Deployment of RSSBased Indoor Positioning Systems
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Abstract
Location estimation based on Received Signal Strength (RSS) is the prevalent method in indoor positioning. For such positioning systems, a massive collection of training samples is needed for their calibration. The accuracy of these methods is directly related to the placement of the reference points and the radio map used to compute the device location. Traditionally, deploying the reference points and building the radio map require human intervention and are extremely timeconsuming. In this paper we present an approach to reduce the manual calibration efforts needed to deploy an RSSbased localization system, both when using only one RF technology or when using a combination of RF technologies. It is an automatic approach both to build a radio map in a given workspace by means of a signal propagation model, and to assess the system calibration that best fits the required accuracy by using a multiobjective genetic algorithm.
Keywords
Positioning systems Propagation models Optimization solvers1 Introduction
The recent progress in portable mobile devices and the proliferation of pervasive applications made contextaware systems of growing interest. Contextawareness is related to the ability of a system to adapt content and presentation of provided services to the user context [1]. Such a context can be defined by means of several elements, but location represents the most considered one. So, in the last years research has spent a massive amount of efforts to devise locationsensing technologies and to support locationaware applications [2]. The key problem to provide locationawareness within the context of mobile computing is to compute the exact physical location of the user; such a problem is named positioning. If positioning in outdoor scenarios is no more an issue thanks to widely adopted solutions, when it comes to deal with indoor scenarios, things have not been settled down and positioning in such environments is still considered an open issue.
Indoor positioning systems can be classified in two distinct groups, which differ with respect to offered accuracy and required infrastructure costs. The first group contains those positioning systems that adopt dedicated infrastructures (e.g., based on ultrasound emissions or ultrawide band), whose only scope is to support positioning operations. On the other hand, the second group contains those positioning systems that adopt nondedicated technologies (e.g., Bluetooth, WiFi or RFID), whose primary function is not related to positioning, but they have been deployed for communication purposes. Using a dedicated infrastructure allows exposing lower accuracy, but also exhibiting strong costs since an exnovo infrastructure needs to be deployed. On the other hand, the spreading of wireless hotspots into many public and private places, as well as the new generation of mobile devices supporting several wireless technologies (e.g., the Nokia C700 ^{1} supports both WiFi and Bluetooth, or new Mobile RFID Reader DL710 ^{2} also provides wireless transfer functions by means of WiFi and Bluetooth) has fostered the development of indoor positioning systems based on standard wireless communication technologies [4]. In fact, both academia and industry have developed several indoor positioning systems based on nondedicated infrastructures [5], which mostly adopt Received Signal Strength (RSS) measures of Radio Frequency (RF) signals as a mean to compute the user location. However, such systems are affected by some serious issues on calibration efforts and achievable accuracy. Specifically, a study presented in [6] has proved that such limits in the accuracy offered by RSSbased positioning systems are intrinsic due to the use of standard RF technologies and is unlike to be further improved if more complex approaches and additional infrastructure are not introduced. To reduce the accuracy exhibited by RSSbased positioning solutions, hybrid approaches have been proposed [7]. They compute user location by combining location information obtained by Access Points (APs), namely reference points or sensors, of different wireless technologies.
The accuracy of an indoor positioning system is affected by how well the system has been configured, i.e., how the RM has been constructed and where reference points are placed. Since the deployment of these APs is not usually made by considering positioning demands, but considering the signal coverage of the overall workspace, the accuracy of the location system may be poor. Using more than one wireless technology allows improving accuracy, but, on the other hand, it further increases the complexity of the deployment and the calibrating of indoor locationsensing infrastructures. Specifically, reference points of different technologies have to be placed in order to maximize the accuracy of positioning as well as to minimize any interference phenomena that may arise among them. Moreover, the number of reference points per each technology has to be chosen in order to maximize the achievable accuracy and to reduce the infrastructure costs. To the best of our knowledge, we argue that such problem has not been fully investigated by the research community. A paper [8] has been recently published on such issues, but it still requires a massive usage of measurements and deals only with the RM construction, while it does not treat sensor placement. An interesting industrial product is Ekahau Real Time Location System (RTLS)^{3}, which is fully integrated with Ekahau Site Survey (ESS)^{4} to minimize deployment time and cost. However, it is tailored only on 802.11a/b/g/n WiFi networks, it does not consider the possibility of using more than one RF technology and it is not equipped with an automatic approach for choosing the best deployment.
 1.
limiting the human intervention when building the RM by modeling the signal propagation in the workspace, and reducing the need of a massive campaign to collect RSS samples;
 2.proposing a methodology to assist the system deployer in the choice of the best placement of the reference points. In particular, possible scenarios that we can consider are the following ones:

The system makes use of infrastructures deployed only for positioning demands. The issue is to estimate how many and what kind of wireless reference points are needed, and where they have to be placed in order to achieve an accuracy that fits the user requirements.

The adopted infrastructure consists of classical wireless APs already deployed in the workspace for communications purposes. The issue is yet to define how many additional, what kind of reference points are needed, and where to place them, so to improve system accuracy.

We have proposed to formulate the issue of deploying a positioning system as an optimization problem. Specifically, we adopt an approach based on a genetic algorithm in order to automatically select the best configuration (i.e., number, kind and locations of the reference points to place in the workspace) that fits the user/application requirements in terms of accuracy. In addition, we have used an analytical model of the signal propagation in order to reduce offline manual efforts needed to build an RM.
The rest of the paper is organized as follows: Section 2 provides a detailed survey of positioning approaches in indoor environments, examining the most adopted ones and the reasons of their success. Section 3 illustrates the issues of calibrating an RSSbased indoor positioning system. It is composed of two subsections: one is about the problems related to calibration, while the other one discusses the state of the art of solutions to the problems formulated in the first subsection. Section 4 presents our approach and how it can be used to built RMs and/or to select the optimal placement pattern. Section 5 speaks about how signal propagation is modeled so to reduce the need of onfield measurements, while Section 6 explains how placement pattern is selected in an automatic manner. Section 7 discusses experimental campaigns we have conducted to assess the effectiveness of our approach. Last, we conclude with Section 8, which contains final remarks on our approach and future work.
2 Indoor Positioning System

InfraRed (IR) Positioning [11]: Infrared technology is adopted to perform location sensing by using shortrange narrowtransmissionangle beam.

UltraSound (US) Positioning [12]: ultrasonic technology is used to measure the location of a tag carried by the user, similarly to the navigating system adopted by bats to move in the darkness. Specifically, a set of receivers are mounted on the ceiling of the indoor environment at known locations, and the user tag periodically broadcasts a short pulse of ultrasound signals.

Ultra Wide Band (UWB) [13]: it requires sending ultrashort pulses (i.e., with a bandwidth lower than 500 MHz).

Visionbased Positioning [14]: several cameras are used to analyze the scene and figure out where the user is located.

Magneticbased Positioning [15]: DC magnetic fields are adopted to locate an user device.
Survey of indoor positioning systems
Prototype  Technology  Accuracy 

Active Badge [3]  IR  n.a. 
Firefly [3]  IR  3.0 mm 
OPTOTRACK PROseries [3]  IR  0.1–0.5 mm 
IRIS_LPS [3]  IR  16 cm 
Active Bat [3]  US  3 cm 
Cricket [3]  US  10 cm 
Sonitor [3]  US  n.a. 
Ubisense [3]  UWB  15 cm 
RADAR [3]  WIFI  3–5 m 
Horus [4]  WIFI  2 m 
DIT [4]  WIFI  3 m 
PinPoint 3DiD [4]  WIFI  1–3 m 
Ekahau [4]  WiFi  1 m 
Robotbased [4]  WIFI  1.5 m 
MultiLoc [4]  WIFI  2.7 m 
TIX [4]  WIFI  5.4 m 
COMPAS [3]  WIFI  1.65 m 
Topaz [3]  BT  2–3 m 
[16]  BT  2.06 m 
[17]  BT  1.5 m 
BLPA  BT  3.76 m 
WhereNet [3]  RFID  2–3 m 
LANDMARC [4]  RFID  <2 m 
SpotOn [4]  RFID  n.a. 
SmartLOCUS [4]  US + RF  2–15 cm 
EIRIS [4]  IR + RF  <1 m 
[18]  RFID + WIFI  260–554 cm 
[19]  RFID + BT  0.25–2.25 m 
[20]  BT + WIFI  2–2.5 m 
A solution to improve the high accuracy of RFbased systems is to combine heterogeneous technologies for the location estimation (Hybrid Positioning) [7]. Such systems have shown a sensible improvement in the accuracy compared to using only one single RF technology (e.g., an accuracy of 22.5 meters with the combined use of BT and WiFi, 260554 centimeters with WiFi and RFID, and 0,252,25 meters with BT and RFID, as listed in Table 1). Using more than one RF technology is not only motivated by accuracy concerns. In fact, a workspace may not be uniformly covered by the RF signals of a given technology, so a positioning system is required to be opportunistic by using the specific technologies that are available in the area within which the user is moving.

Time of Arrival (ToA): time taken by a signal to reach its destination;

Time Difference of Arrival (TDoA): difference among reception instances of a signal at two, or more, spatially separated receiver devices;

Angle of Arrival (AoA): estimation of the direction from which a device receives a signal emitted by a given source;

Received Signal Strength (RSS): power of signals received by a given device.

Triangulation, or multilateration: the user location is computed from given measures of angles and sides of one or more triangles formed by the point where the user is located and two, or more, socalled anchors, i.e., sensors at known location;

Fingerprinting: the strength of the signals received from some reference points is sampled in some areas of the workspace with known location; such samples are called fingerprints. The user position is equal to the area with fingerprint closer to the signal strength measured in the location where the user is placed. This simple approach has been further evolved by more sophisticated ones. A concrete example is the so called Probabilistic Fingerprinting Approach, such as [22]: the location information of each fingerprint is summarized by Probability Density Functions, so to create a probability model of the workspace. Pattern Recognition techniques are used to infer the user location from the probability model by using measured RSS values;

Proximity: the user position is equal to the one of the nearest emitter with known location, and a nearness measure can be formulated in terms of \((i)\) signal time of arrival, i.e., if an emitter is closer to the user device than the other ones, its signals will be the first ones to be received; and \((ii)\) signal reachability, i.e., the user device will receive signals from a given emitter only if located nearby due to the short range of the adopted technology. In case more than one sensor is detected as the closest to the user device (e.g., it is reached by beacons of more than one sensor with the same ToA), then Triangulation can be used to resolve this situation.
Not all the possible combinations between technologies, methods and techniques are feasible in real indoor positioning systems. For a concrete example, due to the short range of the infrared radiation, IRbased systems mainly make use of proximity to estimate user location, or the distance between the ultrasound tags and receivers can be computed through the ToA of the pulse, from which user location is obtained by using the ToA information of at least three receivers by using simple geometrical rules that go back to the Pitagora theorem. With respect to RFbased systems, we have performed an analysis of the most adopted techniques. As shown in Fig. 2c, such positioning systems mostly use Fingerprinting as technique and RSS as method. For this reason, this paper is focused on them; however, any other technique related to RSS is also applicable.
3 Deployment and Configuration Concerns for Indoor RSSBased Positioning
As mentioned, the quality of a given positioning system is formulated in terms of accuracy, which indicates how close the estimated locations are to the real one, and is strongly affected by how well it has been configured, i.e., how adopted RM has been constructed, and where reference points have been placed. In addition, since more than one wireless technology may be used to improve accuracy, the complexity of deployment and calibration of indoor locationsensing infrastructures is further increased. Specifically, reference points of different technologies have to be placed so maximize the achievable accuracy as well as to minimize the infrastructure costs.
3.1 Problem Statement

RM Construction: given a set of reference points, characterized by the same wireless technology or not, we have to obtain a characterization of the signal propagation within the workspace so to extract RSS patterns at known locations and build an RM;

Optimal Placement Pattern: we have to decide which technologies to use, how many reference points per technology to deploy, and where such sensors need to be located so to achieve the optimal positioning accuracy.
Both problems strongly require a computeraided approach in order to reduce the effort of manually tuning the system by automatically generating solutions that best fit the user requirements in terms of accuracy by limiting the usage of onfield measurements. The following two paragraphs provide a detailed description of these two problems.
3.1.1 RM Construction
Traditional measurementsbased solutions to build RMs present a pivotal requirement that can be expressed by the following question: “is it possible to reduce to the minimum the number of needed measurements without compromising the accuracy of the obtained RM?”. In fact, conducting an heavy measurement campaign requires strong efforts in terms of time spent to perform it and money spent to have a person measuring RSS patterns. When tuning the system, a requirement is to keep lower the needed measurements so to minimize the quantity \(T_{C}\) in Eq. 2, and to restrain calibration efforts.
3.1.2 Placement Pattern Selection
 1.
one or more sensors may fail due to hardware malfunctioning, so other ones need to be placed in order to prevent a drop in accuracy;
 2.
one or more sensors have to be moved to new locations without compromising the overall accuracy of the positioning system;
 3.
one or more sensors need to be included in a proper manner so to improve the positioning accuracy.
Selection of the optimal placement pattern exhibits two key requirements. On one hand, it is important to achieve a reasonable radio coverage of the workspace. If there is no coverage in a particular area of the workspace, the system may not be able to compute the user position in there. On the other hand, the system tuned with the selected pattern has to expose an optimal positioning accuracy. Unfortunately, no general guidelines exist when configuring these systems. In fact, the goodness of a placement pattern highly depends on the specific workspace conditions, i.e., wall position and material, space topography, noise sources, number and disposition of the people that attend the place.
 1.
arrange the sensors according to the given pattern;
 2.
measure wireless coverage and accuracy in a set of given points within the workspace;
 3.
assign to the placement pattern a grade that expresses its goodness (which reflects the accuracy of the positioning system deployed by using the given placement pattern).
3.2 Available Solutions for Deploying and Tuning Indoor RSSBased Positioning Systems
In this section, we focus on presenting the state of the art on approaches to deal with the previous problems.
3.2.1 Approaches for RM Construction
Since \(T_{M}\) in the Eq. 2 only depends on the adopted technologies, and \(\epsilon\) on the size of the working area and \(N_{A}\), the traditional ways to lower the calibration efforts are (1) reducing the number of the areas in which the workspace is partitioned (reduction of \(N_{A}\)), and/or (2) spending less time to collect RSS samples at each area (reduction of \(N_{S}\)) [23]. However, such solutions may bring to RMs of lower quality, i.e., it does not fully characterize the features of signal propagation within the workspace, with the consequence to compromise the quality of the overall positioning system [8].
 1.
They are tailored on a given RF technology and do not consider the case where more than one RF technology is used within the positioning system;
 2.
Ray Tracing is an accurate method for indoor signal strength estimation; however, its overhead is quite high with respect to other estimation methods [26].
Since we consider RM construction as a building block of the overall approach to efficient calibration of a given positioning system, we seek a simple and fast method for modeling signal propagation even if this choice slightly compromises the achievable accuracy.
3.2.2 Approaches for Placement Pattern Selection
As formulated in Eq. 3, the calibration time, i.e., \(T_{D}\), is function of the number of solutions to be evaluated, i.e., \(\nu\), and the time to construct an RM for a given placement pattern, i.e., \(T_{C}\). The possible ways to reduce the calibration time is, therefore, to reduce \(\nu\) and/or \(T_{C}\).
A first solution, such as Ekahau Site Survey, consists of introducing a modelbased approach to construct the RM and minimizing the need of an onfield measurement campaign. Despite being successful to address the issue of deploying APs for communication concerns, such a solution presents three drawbacks if we want to use it for dealing with the placement pattern selection: \((i)\) arrangements are made depending operator judgement and not via an automatic approach (i.e., the operator has to select a certain number of possible deployments and evaluate it with the tool), and \((ii)\) only signal coverage is considered, which is not the only factor that negatively affects positioning accuracy, and \((iii)\) only WiFi is considered.

Planning Process for Cellular Networks [27], which consists of two subproblems: Antenna Positioning Problem (APP), i.e., deciding the site location for the antennas, number or type of antennas per each site, and other antenna parameters; and Frequency Assignment Problem, i.e., selecting which available frequencies to assign to the antennas in the network.

Design Wireless adhoc Networks in Indoor Environments [28], whose main objective is to find a configuration of APs so to assure high coverage, low interference level or minimum available throughput.

Coverage Problems in Wireless Sensor Networks [29], which aims at deploying sensors in a way that they are able to observe a certain physical space in an appropriate manner, i.e., at least one sensor covers each location of the physical space of interest. Moreover, deployment is performed by considering additional requirements rather than only coverage, e.g., sensor sensing range may be dynamically adjusted so to conserve energy resources without compromising the sensing coverage objective.
Such problems have been extensively studied in the last decades by formulating them in terms of optimization problems and resolving them by means of highly effective optimization algorithms, such as exact solving approaches or heuristic ones. The fundamental question we have asked to ourselves is “Could we apply approaches contained in such a rich literature to address the calibration issues in RSSbased indoor positioning systems?”. The only answer we came up is “No". In fact, as proved by [30], a placement pattern chosen for only communication purposes (i.e., by maximizing signal coverage or provided QoS), without taking care of positioning concerns, can not be optimal for positioning systems. In fact, such paper shows that even the best placement for communication purposes exhibited a non appropriate accuracy, e.g., around 8 meters, which is completely not suitable for indoor positioning. Our approach to deal with calibration issues in RSSbased indoor positioning systems is to drawn on the experience of planning approaches for wireless and cellular networks and to extend them by including positioning concerns in the formulation of the overall optimization problem and by inserting positioning modelbased emulation in the adopted solving approach.
A last solution is to do not perform the selection process, and to select sensor deployment according to specific guidelines. Literature on USbased positioning contains some papers, such as [31], which provide guidelines to where locate sensors, but they are not applicable for indoor RFbased systems, due to the strong differences in terms of propagation features between RF and UD signals. Moreover, an automatic approach to deploy USbased sensors is also described in [32]. Despite the fact of being tailored on USbased positioning systems and considering TOA technique instead of Fingerprinting, this approach does not fit to our case since it aims to optimize only signal coverage, which, as we have previously said, is not a winning choice for RSSbased indoor positioning systems.
4 An Automated Strategy for Deploying RSSBased Positioning Systems
The rest of this section is structured in two subsections. Section 4.1 describes how the proposed approach is used to build RMs without wasting time to perform any heavy measurement campaigns. Whereas, Section 4.2 illustrates how our approach is used to optimally place reference points in the workspace without requiring an inefficient traditional way of guessing the best deployment by trial and error.
4.1 Building Radio Maps by Reducing Onfield Measurements
As illustrated in Fig. 4, RM Builder is composed of two elements: an RSS Estimator, which returns a characterization of RSS patterns within the workspace given a certain placement pattern, and RM Synthesizer, which constructs an RM starting from the RSS patterns provided as input. In the traditional approaches, the RSS Estimator consists of massive onfield measurement campaigns, while the RM Synthesizer implements the adopted positioning technique, such as Fingerprinting, with one or more technologies. To avoid the recourse to timeconsuming measurements, we propose to implement in the RSS Estimator a model of signal propagation features in the workspace.
 Step1: the user provides a description of the workspace, in terms of the following factors:

space topography, i.e., shape and size of the workspace, and location and type of walls and doors;

deployment, i.e., number and position of the reference points;

tessellation, i.e., size of the areas in which the workspace is partitioned.


Step2: the graphical characterization of the workspace is transformed into a mathematical matrix, which can be used to resolve an analytical signal propagation model.
 Step3: the matrix is provided as input of the propagation model, so to find as output the estimated RSS measures in each area of the workspace. The model is resolved as follows:

Step3.1: the matrix \(D\) is computed, where \(d(i,\,j)\) is the distance of the \(i\)th point of the workspace from the \(j\)th sensor on the direct path;

Step3.2: the matrix \(A\) is evaluated, where \(a(i,\,j)\) is the attenuation of the signal due to the met obstacles, i.e., the second and third terms of the equation in Fig. 7;

Step3.3: the matrix \(PL\) is estimated, where \(pl(i,\,j)\) is obtained using the equation in Fig. 7 considering the distance \(d(i,\,j)\) and the attenuation \(a(i,\,j)\);

Step3.4: the matrix RSS is calculated, where \(d(i,\,j)\) is obtained by subtract to the output gain of the \(j\)th sensor the value of \(pl(i,\,j).\)


Step4: the RM is constructed from the RSS measures obtained from the model resolution.
4.2 Optimal Placement of the Reference Sensors
In Fig. 4, the key element of Placement Path Finder is the Pattern Selection Solver, which searches within the set of all the possible deployment configurations looking for the optimal one. The issue is to find the suitable approach for such a duty.
As said before, the optimal configuration is the one that exhibits the best accuracy. It is quite obvious that, in general, increasing the number of sensors raises the accuracy. However, it also leads to an increase in the costs: having a lot of sensors causes higher static costs, and also implies a strong growth of dynamic costs. Specifically, we witness to a rise of the economic investment needed to acquire and deploy the positioning infrastructure (i.e., static costs), and the time needed to estimate the user location (i.e., dynamic costs). Static costs are paid only once when the system is built, so they are sustainable. On the contrary, dynamic costs strongly affect the efficiency of the positioning system since they are paid every time the system is used, and need to be properly managed. In particular, with respect to dynamic costs, there is an increase of either the time to collect RSS values from all the reference points (i.e., with respect to Eq. 2, having a large number of sensors increases \(T_{M}\)), either the time to query the RM in order to compute the user location (i.e., the fingerprint size grows when the number of sensors increases, so the size of RM and the time to perform a matching between measured fingerprint and stored fingerprint is higher). Even if the first increase is minor due to the low time to measure an RSS, the last one can not be neglected since the positioning system has to be loaded by mobile devices characterized by limited resources (both for processing and storing data). For this reason, the number of sensors can not exceed a certain threshold, otherwise the system cannot be properly used.
So, the number of sensors has to be chosen as small as possible in order to limit such drawbacks, but without compromising the accuracy provided by the system. Therefore, we can formulate the issue of deploying the reference points as a problem where accuracy has to be maximized while sensor number has to be minimized, under the condition of complete wireless coverage of the workspace (if there is no coverage in a particular area of the workspace, the system is not able to compute position in such an area). Such kind of problems are called MultiObjective Optimization Problems (MOOPs), since they have the scope of simultaneously optimizing two or more conflicting objectives, subject to certain constraints.
 Step1: the user provides a graphical representation of the workspace, which is, then, converted in a matrix, as previously mentioned in Step1 and Step2 of the approach to build the RM. In addition, the user uses the Workspace Characterizer as follows:

indicating the wireless technologies that will be adopted within the workspace;

placing within the workspace representation sensors that cannot be moved at will (e.g., sensors alreadydeployed for communication concerns and used also for positioning purposes);

indicating the maximum number of sensors that can be deployed per each technology;

setting proper values for the inputs of the solver.


Step2: the inputs of the user gathered in the previous step is provided to the solver, implemented in the Placement Pattern Finder, which returns a set of suboptimal solutions;

Step3: the returned solutions are presented at the user, which decides the one to use. In fact, welldefined MOOPs do not have a single solution that simultaneously optimizes each objective, but a set of solutions for which each objective has been optimized to the extent that if it is further optimized, then the other objective(s) will suffer as a result.
5 Signal Propagation Model
 1.
PL in free space depends on the logarithm of the distance, namely \(d\), between transmitter and receiver;
 2.
attenuation to pass through all the obstacles met along OLOS (where \(P_{i}\) is the number of obstacles of \(i\)th type found on the OLOS, and \(AF_{i}\) is the attenuation factor associated to the \(i\)th type of obstacle);
 3.
attenuation, namely \(FAF_{n}\), caused if the source and the destination are not placed on the same floor, which is function of the number of crossed floors, namely n;
 4.
attenuation, namely \(CoA_{i,j}\), produced by passive coexistence of two RF technologies, respectively indicated with indexes i and j, that use the same transmission frequency, namely \(\lambda\), and compete on the access to the channel, e.g., using WiFi and Bluetooth in the same workspace results in a potential for reciprocal interference [37].
Typical attenuation factors for obstacles taken from [38]
Obstacle type  Loss (dB) 

Moveable walls  1.4 
Doors  2.0 
Windows  2.0 
Fixed walls  3.0 
Metal partitions  5.0 
Exterior walls  10.0 
Basement walls  20.0 
6 MOOP Solver
In literature, there are several approaches to be used for solving MOOPs [40], and the most widelyadopted ones are the evolutionary algorithms [41] since they have been demonstrated to be general, robust and fast search mechanisms [42]. We have chosen a particular evolutionary algorithm known as MultiObjective Genetic Algorithm (MOGA) [43], since it is simple to implement and efficient (at each iteration of the algorithm, more than one suboptimal solution are generated and evaluated, so to reduce the convergence time), but any other evolutionary algorithm can be used.
MOGA, as any evolutionary optimization algorithm, works on two key elements: Chromosome, i.e., a representation of a certain solution to the given optimization problem, and Population, i.e., a collection of chromosomes that are analyzed at a given iteration of the algorithm. So, the description of the MOGA execution has to provide answers to two crucial questions: “How do solutions are represented by means of chromosomes?" and “How is the solution space explored by means of evolving from one population to another one?".
 1.
The sum of the binary codes of all the strings does not have to exceed the maximum number of sensors indicated by the user;
 2.It is impossible to find two permutation vectors that shares even a single number in its first positions. e.g., let us consider two permutation vectors, namely \(\bar{\alpha}\) and \(\bar{\beta}\), whose relative binary codes are respectively equal to \(n_{\alpha}\) and \(n_{\beta}\), the following condition is never satisfied:$$ \exists i \in \{0, \ldots , n_{\alpha}\} \wedge \exists j \in \{0, \ldots , n_{\beta}\} : \alpha_{i} \in \bar{\alpha}, \beta_{i} \in \bar{\beta} \Rightarrow \alpha_{i} = \beta_{j} $$(4)

Step1: chromosomes for the initial population are randomly calculated, based on user inputs;

Step2: each chromosomes within the current population is evaluated by computing the relative RM through the approach presented in Sect. 5 and a quality score is assigned by estimating the accuracy of the positioning system with the computed RM and the relative signal coverage;

Step3: the chromosomes that present greatest quality score and do not exhibit a positive value of coverage score is stored in an archive. If some of the chromosomes that are already stored in the archive exhibit worse quality scores than the new chromosomes, they are taken away from the archive.

Step4: if the termination condition of the algorithm is verified, the content of the archive is returned to the user. Otherwise, the algorithm proceeds by executing the next step.
 Step5: at this point a new population needs to be generated, so to explore other possible solutions to the problem. Using the chromosomes in the current population, the new ones are determinated using the specific operators of biological evolution:
 Mating new chromosomes are made by recombining the old ones. Two different techniques are applied between strings of the same RF technology for two mating chromosomes:
 Onepoint crossover for the binary part: A single crossover point, namely \(\pi\), is selected. All binary digits beyond that point in either chromosomes are swapped between the two parent chromosomes. The resulting chromosomes are the children:$$ \begin{array}{ccc} \begin{array}{c} 0101101 \\ 0011001 \end{array} &\xrightarrow{\pi = 4} & \begin{array}{c} 0101001 \\ 0011101 \end{array} \end{array} $$(5)
 OX crossover for the permutation part: Two crossover points, namely \(\pi_{1}\) and \(\pi_{2}\), are randomly selected. Everything between the two points is swapped between the parent chromosomes, rendering two child chromosomes:$$ \begin{array}{ccc} \begin{array}{c} 3154679 \\ 2019438 \end{array} & \xrightarrow{\pi_{1} = 4, \pi_{2} = 6} & \begin{array}{c} 2014638 \\ 3159479 \end{array} \end{array} $$(6)


 Mutation a new chromosome is made by arbitrarily changing one value in the old one. Also in this case there are two different techniques depending if we have to mutate the binary or the permutation part of a string:
 Bitflip for the binary part: a point of mutation, namely \(\mu\), is randomly selected, and the binary digit in that place is changed to the opposite value, according to a given probability:$$ \begin{array}{ccc} 0101101 &\xrightarrow{\mu = 4} &0100101 \end{array} $$(7)
 Reciprocal exchange for the permutation part: two points of mutation, namely \(\mu_{1}\) and \(\mu_{2}\), are randomly selected. The order of everything between the two points is inverted, according to a given probability:$$ \begin{array}{ccc} 3154679 &\xrightarrow{\mu_{1} = 4,\; \mu_{2} = 6} &3156479 \end{array} $$(8)

Given the new chromosomes, the algorithm executes the Step2, by assessing their quality in terms of accuracy and coverage.
7 Experimental Evaluations
Based on the methodology introduced in the previous section, we have implemented a Javabased prototype^{5} that provides to a user the abilities of \((i)\) describing its workspace, \((ii)\) obtaining a RM for a given sensor placement pattern, and \((iii)\) computing a set of optimal placement patterns. We used this prototype to evaluate the quality of the proposed approach.
7.1 Signal Strength Model Evaluation
The scope of this subsection is to assess the goodness of the propagation model used within our calibration approach. For this aim, we have performed a measurement campaign by using one AP within the environment of the new CINI laboratory. We have placed it on one of the external walls and made measurements by augmenting the distance between the measuring device and the AP, by moving along the arrow depicted in Fig. 11a. We have repeated each measurement 20 times and made it varying the adopted RF technology. As illustrated in Fig. 11b, we registered an error between the estimated RSS values, namely \(RSS_{mod}\), and the measured ones, namely \(RSS_{meas}\), and it is expected. Specifically, the average error (i.e., the average of the difference between \(RSS_{mod}\) and \(RSS_{meas}\)) is respectively equal to 9,66 for WiFi, 0,47 for Bluetooth and 11,5 for RFID. The next two subsection will investigate how this imperfect modeling of the signal propagation influences RM construction and placement selection.
7.2 RM Construction Evaluation
As shown in figure, the quality provided by our approach is comparable with the best one that empirically builds a RM (i.e., HMMbased curve) considering about 35 training samples at each location and a sampling ratio equal to \(1/2\). Therefore, in order to get the same quality a measurementbased calibration would require about one hour and 45 minutes, while our method spend less than one minute. As shown in box D, when more than one technology is adopted in the workspace, the situation is exacerbated and more samples are required, increasing the time needed for a measurementbased calibration, while we have not witnessed a remarkable performance aggravation when using our modelbased approach.
7.3 Pattern Selection Evaluation
As mentioned in Paragraph 2, there are no general guidelines or standard deployment patterns that we can use for evaluating our selection approach. We have decided to consider two placements of reference points (sensor patterns) belonging to three different technologies (i.e., Bluetooth (BT), WiFi and RFID), which are illustrated in Fig. 12a, and drawn from [44]: Sawtooth Partitioning, which places the sensors according to a sawtooth configuration, and Equal Partitioning, which decomposes the overall environment into four portions and puts a sensor of a technology at the 2.4 frequency (e.g., Bluetooth or WiFi) in the center of each partition and place an RFID sensor at the external walls. These two placements are the ones that someone would come up with if signal coverage and interference avoidance would be the only matters, without making use of any particular automated planning tool. Among the solutions generated by the tool, the placement pattern illustrated in Fig. 12a and indicated as “Approach Placement" has been chosen. Such a placement pattern has been compared with the previous two manual placement patterns. Specifically, we have deployed sensors according to one of the three patterns, and we have considered a fingerprinting RSSbased positioning system that estimates user location by matching the measured RSS and the one stored in the RM. Therefore, we have performed the experiments by randomly selecting several locations within the workspace (whose number is around 50), and we have used the positioning system around 20 times per each location so to obtain the user location in terms of identifier of one of the areas that partitions the workspace. We have defined as accuracy the distance between the real area where the user is located and the area estimated by the positioning system. Then, we have computed the average of such distances so to have a measure of the accuracy of the system. As depicted in the box b of Fig. 12, the placement pattern computed by our approach overwhelms the other two patterns since it presents better values for accuracy.
8 Conclusions and Future Work
Configuring hybrid RSSbased positioning systems is costly and time consuming, because an extensive measurement campaign is needed, and no general guidelines are available to choose which technology to use, how many sensors to deploy and where to locate them. Here, we have described a novel automatic tuning approach for positioning systems that provides twofold innovative contributions to address the issue of calibrating such positioning systems without requiring any heavy measurements campaign, but offering a rigorous method for the placement pattern selection. On one hand, we have proposed to build RM via a simulation model of the signal propagation, in order to compute the RSS patterns without an heavy onfield measurement campaign. Moreover, we have also described an approach to determine the better reference points configuration by formulating such issue as a multiobjective problem, and solving it by means of a multiobjective genetic algorithm. Experimental results presented in this paper proved that this approach is able to construct highquality RM without requiring massive onfield measurements, and to select the optimal placement pattern in terms of lower accuracy offered by the positioning system deployed with this given placement.

In our work we have assumed that all the reference points used the same value for the transmission power. However, adjusting power allocation is an important solution to further optimize accuracy [45]. We have planned to extend our approach so to include the possibility of selecting the optimal power allocation.

We want to include more than one propagation model, so to investigate how a certain model affect the quality of the built RM, and the effectiveness of the selection process carried out by our tool. In addition, we want to study other MOGA solver, so to highlight the effects that the adopted solver has on the overall selection process.

The literature is full of more complex fingerprinting techniques rather than the simple matching between vectors of RSS values. We want to extend our approach for being able to completely describe such techniques and use them to emulate location estimation.

We intend to investigate how a modelbased RM can be used to augment a measurementbased RM, so to reduce amount of required calibration data to a fraction without compromising accuracy.
Footnotes
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