Frequency Hopping for Robust Indoor LocalizationI-Hei Ng∗, Tsung-Han Lin∗, Seng-Yong Lau∗, Te-Yuan Huang∗, Hao-Hua Chu†‡ and Polly Huang∗†§{b91901152, b90901046, sylau, r95921023}@ntu.edu.tw, hchu@csie.ntu.edu.tw and phuang@cc.ee.ntu.edu.tw

∗Department of Electrical Engineering, †Graduate Institute of Networking and Multimedia‡Department of Computer Science and Information Engineering, §Graduate Institute of Communication Engineering

National Taiwan University

Abstract—With an expected market value of $2.71 billion in2016, supporting daily use of real-time location systems in house-holds and commercial buildings is an increasingly importantsubject of study. A growing problem in providing robust locationestimations in real time is the use of wireless transmissions in RFfrequencies. Having implemented a simple RSSI-signature-basedlocation system on a 24-node IEEE 802.15.4-based sensor networktestbed, we are able to analyze the effect of background IEEE802.11 traffic to the localization error. Our previous measurementresults demonstrate that the 80th-percentile of the localizationerror may increase by 141% when the background 802.11 trafficis high. Such performance degradation is a result of RSSI readingloss as the beacon messages collide with background traffic.A common solution to this problem is to extend the time forbeacon message collection. This approach, although effective,adds extra delay before robust estimations can be obtained.Aiming at achieving robust real-time localization, we propose afrequency hopping mechanism that enables the system to adaptto the current interference level. When the interference level ishigh, the system hops to a new channel to avoid the foreseen highloss period. Our experimental results show that the proposedfrequency hopping mechanism can reduce the 80th-percentilelocalization error from 1.82 to 1.32 meters (27%) in a busy hourand from 2.74 to 1.24 meters (55%) in a 20-minute period whenthe 802.11 traffic rate is at its peak.

I. INTRODUCTION

The market for real-time location systems for assets and per-sonnel tracking is expected to reach $1.26 billion by 2011 [1],and $2.71 billion in 2016 [2]. For widespread adoption andeveryday use of real-time location systems in households andcommercial buildings, the systems must be able to provideconsistently accurate location estimations with little delay.

Most indoor localization systems employ an RSSI-signature-based approach which exploits temporal stability inthe received signal strength indication (RSSI) from a set ofpre-deployed beacons at identified locations, which is referredto as the RSSI signature. The RSSI values on the receiving tagon the target are compared to the RSSI signature to identifythe location of the target. Methods of ensuring robust mappingbetween the measured RSSI values and the pre-recorded RSSIsignatures have been studied intensively in recent years [3] [4][5]. Such methods aim to minimize localization errors inducedby unstable RSSI values.

An often overlooked problem is the increasing use ofwireless transmission of RF frequencies in the everyday envi-ronment. Bluetooth (IEEE 802.15.3), WiFi (IEEE 802.11) andZigbee (IEEE 802.15.4) all operate in the 2.4x GHz frequencyband. The stability and availability of RSSI information for

WiFi- or Zigbee-based localization systems may vary depend-ing on interference from other radio sources.

As shown in our previous work [6], the RSSI-based local-ization system is vulnerable to background WiFi traffic. Ourexperimental results have shown that the 80th-percentile of thelocalization error increases from 1.6 to 3.9 meters when theamount of background WiFi traffic increases from 68 to 2,835kbps. Furthermore, the degradation in localization accuracyis mainly contributed by the loss of beacon messages at thereceiving tag due to increased background WiFi traffic, ratherthan the variance of RSSI values. A common solution is toextend the time for beacon message collection. This approach,although effective, adds extra delay at the receiving tag beforeenough beacon messages are collected for robust estimations.

Hence, we proposed a frequency hopping mechanism tomitigate the beacon message loss effect. In wireless commu-nication, frequency hopping [7] is widely used technique toreduce message loss rate by avoiding sending additional dataon channels that are already busy. Our mechanism for RSSI-based indoor localization exploits this same concept. By usingfrequency hopping to reduce beacon message loss rate duringhigh background WiFi traffic, more beacon messages can besuccessfully received by a target for accurate localization.

Our frequency hopping mechanism works as follows. Eachbeacon node runs a diagnostic test periodically to determinewhether the operating channel is experiencing beacon messagelosses. When the level of losses reaches a preset limit, thebeacon node issues a hopping signal to inform all nodes inthe network, including the receiving tag, to hop to the nextchannel. The diagnostic test is essential for the efficiency of thefrequency hopping location system. Insensitive diagnostic testthat responds too slowly to increased background WiFi trafficresults in beacon message loss and inaccurate location esti-mations, while overly-sensitive test that responds too quicklyto flash background WiFi traffic causes unnecessary hoppingwhich would incur even greater beacon message losses andless accurate location estimations. We propose a learning-based approach for the diagnostic test. In that, the value ofthe preset limit is trained by Hidden Markov Model (HMM)offline. The Forward algorithm, which uses the trained valueto decide whether to hop, involves simple computation andis affordable by a sensor node with limited computation andpower.

The 80th-percentile error of the location system is reducedfrom 1.82 to 1.32 meters (27%) in a busy hour and from 2.74

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to 1.24 meters (55%) in the 20-minute period when the WiFitraffic rate is at its peak. The proposed frequency hoppingmechanism enables accurate and stable indoor localizationwith minimum delay.

Although the frequency hopping mechanism is shown effec-tive for an RSSI-signature-based indoor localization system,this mechanism can potentially be applied to any localizationsystem that sends wireless beacon messages for locationestimations, regardless whether the system is for indoor oroutdoor localization and whether the system is based on RSSI-signature or RSSI-ranging.

This study makes the following four contributions:• This is, to our knowledge, the first proposed use of

frequency hopping for localization.• The HMM-based diagnosis test is reasonably simple to

implement on limited sensor nodes.• The proposed mechanism is shown effective in a medium-

scale testbed with realistic WiFi interference.• To be able to repeat experiments with controlled WiFi

interference, we take a unique trace synthesis approachfor the evaluation.

The rest of the paper is organized as follows. We describethe related work in Section 2. The rationale and the designof the frequency hopping mechanism are examined in Section3. Section 4 describes the experimental methodology. Finally,Section 5 reports the results validating the efficiency of theproposed frequency hopping mechanism.

II. RELATED WORK

Co-channel interference is not a new problem, and channelhopping is a popular solution. The problem exists whetheror not radio standards are similar. Srinivasan et al. [8] andZhou et al. [9] have observed the impact of interferencebetween 802.11 and Zigbee signals. Recently Gummadi etal. [10] analyzed the interference of Zigbee and cordless phoneusing 802.11 networks for data communication. Gummadiproposed a channel hopping mechanism to mitigate the impact.Furthermore, Bahl et al. [7] and Mishra et al. [11] both studiedthe channel hopping problem within 802.11 networks fornetwork throughput improvement. Our work differs by usingthe channel hopping mechanism for improving localizationaccuracy.

Indoor localization techniques can be divided into twocategories: range-free and range-based. The former does notlocalize targets based on range estimation [12]. The latteruses absolute angle estimates [13] or point-to-point distanceestimates by measuring signal propagation time [14] [15],signal interference patterns [16] or received signal strengthindicator (RSSI).

In particular, the range-based system that exploits the mea-sured RSSIs infers the location either based on the decaymodel of distance to signal strength [17] [18] [19] or theRSSI fingerprints (also known as the RSSI signatures) to relatean observed set of signal strengths to ones at known loca-tions [20]. The RSSI-signature-based techniques are broadlycategorized into deterministic and probabilistic techniques.

For deterministic method, RSSI readings are first collectedat known locations and the location is the one which RSSIsignature is closest to the measured RSSIs. Probabilistic meth-ods, on the other hand, construct a probability distributionover the target’s location. The extended Kalman filter [21]or particle filter [4] [5] based approach, though can reduceestimation error, requires predictive mobility model which isnot obtainable without aid of other sensors. Our frequencyhopping mechanism is complementary to (and can workswith) these post-processing filtering techniques as they addressdifferent error sources at different times. While our proposedmechanism reduces signal loss at data collection time, the ex-tended Kalman filter and particle filter tackle signal instabilityat data processing time.

III. FREQUENCY HOPPING MECHANISM

A typical RSSI-based localization system works as follows.In the tracking area, some beacon nodes are installed tobroadcast beacon messages periodically. The receiving tag onthe target can record the signal strength of the received beaconmessages which are later used to estimate the location.

To make a RSSI-based localization system robust to back-ground noise, this study proposes a frequency hopping mech-anism consisting of (1) an initialization process for the sensornetwork formed by the beacon nodes, (2) a diagnostic test todetect whether the sensor network is substantially influencedby background noise, and (3) a protocol for signaling all nodesto hop to the next channel. The following subsections describein detail the mechanism components and design rationale.

A. Beacon Network Initialization

Because the beacon signals used by a RSSI-based local-ization system can be interfered by other wireless signalstraveling on the same frequency channel, the resulting beaconmessage losses cause localization errors. To distinguish a busychannel from quiet ones, one needs to establish the criteria forchannel assessment and the base value at the system startuptime.

One obvious criterion is the beacon message reception rateat the receiving tag. However, the receiving tag may appearanywhere in the tracking area. In some regions, particularlythose at the corners where the network connectivity is rela-tively weak, the receiving tag can only receive a small numberof beacon messages even when the channel is quiet. Hence,the number of beacon messages received at the receivingtag is location dependent. For a localization system aimingat tracking mobile targets, a diagnostic test based on thiscriterion would not accurately reflect the interference level ofthe operating channel.

On the other hand, the number of received beacon messagesat beacon nodes will not change much because beacon nodes’positions are fixed. In addition, the effect of beacon messageloss at the receiving tag is observable from the neighboringbeacon nodes. The diagnostic test can thus be performed onindividual beacon nodes by monitoring the reception of thebeacon messages from well-connected neighboring beacons.

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At the beacon network setup phase, the beacon nodessend messages to each other, possibly during non-workinghours when background traffic is low, to determine the list ofwell-connected neighboring beacons [22] [23]. Based on thebeacon packet reception rate (PRR) from these well-connectedneighbors, a beacon node establishes the reference case, i.e.,the base PRR value for a quiet channel.

B. Diagnostic Test

The beacon network decides to hop based on the diagnostictest on the observed PRR. In general, the PRRs from well-connected neighbors decrease as the background traffic in-creases [6]. What complicates the design is that (1) the bound-ary PRR value varies depending on the level of backgroundtraffic and (2) the PRR value does not show a clean cut withor without a fixed level of the background traffic. A simpledeterministic test is typical. In that, a threshold PRR is set.When the measured PRR is lower than the preset threshold,the diagnostic test passes and informs the beacon network tohop to the next channel. The challenge in the deterministicapproach is setting the threshold value. If the threshold is settoo high, the diagnostic test may trigger unnecessary hoppingin response to flash or instantaneous traffic noises, as opposedto sustained background WiFi traffic. Unnecessary hoppingis undesirable because each new hopping incurs a transitiontime when the beacon nodes and the receiving tag in thenetwork perform switching to the new frequency channel.During the transition, the receiving tag may not be able toreceive beacon messages effectively and thus result in beaconmessage loss and increased localization error. Conversely, ifthe threshold is set too low, the beacon may be insensitiveto detect the presence of background traffic. The optimalthreshold requires insights to the impact of lowered PRRs tolocation estimates. To determine the best threshold for all pairsof well-connected beacon nodes, we need to obtain locationestimates and exhaustively try every possible PRR thresholdto discover the optimal one that gives smallest localizationerror. PRR of every beacon pair can be easily collected fromthe beacon network, but localization estimates requires manualdata collection, which is tedious and labor consuming, i.e., notscalable.

Instead of trying to find a hard threshold, this study pro-posed a probabilistic test to infer the level of backgroundtraffic by applying the hidden Markov model (HMM) [24]on the observed PRR. Although more sophisticated methodsin the stochastic process or machine learning literature can beapplied, one should take extra caution on the tradeoff betweenthe accuracy of the diagnostic test and the implementationcomplexity. The diagnostic test needs to run on resourcelimited sensor nodes. Other probabilistic methods need to beanalyzed for their implementation feasibility. While we planto pursue the analysis of more sophisticated methods in thefuture, this study focuses on analyzing and comparing thedeterministic PRR thresholding (baseline) and the probabilisticHMM methods (proposed).

The PRR thresholding as a deterministic approach is very

simple and commonly used in existing frequency hoppingmechanisms for sensor networks, while HMM as a probabilis-tic approach pushes the envelope further. As shown later inSection III-B2, HMM-based diagnostic test is computationallylightweight and feasible for the sensor network platform.HMM is well-known for modeling patterns of temporal depen-dency, which is characteristic of daily WiFi traffic. That is, ifthe data rate of the background WiFi traffic is currently high,it is very likely the data rate remains high. The revealed timedependency in WiFi background traffic also suggests temporalpatterns in PRR and makes HMM a plausible method foraccurate diagnostic test. The HMM method also allows easyclassification of channel state, quiet (no-hop) vs. busy (hop).The location estimates required for accurate diagnosis in thePRR thresholding method will not be necessary.

Hidden Markov model extends the concept of Markovmodels to include the case where the observation is a proba-bilistic function of the state. Thus, hidden Markov model is adoubly embedded stochastic process with a hidden underlyingstochastic process which can only be observed through anotherset of stochastic processes producing the sequence of obser-vations [24]. Using HMM enables modeling of the hoppingdecision (the underlying stochastic process), according tothe sequence of measured PRR (the observable stochasticprocess).

The HMM-based diagnostic test involves two phases, offlinestate modeling phase and runtime state estimation phase. Inthe offline phase, a HMM model is trained by feeding PRR asthe observation sequence into the trainer. The HMM consistsof several hidden states and their corresponding Gaussiandistributions which characterize the observation of each hiddenstate. Applying the Expectation-Maximization (EM) algorithmenables adjustment of model parameters to maximize the prob-ability of the training observation sequences. The hidden statescan be defined as ‘Hop’ or ‘No-Hop’ based on environmentsand strategies. In the runtime phase, every beacon runs theForward algorithm [25] for the state estimation computationby calculating the state probability of each observed PRR.Given its computational simplicity, the Forward algorithm issuitable for resource constrained sensor nodes.

1) State Modeling: Given the continuous stream of PRRof a link as the observation values, the following parametersare estimated by the Expectation-Maximization (EM) algo-rithm. A general HMM is represented by N states, denotedas S1, . . . , Si, . . . , SN . Assuming the observation Ot can becharacterized by a Gaussian distribution Ot ∈ {N(µi, σ

2i )}

with mean µi and variance σ2i , the state modeling problem

can be formulated as follows. Given observation sequenceO = O1, O2, . . . , OT , find a model λ = (N, A, B, π ) thatmaximizes P (O|λ). Additional notations used in our modelare described as follows:• π : initial state distribution

πi = P (q1 = Si), q1 ∈ {S1, S2, . . . , SN}, and qt

represents the estimated state at time t.• A = {aij}, where aij = P (qt = Sj |qt−1 = Si) :

probability distribution of state transition from state i to

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Fig. 1. Illustration of Two-State HMM

state j.• B = {bi(Ot)} : observation probability distribution,

given the state i at time t; the probability that anobservation Ot is observed at state ibi(Ot) = P (Ot ∈ {N(µi, σ

2i )}|qt = Si)

After training, certain hidden states can be designated as‘Hop’, while others are ‘No-Hop’. For example, in the mostconservative way, the state with the lowest observation meanis considered as ‘Hop’ and the others as ‘No-Hop’. Hoppingwould then only occur when PRR is low enough. In thisstudy, two-state and three-state HMMs are both used andonly the state with the lowest observation mean is denotedas ‘Hop’. Figure 1 gives an illustration of a two-state HMMwith continuous observation.

Note that the observation, PRR, is calculated over a certainwindow size Ts. Thus, only Ts+1 PRR observations, i.e.,0, 1, . . ., Ts, are possible; the state machine can therefore bemodeled by discrete observations. However, the window size isin fact an adjustable parameter, and may affect the accuracy ofthe diagnostic test. Because the optimal window size for eachindividual environment is unknown, characterizing the PRRobservations as a continuous Gaussian distribution is moreappropriate.

2) State Estimation: With the derived HMM model λ andthe observation sequence O = O1, O2, . . . , Ot, the probabilityP (qt = Si, O = O1, O2, . . . , Ot|λ) can be found with theForward algorithm. The detailed derivation of the Forwardalgorithm can be found in [24]. The estimated state at timet would be the state with the highest probability. Here, theobservation sequence can be the instantaneous PRR of a goodlink or a look-ahead window of size Ts that records the past Ts

PRR. Since the PRR observation is characterized by Gaussiandistributions, in Forward algorithm, exponential computationwill be needed to compute bi(Ot) = 1√

2πσie−(Ot−µi)/(2σ2

i ),where Ot are the values of PRR observation and µi, σi arethe parameters of the Gaussian distribution in state i. Sincecomputing the exponential function on the sensor nodes is notfeasible on a resource-limited sensor node, such function canbe approximated by a look-up table for a limited number ofPRR values. The look-up table can be computed in advance tocapture the above bi(Ot) function. Given the state machine andan implementation of the Forward algorithm, the beacon nodecan perform the hopping decision inference on board. The For-ward algorithm, whose pseudo code is shown in Algorithm 1,

is simple enough to be within the processing capability ofthe Telos-like sensor node platforms. More precisely, for aHMM with N states, only N(N+1) multiplications and N(N-1) additions are needed for each observation. There will be 6multiplications and 2 additions for the two-state HMM case;and 12 multiplications and 6 additions for the three-state HMMcase.

Algorithm 1: Forward AlgorithmN: the number of states in the HMMπ : the set of prior prob. {πi}, i ∈ {1, . . ., N}A: the set of transition prob. {aij}, i, j ∈ {1, . . ., N}B: the set of observation prob. function{bi}, i ∈ {1, . . ., N}

t: time tOt: observation at time tαt−1(i): the set of prob. of staying at state i at time t-1qt: estimated state at time tInput: N, π, A, B, t, Ot, αt−1

Output: αt, qt

if t == 1 thenforeach state i do

αt(i) = πi × bi(Ot);end

elseforeach state i do

αt(i) = [N∑

j=1

αt−1(j)× aji]× bi(Ot);

endendqt = argmaxi αt(i)

C. Signaling Protocol

The beacon nodes as well as the receiving tag should hopto the next channel when the hopping signal is detected. Ifall nodes could hop in perfect synchrony with no delay, thereceiving tag would continuously receive beacon messageswithout any interruption. However, coordinating all nodes tohop synchronously is impossible in the real world. Thus, a sig-naling protocol, originally designed to avoid self-interferencein a dense wireless ad hoc network [26], was adopted to allowsemi-synchronous hopping in beacon networks.

IV. EXPERIMENTAL METHODOLOGY

Results of the evaluation depend on the interaction betweena Zigbee-based indoor localization system and WiFi noise inan actual environment. However, due to the difficulties ofcollecting long term RSSI and PRR co-traces under realisticWiFi interference, only long-term WiFi traffic were taken andthe short-term RSSI and PRR traces collected at different WiFidata rates were used for synthesizing long-term traces. Withthe synthesized data, trace-driven simulations were conductedto evaluate the proposed frequency hopping mechanism. Asfollows are the description of the testbed, the implementationof the localization system and the methodology of tracecollection and synthesis.

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Fig. 2. Testbed Layout. The tracking area is denoted as blue.

A. Testbed

The experimental evaluation was carried out on our BL-live testbed [27]. As show in Figure 2, twenty-four beaconnodes were deployed on the 6th floor of a department buildingat our university. The beacon nodes are Telos-like modules[28] equipped with TI MSP430 microcontrollers and CC2420802.15.4 radios. These beacon nodes are connected, via USBhubs and USB extender, to two PC gateways. The USB inter-face on the PC gateways, is then used for code dissemination tobeacon nodes and data collection from the beacon nodes. Thetestbed is supplied by permanent power source to eliminatethe labor cost of battery replacement and to enable long-termmeasurements. The software is implemented on TinyOS, andthe default MAC, a CSMA/CA-like mechanism, is on for allbeacon packet transmissions.

B. Localization System Implementation

This study implements a RSSI-signature-based localizationsystem based on the well-known RADAR [20] algorithm. Thebeacon nodes periodically transmit short packets containingthe beacon ID. The packet sending interval, denoted as thebeacon cycle, is set to 200ms. To avoid packet collisionsamong the beacons, the DESYNC [29] protocol is imple-mented. The protocol ensures that neighboring beacons havedifferent sending time to avoid collisions. The RSSI values ofpackets received from pre-deployed beacons per beacon cycleis referred to as the RSSI vector.

This system typically operates in two phases, training andtracking phases. In the training phase, a receiving tag isconnected to a portable PC held by the user, who walksalong the tracking area. After collecting forty RSSI vectors,the received RSSI vectors are averaged to generate a singleRSSI signature for each sampled location. The set of RSSIsignatures collected at various locations constructs the radiomap.

In the tracking phase, the receiving tag collects the beaconpackets for every beacon cycle and sends the RSSI vector backto the localization system. The system compares this RSSIvector to the reference RSSI signatures in the radio map toidentify the closest possible location. The k-nearest-neighbor(KNN) method is used for location inference. The coordinatesof the k sample locations with RSSI signatures closest to thecollected RSSI vector are weighted averaged by the Euclideandistances.

We observe that even when the channel is quiet, the packetreception rate is not going to be perfect all the time, i.e.,the mobile tag does not always receive the complete RSSIvector. For the computation of KNN, the missing valuesare traditionally filled in with the minimum RSSI, which is-100 dBm in CC2420. However, the relationship betweenRSSI and PRR is not linear [30]. A higher RSSI does notnecessarily imply a higher probability to successfully receivethe packet. Setting the missing RSSI values to the minimumgives bias to sample points with lower RSSI values. To removesuch bias, we filter out the missing values from the locationestimation computation. The proposed method is referred toas the normalized KNN (NKNN), in which the Euclideandistance is further divided by the number of beacons fromwhich RSSI values are actually received.

C. Trace Synthesis

To collect long-term RSSI, PRR and WiFi co-traces, a sim-ple approach would be to let the receiving tag, beacon nodes,and the WiFi traffic logger run simultaneously for severaldays. However, since the system was installed in a public area,continuously monitoring the receiving tag throughout the ex-periment would not be possible because leaving the receivingtag in the hallway unmonitored would raise both technical andsecurity concerns. Additionally, pedestrians walking by the re-ceiving tag would have significantly increased RSSI variance.Factoring out the effect of nearby obstacles in the evaluationwould be difficult without knowing the pedestrian traffic inthe hallway. The receiving tag might also be removed bycurious trespassers. Early attempts to collect long-term tracesby leaving the receiving tag in the hallway also generatedcomplaints from other residents in the building. Therefore,only long-term WiFi traces were taken. The long-term RSSIand PRR traces were synthesized by using the short-term RSSIand PRR traces collected at different WiFi traffic rates. Theaverage data rate of the collected long-term WiFi traffic wascalculated once per minute, and a one-minute segment wasrandomly selected from the RSSI and PRR traces at the closestWiFi data rate. All the selected one-minute segments weremerged into hours of RSSI and PRR traces.

To generate WiFi traffic at different levels, a laptop PCwas connected to the Internet via the selected AP and a largefile was downloaded from an FTP server an FTP client withupload/download speed limit function to generate differentWiFi traffic rates. Another laptop PC near the WiFi sourcewas used as a sniffer to log all WiFi traffic in the channel andto ensure no unexpected extra traffic occurred. Dumpcap [31],a Linux packet header capturing tool built on the pcap library,was used to log the packets. The WiFi log, referred to as’WiFi’ data, was used to measure the background noise. Theexperiments were conducted at midnight during weekends.Only a very small amount of traffic other than the generatedone was observed by the sniffer. This ensured that the interfer-ence patterns observed were coming from the same AP. In thefive sets of experiments, the average background WiFi trafficrates were 68, 264, 1,308, 1,705, and 2,835 kbps. The traffic

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rate reported here is not exactly the same as the traffic in thechannel because the sniffer cannot capture corrupted packets.Also, no kernel loss is reported by the packet capturing tool.

The receiving tag was placed on the tracking area andconnected to a laptop PC. Each rate-limited file transfersession was slightly longer than 10 minutes. During thatperiod, we record every beacon messages received by thereceiving tag and the beacon nodes in the testbed. The RSSIvalues in the beacon messages collected by the receiving tagwere used to infer the localization errors. From the beaconmessages collected within a beacon cycle, the location of thereceiving tag was estimated. Each run produced 3,000 locationestimations. The beacon messages collected at the neighboringbeacons were used to calculate the beacon PRR. The beaconPRR was calculated by zooming into the beacon link near theAP where the generated background traffic emerged. Takinga sliding window of 50, the percentage of beacon packetsreceived in the past 50 cycles was calculated.

With the trace synthesis method described above, three one-hour segments were selected from the synthesized traces forevaluation, i.e., during busy (peak hours in a day), normal(throughout weekdays), and quiet (after midnight) hours. (seeFigure 3).

V. RESULTS

The diagnostic test to determine whether or not the beaconnetwork should hop is critical to a noise-resilient RSSI-basedlocalization system. In the following subsections, we describehow the above traces are used and examine qualitativelyand quantitatively the state decision behaviors using the PRRthreshold (baseline) and HMM (proposed) approaches.

A. PRR Thresholds

As mentioned in Section III, a naive, though not scalable,solution for making hop decision is to set a threshold on

Fig. 5. Hopping Decision of PRR-Thresholding. Red dots: Hop. Green dots:No-Hop.

the observed PRR. The challenge is how to find a properthreshold. A brute-force approach is to conduct a trace-drivensimulation on every possible threshold setting and select theone that can minimize localization error. We take the normal-hour PRR trace for the simulations. Taking one PRR valueat a time, if the observed PRR is lower than the threshold,a ‘Hop’ decision would be made; otherwise, a ‘No-Hop’decision would be made. When the ‘No-Hop’ decision ismade, the simulation then takes the next PRR data in thetrace and repeats the decision making process. When ‘Hop’is indicated, the simulation moves to a data point randomlyselected from the PRR trace to simulate hopping to the “new”channel. We assume no beacon messages are received in thefirst period after hopping, i.e., the first localization error inthe new channel is set to be a predetermined maximum.If the simulation reaches the end of the trace, it rounds tothe beginning of the trace. An implicit assumption in suchsimulations is that all channels behave similarly during thenormal hours. Each simulation runs for 3 hours. Note that,simulating in this fashion, when PRRs are computed usinga sliding window, the first PRR value should be calculatedbased on the dynamics of the beacon messages in the firstand last forty-nine cycles. The first forty-nine PRRs should becomputed similarly.

Figure 4 shows the 80th-percentile localization errors bysetting different PRR thresholds from 20% to 80%. From thesimulation results, setting PRR threshold at 48% can achievethe most accurate localization estimation. The localizationerror is higher for PRR thresholds below 48%, because lowerthresholds caused the system to miss some background trafficand resulted in higher packet losses. The localization is

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(a) Two-state Model (b) Three-state Model (c) Three-state Model (Window Size=10)Fig. 6. State Prediction of HMM. Red dots: Hop. Green dots: No-Hop.

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(b) Zoom in to busy 20 minutesFig. 7. Localization Accuracy in Busy Hour

also higher for PRR thresholds above 48%, because higherthresholds caused the system to make frequent unnecessaryhopping and again resulted in higher packet losses.

Setting 48% as the PRR threshold, another set of simulationwas carried out with the busy-hour trace. Figure 5 shows thedata points predicted as ‘Hop’ in red (dark) and those predictedas ‘No-Hop’ in green (gray). The ‘Hop’ data points generallycorrespond to the 20-minute interval during which a surge ofWiFi traffic occurs. A substantial number of false negativewere noted while no false alarms were detected. Here, thefalse negative is defined as a data point that is within theWiFi traffic burst and results in high localization error, butthe diagnostic test reveals a prediction of ‘No-Hop’. The falsealarm is defined as a data point that is beyond the WiFi trafficburst but is predicted as a ‘Hop’ point.

B. Hidden Markov ModelInstead of brute-forcely searching for a good threshold, with

HMM the system can learn to distinguish busy and quietchannel from measured PRRs and make hopping decisions. Totrain a model, the normal-hour is applied, and the initial valuesfor parameters µ and σ in each state are derived from the K-means algorithm. The K-means algorithm identifies partitionssuch that the data points within the same state are as closetogether as possible, and the data points in different states are

as far apart as possible. For the HMM-related computation, aMatlab HMM toolbox was employed [32].

A two-state HMM is first employed, since there is a straight-forward mapping between the two states and the two decisions,‘Hop’ or ‘No-Hop’. The state machine was trained withthe normal hour trace. The state with lower PRR mean isdenoted as ‘Hop’, while the other is ‘No-Hop’. A trace-drivensimulation based on the derived model then runs with thebusy-hour trace, and the result is shown on Figure 6(a). Inthe figure, the red (dark) points are the data points predictedas ‘Hop’, while the green (gray) points are those predicted as‘No-Hop’. As in the previous section, the ‘Hop’ data pointsgenerally correspond to the 20-minute interval during which asurge of WiFi traffic occurs. However, a substantial number offalse alarms were also noted. Frequent false alarms may causethe system to hop unnecessarily. In this case, the receiving tagwould be unable to reliably receive beacon messages duringthe hopping transition and the accuracy of the location systemwould deteriorate.

Compared to the results of PRR thresholding in Figure 5, wehave observed that those false alarms are composed by the datapoints which only suffered from mild packet losses and stillcan achieve high localization accuracy. This phenomenon canalso be found in our previous work [6], the localization error

8

remains low while the number of receiving beacon packetsdecrease to 8 or 7 packets. An optimization of this two-stateHMM is to create another hidden state to capture the PRR datapoints which are only affected by mild background traffic.

We then evaluate a three-state HMM, and classify the threestates in the most conservative way with two ‘No-Hop’ statesand one ‘Hop’ state. Only the states with the lowest PRRmean are designated ‘Hop’, while others are ‘No-Hop’ states.Figure 6(b) shows that three-state HMM can effectively lowerthe false alarm rate by accommodating the above mentioneddata points with one more ‘No-Hop’ state.

C. Localization Error with Frequency Hopping

Figure 7(a) shows the CDF of localization errors duringa busy hour using two-state HMM, three-state HMM, the48% PRR threshold, the 42% PRR threshold, as well as thelocalization errors without frequency hopping. The 48% PRRthreshold was selected based on brute-force method showed inprevious subsection. We can also choose a threshold blindly,and a reasonable choice would be in the range of 40% to60%. Hence, we chose 42% threshold to represent a blindlyrandom choice threshold. As show in the figure, both two-stateand three-state HMMs improve the 80th-percentile localizationerror over the without frequency hopping method. For three-state HMM, the improvement is as high as 28% (from 1.82 to1.32meters) and achieved similar accuracy as the brute-force48% PRR threshold setting. Accuracy of the 42% thresholdsetting is slightly worse than the three-state HMM and 48%threshold, but better than two-state HMM. The above resultsshow that the frequency hopping mechanism can avoid un-necessary beacon packet losses and still maintain localizationaccuracy. Conversely, the original localization system withoutfrequency hopping must undergo a period of high localizationerror.

The 50th-percentile localization errors, however, are similarbecause the interference level is not high during most of theone hour period. The frequency hopping mechanism is not in-tended to improve the average error of the localization system.Instead, it aims at minimizing the variance in localization errorby avoiding occasional surges of background traffic. This taskis particularly important if the system is to be deployed foreveryday use.

To further highlight the advantage of frequency hopping,we zoom into the busiest 20 minutes. The 80th-percentilelocalization error, as shown in Figure 7(b), can be reducedfrom 2.74 to 1.24 meters . In this figure, three-state HMM hasthe best performance, slightly better than the 48% thresholdsetting. The random chose 42% threshold become worse, the80th-percentile localization error for this setting is 1.74 meters.The result shows that, although intuitively setting a thresholdis the simplest way, but could lead to a larger localization error.Setting a threshold by the brute-force method can achievebetter performance, is tedious and labor consuming. On theother hand, providing similar localization accuracy to the 48%threshold, the three-state HMM only needs PRR to train thetraining of the model rather than the location information

0.0 0.5 1.0 1.5 2.0

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Fig. 8. Localization Accuracy in Quiet Hour

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window size=10window size=20window size=30window size=40window size=50window size=60window size=70window size=80window size=90without hopping

Fig. 9. Impact of Window Size on Localization Accuracy

which is required to find an hard threshold. In this regard,HMM is preferable than PRR thresholding for diagnostic testsin terms of performance and feasibility.

1) Busy vs. Quiet Hour: Figure 8 shows the CDF of local-ization errors during a quite hour. The ‘Without Hopping’ caseshows slightly better 80th-percentile localization error than allthe other cases. This is because any hopping in this trace isunnecessary. In addition, even if the system successfully hopsto a very quiet channel, no particular benefit can be achieved.In fact, there is a slight penalty of not being able to receivebeacon messages during the transition of hopping.

2) Sliding Window Size: The sliding window size forcomputing the PRR is a tunable parameter in our localizationsystem. PRR represents the beacon message reception rateover a period of time, which is the sliding window size. Ifthere is a WiFi traffic burst, it would take a certain amountof time for the PRR to reflect the change. The delay canbe reduced by setting a smaller window size. However, thefalse alarm rate becomes higher as a smaller window size ismore sensitive to short-term noise. As shown in Figure 6(b)and 6(c), a window size of 10 incurs substantial amount ofunnecessary hopping while a window size of 50 makes thesystem more stable. To observe the effect of different windowsizes, we take the busy-hour trace and 3-state HMM methodand simulate the localization error varying the window sizefrom 10 to 90. Figure 9 are the resulting localization errors.As window size increases from 10 to 40, the error decreasesand reaches smallest when the window size is around 50 to 70.Then the error increases again when window size goes from80 to 90. In this sense, a window size of 50 gives a goodtradeoff between delay and false alarm rate.

9

VI. CONCLUSION AND FUTURE WORKS

We have demonstrated in this study that the proposedfrequency hopping mechanism can achieve accurate, stableindoor localization in daily environments. The 80th percentileand 50th percentile localization errors are kept low to ap-proximately 1.3 and 0.6 meters, even when the environmentis experiencing heavy interference. Although using a longerbeacon message collection time may also mitigate the lo-calization error due to beacon message loss, the proposedfrequency hopping mechanism pushes the envelope further. Itenables accurate and stable indoor localization with minimumdelay, i.e., the real-time location systems with a rising marketdemand.

Our intention is to implement the frequency hopping mech-anism on our localization testbed and evaluate the long-termstability under daily WiFi influences. The implementation ofthe Forward algorithm and the signaling protocol is relativelystraightforward. Obtaining the HMMs, however, requires anextended measurement study with WiFi traffic systematicallygenerated at different locations. This is top on our future planpursuing research in robust real-time location systems.

In the design of our frequency hopping mechanism, theaccuracy of the diagnostic test is crucial to the decision offrequency hopping and the ultimate localization accuracy. Weevaluated the performance of PRR thresholding and HMMapproaches which are proven feasible on resource-constrainedsensor nodes. Other sophisticated pattern recognition methodswill also be a subject to our future study.

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