=Paper=
{{Paper
|id=Vol-2498/short20
|storemode=property
|title=Azimuth estimation for indoor localization using redundant planar circular photodiode array
|pdfUrl=https://ceur-ws.org/Vol-2498/short20.pdf
|volume=Vol-2498
|authors=Gergely Zachár,Gergely Vakulya,Gyula Simon
|dblpUrl=https://dblp.org/rec/conf/ipin/ZacharVS19
}}
==Azimuth estimation for indoor localization using redundant planar circular photodiode array==
https://ceur-ws.org/Vol-2498/short20.pdf
Azimuth Estimation for Indoor Localization Using
Redundant Planar Circular Photodiode Array
Gergely Zachár1, Gergely Vakulya1, and Gyula Simon1
1
Pázmány Péter Catholic University, Budapest, Hungary
simon.gyula@ppke.hu
Abstract. A novel sensor architecture, called Planar Circular Photodiode Array
(PCPA) is proposed to provide azimuth measurements for indoor localization
systems. The transmitters are blinking LEDs, where the unique blinking fre-
quency identifies the transmitters. The inexpensive sensor device contains a cir-
cular photodiode (PD)-array, where each PD measures the intensity of each trans-
mitter. The directions of the transmitters are determined by a Least Squares
method, using the reference sensitivities of the sensors. The paper provides sim-
ulation analysis to determine the achievable angle measurement accuracy, and as
illustrations, the corresponding localization accuracy for some setups. Real phys-
ical measurements are also provided, showing potential accuracy below 1 degree.
Keywords: Azimuth Estimation, Angle of Arrival, Position Estimation, Photo-
diode Array.
1 Introduction
Angle of Arrival (AoA) and Angle Difference of Arrival (ADoA) localization schemes
were proven successful in various localization systems. For such solutions bearing
measurements of either the target or the deployed beacons are necessary. In the first
case the target emits a signal and multiple receivers, deployed in known locations,
measure the direction of the signal source (e.g. [1], [2]). In the second case multiple
deployed beacons in known locations emit signals and the receiver on the target
measures the directions of the beacons (e.g. [3]-[7]). In both cases some kind of trian-
gulation provides the target location.
In AoA/ADoA applications typical signal sources are optical (e.g. blinking LEDs)
or acoustic (e.g. weapons as targets or ultrasound emitters as beacons). In this paper we
focus on optical sources (LEDs) only. In this case the receivers may be cameras [4],
photosensitive devices [2], or simple photodiodes [3]. The target localization can be
done in general using 3-D measurements (i.e. both azimuth and elevation [7]) or using
only azimuth measurements [4], [5]. In the latter case some restrictions apply to the
sensor; either the sensor’s direction must be known (e.g. the sensor is looking upwards)
[4], or it must be measured with auxiliary sensors (e.g. by a three-axis accelerometer)
[5]. However, azimuth only estimation was proven more efficient from the calculation
point of view [1]. Moreover, in many applications only the 2-D location is important
2
and the elevation information is not required. In such cases azimuth-only estimation is
both computationally efficient and accurate.
In this paper we will propose an azimuth-only measurement method using inexpen-
sive devices. The light sources are LEDs, which transmit their identifier using Visible
Light Communication. The proposed receiver is called Planar Circular Photodiode Ar-
ray (PCPA), which is a redundant sensor device: the source intensity is sensed by many
sensors at the same time, and from the detected intensity differences of the sensors the
direction of the source can be determined. The direction estimation is based on the sen-
sors’ varying radiant sensitivity as the angular displacement of the source changes.
In the literature various sensors were proposed to measure the bearings of light
sources. In [8] a pinhole camera was created with a movable hole, from a Thin-Film-
Transistor (TFT) unit of a TFT display, and a photodiode. Instead of the pinhole cam-
era, several systems use ordinary cameras, as receivers [4]-[7]. In the system of [3]
three orthogonal silicon photodiodes (PDs), forming a cube, were used to measure the
azimuth and elevation of light sources. A special camera was created in [13], placing a
microlens above an image sensor. A Quadrant Photodiode Angular Diversity Aperture
(QADA), combined with an aperture was used in [14]. In this paper an inexpensive PD-
array will be used for sensing. Our proposed system will apply ideas from [3], i.e. the
sensor’s varying radiant sensitivity vs. the angular displacement will be utilized, and
the transmitters will be identified using frequency modulation. New contributions are
the proposed redundant PCPA sensor architecture, which provides enhanced robustness
and noise resilience, with field of view of 360; and the associated Least Squares direc-
tion estimation method.
2 Proposed Measurement System
2.1 Measurement Method
Fig. 1 shows the architecture of the measurement method. The transmitters are
LEDs, blinking with different frequencies (in the figure three transmitters are shown
with frequencies , , … , ). In the proposed Planar Circular Photodiode Array
(PCPA) the PDs are arranged evenly in the outer surface of a cylinder to form a circle,
looking outwards in radial directions. We assume that the transmitters are in the same
plane as the receivers. Each PD implements a measurement channel. The radiant sen-
sitivity of the channels, as a function of incoming angular direction, is shown in the
figure (in this specific example the sensitivity curve is a circle, shown by different col-
ors for each channel). Each channel measures the amplitude of each transmitter’s signal,
the measured spectra are also illustrated in the figure. Based on the measured signal
amplitudes and the calibrated reference sensitivities, the azimuth values , , for each
transmitters are estimated. The figure also illustrates a possible localization scenario:
from the estimated azimuth values and the known transmitter (beacon) positions, the
location and orientation of the receiver can be determined by any triangulation method.
3
Fig. 1. The architecture of the proposed angle measurement device, and its application in a lo-
calization system. From left to right: blinking LED using unique frequencies; PCPA with 6
channels, colored circles represent the PDs’ radiant sensitivity characteristics; amplitude meas-
urement using FFT of each channel; azimuth estimation and localization.
2.2 Azimuth estimation
Let and denote the number of channels in the PCPA, and the number of transmit-
ters, respectively. The × reference matrix contains the calibration data as fol-
lows: row (1 ≤ ≤ ) represents sensor , while column represents direction
= ∙ 360°/ , where is measured in the coordinate system of the sensor unit,
and 1 ≤ ≤ . The th column of contains the normalized reference light
intensities of all sensors in the sensor unit, for light source in direction , such that
the maximum value in each column is one. Thus
=[ … ], =[ , , … , ] (1)
where ( . ) is the transpose operator and max , = 1. Let denote the measured
intensity value of transmitter , 1 ≤ ≤ , by sensor . Vector contains the
measurements of all sensors as follows:
=[ … ] . (2)
The applied cost function is the following:
= min ( ) = min‖ − ‖. (3)
where is a scaling factor to compensate for the unknown source light intensity. The
minimum of ( ) is at value , where ( ) = 0, thus = . If is
the direction index for which is minimal then the azimuth estimation for trans-
mitter is
= . (4)
Note: The reference points are stored in matrix . The resolution can be increased
by applying interpolation between consecutive points , and , .
4
3 Simulation results
3.1 Azimuth Estimation
In this section simulation test results on the accuracy of the proposed azimuth measure-
ment method, as a function of the number of sensors and the angle of half sensi-
tivity of the sensors, will be presented. In the simulations values of = 6, 12, 24, 48
and = 15°, 30°, 60° (typical values for PDs) were used. The radiant sensitivity for
channel ( = 1,2, … ), as a function of angular displacement , was simulated as
cos − if − + ≤ ≤ +
= (5)
0 otherwise
The resolution was set to = 3600. Various amount of noise was added to the ideal
measurements of each channel, to simulate measurement errors. To each measured sig-
nal amplitude (the highest of which was normalized to 1) a zero mean Gaussian noise
was added, with variance of = 0.010, 0.025 and 0.050. The simulation results
are presented in Fig. 2, showing the absolute mean of the estimated azimuth error with
symbols and its standard deviation (std) with whiskers.
Angle estimation error (deg)
Fig. 2. Azimuth estimation error of the PCPA azimuth measurement method, as a function of
the number of channels (vertical axis), the angle of half sensitivity (blue: ±60°, red: ±30°,
black: ±15°), and the std of the measurement noise (o: 0.05, x: 0.025, dot: 0.01).
It is apparent that higher number of channels gives lower estimation error. Smaller an-
gle of half sensitivity also provides better results. With the smallest noise level of
= 0.01 the mean azimuth estimation error is 0.07° with std of 0.05°, for = 48
and = 15°. For = 6 and = 60° the same noise level produced mean error of
0.38° with std of 0.29°. For higher noise levels the estimation error increases approxi-
mately linearly with the noise level.
3.2 Localization Accuracy
Using Gaussian azimuth error (0,0.75°), simulations were conducted to determine
the potential localization accuracy. The number of transmitters in two setups were 3
and 8. The layout of the 5m × 4m test area is shown in Fig. 3, the transmitters are
5
denoted by red dots. The 15 test points were on the 0.5m grid, between (1.5m, 1.5m)
and (3.5m, 2.5m). In each setup 50 independent test were conducted for each test loca-
tions, the estimated positions are shown by colored points around the ideal location.
For = 3, shown Fig. 3(a), the geometric dilution of precision (GDOP) is apparent
towards the upper right corner, where there is no transmitter. The mean localization
error in this scenario was 5.3cm with std of 3.3cm. The other setup contained 8 trans-
mitters, as shown in Fig. 3(b). Here the effect of GDOP is not visible, and the mean
localization error was 1.9cm with std of 1.1cm.
Fig. 3. Simulated position estimation errors in 3-beacon and 8-beacon scenarios.
4 Measurement results
4.1 System Architecture
The block diagram of the measurement system is shown in Fig. 4. The high-power
infrared LED was switched with an IRF540 MOSFET, which was driven by a
PIC16F18313 microcontroller, using the NCO peripheral, allowing the setting of the
switching frequency with sub-Hz precision. In the experiments the following frequen-
cies were utilized: = 4219Hz, = 4570Hz, = 4883Hz.
Fig. 4. The hardware architecture of the PCPA
In the receiver six Vishay BPW41N infrared photodiodes (with = ±65°) were uti-
lized. The signal of each channel was preamplified by a transimpedance amplifier. The
gain of this stage was chosen to provide enough sensitivity, but to avoid saturation by
the DC component caused by normal daylight infrared radiation. The second stage am-
plifier is AC-coupled. The corner frequency of both stages was set to 10 kHz to sup-
press the higher harmonics of the received square wave. The conditioned signals were
6
connected to six ADC pins of a dsPIC33 microcontroller and each channel was sampled
with 40 kHz. The received signal amplitudes were calculated using a 1024-point FFT
with flat-top window.
4.2 Reference channel sensitivities
The rows of the reference matrix represent the relative radiant sensitivity of the chan-
nels of the PCPA. The reference matrix was measured in ideal circumstances: we used
one beacon in fixed position, no other light sources were present (dark room). Using an
automatic turntable, = 360 was provided. The values are the average of 20 inde-
pendent measurements. The channel sensitivities are shown in Fig. 5. Notice that the
curves are quite similar but still there is a visible difference between them.
(a) (b)
Fig. 5. Radiant sensitivity of the six channels of the PCPA.
(a) Polar coordinates, (b) Cartesian coordinates.
4.3 Azimuth estimation
Test were conducted to determine the azimuth measurement error of the proposed
PCPA. In the tests three transmitter units were utilized simultaneously. The positions
(direction and distance) of the transmitters were varied around the PCPA. Test results
obtained using artificial lighting, daylight condition, and a special scenario with a re-
flective surface 1m from the sensor are summarized in Fig. 6.
Fig. 6. Azimuth estimation error of the PCPA.
7
4.4 Localization example
An illustrative localization test was performed using = 3 transmitters in a room
of size 5m × 4m. One of the transmitters and the 6-channel PCPA, mounted on the
turntable, are shown in Fig. 7(a). The localization results are shown in Fig. 7(b). The
test setup is the same as in the 3-beacon simulation, presented in Section 3.2 in Fig.
3(a). The positions of the transmitters are denoted by red dots, the positions of the 15
reference points were also the same (on grid points). From each reference points 36
independent measurements were made by rotating the sensor unit by 10 degrees be-
tween the measurements. From each measurement the location estimate was calculated
using a least squares method, the results are shown by colored points in Fig. 7(b). The
measurement results correspond well with the simulations. However, on the left hand
side the precision is higher, which severely degrades towards the upper left corner, and
becomes significantly higher than in the simulations. The reason is due to two effects:
the GDOP is higher towards the upper right corner, as can be seen in Fig. 3(a). Also,
the angle measurements in these locations produced high errors (occasionally as high
as 8 degrees), probably due to reflections. The two reinforcing effects resulted in a high
position error. For all the 15 test points the mean localization error and std were 8.7cm
and 7.2cm, respectively. Excluding the three points on the right hand side, the remain-
ing 12 test points produced mean error and std of 5.3 cm and 4.1 cm, respectively.
5 Summary
A novel sensor to measure the azimuth of modulated light sources was proposed, using
a Planar Circular Photodiode Array (PCPA). According to simulation analysis, the pro-
posed measurement method with the redundant PCPA allows the measurement of the
azimuth of the light source with accuracy in the range of 0.5° − 2°, depending on the
size of the array. The proposed low-cost solution can be a good alternative of more
costly (e.g. camera-based) sensors in AoA/ADoA localization systems. In an illustra-
tive localization example using a 6-channel PCPA and only 3 beacons, the mean local-
ization error was below 0.1m in a 5m × 4m room.
(a) (b)
Fig. 7. (a) The measurement setup with a beacon (left) and the 6-channel PCPA (right),
deployed on an automatic turntable. (b) Localization results using 3 beacons.
8
Simulation studies suggest that sensors with more channels provide higher measure-
ment accuracy (e.g. the accuracy of a 24-channel PCPA is twice of that of a 6-channel
one). Utilization of higher number of beacons also increases the localization accuracy.
The accuracy of the proposed system is comparable with that of radio time of flight
systems, with the additional advantage of the possible orientation estimate. The appli-
cation of the proposed system requires that the transmitters and the PCPA be at the
same plane. Uncontrolled elevation of the transmitters may cause additional error. The
effect of reflections may also cause performance degradations in environments with
highly reflective surfaces. These effects are subject of further studies.
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