Indoor localization with smartphone using BLE ibeacon

VIETNAM NATIONAL UNIVERSITYUNIVERSITY OF ENGINEERING AND TECHNOLOGYDuong Ngoc Son INDOOR LOCALIZATION WITH SMARTPHONE USING BLE IBEACON MASTER THESIS IN ELECTRONICS AND TELECOMMUNICATION

VIETNAM NATIONAL UNIVERSITYUNIVERSITY OF ENGINEERING AND TECHNOLOGY

Duong Ngoc Son

INDOOR LOCALIZATION WITH SMARTPHONE

USING BLE IBEACON

MASTER THESIS IN ELECTRONICS AND TELECOMMUNICATIONS

SUPERVISOR : PHD DINH THI THAI MAI

HANOI - 2020

Publication thesis option

This thesis would consist of the following six articles:

Paper 1: Thai-Mai Thi Dinh, Ngoc-Son Duong, Kumbesan Sandrasegaran, based Indoor Positioning Using BLE iBeacon and Reliable Lightweight Fingerprint Map”,IEEE Sensors Journal, 2020 In press https://doi.org/10.1109/JSEN.2020.2989411

“Smartphone-Paper 2: Ngoc-Son Duong, Thai-Mai Dinh, “Develop a true real-time iBeacon-basedindoor positioning system using smartphone”, to be submitted to IEEE Transactions onInstrumentation and Measurement

Paper 3: Ngoc-Son Duong, Thai-Mai Dinh, “Indoor Localization with lightweight RSSFingerprint using BLE iBeacon on iOS platform”, in 19th International Symposium onCommunications and Information Technologies (ISCIT), Vietnam, Sept 2019

Paper 4: Thai-Mai Dinh, and Ngoc-Son Duong “Smartphone Indoor Positioning tem based on BLE iBeacon and Reliable region-based position correction algorithm”, inInternational Conference on Advanced Technologies for Communications (ATC), Viet-nam, Oct 2019

Sys-Paper 5: Ngoc-Son Duong, Tuan-Anh Trinh Vu, and Thai-Mai Dinh, “Bluetooth LowEnergy Based Indoor Positioning on iOS Platform”, in IEEE 12th International Sym-posium on Embedded Multicore/Many-core Systems-on-Chip (MCSoC), Vietnam, Dec.2018

Paper 6: Ngoc-Son Duong, and Thai-Mai Dinh, “Smartphone Indoor Positioning Based

on Enhanced BLE Beacon Multi-lateration”, TELKOMNIKA, submitted, in revision

“I hereby declare that the work contained in this thesis is of my own and has not beenpreviously submitted for a degree or diploma at this or any other higher education institu-tion To the best of my knowledge and belief, the thesis contains no materials previouslypublished or written by another person except where due reference or acknowledgement ismade.”

Hanoi, 2020

Student

This thesis would never have been done without the support of many colleagues, friends,and my family

Firstly, I would like to thank my advisor, PhD Dinh Thi Thai Mai, who has given

me all the support and guidance I needed as a master student I am very grateful to havehad her trust in my ability, and I have often benefited from her insight and advice duringthe time I conducted my thesis work

I am grateful to other teachers and friends in Communication Systems Laboratory, ulty of Electronics and Telecommunications, University of Engineering and Technology

Fac-I would like to also acknowledge my family and my beloved ones for cheering and porting me during my six years at the university Your sentimental values mean a lot tome

sup-This work has been supported by Vietnam National University, Hanoi (VNU), underProject No QG.19.25

as low energy consumption, wide-coverage, easy deployment, and potential high accuracy.

To achieve high location accuracy, this thesis proposes a real-time indoor positioningsystem which combines iBeacon technology and smartphone sensors Two main tech-niques are used for positioning, i.e, Pedestrian Dead Reckoning (PDR) and Range-basedusing Least Square Estimation (LSE) These two methods help each other create a highlyaccurate system Firstly, we offer a solution for Received-Signal-Strength-based (RSS-based) continuous positioning problem by investigating heterogeneity in RSS Secondly,

we propose a method of improving accuracy for LSE We consider PDR-based positionand improved LSE-based position both have a Gaussian uncertainty that comes from ini-tial position plus drifting and RSS-to-distance conversion, respectively Then, two kinds

of Normal distribution will be fused by the Kalman filter to produce more precise tions The method is intended to design a real-time system for locating moving target.The results show our proposed solution is not only highly accurate but also feasible inactual deployment

1.1 Motivation 1

1.2 Approach 3

1.3 Contribution 3

1.4 Outline 5

2 Background 6 2.1 Positioning Technology 6

2.1.1 Bluetooth Low Energy 6

2.1.2 Inertial sensor 7

2.2 RSSI-based Positioning Techniques 10

2.2.1 Fingerprinting Method 10

2.2.2 Range-based Method (Lateral) 11

2.3 Bayesian Filtering - From Kalman Filters to Particle Filters 12

2.3.1 General Bayes Filtering problem 12

2.3.2 Kalman Filter 13

2.3.3 Particle Filter 14

3 Proposed System 18 3.1 System overview and architecture 18

3.2 PDR subsystem 19

3.2.1 Embedded Sensor Block 19

3.2.2 Sensor–based positioning method 19

3.2.3 Step Length Estimation 19

3.3 LSE subsystem 20

3.3.1 RSS Uncertainty Analysis 20

3.3.2 RSSI-to-Distance Conversion 25

3.3.3 Location Estimation 26

3.4 Kalman Fusion 27

4 Evaluation 30 4.1 Experiment Setup 30

4.1.1 Device and Software 30

4.1.2 Experiment Setting 30

4.2 Results and Discussion 30

4.2.1 Ground Truth and Accuracy Comparisons 304.2.2 Performance evaluation under impact of different velocity 324.2.3 Performance evaluation under impact of different beacon density 324.2.4 Compare to Fingerprinting 34

5.1 Conclusion 365.2 Future Work 36

Abbreviations

List of Figures

1.1 Comparison of different signals for smartphone-based indoor localization

[18] 1

2.1 Channel configuration of BLE 6

2.2 BLE iBeacon protocol architecture 8

2.3 INS axis system on iPhone (source: Apple) 8

2.4 Accelerometer measures changes in velocity along the x, y, and z axes 9

2.5 Gyrocopter measure rotation rate in the x, y, and z axes 9

2.6 Fingerprint Concept 10

2.7 Least square position algorithm of three beacons 11

2.8 Comparison of raw RSS and KF-filtered RSS 15

2.9 The estimated position using Kalman filter 15

2.10 Illustration of importance sampling method 15

3.1 System overview and architecture 18

3.2 Change of acceleration as the user moves 20

3.3 RSS uncertainty at different distances Legend: The bar charts represent observed data histograms at at different distances Each environmental case at each distance includes 400 samples Blue bar, light orange bar, purple bar, green bar denote LOS, 1 wall blocked, 1 column blocked, 2 wall blocked situation, respectively; The dashed lines represent fitted line from data specified by Normal distribution; The solid lines represent the fused distribution of possible cases 23

3.4 Linear approximations of distance path loss model 25

3.5 Visual view of our proposed method 27

3.6 Fusion of LSE-based position and PDR-based position 28

4.1 The position of the iBeacons and true path on the experiment area 31

4.2 Ground truth and accuracy comparisons a) Distribution of corrective points b) Trajectories of true path, PDR path and proposed method path c) Cumulative localization error distributions of our proposed method 32

4.3 Cumulative localization error distributions in 2 cases: running and walking 33 4.4 Average localization error given different number of iBeacon 33

4.5 Comparison between different positioning methods a) Box-and-whisker plot of localization error for specific cases b) Trade-off between positioning accuracy and efforts of calibration time 34

List of Tables

1.1 Comparison between Wi-Fi or BLE Beacons for indoor location 2

1.2 Pros and cons of the positioning methods 4

2.1 Classic Bluetooth vesus BLE 7

3.1 Mean RSS and its standard deviation at different distances 24

3.2 Distance calculation model for each RSSI range 26

Figure 1.1: Comparison of different signals for smartphone-based indoor localization [18].

Since its inception, Global Positioning System (GPS) technology [35] has really changedthe way people pinpoint the location and find their path on the planet The ideal conditionfor GPS to achieve the highest accuracy is the Line-of-Sight (LOS) or few obstructions.However, the rapid development of the construction architecture somewhat hinders thereception of GPS signals, especially in the basement or deep hall Position errors in thesecases can be up to hundreds of meters Therefore, Indoor Positioning System (IPS) hasbeen studied to be able to locate objects or people in the indoor environment Basically,the concept of Indoor Positioning System inherits the characteristics of the Global Posi-tioning System Receivers gathering information from the transmitter to get the location.The thing makes IPS different from GPS is the transmitter technology Instead of usingsatellites, IPS utilizes other technologies based on radio frequency (RF-based) such as Wi-

fi [3], Radio Frequency Identification (RFID) [4], Ultra-wideband (UWB) [5], FM source[16] or non-RF-based such as magnetic field (a.k.a geomagnetism or earth magnetic field)[36], photo-based (camera-based) [37], IMU-based [16] The criteria for a proper IPS arehigh accuracy, low cost, high energy efficiency, high stability, and platform independence

In order to have a clear view, Suining et al [18] make a comparison of some technologies

in terms of two most impact aspects, i.e, accuracy and cost in deployment, as shown inFig 1.1 This figure shows geomagnetism seems to be suitable for IPS but note thatthe magnetic field is time-varying and its change not following any law, this leads to notfeasible in deployment Other possible solutions lie in the center of the figure, such asWi-fi and BLE A detailed comparison between Wi-fi and BLE is shown in Tab 1.1

Table 1.1: Comparison between Wi-Fi or BLE Beacons for indoor location

Compatible with iPhones? Yes

Yes, but iOS doesn’t supportranging for Wi-Fi

Consequently, positioning

is difficult and inaccurate

Is maintenance required? Battery replacement

process after 5 years

Calibration process requiredand regular upkeep

Out of these, BLE seems to be the best solution We can make it possible to performindoor positioning through received signal strength (RSS) There are two kinds of RSSI-based technique: Fingerprinting [42] and Lateral method (range-based method [45]) Inthe localization problem, Lateral method uses estimated distance from the path-loss model

to estimate user’s position Meanwhile, Fingerprinting relies on map survey step to build

a RSS database of an interested area Then, position decision is made based on onlinesignals and offline database using a matching algorithm

Due to the instability of the BLE signal, indoor localization using only BLE beaconresult in large errors Thus, many studies have combined BLE beacon with other technolo-gies and techniques to yield higher accuracy In [6], sensors embedded in smartphones areexploited to combine with BLE beacons to determine the location of the object In thiswork, the Pedestrian Dead Reckoning (PDR) is applied for localization using smartphonesensors and extended Kalman filter is chosen as a fusion algorithm The user’s position isupdated when a user moves into a three meters reliable calibration range Exploiting Wi-

Fi access points, Zou et al [7] introduced an indoor navigation and tracking system usingbuilt-in smartphone sensors In this work, the authors use particle filter-based fusion,iBeacon measurements are only used to compute the particle’s weight when the user is in

a poor Wi-Fi coverage area Otherwise, if the user is in a good Wi-Fi coverage area, theWi-Fi-based positions are used to compute the weight instead Along with the particlefilter, a group of authors in [8] introduced a map constraint-based method to improvethis filter In prediction phase, they leveraged MEMS sensors in smartphone to computethe new position of each particle In observation phase, they used the position obtainedfrom RSSI Least Squares - based position estimation method to update the weight of theparticle The key of this research is map constraints According to their arguments, onthe map, there are unreachable positions such as the wall, columns, etc Therefore, theparticles, which represent for user position, are absurd if they reside in those areas andthen they must be removed The same thing happens with the route The weight of aparticle is only updated when it is in an accessible area and on an accessible route The

work in [9] is also a study on iBeacon and IMU-based indoor positioning systems usingFingerprinting In the map matching algorithm, instead of applying conventional kNN,they applied Bayesian estimation as a probability method to encircle reference points thatlikely to be the exact position Recent studies tend to apply machine learning into indoorpositioning systems [10] is one of the most detailed studies on the use of machine learningalgorithms Most machine learning and deep learning algorithms are reviewed By usingmachine learning in combination with XBee, Wi-Fi, BLE technology and device’s sensor,research shows that the system can achieve high accuracy.

In some senses, all of them provide high-precision systems but they are far removedfrom reality Some of them get high complexity and does not seem to be appropriatefor finite resources such as a phone [6, 10] The others require a lot of time to collectdata for reference points (high-resolution fingerprint) [10, 29] In general, there are threelimitations of previous works, i.e: i, can not provide real-time update ability ii, onlyapply for static positioning iii, not practical in actual implementation Therefore, thekey motivation of this work is originated from the problem associated with feasible real-time positioning solution for moving target with meter-level accuracy requirement

1.2 Approach

This work chooses BLE iBeacon – smartphone sensors fusion as the main approach forindoor positioning as well For BLE iBeacon, we can use RSS to locate user positionvia range-based method or Fingerprinting-based method For smartphone itself, we canalso exploit embedded IMU to compute the phone displacement We make comparison ofthree techniques in Tab 1.2, where we can see both side - pros and cons of them Since

we wish to build a system with highly position update rate, PDR is the best solution.With known initial position, PDR provides quite high positioning accuracy However, inlong distance movement, PDR’s trajectory can be drift over time due to sensor noise sothat it leads to a high cumulative error Fortunately, this drawback can be compensated

by using BLE signal So, it is reasonable to have a combination of PDR and based method or PDR and Fingerprinting For Fingerprinting, it is a sort of supervisedmachine learning method include Offline phase (corresponding to training phase, labelingphase in ML) and Online phase (corresponding to testing phase in ML) That meanscomputational ability might perform inefficiently in limited resource of mobile phone Inaddition, Fingerprinting need a large of data base for ensuring high accuracy Therefore,

range-it would be unreasonable to save all data of radio map in a phone Consequently, resulting

in delay if data must send via network or directly handled in mobile phone Of note that

it is not about what we expect at our system For real-time requirement, we wish all

of data about the map and computational task must reside in the user’s smartphone.For this aspect, range-based method seems to be appropriate rather than Fingerprinting.Comparing to Fingerprinting, all of range-based method need is coordinates of the beacon.Since we only need to survey for distance model, time for data collection task of range-based method is much shorter than Fingerprinting Moreover, algorithm of range-basedmethods usually are simple so that computational ability can perform in phone directly.Subsequently, real-time requirement is satisfied

1.3 Contribution

In this thesis, we propose a real-time and highly accurate smartphone localization systemfor moving target using BLE iBeacon This work aims to develop a fine-grained local-

ization technique for wide range applications, for example, meter-level indoor navigationfor both emergency and casual cases, proximity marketing, and potentially for roboticindoor mapping and navigation In details, the main contributions of this work are listed

as follows:

• Creatively introduce heteroscedasticity phenomenon to measure the uncertainty ofBLE RSSI RSS is considered as a Gaussian random variable and its uncertaintylinearly decrease as the RSS decreases To ensure reliability, we only make use of areliable RSS range for reliable position estimation

• Introduce a method to improve the accuracy of a hybrid system using PedestrianDead Reckoning and Least Square Estimation Firstly, we proposed a method ofimproving the accuracy of the LSE algorithm by giving higher weights for iBeaconwhich has the highest RSS Secondly, we apply fusion for the improved LSE-basedand PDR-based position for producing a more accurate position

1.4 Outline

The rest of my thesis is organized as follows:

Chapter 2 firstly presents overview the two of technologies which are used in the proposedsystem, i.e: BLE and IMU Then, we briefly present two kinds of RSS-based techniques,i.e: Fingerprinting and Lateral Finally, fundamental of Bayes filters are introduced

Chapter 3 presents the proposed indoor positioning system including PDR subsystemand LSE subsystem In LSE subsystem, I discusses RSS measurement and its uncertainty

in the first half Then, a ranging scheme is presented in the rest

Chapter 4 presents experimental results and discussion

Finally, Chapter 5 concludes this thesis and suggests some ideas for the future work

Chapter 2

Background

2.1 Positioning Technology

Bluetooth Low Energy Overview

Bluetooth technology [25], managed by Bluetooth SIG, has been a well-known wirelessstandard for short-range communication for over a decade It has widely used in PAN as analternative to wired communication, for example, replacing wired line in computer mouse

or headset With the demands of better technology, Bluetooth (a.k.a Bluetooth Classic)

is replaced by intervention of Bluetooth Low Energy BLE is intentionally designed forIoT purposes rather than for short-range devices communication Compare to Bluetooth,BLE consumes less power, provide higher range communication, less latency and moresecurity Tab 2.1 summarizes the key feature of Bluetooth Classic and BLE

BLE operates in the 2.4 GHz ISM spectrum band into 40 channels In which, channel

37 (2.42 GHz), 38 (2.426 GHz) and 39 (2.48 GHz) serves for advertisement purposes andthe rest for data exchange When a BLE device work on channel 37–39, it is known

as beacon BLE beacon broadcasts its advertising packet periodically in constant timeinterval The shorter the advertising interval, the more the packet can be broadcasted inone second

37 0 1 2 3 4 5 6 7 8 9 10 38 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 39

2400 Frequency (MHz) 2480

Advertising Channel Data

Figure 2.1: Channel configuration of BLE

Table 2.1: Classic Bluetooth vesus BLE

Feature Bluetooth Classic BLE

Throughput 0.7-2.1 Mbps 305 kbpsConnection Latency 100 ms <6 ms

Comunication Mode One to One One to Many

Usage of BLE in Indoor Positioning System

Before BLE is introduced, Bluetooth-based indoor localization is not a reasonable ideabecause of its communication method (one-to-one communication) We only can makeindoor positioning possible after its debut With many advantages, BLE beacon seems

to be better than Wi-fi in the indoor positioning field It holds unique features that

no IoT device has such as small, better power efficiency, wide range, cost-effective and

so on Currently, most BLE positioning methods typically use RSSI Range-based IPS

is designed using path-loss models to estimate the distance between smartphone andbeacon However, path-loss models could not work well in heterogeneous environments asindoor and then resulting error in positioning To deal with this problem, we can use awell-known technique, called Fingerprint The data set of Fingerprint for each referencepoint on map models the specific elements of structures in the indoor environment Thetrade-off of this technique is time-consuming in the data collection task

iBeacon and iOS indoor positioning application

With aims to seek a feasible solution for indoor positioning with high accuracy, Appleintroduced iBeacon - a protocol running on a small, battery-powered device that usesBluetooth Low Energy (BLE) technology for broadcasting its message to a compatiblesmartphone within its range It holds very unique features that none of the technologycan provide for indoor localization such as small size, high energy efficiency, low cost,and less interference Beacons that use with iBeacon protocol promote their presence viathree identifiers namely, UUID, Major, and Minor [1] (For brevity, in the rest of the thesis,iBeacon is implied as beacon using iBeacon protocol) As the name implies, an iBeacondevice acts as a lighthouse Instead of emitting light to provide navigation for ships,iBeacon device broadcasts BLE signals to let smart-phone know their location context.The signal needs to be read and converted into relevant information by applicationsrunning on smartphones Some places that use iBeacon include Brooklyn Museum, LutonAirport, Los Angeles Zoo

Inertial navigation is the concept of only utilizing internal motion sensors to calculate theposition The favor approach is Pedestrian Dead Reckoning (PDR) [20, 22] Accelerome-ter, gyrocopter and magnetometer are three types of sensor which are commonly used in

(1 byte)

Access Address

(4 bytes)

PDU (2-39 bytes)

CRC (3 bytes)

Header (2 bytes)

MAC (6 bytes)

Data (up to 31 bytes)

iBeacon Prefix (9 bytes)

an iOS device is shown in Fig 2.4

Gyroscope

A gyroscope is responsible for measuring the rate at which a device rotates around aspatial axis Rotation rate are measured in radians per second around the given axis

Figure 2.4: Accelerometer measures changes in velocity along the x, y, and z axes

(as shown in Fig 2.3) Rotation values may be positive or negative depending on thedirection of rotation An measurement of rotation rate in iOS device is shown in Fig 2.5

2.2 RSSI-based Positioning Techniques

In general, the approaches used in indoor localization can be classified into four categories:Time of Arrival (TOA), Angle of Arrival (AOA), Hybrid TOA/AOA and, Received SignalStrength Indicator (RSSI) This thesis aim to the most commonly method for indoorlocalization, RSSI [41]

User

Online Received RSS Reference Point

Figure 2.6: Fingerprint Concept

Fingerprinting is by the far the most favored positioning method for researching onindoor localization based on radio frequency In Fingerprinting method, the positionobtained from Fingerprinting must be pass through two phases: Offline/Training phaseand Online/ Execution phase In the Offline phase, the area is divided into grid point orreference point, then collect data for each one These data are then saved in the form ofvectors and stored in a database Suppose we have Q beacons, and P reference points(RPs) in the area We need to collect data for a location at RPs in the shape of a vector.Each vector normally has the form as following:

Vp = {xp, yp; RSSp1, , RSSpq, , RSSpQ}, p ∈ [1, P ] , q ∈ [1, Q] (2.1)

in which, {xp, yp} is coordinate of p th RP and RSSp1, , RSSpq, , RSSpQ are RSS valuesfrom Q beacons respectively All of these reference points will contribute to creating aradio map The problem of Fingerprinting is estimating a position when RSS valuemeasurement on-the-fly of an unknown position is available:

Va = {RSS10, , RSSq0, , RSSQ0 }, q ∈ [1, Q] (2.2)This task will be done in Online phase by using a matching algorithm such as k-NN, SVM,Neural Network and so on Fingerprinting’s advantage is not dependent on convertingRSSI to distance The stability of Fingerprinting is higher than range-based methodbecause the position is fixed into reference points Besides, the major problem of Fin-gerprinting is several reference points have similar data vectors This lead to decreasethe localization accuracy Fingerprinting in combination with k-Nearest-Neighbor is alsocommon method in indoor positioning research Based on kNN algorithm, online vector

and offline vecotr are compared with each other by calculating the following Euclideandistance:

d(Va, Vp) =

vuut

QXq=1

Another method for finding tag device position is known as Lateral or Lateration UnlikeFingerprinting, Lateral method does not have an offline phase However, it requires adatabase of the anchor node’s coordinate

The most common way to find tag device position is to use Least Square Estimation.Assuming that the mobile phone is located at (x, y), and the ith beacon is located at(xi, yi) The true distance between the mobile phone and the ith beacons, di, can beexpressed as:

b = 12

m for moving devices and 0.7 m for static devices

2.3 Bayesian Filtering - From Kalman Filters to

Par-ticle Filters

Considering a discrete-time nonlinear state model which is consist of a hidden state{xk, k ∈ N}:

are available In other word, it is required to calculate the pdf p(xk|z1:k) This can bedone in the recursive form of Bayes filter which includes two phases, i.e, prediction phase,and update phase.

The prediction phase involves using the system model (2.8) to obtain the prior pdf ofthe state at time k via the Chapman–Kolmogorov equation:

p(xk|z1:k−1) =

Zp(xk|xk−1)p(xk−1|z1:k−1)dxk−1 (2.10)

Note that in Eq 2.10, the required pdf p(xk−1|z1:k−1) is assumed to be known in advanceand the probabilistic model p(xk|xk−1) is defined by (2.8) with known statistics of vk−1

We can use a observation zk at time step k to update the prior (update phase) via Bayeslaw:

Kalman filter [39, 40] has been widely used in control, sensor fusion, noise filtering andtracking problem The Kalman filter assumes that the posterior density at every timestep is Gaussian There is several conditions that need to be satisfied to have a optimalsolution, i.e:

• vk−1, nk are both considered to be Gaussian

• fk(xk−1, vk−1) is known linear function of xk−1 and vk−1

• hk(xk, nk) is known linear function of xk and nk

Then, Eq (2.8) and (2.9) can be rewritten as:

p(xk−1|z1:k−1) = N (xk−1; mk−1|k−1, Pk−1|k−1) (2.14a)p(xk|z1:k−1) = N (xk; mk|k−1, Pk|k−1) (2.14b)p(xk|z1:k) = N (xk; mk|k, Pk|k) (2.14c)where

Pk|k−1= Qk−1+ FkPk−1|k−1FkT (2.15b)

mk|k = mk|k−1+ Kk(zk− Hkmk|k−1) (2.15c)

Pk|k = Pk|k−1− KkHkPk|k−1 (2.15d)

In Eq (2.15), (·)k|kand (·)k|k−1represent the filtered state and predicted state of operation(·), respectively Kk is known as the optimal Kalman gain Normally, Kalman gain is aweighting factor calculated on basis of error covariance of the transition model and theobservation model It tells how much to change the predicted state to reflect an observedstate Kk equals to:

Kk = Pk|k−1H

T k

HkPk|k−1HT

In the simplest case, Kalman filter can help to reducing noise from RSS For RSS, noise isoften known for short-term fading, which is caused by surrounding pedestrians RSS canfluctuate sharply in a short period of time To reduce its impact, especially in situationswith strong fluctuations, we apply Kalman filter for RSS model:

Algorithm 1: Kalman Filter Algorithm

Initialize: State mean: Γ0 = z0

State covariance: ρ0 = 1

1 Predict state: ˆΓ−k = ˆΓk−1

2 Predict state covariance: ˆρ−k = ρk−1

3 Calculate Kalman filter gain: Kk= ρ−k(ρ−k + R)−1

4 Update state: ˆΓk = ˆΓ−k + Kk(zk− ˆΓ−k)

5 Update state covariance: ρk = (1 − Kk)ρ−k

In Fig 2.8, the red line represents nature RSS at a distance of 2.5 m under LOScondition and the blue line represents filtered RSS using Kalman filter At some timesteps, the red line sharply attenuated due to the presence of pedestrians We easily seethe Kalman filter somewhat reduced the impact of the RSS fluctuations in blue line.Moreover, KF can help reduce the uncertainty of position in some circumstance As wecan see in Fig 2.9, when not using the Kalman filter, the estimated positions show alarge dispersion After filtering, estimated positions show an opposite trend

Sequential Importance Sampling (SIS)

In practice, it is not easy to calculate (2.11) directly In this case, we can use MonteCarlo method to approximate posterior density function by using a set of samples withassociated weights, following below equation:

p(x0:k|z1:k) ≈

N s

Xi=1

Figure 2.8: Comparison of raw RSS and KF-filtered RSS

9 9.5 10 10.5

11

Filtered Position True Position

Figure 2.9: The estimated position using Kalman filter

q(x)

p(x)

Figure 2.10: Illustration of importance sampling method