1. Introduction
Indoor positioning forms an integral part in the development of future technologies and its importance in daily activities cannot be overemphasized. Application areas for indoor positioning systems range from smart monitoring of people and facilities in an indoor location to enhanced search and rescue operations during emergencies [
1,
2]. As a result, indoor positioning has been the subject of increasing research interest over the past decade. The central idea behind the design of an indoor positioning system is to establish a ‘transmitter-receiver communication’ link and use a signal parameter to determine the location of the receiver [
3]. Using radio frequency (RF) communication channels, ZigBee, Bluetooth, ultra-wideband, and WiFi have all been used to develop indoor positioning systems [
4]. However, the possibility of multipath reflections and interference with other RF-based devices makes RF unsuitable for indoor positioning [
5]. The use of magnetic or induction-based systems and ultrasound systems has been investigated for indoor positioning, but these systems come with high installation costs [
6,
7]. In addition, magnetic systems can interfere with other sensitive electromagnetic signals (such as those in hospitals).
Light emitting diodes (LEDs) have been receiving attention recently in the context of positioning due to their cost, lighting characteristics, and ability to communicate. LED-based positioning has been extensively investigated with major techniques such as received signal strength (RSS) [
8], proximity [
9], fingerprinting [
10], arrival techniques (which include angle of arrival (AoA) [
11], time of arrival (ToA), time difference of arrival (TDoA), phase difference of arrival (PDoA), and image-based positioning [
3]. The proximity technique has the simplest positioning algorithm and is the most inexpensive to implement, however the accuracy of such systems is usually low [
12]. RSS, AoA, fingerprinting, and image based techniques are also popular forms of LED-based indoor positioning with a very high accuracy [
13,
14]. Despite the high accuracy these techniques promise, LED-based indoor positioning and indoor positioning in general has been reported as a problem yet to be solved [
5]. This is because these highly accurate positioning techniques have been approached with a view to increasing accuracy alone. However, in real life situations, the complexity of the receiver (or mobile unit), the size (weight and volume) of the deployed hardware, the wearability of the receiver, and the positioning time are equally important factors. Ignoring these factors leads to systems that have complex algorithms which are computationally intensive and very expensive to implement [
5]. When implemented, the receiver requires hardware of a large size which requires high amounts of electrical power for their operation. Previous works on LED-based positioning which implement their algorithms are presented in
Table 1. By the use of heavy and large receiver systems, it can be observed that the wearability of the receiver system has not been properly considered in various indoor positioning system (IPS) design techniques.
From
Table 1, the simplest algorithm is the proximity method but this technique has the highest amount of errors. Methods to improve the accuracy of this system have been investigated but all solutions make the system much more complex. An advanced overlap-based proximity technique called the multiple LED estimation model (MLEM) is chosen as a motivation for further research in an attempt to improve the performance of proximity based IPS while keeping the complexity and cost of the system low [
66].
Although smart phones have been used as mobile receivers, holding a phone round the clock for the sole purpose of positioning might not be convenient. To the best of the author’s knowledge, wearable receivers for indoor positioning were first demonstrated in Reference [
66]. The system uses the proximity technique of LED-based positioning due to its simple algorithm. However, since the optical power from LEDs follows a Lambertian distribution, the performance of the IPS is observed to change when the receiver moves towards the edges of the LED beam, which are called the optical boundaries. As a mobile receiver moves from the region of one LED to another, it crosses optical boundaries where the optical power is drastically reduced (almost to zero).
There has not been much emphasis on optical boundaries affecting optical wireless communication (OWC) because the focus has been placed on meeting high data-rate demands [
67,
68,
69]. Conditions that provide sufficient optical power for OWC have been used for investigations to achieve higher data rates. In situations where the receiver is subject to harsh channel models, optical link budget analysis or advanced optical modulation techniques are used to design the optical system. Short distance investigations in Reference [
70,
71,
72] with stationary receivers have been used for indoor measurements, while for outdoor investigations, lasers or collimating lenses have been used [
73,
74]. Although collimated light beams have their advantages in long distance optical signal propagation, the dispersed light beams from off-the-shelf LEDs are a better choice for the low data rates needed in indoor positioning systems. On a horizontal plane, the region covered by the dispersed beam from an LED, called the optical footprint, does not have a well-defined boundary. Information on the LED footprint has always been communicated in terms of the angle at half power from various manufacturer datasheets. However, as is shown in this work, this information suffices for the use of such LEDs in optical wireless communication, but not in optical proximity-based positioning. This is because, in optical proximity positioning, the LED footprint is very important in determining the accuracy of the positioning. In addition, a moving person may bend toward or away from the LED transmitter. This bending that turns the receiver away from the transmitter is known as receiver tilt.
Optical proximity-based IPS determines the location of an object based on the signal information received [
16]. A mobile receiver can only receive this information if the receiver is within the LED footprint. The accuracy of positioning is dependent on the size of the footprint of the LED. Proximity-based indoor positioning systems have been shown to improve accuracy with the use of overlapping LED beams in a MLEM while keeping the receiver wearable [
19,
75]. By uniquely programming each LED, more identifiable regions are created as illustrated in
Figure 1a,b.
Figure 1a shows the conventional proximity LED IPS which only identifies a room [
16,
76].
Figure 1b shows the use of MLEM, with seven additional identifiable regions which are used to increase the positioning accuracy [
77]. However, this model has the possibility of LED data packet collisions in the overlap regions. By using packet duration multiplexing (PDM), the collision can be reduced [
75,
78]. However, Ref. [
12,
16] this assumes that an LED beam with a definite cut-off angle is used to define overlap conditions for an increase in positioning accuracy.In practice, this is not so. Moreover, when the receiver is tilted as illustrated in
Figure 1c, the optical boundaries change.
This paper investigates the performance of transmitted optical signals at the optical boundaries and its effect on LED-based positioning. This effect is quantified by measuring the positioning time, which is the time required to know a position. The effect of considering optical boundaries on positioning accuracy is also examined. Investigations of the effect of encoding design and receiver tilts on positioning near the optical boundaries are also carried out and suggestions are given for LED positioning protocol designs based on the results of these investigations.
The rest of the paper is organized as follows: in
Section 2, the system model showing the problem is described. The derivation of the threshold angle for defining optical boundaries is presented in
Section 3. Investigation of the effects of encoding protocol design, and the effects of overlap and receiver tilt in the optical boundaries on positioning are explained in
Section 4. The results and discussion are given in
Section 5. Finally, in
Section 6, the conclusions are presented.
2. System Model
The system model for investigating the optical boundaries is developed based on the transmitter front end as shown in
Figure 2.
Considering a typical room size of dimensions 5 m × 5 m × 3.5 m, where the receiver is on a horizontal plane at a distance of
h m from the transmitter. The power received at a location in the room is given by
, where
is the optical power transmitted from the LED, and
is the DC channel gain for directed line of sight (LOS) given in Reference [
34,
79,
80] as
where
A is the physical area of the PD,
d is the LOS distance between the transmitter and the receiver,
is the angle of irradiance with respect to the transmitter’s perpendicular axis, and
is the angle of incidence with respect to the receiver axis.
is the transmission of the optical filter and is assumed to be in unity for this work as this assumption does not affect generality [
81],
is the field of view of the receiver,
is the gain of the optical concentrator given as a function of the refractive index
n as
m is the order of the Lambertian source and is
where
is the half angle of the LED transmitter.
In this work, the received optical power as the mobile receiver moves along the horizontal plane is expressed in terms of the angle of irradiance at the receiver with respect to the transmitter’s perpendicular axis. On the basis of
Figure 2, the horizontal displacement
x can be evaluated from this figure as
.
Problem Description
In this section, the problems with indoor positioning at the boundaries of the LED footprints are identified. Given that the distance between the transmitter and receiver plane
h is 3 m, the plots of the normalized received optical power of two LEDs (OSRAM SFH 4554 and VISHAY TSFF 5510 called LED
and LED
) with the properties given in
Table 2 are shown in
Figure 3. The normalized received optical power is the ratio of the received optical power to the peak received optical power. Taking the region beyond which the optical power is not detectable as the optical boundary. Peak optical power is received at the
angle of incidence point for both LEDs. The received optical power starts to reduce, as the mobile receiver moves towards the half angle. At the half angle, the optical power is still sufficiently high to give accurate positioning. Therefore, this angle is not suitable in defining the optical boundary for indoor positioning. At the full angle, which is twice the half angle (
for LED
and
for LED
), the normalized optical power for LED
is
, while that for LED
is almost 0. These inconsistencies around the half- or full-angle-based boundaries of the LED cause a mobile receiver to perform inconsistently when it is in the boundary region. In addition, wearable mobile receivers are subject to tilting. The received optical power as the PD moves along the horizontal plane is presented in
Figure 4 for when the PD in
Figure 2 is tilted at
,
,
, and
to the right of LED
. The boundary for positioning is seen to vary with the angle of tilt for a receiver. Consequently, neither the half angle nor full angle is enough to determine the boundary of proximity-based IPS. In view of this, a threshold angle, based on the receiver design, which suffices in determining the boundaries for positioning is defined in this work.
6. Conclusions
The boundary of LED footprints plays a vital role in position estimation of proximity LED-based IPS. In this work, the boundary of an LED footprint is defined based on the properties of a mobile receiver. This technique can be used in RSS, AoA, and fingerprinting positioning systems that involve overlap of LED beams and use the PDM multiplexing technique. This work shows that by properly defining the optical boundary, unnecessary delays in positioning time can be prevented. It first establishes and validates a relationship between the BER and PDR of packets received at the receiver and then shows the effect of encoding protocol design on the BER. These relationships are used to show how signal quality deterioration due to undefined optical boundary affects the positioning time of the IPS. For a single LED transmitter, the defined optical boundary reduced the positioning delay by a factor of 13 for a 4-bit packet and by 230 for 12-bit packets. When overlap, which is used to improve positioning accuracy, is considered, the defined optical boundary reduces the positioning delay by a factor of 12 and 287 for 4-bit and 12-bit packets, respectively. The effect of a tilted receiver is also studied, and this work shows that for a tilt, the positioning time is improved by a factor of 22 and 1464 for 4-bit and 12-bit packets, respectively. In conclusion, full angle boundaries waste positioning time, and hence are not usable for LED based positioning. In terms of positioning accuracy, the use of a threshold angle maintains a systems positioning accuracy by changing the number of LEDs required. With 32 LEDs, a positioning error of mm is achieved, and the error reduces as the number of LEDs increases. This work has shown that a desired positioning accuracy can be achieved while using a receiver based threshold angle in the positioning system design to reduce positioning delay significantly. This facilitates the design of a simple lightweight wearable receiver for indoor positioning.
For future work, the effect of using other encoding schemes to design the positioning protocol will be determined.