function from the eighth layer to multiple outputs. As for thenumber of units, it is known that the accuracy increases due
to avoiding overfitting when the number of units decreases
by 0.6 times from the first layer until one layer before theoutput layer, so we utilized this design here as well [11].
The number of units in the first layer was set to 1800, which
was highly accurate due to random sampling.
It is possible to calculate sub-area and direction probabilities from the output of the trained network shown in Fig. 9.
In addition, the network can be fine-tuned by separating theoutput shown in Fig. 9 and combining the 286 sub-areas and
12 directions as outputs (Fig. 10).

Fig. 7.

Four direction labels.

VI. EXPERIMENTAL RESULTS
The network described in the previous section was learned
and the performance was then evaluated. We used an
NVIDIA RTX 4090 for learning. The experimental data is
600 meters square of a W3D global high-resolution 3D map
acquired by Maxer satellites, and its center is 139.108 east
longitude and 36.624 north latitude. Four 500-meter squareareas were taken in a 600-meter square area with a 25meter shift (Fig. 11). Each 500-meter square was divided into
25 and labeled. We randomly sampled 80% of all the datafrom the 289 (= 17 × 17) sub-areas as training data and theNumberof units

Input layer (100 dim.)
ReLU

Four-direction estimator 1

8th

Label: A

Fully connected25

289 sub-areas

Label: B

Label: D

Fully connected4

Softmax

Softmax

Fig. 10.

Estimated direction

12 directions
Fine-tuning network.

Label: C

Four-direction estimator 2

remaining 20% was validation data. We initially used Adamas the optimizer, but the validation accuracy decreased in the
middle of learning, so we used RMSprop instead.

Label: E
Label: H

Label: FLabel: G

Four-direction estimator 3
Label: L
Label: I

Label: K
Label: J
Fig. 8.

Estimation of 12 directions.
Fig. 11.

3D map acquired by Maxer satellites.

A. Positon Estimation Results
Input layer (100 dim.)
ReLU

1st hidden layer (fully connected)

Numberof units
1800

ReLU

2nd hidden layer (fully connected)

1080

ReLU

3rd hidden layer (fully connected)

TABLE IESTIMATION ACCURACY OF EACH LATTICE

648

ReLU

4th hidden layer (fully connected)

After learning for 1000 epochs, the performance of 25
areas of each lattice was estimated as shown in Table I.
Figure 12 shows the learning curve of lattice 1.

388

Lattice 1
85.6%

Lattice 2
86.1%

Lattice 3
86.2%

Lattice 4
85.7%

ReLU

5th hidden layer (fully connected)
ReLU

6th

Fully connected

Fully connected
ReLU

7th

Fully connected
Fully connected
Softmax

Output of lattice 1 to 4
Fig. 9.

139

ReLU

Fully connected

ReLU

8th

232

ReLU

83

ReLU

25

Fully connected4

Softmax

Output of direction 1 to 3

Implementation of deep neural network.

By superimposing the four grids, 289 sub-areas werecreated. When the sub-areas were estimated by adding theprobabilities that drones exist in each area, the accuracy was
67.4% at a chance rate of 1/289.
We created a heat map to clarify what kind of position estimation errors occurred. As shown in Fig. 11, we found that
32.6% of the data was incorrect. The blue square indicatesthe estimated area, and the red square indicates the correct
area. The numbers in the heat map are the sum of the correct
answer probabilities of the four lattices, where the maximum
and minimum values are 4 and 0, respectively. Even if theestimation was incorrect, as shown in Figs. 13(a)–(c), theadjacent position was often inferred. However, in a numberof cases, another position was estimated, as shown in (d).

accuracy can be improved. Therefore, we performed finetuning using the network in Fig. 10, in which 289 sub-area
units and 12 directional units with softmax functions are
combined with the trained network from the input to theeighth layer.
After fine-tuning, the accuracy of position estimation withthe 25-meter square resolution was 96.8%, and the accuracyof 12-direction estimation was 92.6%. Learning did not
progress when the network in the initial state was usedinstead of fine-tuning.

Output1 accuracy

Output1 Area1

VII. CONCLUSION

Epoch

Fig. 12.

Learning curve of lattice 1.

B. Direction Estimation Results
The accuracy of each estimator for direction estimation
is listed in Table II. Figure 14 shows the learning curve of
direction estimator 1.
TABLE IIESTIMATION ACCURACY OF EACH DIRECTION ESTIMATOR
Estimator 1
79.0%

Estimator 2
78.5%

Estimator 3
78.9%

When the directions were estimated by adding the resultsof the three direction estimates, the accuracy was 59.4% at
a chance rate of 1/12.
The graph shown in Fig. 15 was created to clarify theerrors that occurred in direction estimation. We found that
40.9% of the data was incorrect. The estimated and correct
directions are shown in orange and brown, respectively.
The polar coordinate numbers are the sum of the correct
answer probabilities of the three estimators, with a maximum
and minimum value of 3 and 0, respectively. As shown in
Figs. 15(a)–(c), there were many cases where the adjacentdirection was estimated even if the estimation was incorrect.
However, in a number of cases, another direction was estimated, as shown in (d).
C. Fine-Tuning Results
We improved the resolution by summing the output of four
lattice probabilities for position estimation and the outputsof three estimators for direction estimation. In this method,
if even one of the lattices or estimators is misestimated,the final position or direction will be wrong. Therefore, theestimation accuracy was low compared with one lattice or
one estimator.
Even when an estimation error occurred, there were many
instances in which the estimated area was adjacent to thecorrect area due to a slight difference in probability. If thisprobability can be adjusted, there is a possibility that the

We proposed a method for estimating the position anddirection of drones by learning the ground surface vector
acquired by LiDAR with a multi-output deep neural network.
The main contributions of this paper can be summarized asfollows.
Improved resolution of area estimation: While the sizeof the area to be estimated was 100 meters square, the area
estimation multiplexing made it possible to estimate a subarea of 25 meters square. The sub-area could be estimatedwith an accuracy of 67.4% at a chance rate of 1/289. Evenfor the incorrect estimation, which was 32.6%, most of theerrors were related to the adjacent sub-area.
Direction estimation: Previously, it was assumed thatthe drone would always fly northward, but by learning thesurface vectors in all directions (i.e., 360 degrees), we wereable to estimate the direction of the drone. It was possible toestimate the sub-area with an accuracy of 59.4% at a chance
rate of 1/12. Most of the incorrect answers (40.9%) were
estimation errors in adjacent directions.
Fine-tuning: After fine-tuning using a network that combines 289 sub-areas, 12 directional units, and the learned
network from input to the eighth layer with softmax, theposition estimation accuracy with a resolution of 25 meterssquare was 96.8%, and the 12-direction estimation accuracy
was 92.6%.
Improved resolution in estimating drone position andorientation: Our previous deep learning-based position detection method suffered from a drop in accuracy when we
attempted to improve the resolution. The experimental results
showed that multiple lattices and direction estimators canimprove resolution without a significant loss of accuracy.
Our next steps are as follows.
Further improvement in resolution: Our proposed
method can further improve the resolution by setting the shiftof the lattices and direction estimators very small. We willverify the extent to which the resolution can be improved
without a significant drop in estimation accuracy.
Network construction corresponding to changes inaltitude: In the experiment, it was assumed that the drone
would fly at a fixed altitude of 30 meters, but in actual flight,
altitude changes occur. Therefore, we plan to divide the areain the altitude direction and perform learning and estimation.
Learning in a large area: A problem with current
learning networks is that once the drone leaves the training
area, it loses its position. To prevent this, we need to prepare

(a)

(b)

(c)

(d)

Fig. 13.

Heat map of position estimation error.

Output5 accuracy

Output5 Direction1

shape of a flower. We plan to enable faster estimation by
inputting one petal pattern or one curve pattern into the
network.
Field flight experiments: A trained network can estimate
position and direction in real time with a small computer.
We plan to carry out a field flight experiment by mounting
the computer on an unmanned aircraft operated by the Japan
Aerospace Exploration Agency (JAXA).
ACKNOWLEDGMENT
This work was supported by the Japan Society for the
Promotion of Science (JSPS KAKENHI Grant Number
17K19972).
R EFERENCES

EpochFig. 14.

Learning curve of direction estimator 1.

a large labeled area around the area where the flight isplanned. We are planning to evaluate the performance in alarge area.
Non-repetitive scanning 3D LiDAR: Although 2D LiDAR was used in the experiments in this paper, a numberof 3D LiDARs perform non-repetitive scanning [21]. They
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