A Study on Acquisition of 3D Self-Localization by Fluorescent Lights

Rikuto Ozawa

and Hiroyuki Kobayashi

Graduate School of Robotics and Design, Osaka Institute of Technology, Kita-ku, Osaka, Japan

Keywords:

Machine Learning, Neural Network, Robotics, Self-Localication, CEPHEID.

Abstract:

The authors proposed a method called “CEPHEID” in previous study. This method utilizes individual dif-

ferences in power spectra obtained from illumination lights to identify individuals, allowing for self-location

estimation using lighting ﬁxtures embedded in the ceiling as landmarks. However, the information obtain-

able through this method is limited to a two-dimensional plane. To overcome this limitation, in this study, we

introduced a regression model in addition to the deep learning model used for individual identiﬁcation. The re-

gression model aims to estimate the distance to the illumination light, enabling the acquisition of self-position

information in three dimensions. This paper presents the evaluation of the accuracy of the regression model’s

distance estimation.

1 INTRODUCTION

In recent years, signiﬁcant progress has been made

in the ﬁeld of robotics, particularly in areas such as

autonomous driving and automation of restaurant ser-

vices. These advancements have had a profound im-

pact on society, and as a result, much research on self-

location estimation, which is necessary for these pur-

poses, has been actively conducted.

Currently, two primary methods are commonly

used for self-location estimation: one that combines

external and internal sensors, and another that relies

solely on external sensors.

An example of the former method is Odome-

try. This method calculates displacements based on

the rotation angles of wheels or steering in a robot

(Tomonou, 2016)(Chenavier and Crowley, 1992).

The robot’s position is estimated using cumulative

calculations. Odometry is a versatile positioning tech-

nique that is less affected by the surrounding environ-

ment. However, it is prone to a problem known as

error accumulation. Therefore, the use of values from

external sensors is necessary to correct these errors

and improve accuracy.

On the other hand, GPS (Global Positioning Sys-

tem) is an example of the latter method. It relies on ra-

dio waves transmitted by satellites orbiting the Earth.

GPS is widely utilized in smartphones and IoT de-

vices due to its low cost and high accuracy, becoming

https://orcid.org/0009-0009-3359-5972

https://orcid.org/0000-0002-4110-3570

an essential part of our daily lives. However, GPS

has its limitations. It can experience reduced accu-

racy or, in some cases, fail to estimate position in ar-

eas where radio waves cannot reach, such as indoors

or underground. To address this issue, various meth-

ods have been proposed, including the combination of

GPS with WiFi, Bluetooth, etc. (Ban et al., 2014)(Fu-

jihara et al., 2020). Nonetheless, these methods re-

quire additional equipment installation, posing prac-

tical challenges.

In this context, we proposed ”CEPHEID (Ceil-

ing Embedded PHoto-Echo ID)” (Yamano and

Kobayashi, 2017a)(Yamano and Kobayashi, 2017b) a

novel approach that leverages a deep learning model

generated from the ﬂickering patterns of lighting de-

vices to enable self-position estimation. However,

the current implementation of CEPHEID is limited to

two-dimensional information. Therefore, the primary

objective of this study is to achieve self-position es-

timation in three-dimensional space by incorporating

the height of the lighting devices.

This paper is structured as follows: Section 2 pro-

vides an explanation of CEPHEID as the fundamental

basis for this study. Section 3 explains the method

for creating a deep learning model capable of esti-

mating the distance to the lighting sources. Section 4

discusses the accuracy and performance evaluation of

the developed deep learning model. Finally, Section 5

concludes the paper by summarizing the ﬁndings and

presenting future prospects.

Ozawa, R. and Kobayashi, H.

A Study on Acquisition of 3D Self-Localization by Fluorescent Lights.

DOI: 10.5220/0012212200003543

In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2023) - Volume 1, pages 285-290

ISBN: 978-989-758-670-5; ISSN: 2184-2809

285

2 CONCEPT

CEPHEID is named after the initials of “Ceiling Em-

bedded PHoto-Echo ID”. Unlike conventional meth-

ods (Fushimi et al., 2009) that require additional

known information in the equipment, CEPHEID per-

forms identiﬁcation based on individual differences in

ﬂickering patterns of the lighting ﬁxtures.

Figure 1 shows the power spectrum obtained from

two different lighting ﬁxtures in a room. In this im-

age, both waveforms show a strong peak at 120Hz,

and similar waveforms can be observed in other fre-

quency bands as well. However, it can be noted that

there are differences in the peaks at certain points.

The exact cause of this phenomenon has not been

fully revealed. We believe it is likely due to slight

individual variations in electrical components. In any

case, lighting devices have identiﬁable individual dif-

ferences, and CEPHEID enables the identiﬁcation of

lighting sources through the use of a deep learning

model.

A similar study (Zhang and Zhang, 2017) exploits

individual differences observed in the MHz band. In

contrast, CEPHEID utilizes individual differences in

human audible frequencies, typically within the range

of 20kHz. This enables the use of widely avail-

able 3.5mm audio jacks and A/D conversion circuits,

which are currently prevalent.

Previous studies (Kobayashi, 2019)(Kobayashi,

2020) have shown that the model achieves an accu-

racy of approximately 97% in classifying 48 light-

ing sources. Furthermore, it has been determined that

the same level of accuracy can be obtained when per-

forming the same test again 22 days after model gen-

eration. While CEPHEID has proven to be useful in-

door positioning method, one challenge is that it is in-

herently a classiﬁcation problem and the information

is limited to a two-dimensional plane.

This study aims to explore the feasibility of three-

dimensional self-position estimation, considering the

height of the illumination source. In this paper, we ex-

plore the introduction of a regression model that pro-

vides continuous distance values to the illumination,

in addition to a classiﬁcation model.

3 MODEL CREATION

3.1 Data Acquisition

Figure 3 shows the dongle utilized for data acqui-

sition, along with its circuit diagram. This circuit

consists of a 1KΩ carbon resistor and Si photodiode

(Hamamatsu Photonics S2506-02). This conﬁgura-

Figure 1: Power spectrum acquired from two difference

lighting sources.

Figure 2: Power spectrum acquired at two difference dis-

tances(speciﬁcally, at 0.4m and 2.0m).

tion enables us to acquire data at a very low cost. In

this study, the dongle is used to capture the ﬂicker-

ing patterns of illuminations for a duration of 30 sec-

onds. These captured patterns are subsequently used

as training data for the deep learning model.

3.2 Data Padding

First, the 30 seconds of WAV data is divided into

10 segments, each separated by a 3-second interval.

Then, because the division of the data may cause

noise, a window function (Hanning window) is ap-

plied to weight the data, resulting in a gradual ampli-

tude reduction at the beginning and end of the audio.

Subsequently, the resulting data from these processes

is subjected to the following padding methods com-

monly employed in speech recognition problems:

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MIC

GND

Figure 3: CEPHEID dongle.

• Pitch: Modifying the pitch of the audio.

• Shift: Shifting the starting point of the data back-

wards and aligning any overﬂowed portion to the

beginning.

• Stretch: Accelerating the playback speed of the

audio.

Using these methods, a total of 220 variations of data

are generated from a single 30-second segment.

3.3 Data Processing

Perform a discrete Fourier transform on each of the

padded data sets to obtain the following power spec-

trum P

input

= [ f

, f

, ...] (1)

Because P

input

is a complex vector, its magnitude is

obtained using equation (2).

(Re( f

)

+ Im( f

)

) (2)

Deﬁne P

raw

as a summary of p

. In this context, i rep-

resents the frequency corresponding to each of them.

raw

= [p

, p

, ...] (3)

The power spectrum within the audible frequency

range can be obtained using this method. However,

the dimensionality is too large, with several tens of

thousands, so it is necessary to reduce the number of

dimensions. Here, we divide P

raw

equally along the

linear axis and perform averaging within each inter-

val. As a result, the ﬁnal feature vector P becomes

1024 dimensions.

P = [p

′

, p

′

, p

′

, ..., p

′

1024

] (4)

3.4 Model Structure

The structure of the model developed in this study is

shown in Figure 4. The model consists of a 1D convo-

lutional layer, a fully connected layer (Dense layer),

and a dropout layer. The activation function for each

layer uses the Rectiﬁed Linear Unit (ReLU) function,

as shown in the following equation (5). Only the ﬁnal

layer was not speciﬁed.

ϕ(x) = max(0, x) (5)

The loss function utilized during training is presented

in equation (6).

Loss =

n−1

∑

i=0

−

)

(6)

In this equation, y

represents predictions,

repre-

sents the ground truth, and n indicates the number

of data points. We have chosen Mean Square Error

(MSE) as our loss function. This choice aims to en-

sure that the model’s output represents a continuous

value, reﬂecting the distance to the illumination light

source.

(725,20)

Conv1D

(14500)

Flatten

(2048)

Dense

(1024)

Dropout (2048) Dense

(256)

Dense

(1024)

Dense

(64)

Dense (1)Dense

(1024)

input

output

Figure 4: Model structure.

4 EXPERIMENT

4.1 Purpose

In this section, we report the experimental results.

We created two deep learning models that output dis-

tances to the illumination light source as continuous

values. One was trained using data collected at 0.2m

intervals, while the other was trained using data col-

lected at 0.4m intervals. Please note that both models

were trained using data collected between 0.4 meters

and 2.0 meters from the illumination light source, and

the evaluation data was gathered one week after the

training data.

To validate the effectiveness of our approach, we

conducted the following three experiments:

• Experiment 1: Accuracy evaluation of deep learn-

ing models trained on data acquired every 0.2m

• Experiment 2: Accuracy evaluation of deep learn-

ing models trained on data acquired every 0.2m

A Study on Acquisition of 3D Self-Localization by Fluorescent Lights

287

Table 1: Detailed values of experiment 1.

distance [m]

true 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

light 1 0.395 0.593 0.766 0.931 1.121 1.353 1.662 1.809 2.058

light 2 0.410 0.591 0.816 0.996 1.157 1.398 1.582 1.755 1.898

light 3 0.396 0.618 0.830 1.024 1.154 1.408 1.635 1.715 1.939

light 4 0.389 0.594 0.809 1.041 1.185 1.377 1.609 1.795 1.980

light 5 0.378 0.603 0.748 1.037 1.172 1.401 1.555 1.766 2.025

• Experiment 3: Using the model trained in Experi-

ment 1, we evaluated the model’s performance by

inferring data with randomly varying amplitudes.

In particular, Experiment 3 was conducted to conﬁrm

that the light intensity was not explicitly learned by

the model. It is commonly known that light intensity

is inversely proportional to the square of the distance,

and by conducting this experiment, we aimed to ver-

ify that the model relied on other factors instead of

explicitly learning the inverse square law.

4.2 Procedures

The experimental procedure is shown below.

1. Acquire data directly underneath the ﬁve lighting

devices (Figure 5).

2. Create a deep learning model using the acquired

data.

3. Evaluate the accuracy based on the inference re-

sults of the model.

Figure 5: Lighting devices to be veriﬁed.

4.3 Results

4.3.1 Experiment 1

Figure 6 shows the inference results, and Table 1

shows the detailed values. The horizontal axis rep-

resents the actual distance, while the vertical axis rep-

resents the inference results. The graph illustrates that

if each dashed line closely resembles a long straight

line, it indicates good accuracy. Based on Figure 6,

it can be observed that the overall inferences are cor-

rect. In addition, according to Table 1 the largest error

was approximately 0.1m, and the average error across

all measurements was within 0.05m.

0.0

0.5

1.0

1.5

2.0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

predict distance[m]

original distance[m]

original light1 light2 light3 light4 light5

Figure 6: Inference result of experiment 1.

4.3.2 Experiment 2

0.0

0.5

1.0

1.5

2.0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

predict distance[m]

original distance[m]

original light1 light2 light3 light4 light5

Figure 7: Inference result of experiment 2.

Figure 7 shows the inference results, and Table 2

shows the detailed values. The view of the ﬁgure 7

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Table 2: Detailed values of experiment 2.

distance [m]

true 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

light 1 0.338 0.550 0.739 0.878 1.075 1.295 1.572 1.788 2.092

light 2 0.325 0.456 0.740 0.980 1.056 1.382 1.510 1.700 1.871

light 3 0.339 0.444 0.747 1.009 1.163 1.486 1.619 1.636 1.812

light 4 0.323 0.462 0.752 0.924 1.078 1.315 1.494 1.727 1.849

light 5 0.300 0.376 0.791 1.096 1.163 1.418 1.532 1.730 2.010

is the same as in Experiment 1. Based on Figure 7, it

can be observed that the overall inferences are correct.

In addition, according to Table 2 the largest error was

approximately 0.22m, and the average error across all

measurements was within 0.08m.

From these result, It was found that doubling the

interval between data to be acquired approximately

doubles the error.

4.3.3 Experiment 3

The ﬁgure and table are omitted because this experi-

ment yielded identical results to Experiment 1. Based

on the ﬁndings from this experiment, it was observed

that the trained model generated this time is not re-

liant on light intensity.

5 CONCLUSIONS

This paper presents the results of a deep learning

model for estimating the distance of multiple lighting

devices. In Experiment 1, the maximum error was ap-

proximately 0.1m. This indicates the generation of a

useful learning model. Experiment 2 exhibited an av-

erage error of approximately 0.2m, which was slightly

larger than the error in Experiment 1 but overall dis-

tance estimation remained accurate. Experiment 3 re-

vealed that the learning model did not capture the in-

tensity of light.

Based on the above ﬁndings, the model demon-

strated the ability to estimate distances effectively,

providing practical applicability. However, because

the inference results were derived from static data, the

actual sensitivity of the model has yet to be veriﬁed.

Therefore, we plan to verify the effectiveness of this

method in real-time scenarios.

This method also presents a challenge due to the

time-consuming nature of preparing training data,

as it requires multiple shots for each illumination.

Therefore, our goal is to develop a method that sim-

pliﬁes the process of preparing training data.

ACKNOWLEDGEMENTS

This work was supported by JSPS Grant-in-Aid for

Scientiﬁc Research JP20K12016.

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