Particle Filtering and Sensor Fusion for Robust Heart Rate Monitoring using Wearable Sensors

Transcription

1 Paricle Filering and Sensor Fusion for Robus Hear Rae Monioring using Wearable Sensors Viswam Nahan, IEEE Suden Member, and Roozbeh Jafari, IEEE Senior Member Absrac This aricle describes a novel mehodology leveraging paricle filers for he applicaion of robus hear rae monioring in he presence of moion arifacs. Moion is a key source of noise ha confounds radiional hear rae esimaion algorihms for wearable sensors due o he inroducion of spurious arifacs in he signals. In conras o previous paricle filering approaches, we formulae he hear rae iself as he only sae o be esimaed, and do no rely on muliple specific signal feaures. Insead, we design observaion mechanisms o leverage he known seady, consisen naure of hear rae variaions o mee he objecive of coninuous monioring of hear rae using wearable sensors. Furhermore, his independence from specific signal feaures also allows us o fuse informaion from muliple sensors and signal modaliies o furher improve esimaion accuracy. The signal processing mehods described in his work were esed on real moion arifac affeced elecrocardiogram (ECG) and phooplehysmogram (PPG) daa wih concurren acceleromeer readings. Resuls show promising average error raes less han 2 beas per minue (bpm) for daa colleced during inense running aciviies. Furhermore, a comparison wih conemporary signal processing echniques for he same objecive shows how he proposed implemenaion is also compuaionally more efficien for comparable performance. Index Terms Paricle Filer, Physiological Signal Processing, Moion Arifacs, Hear Rae, Wearable Sensors I I. INTRODUCTION N recen imes, a significan amoun of research has been dedicaed o realizing he goal of pervasive, around-heclock personal physiological monioring ha is boh easy o use and accurae. The radiional norm is o rely exclusively on hospial visis, however his model of healhcare could be significanly augmened wih he help of dedicaed wearable and environmenal sensors. Apar from generally being more convenien and cheaper, coninuous monioring wih a wearable device will be invaluable for idenifying medical condiions for which sporadic monioring is insufficien. Among he various physiological measures, here has been significan ineres in wearable coninuous hear rae (HR) monioring, and i would be useful for boh finess and healh applicaions. For example, hear rae variabiliy is a condiion Submied for review on Augus 30 h, This work was suppored in par by TerraSwarm, one of six ceners of STARne, a Semiconducor Research Corporaion program sponsored by MARCO and DARPA. V. Nahan is wih he CSE deparmen and R. Jafari is wih he BME, CSE ad ECE deparmens a Texas A&M Universiy, College Saion, Texas, 77843, USA. ( s: {viswamnahan,rjafari}@amu.edu ). ha could be an indicaor of myocardial ischemia [1] and coninuous monioring of he hear rae would increase he chances of a successful diagnosis. Wearable hear rae moniors could also enable general finess applicaions. For example, users would be able o ailor heir exercise rouines according o how heir body is responding o he workload. Coninuous cardiac aciviy monioring could also be used for user auhenicaion purposes, as shown in a recen work [2]. However, he increased comfor and convenience of hese sensors ofen comes a he cos of an increased amoun of noise as well; for example, for bio-poenial sensors, he skin conac would likely have o be a dry elecrode, poenially non-conac elecrodes, which in urn means an increased amoun of noise compared o we or gel-based inerfaces which are sill he sandard for medical grade equipmen [3]. Moreover, aciviies of daily living are likely o lead o moion arifacs in he signals, such as in he case of a smar wach monioring hear rae while he user is jogging. A recen sudy exploring coninuous monioring of hear rae of consrucion workers o manage workload showed ha moion arifacs were he primary source of error in hear rae esimaion [4]. There are muliple modaliies, sensor ypes, and sensor locaions ha can be used o capure hear rae. The hear rae can be inferred from he ECG, PPG or even he changes in bio-impedance of a cerain region of he skin. The ype of sensors can be gel-based paches, or dry meal elecrodes or an LED-phoodiode combinaion as is he case for PPG. Finally, he sensors could be available in muliple locaions depending on he conex such as on a T-shir, on a wris wach, or on he sides of reading glasses. No o menion he possibiliy of environmenal sensors opporunisically measuring he hear rae, such as a seering wheel capuring ECG aciviy wih elecrodes placed on eiher side of he wheel. Moreover, apar from all hese sources for measuring he signal, we can also easily imagine sources ha measure he noise. An obvious example would be acceleromeers ha are already par of porable devices such as smar waches; hese signals could be correlaed wih he moion noise ha clouds he esimaion of hear rae. The inerne of hings (IoT) would very much include physiological and moion sensors, and i is very likely ha successful signal processing echniques would ake advanage of he expeced muliude of sensors. Therefore, we srive o show ha he proposed implemenaion is capable of supporing muliple simulaneous and heerogeneous sensors and fusing hem effecively for more accurae esimaes. Finally, an imporan consideraion when designing

2 wearable sensors is he compuaional power. Due o form facor and baery lifeime consrains, he processors in hese sysems are relaively modes, and hence i is imporan o ensure ha he compuaional load due o signal processing algorihms is minimized as much as possible. In his work we describe he use of a paricle filer o esimae arge physiological phenomena from a variey of signal modaliies, as well as he fusion of hese. The paricle filer is a sequenial Mone Carlo rouine ha probabilisically esimaes he rue sae of a given sysem by updaing he weighs and redisribuing a se of paricles. More deails on he working of he paricle filer will be provided in his aricle and can also be found in oher works [5]. Moreover, while he focus of his work is on hear rae monioring, he proposed implemenaion of he paricle filer could also be used for esimaing oher physiological parameers ha are relaively slow-changing and consisen over shor ime inervals. As will be explained in deail laer, based on sensor observaions, he paricle filer racks muliple possibiliies for he arge parameer and rewards hose ha are consisen over ime. We know ha he human hear rae is relaively seady over shor ime inervals, bu his applies o oher phenomena as well, such as respiraion rae or coninuous arerial blood pressure (ABP). Coninuous ABP can be esimaed by measuring he pulse ransi ime [6], which in urn can be esimaed wih he same signal modaliies discussed in his work. As such, no only is he proposed implemenaion independen of specific signal modaliies or feaures, i is also poenially adapable for oher applicaions in he same domain. The conribuions of his work are: 1. A paricle filer formulaion for esimaion of hear rae from noisy sensor sreams wihou dependence on specific signal feaures; i insead works wih naïve, greedy observaion mechanisms and leverages he expeced seady changes of he human hear rae. 2. Demonsraion of he efficacy of he echnique using real moion-arifac affeced ECG and PPG daa. 3. Showcasing our implemenaion s poenial for fusion of muliple signal modaliies o improve hear rae esimaes. 4. Demonsraion of improved compuaional efficiency of our soluion compared o conemporary relaed works. II. RELATED WORKS There have been many proposed approaches in he lieraure o obain an accurae hear rae esimae from a noisy cardiac signal. Several works have been based on he use of an adapive filer, bu such echniques always rely on he presence of an exernal reference signal, such as acceleromeer daa [7, 8] or elecrode issue impedance [9], which may no always be available. Moreover, differen reference signals may be beer correlaed wih differen ypes of moion arifacs and hus a sysem based on only one reference signal may no represen a generalized soluion o handle arifacs from a variey of user acions. Mehods based on a Kalman filer do no rely on an exernal reference [10], bu hese echniques assume ha he signal and observaion models are linear funcions and ha he noise is Gaussian, which is no always he case for biomedical applicaions [11]. The exended Kalman filer was inroduced o circumven he disadvanage of he lineariy assumpion [12], bu jus like he regular Kalman filer i sill suffers from he fac ha only unimodal Gaussian disribuions can be racked [11]. In oher words, only one possibiliy for he rue sae can be racked a a ime and if he esimae diverges from he rue sae, i may coninue o diverge beyond recovery. Apar from hese, here have been a few works ha successfully combine several signal processing echniques along wih heurisic knowledge of signal characerisics o build a hear rae deecion algorihm. There have been hree recen relaed works of noe ha ackle he problem of hear rae esimaion in he presence of exreme moion arifacs when running. The firs, dubbed TROIKA [13], involves primarily singular value decomposiion, an opimizaion approach o find a sparse signal represenaion of he PPG frequency specrum and finally specral peak racking approaches o esimae he hear rae. The second echnique developed by he same auhor, called JOSS [14], has a similar approach excep i joinly esimaes he specra of he acceleromeer as well as he PPG and does away wih cerain seps o save on compuaion ime. The hird and final work for PPG signals wih moion arifacs [15], which we will refer o as Robus EEMD, is based on ensemble empirical mode decomposiion (EEMD), followed by a recursive leas squares (RLS) adapive filer using he acceleromeer signal as reference. These wo echniques are followed by several specral peak racking approaches as well as heurisic condiional seps o rack he hear rae frequency. Laer in his paper, we will presen a comparison of our proposed pariclefiler based approach wih hese hree works, boh in erms of esimaion accuracy as well as compuaional efficiency. The paricle filer is a probabilisic mehod ha does no depend on any exernal reference signal nor assume a specific disribuion for eiher he signal or he noise as is he case for he Kalman filer. I is robus and has he poenial o recover from incorrec esimaes since i can keep rack of muliple possibiliies. I is generalizable and can be adaped o handle a variey of signal and noise models. I is also sraighforward o adjus he number of paricles in use, o rade-off beween compuaion ime and accuracy depending on he applicaion. The paricle filer has been previously employed in oher similar applicaions, such as idenifying he various segmens of an ECG in saionary condiions. However, apar from no dealing wih moion arifacs, hese works usually incorporae a complex dynamical model for he ECG ha involves several sae dimensions, which in urn increases he compuaional cos [16, 17]. Anoher work based on an ECG model has a much reduced dimensionaliy for he sae space; however i is only esed for ECG conaminaed by whie or pink noise [18]. A paricle filer has also been employed for muscle arifac affeced ECG de-noising, however his also relies on a sophisicaed model ha is specific o he progression of ECG wih muli-dimensional saes and does no seem o be validaed on ECG signals wih a significan amoun of noise [19]. Moreover, in all of he above, he approach ha relies on

3 he use of a single rigid and specific mahemaical model may no be generalizable o be used for a wider variey of signals from differen subjecs [20]. The key difference in our proposed framework is ha he hear rae iself is direcly used as he sae o be esimaed in he paricle filer model equaions, and we design he observaion densiies such ha he paricle filer simply rewards hose observaions ha are consisen wih he expeced behavior of a human hear rae. Moreover, he use of only a single sae dimension in he formulaion grealy eases he compuaional load compared o previous paricle filer implemenaions in his domain. A. Paricle Filer III. BACKGROUND In order o formulae he sae esimaion problem for hear rae deecion, we firs define he sae space represenaion: X ~π x (X ) (iniial disribuion) Z X ~ g(x ) X +1 X ~ f(x ) where X denoes he rue sysem sae, i.e., he rue hear rae a ime, π x (X ) denoes he iniial disribuion of he sysem saes based on some prior knowledge, Z denoes a se of discree observaions, g( ) is a funcion represening he observaions condiioned on he rue hear rae, and f( ) is he sae dynamics or ransiion model ha characerizes he hear rae dynamics as a funcion of ime. In essence, he funcion g(x ) denoes he likelihood of observaions given he rue sae, and he funcion f(x ) describes he progression of he rue sae due o is own dynamics over ime. The sae esimaion problem can be delegaed o a paricle filer, which is a sequenial Mone Carlo mehod ha solves he problem by mainaining a se of weighed paricles, each being a candidae sae esimae, is weigh being proporional o he likelihood of ha paricle represening he rue sae. A each sep of he paricle filering problem, he goal is o esimae he poserior sae disribuion (p(x Z )), i.e., he probabiliy disribuion of he curren rue sae given a se of observaions. This is esimaed by he weighed sum: N p p(x Z ) = p=1 W X pδ( X X p ) (1) X p is he p h paricle a window, W p X denoes he weigh of paricle X p, N p is he oal number of paricles and δ( ) is he Dirac dela funcion, used o place a mass a he paricle s locaion in he poserior probabiliy densiy funcion. Once his poserior probabiliy disribuion is updaed in each ime insance, a suiable mehod can be used o bes esimae he arge sae a each ime. In his work, we use he maximum a poseriori (MAP) esimae. B. Problem Characerisics (observaion densiy) (ransiion densiy) There are a number of reasons why he paricle filer is a good fi for he paricular problem of hear rae esimaion in noisy signals, when compared o oher similar echniques. For example, if we consider he problem of hear rae esimaion using peak deecion on he ECG, a common source of noise is moion ha causes spike-like arifacs. These could lead o false posiives for a peak deecion algorihm. If we consider a specific insance wih a rue hear rae of 60bpm, if here is a false posiive peak beween wo rue peaks, hen he average esimaed hear rae for ha period becomes, say 120bpm. Thus, i is clear ha he noise canno be modeled as a Gaussian disribuion around he rue value. The probabiliy disribuion of he hear rae is in fac muli-modal wih several disinc possible hear raes in he probabiliy space. This is precisely why, as menioned earlier, i may be unsuiable o use he Kalman filer which assumes linear Gaussian models, and he Exended Kalman filer ha can rack only one of hese muliple possible modes. Moreover, given his mulimodal probabiliy disribuion space where he differen modes can be very far apar in erms of hear rae, we decided o minimize he average error by aking he MAP esimae. The key insigh is ha he human hear rae is ypically a seady, consisen signal over shor ime windows; in he following secions we will describe he observaion mechanisms ha allow he paricle filer o essenially become a srucure ha amasses paricles in sae space regions ha show more consisency. In he dimension of ime, since he curren disribuion of he paricle filer depends on previous disribuions, here is an inheren sense of memory o faciliae rewarding of consisency. In he dimension of sae space, N differen paricles can rack N differen possible hear raes, hus allowing a parallel search for consisency which reduces he chances of permanenly going off rack. Anoher salien poin o noe is ha he paricle filer, as implemened in his work, is decoupled from he signal characerisics. In oher words, he paricle filer simply receives noisy observaions of hear rae, bu is agnosic o how hese observaions were obained and o wha signal modaliies and feaures were used. Thus, he paricle filer is no married o he paricular observaion mechanisms described in his work, and any changes o hese mechanisms for example o add sophisicaion, or make i more suiable for he given sensor or applicaion scenario can be easily inegraed ino he same paricle filer framework. More imporanly, oher signal modaliies for hear rae deecion, such as he ballisocardiogram (BCG), seismocardiogram (SCG) or bio-impedance, could also fi ino he same framework and be fused wih esimaes from exising sensors. C. Signal Characerisics Elecrocardiogram Signal: The ECG is a represenaion of he elecrical aciviy of he hear. In his work we are ineresed only in he hear rae, and one of he mos common ways o esimae he hear rae from ECG is using he R-peaks. The R-peak denoes he poin of elecrical depolarizaion of he venricles of he hear a he sar of each bea. The ime beween successive R-peaks can be used o calculae he bea-o-bea hear rae (Figure 1). However, as menioned before, spike -like effecs caused by moion arifacs could be falsely idenified as R-peaks. This

4 naurally leads o overesimaion of he hear rae when using peak deecion based approaches. arifacs caused by moion or oher noise sources. In he example in Figure 3, four differen hear rae observaions will be considered based on he peak-o-peak pairs shown. Figure 1 - R-peak and R-R inerval in an ECG waveform Phooplehysmogram Signal: The PPG is obained by ransmiing ligh of suiable wavelengh ino he skin and using a phoodiode o capure he refleced response ha is modulaed by he flow of blood, as shown in Figure 2. Unlike ECG, since here is no clear ime domain feaure, we insead use frequency domain observaions for he PPG as will be described in Secion IV A. Figure 2 PPG waveforms showing periodic hearbea Acceleromeer Signal I is quie probable ha frequencies due o he cadence of walking or running moions would be prominenly presen in boh ECG and PPG signals. Since hese frequencies would also be presen in he acceleromeer s daa, we can leverage his o beer inform he esimaion process. This is paricularly imporan in insances where he moion resuls in a periodic noise in eiher he ECG or PPG signal. The paricle filer is designed o exploi he assumed quasi-periodiciy of he hearbea and randomness of moion arifacs; hus in he specific insance of noise due o periodic moion, he acceleromeer observaions can prove criical o disinguish his from periodic hear rae. IV. METHODS A. Observaion Mechanism The sensors provide observaions of he hear rae, and he paricles updae heir weighs according o each of hese. Phooplehysmogram Observaions The PPG signal is firs bandpass filered beween 0.5 and 15Hz o remove baseline wander and unrelaed high frequency noise. Subsequenly, we use a specrogram based approach, aking moving, overlapping windows of he PPG sream and applying he shor-ime Fourier ransform. The window size was se o be 8 seconds, wih an overlap of 2 seconds beween successive windows. The frequency specrum from a window of PPG consiues one se of observaions. Elecrocardiogram Observaions When processing he ime domain ECG signal, we use wo back-o-back non-overlapping windows dubbed W sar and W end. For he purposes of calculaing hear rae, we only consider peak-o-peak inervals ha begin wih a peak in W sar and end wih a peak in W end. All such inervals aken ogeher consiue a se of observaions for a given ime window. Noe ha he peaks ha consiue hese pairs may or may no be W sar W end Figure 3 - Windowing illusraion on ECG signal We use windows of size 2 seconds in his work, wih a sep size of approximaely 0.27 seconds. This sep size was chosen o accommodae he fac ha we expec hear raes as high as 220 beas per minue, and a sep size bigger han his could poenially mean skipping rue peak-peak observaions in hose scenarios. The peak deecion is hen done as follows: findpeaks(w i, A min, T min ) {P 1, P 2,, P k } = P Wi (2) findpeaks(w i, A min, T min ) finds he ime of occurrence of all peaks in he signal W i ha have ampliude a leas A min and such ha no wo peaks are wihin T min ime of each oher, P Wi is he se of peak locaions in ime, {P 1, P 2,, P k }, reurned by he findpeaks funcion. This funcion is he defaul implemenaion found in MATLAB. This peak deecion on is own however is somewha naïve, so we add an addiional sep in he procedure for ECG o reduce he number of false posiives. We used he coninuous wavele ransform (CWT) on he ECG signal wih he Mexican Ha wavele, a cener frequency of 0.25Hz and a scale of 5.29 as suggesed by a previous work [21]. This helped o accenuae peaks ha more closely resemble an R- peak and diminish oher rivial peaks. The sep described in Equaion (2) is hen performed on he wavele ransformed signal o obain he peak locaions. I mus be noed ha his merely reduces he number of false posiives bu does no eliminae hem. Peak-deecion based hear rae esimaion based solely on he CWT esimae would sill overesimae due o false posiives, as shown in our previous work [22]. The hear rae observaions are hen obained as follows: P Wsar = {P 1, P 2,, P k } (3) P Wend = {P 1, P 2,, P m } (4) PP Se of all (P b P a ) P a P Wsar, P b P Wend Z n = ( fs PP (n) ) 60 (5) P Wsar and P Wend refer o he ses of peak locaions in a saring and ending window respecively, fs is he sampling rae, PP is he se of peak-o-peak inervals wih he firs peak in a saring window and second peak in an ending window, Z n is he n h hear rae observaion of window expressed in beas per minue (bpm). Taking all Z n in a given window corresponds o he se of observaions Z referred o in Secion III A when describing

5 he paricle filer s observaion model. I mus be noed ha we ake seps o avoid duplicae observaions, i.e., prevening he same wo peaks aken as a pair in muliple ime windows. We also ake seps o ensure any observaion included in he se is consisen wih oher observaions of similar hear rae from he same ime window already in he se; for example, when we have muliple false peaks we could very well have 4 observaions of 50bpm wihin a 2 second window, bu i is clearly impossible in realiy for all hese observaions o be rue. So in his example, only hose pairs of peaks corresponding o 50bpm ha are consisen wih each oher are aken ino he se. This sep is necessary o avoid an undue preponderance of lower hear rae observaions jus because of he naure of our relaively naïve observaion mechanism. Acceleromeer Observaions The acceleromeer daa (denoed as ACC) is processed using he same specrogram approach used for he PPG signal, wih idenical windowing procedures. Since here are 3 axes on he acceleromeer, we srived o combine hem ino a single specrogram o provide a unified source of observaion for he moion noise over ime. Using only one axis on is own was no an opion because here was no cerainy abou which axis capured he mos aciviy across he differen subjecs in he daabase. This is presumably due o variaions in sensor placemen and running syles among he differen subjecs. We compued he specrogram for each of he 3 axes, and hen siched ogeher a combined specrogram ha always included only he maximum of he hree available powers for each of he frequencies in each ime window. This greedy approach allows o always capure he moion frequencies wihou unduly diminishing heir relaive power. B. Paricle Filer Implemenaion The iniial disribuion for he paricle filer, π x (X ), is defined as follows: X ~π x (X ) = U(HR min, HR max ) (6) Where U( ) denoes a uniform disribuion beween HR min and HR max, he assumed lower and upper limis of he hear rae defined by reasonable human physiological bounds. We made he iniial disribuion uniform since we have no prior knowledge on he iniial hear rae, oher han exreme limis. For he PPG, he probabiliy of an observaion wih respec o a given sae of hear rae is compued as follows: φ i i = S F n n=1 S, i (1, F) (7) p(z X ) = g(x ) d = φ (8) i S is he i h elemen of he vecor of observed power specrum ampliudes (measured as described in Secion IV A) in ime window for he PPG signal, F is he oal number of frequencies under consideraion, i φ is he i h elemen of φ, he probabiliy densiy funcion ha resuls from normalizing he values of he observed power specrum o be beween 0 and 1 in ime window, d, refers o he frequency in he power specrum ha is closes o he hear rae X. d φ is he probabiliy of he even ha he corresponding frequency represens he rue hear rae. This formulaion is based on he assumpion ha a higher power a a given frequency means he more likely i is ha ha frequency represens he hear rae. However, we know ha wih moion arifacs here could be high power a cerain frequencies as a resul of he cadence of moion. This is where he observaions from he acceleromeer sensor come in; we formulae he acceleromeer observaion funcion such ha we reduce he likelihood of a given frequency represening he rue hear rae if i is presen in high power in he acceleromeer power specrum. The formulaion is as follows: φ i = i+1 i=i 1 S i F n=1 S n, i (1, F) (9) p(z X ) = g(x ) = (1 φ d ) (10) S i is he i h elemen of he vecor of he observed power specrum ampliudes in ime window of he acceleromeer specrogram, F is he oal number of frequencies under consideraion, φ i is he i h elemen of φ, he probabiliy densiy funcion for moion noise ha resuls from normalizing he values of he observed acceleromeer power specrum o be beween 0 and 1 in ime window, d, is he index of he power specrum corresponding o he frequency ha mos closely maches he hear rae X. φ d is he probabiliy of he even ha he corresponding frequency is no he hear rae, which for our purposes means i is noise. For he ECG, in order o creae a coninuous probabiliy disribuion ou of he discree observaions, we fi Gaussian disribuions around each of he observaions resuling in a Gaussian mixure. The probabiliy of a se of observaions is hen compued as follows: O p(z X ) = g(x ) = p(z n X ) O n=1 = n=1 N(Z n, X, σ z ) (11) n Z refers o he n h hear rae observaion in window, O is he oal number of observaions in window. N(Z n, X, σ z ) denoes a Gaussian disribuion wih mean equal o he hear rae X in window, and sandard deviaion σ z reflecing he maximum olerable deviaion beween he rue hear rae and he observaion, evaluaed a Z n. σ z is heurisically se o be 3bpm in his work, o ensure ha a given paricle is reasonably close o an observaion o gain weigh. Making his parameer oo high would mean even unrelaed paricles gain weigh from a given observaion, whereas making i oo low would oo sricly require paricles o exacly mach he observaion o gain weigh. The paricle filer is iniialized as follows: X p 0 = U(HR min, HR max ) (12) W p X0 = 1 (13) N p p (1, N p ) X p 0 is he p h paricle sampled from he uniform disribuion beween HR min and HR max, defined o be 40 and 220 bpm respecively for his work, a ime = 0, W p X0 is he iniial weigh of paricle p a ime = 0. N p is he oal number of paricles, se o be 300 in his work. Choosing he number of paricles affecs a rade-off beween esimaion accuracy and compuaion ime, which we will elaborae furher on in Secion VI F.

6 Afer his iniializaion, wih each succeeding ime window, he paricle weighs are updaed as shown in (14). Noe ha we use he so-called boosrap filer wherein he sae ransiion densiy is used as he imporance disribuion, making he weighs of he paricles direcly proporional o he observaion densiy [5]. We chose o do his o simplify he compuaional load considering he applicaion domain. O W p X = p(z X p n=1 N( Z n, X p, σ z ), for ECG ) = { φ d, for PPG (1 φ d ), for ACC p (1, N p ) (14) X p is he p h paricle of window, W p X is he weigh of paricle X p, N(Z n, X p, σ z ) is he value of a Gaussian disribuion wih mean X p and sandard deviaion σ z evaluaed a Z n, d φ is he probabiliy of he even ha he frequency corresponding o X p represens he rue hear rae. φ d is he probabiliy of he even ha he frequency corresponding o X p is no he hear rae, which for our purposes means i is noise. The weighs are all hen normalized o be beween 0 and 1: N p r=1 W p X = W p X W r Xi (15) p (1, N p ) W X p is he weigh of he p h paricle of window normalized so he weighs form a probabiliy mass funcion. Once he paricle weighs are calculaed he well-known sampling imporance resampling (SIR) procedure is employed o preven paricle degeneracy [5]: M p p = W X r r=1, p (1, N p ) (16) u = argmin a R a U ~ U(0,1) M (17) X p u = X, p (1, N p ) (18) M p is he p h elemen of a cumulaive sum vecor of he normalized paricle weighs X p is he updaed sae of he p h paricle of window afer resampling, and R U is a randomly seleced number from he uniform disribuion beween 0 and 1. Afer his sep, he disribuion of paricles approximaes he poserior probabiliy disribuion of he rue hear rae sae. To ge an esimae for he hear rae in he curren ime window, as menioned before, we use he MAP esimae. Since he paricle weighs are now equalized, we insead look o he disribuion of paricles o capure he mos likely esimae. We cluser he paricles belonging o a similar hear rae ogeher, and can say ha he larges cluser represens he mos likely sae as i is analogous o aking he highes weigh paricle wihou he SIR procedure. The clusers and he hear rae esimae are hus calculaed as follows: C n Se of all X m X m X n < CS m (1, N p ), n (1, N p ) E = i i C max C max (19) C n is he n h cluser of paricles CS is he maximum spread of a cluser (se o be 3 bpm) i C max refers o he i h member of he larges cluser C max, and E is he esimae for ime window. For his specific applicaion, he esimae is hear rae in bpm. The final sep in a given ieraion of he paricle filer is he model-based updae ha reflecs he sae ransiion model defined earlier in Secion III. Essenially, as ime progress he rue hear rae is expeced o be dynamic o an exen, and no remain consan. Therefore, he paricles are updaed accordingly a he end of each ime window o approximae his behavior. We assume ha he model governing he human hear rae changes over ime is a normal disribuion: p ~f(x p )~ N(X p i, σ x ) = X p i + (σ x R N ~N(0,1)) (20) X +1 p (1, N p ) R N is a randomly generaed number from he sandard normal disribuion, and σ x is he sandard deviaion capuring he expeced change in hear rae from one window o he nex. Wih he window sep size being 2 seconds, σ x is heurisically se o be 6 bpm. The window hen shifs o a new secion of he signal and he paricle filer coninues o rack he hear rae in his manner ieraively over successive windows. C. Paricle Weighing Assumpions I can be seen from he formulaion for ECG ha for a given se of observaions in one ime window, we consider all he observaions as equally likely. We deemed i more generalizable o no rely on any specific feaures among a se of observaions o differeniae hem. Insead, we assume ha he rue hear rae for he subjec would make relaively smooh, coninuous and gradual changes over ime. Leading on from his, we also assume ha he observed hear raes as a resul of false posiive peaks are more random and inconsisen. Wih hese assumpions, our expecaion is ha even hough all observed hear raes are considered equally likely, he paricles will build over he correc hear rae as ha is observed more consisenly over successive ime windows. D. Fusion Technique Since we have formulaed he paricle filer wih only he hear rae as he sae o be esimaed, muliple signal modaliies and heir observaion mechanisms can be fused in he same framework. The paricle weighing for an arbirary number of observaion sources, i.e., sensors, is given by: W fusion p X = S p(z s X p s=1 ) (21) W fusion p X is he weigh assigned o paricle X p when fusing he informaion from muliple sources of observaion S is he oal number of observaion sources Z s is he se of observaions in ime window from source s In essence we assume ha since he differen sources are observing he same arge phenomenon, paricles corresponding o saes ha are observed wih higher weigh across muliple sources should be rewarded. Conversely, i is unlikely ha he same false sae would be observed wih high probabiliy across muliple sources. In oher words, i would be rare for a source of noise o affec sensors wih differen modaliies placed in differen locaions in he same way.

7 In his work, for he fusion of ECG, PPG and ACC sensors, he paricle weighing process is modified as follows: W fusion ECG p X = p(z X p PPG ) p(z X p ACC ) p(z X p ) (22) O ECG p(z X p ) = n=1 N( Z n, X p, σ z ) (23) p(z PPG X p ) = φ d (24) p(z ACC X p ) = (1 φ d ) (25) Similarly, in he daabase o be described in more deail in Secion V, here are wo separae PPG sensors in addiion o he acceleromeer in a wach-like device; so he formulaion above is modified by simply replacing he observaions from ECG wih he observaions from he second PPG sensor. Wih his formulaion, we can also ge an idea of he conribuion of each sensor or signal modaliy o he overall paricle filer esimae in each ime window, as shown below: β s = p p(z s X p X ) Cmax, s S (26) s β is he conribuion of sensor s o he paricle filer esimae in ime window X p is a paricle in he maximum clique C max for window s Z is he se of observaions in ime window from sensor s S is he se of all sensors or signal modaliies This conribuion can hen be normalized wih respec o all he sensors in he sysem and expressed as a percenage: β s = (β s m m S β ) 100 (27) Sensors producing random, noisy observaions will likely have a low conribuion o he overall paricle filer esimae, hus poenially informing dynamic adjusmens o he conribuions of individual sensors based on perceived signal qualiy in real ime. Moreover, prior knowledge of he increased reliabiliy of one sensor could allow increased weighage of observaions originaing from ha sensor. In his iniial work however, we keep i simple and do no assume ha any one signal sensor is inherenly beer han he oher. The advanage of his overall mehod of fusion is ha i is simple and generalizable and can easily be reused for differen applicaions as well as an arbirary number of sensors. E. Addiional Improvemens While he paricle filer framework is complee wih he above implemenaion, we found during he course of our experimens wih he daa ha we could make addiional improvemens o he algorihm o furher reduce error for his specific scenario of esimaing HR for a running subjec: Hard Thresholding of ACC We assume ha he power of a frequency in he acceleromeer specrum is direcly proporional o he probabiliy of ha frequency represening moion noise. However, in a few subjecs daa here was a harmonic of he movemen frequency ha was somewha low in srengh bu sill high enough o mislead he paricle filer. Therefore, we modified he ACC probabiliy funcion o remove from consideraion an observaion if he power of he corresponding frequency was greaer han 10% of he maximum power observed in he acceleromeer for ha ime window. Deecing ACC Overlap wih Hear Rae Frequency There were a few insances wherein he dominan ACC frequency happened o overlap wih he rue hear rae frequency. This would be especially problemaic wih he hard hresholding inroduced above. Therefore, we implemened a rough frequency margin around he expeced hear rae, and if he ACC frequency under consideraion was wihin his zone, we did no perform he hresholding. This ensured ha we did no effecively remove from consideraion paricles corresponding o he hear rae simply because he ACC frequency was close. The bounds for he margin were se by aking he average of he previous 3 hear rae esimaes in Hz and making a conservaive bound of +/- 0.1 Hz. This corresponds o an assumpion ha he hear rae would no change by more han 6 bpm in eiher direcion from one ime window o he nex. Deecing Resing Sae In all of he daa, he subjec sars a res a leas for a few seconds before beginning any aciviies. I makes lile sense o include he acceleromeer observaions in hese saes. Therefore, we firs find he magniude of acceleraion in each ime window as follows: τ = (a x ()) 2 + (a y ()) 2 + (a z ()) 2 (28) a x () is he x-axis acceleraion for he given ime window a y () is he y-axis acceleraion for he given ime window a z () is he z-axis acceleraion for he given ime window The observaions of he acceleromeer are aken ino consideraion for he final hear rae esimae only if his magniude was above a cerain hreshold. The hreshold was heurisically deermined o be 1.04 g by examining he daa. This parameer has o be heurisically se his way in he absence of more sophisicaed aciviy deecion algorihms. Changing Model for Ramping Up of Hear Rae When he subjec ransiions from a resing sae o walking or running, here is naurally a sudden increase in hear rae in response o he increased workload. There were a few insances where he paricle filer was slow o cach up simply because here happened o be observaions corresponding o he slower resing sae hear rae which urned ou o be false observaions. In hese siuaions, here is an error in hear rae for a few ime windows because he paricle filer already had a preponderance of paricles around he resing hear rae and coninued o see observaions consisen wih ha hear rae. So in a sense here may be some laency for he paricle filer esimaes o cach up o he rue hear rae when here is an abrup change in he dynamics. Therefore we waned o inroduce he noion of conexawareness and have muliple operaing modes for he paricle filer. When we have he acceleromeer, we have an independen source of informaion ha provides addiional conex for he user s curren sae. When he subjec is a res or running seadily, we do no expec rapid changes in hear rae and so he paricle filer model sae updae (described in equaion (20)) will be conservaive. Conversely, when he subjec s aciviy level increases rapidly, we can accordingly adjus he model for sae updae o emporarily allow for

8 greaer changes. A similar idea for his adapive changing of model equaions based on he curren conex has been previously implemened in oher applicaion areas [23]. For our problem, when he subjec was previously a res (as deermined by he magniude hreshold) and he ACC magniude from (28) changes by a significan margin from one ime window o he nex, we can assume ha increased aciviy has begun. Then for he nex few ime windows, insead of using he sae updae equaion described in (20), we use he following: p ~f(x p )~ N(X p i, σ x ) = X p i + (R N ~N(α, σ x )) (29) X +1 p (1, N p ) R N is a randomly generaed number from he normal disribuion wih mean α and sandard deviaion σ x α is a posiive bias mean o indicae ha on average, he hear rae is expeced o increase. I is se o 6bpm in his work. σ x is he sandard deviaion capuring he change in hear rae from one window o he nex. I is se o be 10bpm, a larger number o reflec he possible rapid changes in hear rae. The hreshold for required change in acceleraion magniude is se o be 0.04 g, and when such a change occurs he alernae updae equaion (29) is used for a period of 5 ime windows. Noe ha we do no assume he hear rae definiely mus increase whenever higher ACC aciviy is deeced, as ha is placing oo much rus in a rudimenary aciviy deecion approach. Raher, we simply allow he paricles o be more spread ou han usual for a few ime windows when we deec a possible sign of volailiy in he hear rae. In oher words, here will be more paricles han usual in he higher hear rae regions in anicipaion of a sudden increase, bu here will coninue o be paricles corresponding o he previous seady sae, lower hear raes, and everyhing in beween. This is one of he core advanages of he paricle filer, wherein paricles can rack muliple possible saes in parallel. Wih his conex-aware mode-swiching approach, he insances of paricle filer esimae laency due o sharp hear rae changes was reduced. We did no observe his laency effec for longer han 3 ime windows or 6 seconds across all subjecs esed in his work, and here was no laency a all for many subjecs. A. PPG Daabase V. EXPERIMENTAL SETUP Moion arifac affeced PPG daa was aken from he daabase used as par of he 2015 IEEE Signal Processing Cup (SP Cup) [13]. This daa was recorded a a sampling rae of 125Hz using a wris-worn dual PPG sensor (i.e., wo simulaneous channels of PPG) from 12 subjecs. The sensor also included a 3-axis acceleromeer. Each rial for a subjec consised of 30 seconds of resing, followed by four sages of aciviy each for 1 minue, and finally 30 seconds of res again. The four periods of aciviy consised of alernaing beween relaively slower (6km/h or 8km/h) and faser (12km/h or 15km/h) readmill speeds. ECG was also simulaneously recorded from he ches using we sensors, and his is used o obain he ground ruh hear rae. Since he hree relaed works menioned earlier TROIKA, JOSS and Robus EEMD also all worked on he same daase, we can direcly compare he average errors in hear rae esimaion. A his juncure, we noe ha he JOSS work resampled he daa o 25Hz (presumably o ease he compuaional load) and also runcaed he daa for 6 of he 12 subjecs; his is because ha algorihm is enirely dependen on a clean sar for he racking, and half he subjecs had signals wih some noise o varying degrees even a he iniial resing sage. Therefore, o compare wih JOSS we also perform he resampling as well as he runcaions described in ha paper [14]. However, one of he key advanages of he paricle filer is he increased abiliy o recover from going off-rack due o he presence of muliple differen paricles in he sae space. So we will also presen he resuls from he un-runcaed daases and show ha he paricle filer effecively recovers from hese false sars. B. ECG Daabase wih Simulaed Noise As he daase described in he previous secion had only clean ECG, we waned o find anoher soluion o obain moion arifac affeced ECG o es he paricle filer on he esimaion of hear rae from he fusion of simulaneous noisy ECG and noisy PPG. To he bes of our knowledge here was no exising daabase ha provided simulaneously recorded ECG and PPG daa ha were affeced by real moion arifacs and also had he ground ruh hear rae available. Therefore, we urned o he MIT-BIH Noise Sress Tes Daabase o ge real moion arifac noise and add i o he exising clean ECG signals from he aforemenioned Signal Processing Cup daabase [24, 25]. The MIT-BIH daabase, including he echniques o synheically inroduce realisic moion arifac noise, is well respeced and has been used in several previous works. The owners of he daabase hemselves provided a echnique o add calibraed amouns of moion noise daa o any given ECG record from heir own daabase such ha he desired SNR level is obained. We have simply adaped his approach o injec he moion arifac noise ino he ECG daa from he SP Cup daabase. In order o es he fusion approach, we used he ECG daa injeced wih moion arifacs in conjuncion wih he PPG daa ha is already presen in he same daabase wih real arifacs due o he running aciviy. The paricle filer esimaes from hese fused observaions are compared o he hear rae from he unaffeced clean ECG daa in he daabase. We ensure ha he added moion arifac noise for ECG is proporionally increased in inensiy as and when he running speed increases in a given daa record. We chose SNR levels of 3dB and -3dB respecively for he slower and faser speeds. Generaing his noisy ECG allows us o illusrae how he paricle filer can fuse muliple modaliies o improve hear rae esimaes compared o using individual sensors. C. Experimenal Daa Collecion Even hough we believe he mehodology of adding noise o he ECG described in he previous secion is sound, we readily concede ha he ideal scenario would be o have simulaneously colleced ECG and PPG daa ha were boh affeced by real moion arifacs during he course of he daa

9 collecion. Since such a daabase is lacking in he lieraure o our knowledge, we conduced a limied daa collecion of our own o bolser our experimenal conclusions. We used a previously developed sysem called he BioWach [26] ha colleced one channel of PPG signals from he wris and also included an acceleromeer. For he ECG, we used a cusom plaform based on he TI ADS1299, an analog fron end for bio-poenial signals. One channel of ECG was recorded from he ches using adhesive gel elecrodes in a Lead II configuraion o be used as he ground ruh. A second channel was recorded using a dry elecrode ha was secured o he forearm jus above he BioWach using medical ape. This was mean o provide an ECG signal ha was more suscepible o moion arifacs. Boh devices sampled daa a a rae of 125Hz and ransmied daa o a PC wirelessly using Blueooh. Daa was colleced from 5 subjecs running on a readmill afer informed consen and proocol approval by he IRB a Texas A&M Universiy (IRB D). The experimenal proocol was designed o be similar o ha of he daabase described earlier: 30 seconds of res, followed by four 1- minue periods alernaing beween walking and running, and 30 seconds of res a he end. Examples of he signals from our sysem afer pre-processing (0.5 o 15Hz bandpass for PPG and 0.5 o 30Hz bandpass for ECG), for boh sanding and running scenarios are shown in Figures 4 and 5 respecively. Figure 4 ECG, PPG and Acceleromeer signals wih subjec a res Figure 5 ECG, PPG and Acceleromeer signals wih subjec running VI. RESULTS A. Hear Rae Esimaion Accuracy PPG Daabase Table I shows he average hear rae esimaion error in bpm for each of he 12 subjecs in he SP Cup daabase as well as he overall mean and sandard deviaion of error. We can see ha he average error is < 2bpm for mos subjecs. Also shown for comparison are he corresponding resuls from he JOSS, TROIKA and Robus EEMD works. Noe ha Table I shows he resuls for he runcaed daa, and resuls are presened for our proposed work as well as he Robus EEMD a boh 25Hz and 125Hz sampling rae. The average errors are more or less similar for he differen mehods, wih he Robus EEMD marginally beer, whereas he proposed mehod a 125Hz shows he lowes sandard deviaion of error. The resuls for he un-runcaed daa are in Table II, and we can see ha he error from he paricle filer esimaes are hardly affeced despie he noisy iniial periods ha prohibied he use of he JOSS algorihm. In Figure 6 below is shown he Bland-Alman plo for he paricle filer esimaes agreemen wih he ground ruh a he full 125Hz sampling rae. Figure 6 Bland-Alman plo for paricle filer agreemen wih ground ruh The limis of agreemen (LOA) were defined following sandard pracice as [µ σ, µ σ], where µ is he average difference and σ is he sandard deviaion, 2.35 bpm in his case. The LOA were [-4.75, 4.45] bpm, and 95% of he difference values were wihin his confidence inerval. B. Hear Rae Esimaion Accuracy ECG Daabase and Fusion of ECG + PPG Table III shows he esimaion error when using he paricle filer o esimae hear rae from he noisy ECG simulaed as described in secion V B. For comparison, we show he average esimaion error for hear raes as compued by our implemenaion of he well-respeced Pan-Tompkins algorihm, which was designed specifically o esimae hear rae from ECG signals [27]. Of course, he Pan-Tompkins algorihm was no designed for his inensiy of moion arifacs, bu we included i o show he exen of noisiness in he ECG which causes significan issues for an esablished algorihm. We can see how he paricle filer also works well wih his differen modaliy wih low error raes. In addiion, also shown in he able are he resuls of fusion of his noisy ECG wih he wo noisy PPG channels and he acceleromeer. We can see how he fusion almos always improves he accuracy, showing how he paricle filer was able o effecively reward he consisen rue observaions across he differen sources and make he bes of he sensors available. The paricle filer racking over ime for Subjec 1 is also shown in Figure 7 for illusraive purposes. In his figure, Findpeaks esimae refers o he hear rae esimae based solely on he CWT-based peak observaion mehod on ECG, and i can be seen how i ends o overesimae as soon as he moion sars, whereas he paricle filer coninues o keep rack even as he subjec s hear rae changes subsanially during periods of moion aciviy. Figure 7 Hear rae esimaion performance on a single subjec

10 TABLE I. MEAN ABSOLUTE HEART RATE ESTIMATION ERROR (IN BPM) FOR THE VARIOUS ALGORITHMS ON THE TRUNCATED DATASETS Subjec # Mean ± SD JOSS [14] (25Hz) ± 2.61 TROIKA [13] (25Hz) ± 2.86 Robus EEMD [15] (25Hz) ± 1.79 Paricle Filer (25Hz)(Our mehod) ± 2.07 Robus EEMD [15] (125Hz) ± 2.02 Paricle Filer (125Hz) (Our mehod) ± 1.73 TABLE II. MEAN ABSOLUTE HEART RATE ESTIMATION ERROR (IN BPM) FOR THE VARIOUS ALGORITHMS ON THE UN-TRUNCATED DATASETS Subjec # Mean ± SD TROIKA [13] (25Hz) ± 3.45 Robus EEMD [15] (25Hz) ± 2.17 Paricle Filer (25Hz) (Our mehod) ± 2.17 TROIKA [13] (125Hz) ± 0.82 Paricle Filer (125Hz) (Our mehod) ± 2.01 TABLE III. MEAN ABSOLUTE HEART RATE ESTIMATION ERROR (IN BPM) FOR THE ECG AND FUSION (ECG+PPG) PARTICLE FILTERS, AND PAN-TOMPKINS Subjec # Mean ± SD ECG Paricle Filer (Our mehod) ± 2.02 ECG+PPG Paricle Filer (Our mehod) ± 1.32 Pan-Tompkins[27] ± C. Hear Rae Esimaion Experimenal Daa Collecion In Table IV we also presen he resuls of hear rae error from he fusion paricle filer on he daase colleced ourselves, which guaranees real simulaneous ECG and PPG affeced by moion arifacs. This shows ha he paricle filer performance coninues o be effecive even in his scenario. Again, for comparison is shown he error raes when using he Pan-Tompkins algorihm on he noisy ECG. Noe ha for Subjec 4 he Pan-Tompkins algorihm s adapive parameers compleely wen off rack early on in he daa record due o excessive noise, and did no recover esimaes hereafer. TABLE IV. MEAN ABSOLUTE ESTIMATION ERROR FOR FUSION PARTICLE FILTER AND PAN-TOMPKINS ON OUR EXPERIMENTAL DATASET Subjec # Error for Paricle Filer (bpm) Error for Pan-Tompkins [27] (bpm) figure, we plo only a subse of he ime windows, spanning abou 1 minue. Moreover, overlaid in red is he paricle filer hear rae esimaion error for each of hose windows. The error rises o almos 20 beas per minue around window 10, bu soon afer his he conribuion of he ECG o he overall esimae increases. I is clear ha he paricle filer fusion rewards he more consisen observaions from he ECG, and correspondingly he overall error drops sharply. We see a similar rend on a smaller scale around ime window 40, where he error is relaively high unil he ECG conribuions become higher and he overall esimaion performance becomes beer. In fuure work, we aim o implemen echniques ha can recognize hese rends of qualiy of observaions and explicily re-weigh individual modaliies in he fusion formulaion N/A Mean ± SD 1.4 ± ± D. Fusion Conribuion Analysis In order o furher illusrae how he fusion of modaliies works, we ake a closer look a he performance on Subjec 10 from he daabase. As can be seen in Tables I and II, esimaion performance on his subjec is noiceably worse, for our algorihm as well as hose of oher previous works. This suggess ha he PPG signals hemselves were relaively more unreliable for his subjec. However, we see ha in Table III when using he noisy ECG he performance is much beer; so we can assume in his insance ha he ECG is a more reliable signal a leas for cerain segmens of he daa. Figure 8 shows he relaive conribuion of each modaliy ECG and he wo PPG sensors over ime for Subjec 10, compued as described in equaions (26) and (27). In his Figure 8 Relaive conribuion of ECG and PPG modaliies o overall fusion paricle filer esimae over ime for Subjec #10 E. Discussion of Esimaion Performance The esimaion errors are low, bu in order o provide furher conex, we have compared he resuls o hose of recen sae-of-he-ar works on hear rae esimaion in he presence of moion arifacs. The esimaion error levels are comparable o he mos recen relaed works in he area. We noe ha he oher relaed works were specifically developed and opimized for he objecive of hear rae monioring using PPG signals wih several heurisics; for insance, TROIKA and JOSS use heurisics such as a rigid arificial bound on he variabiliy of repored hear rae esimaes from one window o he nex, hresholds for wha consiues a big enough peak in he PPG frequency specrum, and polynomial curve fiing based on previous hear rae esimaes o predic he nex esimae when he racking does no reurn a saisfacory resul. Similarly, he Robus EEMD work, in addiion o

11 JBHI using EEMD and an adapive filer, has an arbirary absolue crierion o designae a reliable peak in he PPG specrum for hear rae and hresholds for wha consiues a srong enough peak in he PPG specrum. The algorihm also delees or removes segmens of he signal from consideraion if he corresponding acceleromeer magniude is oo high. Moreover, wih he EEMD approach he user is required o manually deec in a raining phase which of he several inrinsic mode funcions has he perinen hear rae frequency informaion, and his also changes wih sampling rae. I is herefore noable ha he relaively more generalized paricle filer framework inroduced here wih minimal heurisics or rule-based seps, no requiremen for clean sar, no deleion of daa, which can work wih oher signal modaliies as shown wih ECG, and can also be applied o oher physiological signal esimaion problems, exhibis comparable performance o conemporary works ha were purpose-buil for he hear rae esimaion problem on PPG signals. Moreover, as will be noed in he nex secion, his comparable esimaion performance is achieved wih an algorihm ha is far more compuaionally efficien compared o hese works. F. Compuaion Time In his work, due o he formulaion wih he hear rae sae, we miigaed he compuaional load by racking only one sae dimension wih jus 300 paricles. Indeed, he conemporary works we can compare his o are significanly more compuaionally inensive. The auhors of he Robus EEMD work [15] noe ha he TROIKA algorihm akes abou 17 minues and 30 seconds on average o complee hear rae esimaion on a single subjec a a sampling rae of 125Hz; whereas he Robus EEMD algorihm iself akes abou 55 seconds per subjec. Similarly, a a sampling rae of 25Hz, he JOSS algorihm akes abou 25s on average per subjec and he corresponding Robus EEMD algorihm akes abou 16s. When we measured he execuion ime of our paricle filer implemenaion on MATLAB, he average ime per subjec was only abou 1.04 seconds for he 25Hz sampling rae, and 1.18 seconds for he 125Hz sampling rae. I mus be noed ha he execuion imes repored above for he relaed works were gahered from a work ha used MATLAB 2013a, whereas we use MATLAB 2017a. However, his alone canno accoun for he highly significan difference in compuaion ime. Furhermore, he machine used o exrac hese resuls has similar specificaions o he one used o repor he resuls for he relaed works [15]. In paricular, we used a Windows bi PC wih an Inel i processor a 2.60 GHz and 16GB of RAM. We also analyzed he rade-off beween he accuracy and compuaional cos as a funcion of he number of paricles. Figure 9 shows a comparison of he error raes and compuaion ime per minue of daa for our paricle filer as he number of paricles is varied for a single subjec. As a reminder, we used N = 300 paricles in our work. While he esimaion performance does improve as we increase he number of paricles, as expeced, i is likely ha he higher values of N would make i impracical o compue hese esimaes in real-ime, especially on wearable sensors. On such sysems, one can easily adjus he number of paricles subjec o he availabiliy of compuaional resources. Figure 9 Changes in average esimaion error and compuaion ime per minue of daa on a single subjec as he number of paricles is changed G. Limiaions We did no es on paiens wih hear rae variabiliy or oher cardiac condiions; his will likely require some uning of he parameers, bu his would be applicable o oher conemporary signal processing echniques as well. Tesing on subjecs wih abnormal cardiac aciviy will be lef for fuure work. We also noe ha precise compuaional benchmarking is no he primary goal of his work; he previous secion was only mean o provide a rough guide indicaing a definie compuaional advanage over conemporary relaed works in he area. Deploymen of he algorihm on a sysem is ou of he scope of his work; however we submi ha he design of such a sysem is eminenly feasible, especially if we leverage cloud compuing resources or oher echniques o circumven he compuaional consrains on ypical wearable sysems. VII. CONCLUSION In his work, we have inroduced a generalized paricle filer framework ha can be used o rack hear rae and proved he feasibiliy of he echnique on real world PPG and ECG signals affeced by moion arifacs. Furhermore, we showed how he paricle filer can be used o successfully improve esimaion accuracy by combining informaion from muliple modaliies simulaneously measuring he same arge phenomenon or even he noise associaed wih he arge. This will prove useful in he conex of he upcoming IoT ecosysem where here are muliple wearable and environmenal sensors coninuously monioring he physiological saus of he user. ACKNOWLEDGMENT This work was suppored in par by he Naional Science Foundaion, under grans CNS and EEC , and by TerraSwarm, one of six ceners of STARne, a Semiconducor Research Corporaion program sponsored by MARCO and DARPA. Any opinions, findings, conclusions, or recommendaions expressed in his maerial are hose of he auhors and do no necessarily reflec he views of he funding organizaions. REFERENCES [1] G. E. Prinsloo, H. L. Rauch, and W. E. Derman, A brief review and clinical applicaion of hear rae variabiliy biofeedback in spors, exercise, and rehabiliaion medicine, The Physician and Sporsmedicine, vol. 42, no. 2, pp , [2] F. Lin, C. Song, Y. Zhuang, W. Xu, C. Li, and K. Ren, Cardiac Scan: A non-conac and coninuous hear-based auhenicaion sysem, in 2017 ACM Inernaional Conference on Mobile Compuing and Neworking (MobiCom), Ocober [3] S. Ha, C. Kim, Y. M. Chi, A. Akinin, C. Maier, A. Ueno, and G. Cauwenberghs, Inegraed circuis and elecrode inerfaces for

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Tompkins, A real-ime QRS deecion algorihm, IEEE Transacions on Biomedical Engineering, vol. BME-32, pp , March Viswam Nahan (M 14) received his B.S. and M.S. degrees in compuer engineering from UT-Dallas in 2012 and 2015 respecively. He is currenly working oward his Ph.D. in compuer engineering a Texas A&M Universiy. His research ineress include design and developmen of wearable and reconfigurable healh monioring devices, and associaed signal processing echniques. Roozbeh Jafari (SM 12) is an associae professor in Biomedical Engineering, Compuer Science and Engineering and Elecrical and Compuer Engineering a Texas A&M Universiy. He received his Ph.D. in Compuer Science from UCLA and compleed a posdocoral fellowship a UC-Berkeley. His research ineres lies in he area of wearable compuer design and signal processing. His research has been funded by he NSF, NIH, DoD (TATRC), AFRL, AFOSR, DARPA, SRC and indusry (Texas Insrumens, Tekronix, Samsung & Telecom Ialia). He has published over 100 papers in refereed journals and conferences. He has served as he general chair and echnical program commiee chair for several flagship conferences in he area of Wearable Compuers. He is he recipien of he NSF CAREER award in 2012, IEEE Real-Time & Embedded Technology & Applicaions Symposium (RTAS) bes paper award in 2011 and Andrew P. Sage bes ransacions paper award from IEEE Sysems, Man and Cyberneics Sociey in He is an associae edior for he IEEE Transacions on Biomedical Circuis and Sysems, IEEE Sensors Journal, IEEE Inerne of Things Journal and IEEE Journal of Biomedical and Healh Informaics. He serves on scienific panels for funding agencies frequenly and is presenly serving as a sanding member of he NIH Biomedical Compuing and Healh Informaics sudy secion.