ieee sensors journal, vol. 13, no. 12, december 2013 4977...

IEEE SENSORS JOURNAL, VOL. 13, NO. 12, DECEMBER 2013 4977

Physiological Tremor Estimation WithAutoregressive (AR) Model and Kalman

Filter for Robotics ApplicationsSivanagaraja Tatinati, Kalyana C. Veluvolu*, Senior Member, IEEE, Sun-Mog Hong, Member, IEEE,

Win Tun Latt, and Wei Tech Ang, Member, IEEE

Abstract— This paper focuses on developing a simple andefficient tremor estimation algorithm suitable for real-time appli-cations. Autoregressive model in combination with Kalman filteris employed for tremor estimation in robotics devices. A researchis conducted with tremor data recorded from surgeons and novicesubjects for model identification and characteristics. Resultsshow that appropriate choice of model parameters improves theestimation accuracy. Comparison with existing tremor estimationmethods is performed to analyze the performance. Experimentalresults for 1-DOF tremor estimation are provided to validate theapproach.

Index Terms— Tremor, inertial sensors, AR modeling, Kalmanfilter, real-time estimation.

I. INTRODUCTION

TREMOR is defined as “an involuntary, approximatelyrhythmic and roughly sinusoidal movement of a body

part” [1], [2]. Tremor exists in all humans with a smallamplitude and generally termed as physiological tremor. Fur-ther, there exist pathologies with various disabling forms oftremors [3]. Pathological tremor has a different aetiology andexhibits different characteristics in both time and spectraldomains [4]–[6], serious neurological disorder compared to thecommonly existing physiological tremor. Pathological tremorpossesses high amplitude, has a single dominant frequency[4], [7], where as the physiological tremor has low amplitudeand multiple dominant frequencies distributed within a smallbandwidth [8]. The amplitude of physiological tremor ranges50 to 100 μm in each principal axis and the frequency rangeis from 8 to 12 Hz [1], [2].

Microsurgical procedures demand a high level of manualaccuracy and restricts the number of qualified surgeons. For

Manuscript received April 23, 2013; accepted June 26, 2013. Date ofpublication July 3, 2013; date of current version October 10, 2013. Thiswork was supported by the Basic Science Research Program through theNational Research Foundation of Korea funded by the Ministry of Education,Science and Technology under Grant 2011-0023999. The associate editorcoordinating the review of this paper and approving it for publication wasDr. Ashish Pandharipande. (Corresponding author: K. C. Veluvolu.)

S. Tatinati, *K. C. Veluvolu, and S.-M. Hong are with the School ofElectronics Engineering, College of IT Engineering, Kyungpook NationalUniversity, Daegu 702-701, Korea (e-mail: [email protected]; [email protected]; [email protected]).

W. T. Latt is with the School of Mechanical and Aeronautical engineering,Singapore Polytechnic, 139651 Singapore (e-mail: [email protected]).

W. T. Ang is with the School of Mechanical and Aerospace Engi-neering, Nanyang Technological University, 639798 Singapore (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSEN.2013.2271737

example, treatment of retinal vein occlusions which occurswhen a clot forms in the central vein of the retinal circula-tion. This tremor leads to an intolerable imprecision in thesurgical procedure (e.g. vitroretinal surgery) which requiresa positioning accuracy of about 10 μm [9]. Apart from thesurgical applications, physiological tremor also causes a dis-turbance to camera during photography [10], [11]. With age,the hand tremor amplitude increases and the manual accuracyfurther deteriorates. Optical image stabilization (OIS) [12],[13] technique is employed to compensate hand tremor byadjusting either the lens system or the image sensor. Typically,an accelerometer is employed for position estimation.

In hand-held robotic instruments [14], [15], filtered tremorsignal from the sensed motion is used to generate an opposingmotion to compensate the physiological tremor motion in real-time. For effective tremor compensation, zero-phase lag isrequired in the filtering process. Linear filters are successful infiltering the tremor but their inherent time delay [16] severelyaffects the compensation. In [17], it was shown that a delayas small as 30 ms may degrade the performance in human-machine control applications.

To overcome these issues, adaptive algorithms becamepopular for tremor estimation [18]–[22]. Fourier series basedmethods and their variants have been developed over recentyears. In [18], weighted-frequency Fourier linear combiner(WFLC) was proposed. Later, a two stage algorithm WFLCand Kalman filter (KF) [21] was developed for pathologicaltremor estimation from gyroscopic data. Both WFLC andWFLC with KF (WFLC-KF) rely on a single (i.e. dominant)frequency component estimation. The estimation accuracy ofWFLC based algorithms decrease if the frequency variationsare too fast or if the signal contains multiple dominantfrequencies.

Recently, it was shown that the physiological tremorof trained surgeons contains multiple dominant frequencieswithin a bandwidth of 3-4 Hz [19]. Furthermore, the analysiswith the data from surgeons also revealed that the multiplepeaks in the fast Fourier transform (FFT) spectrum are dueto the existence of multiple simultaneous oscillators in thetremor signal [19]. To solve these issues, band limited multipleFourier linear combiner (BMFLC) that estimates the signalswithin a pre-defined frequency band was developed [19].Both BMFLC and BMFLC with KF (BMFLC-KF) [23], relyon simultaneous estimation of multiple frequency componentsin the tremor signal. Recently, BMFLC was employed fortremor cancellation in tele-robotic systems [24]. Comparative

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4978 IEEE SENSORS JOURNAL, VOL. 13, NO. 12, DECEMBER 2013

performance of all tremor estimation methods can be foundin [23].

Although the accuracy of BMFLC-KF for tremor estimationis very high, it requires the knowledge of tremor characteristicsof the subject (for example, bandwidth and frequency range).If the subject’s tremor characteristics are not accurately known,the algorithm requires a wide band and the algorithm becomessusceptible to high frequency noise. Further, the stability ofthe algorithm will be affected. BMFLC is only accurate if thesubject’s tremor characteristics are known and the method iscustomized for the subject. Hence for applications like camerasystems, where subject-specific tremor characteristics are notknown a priori, BMFLC cannot be used for modeling thetremor. Furthermore, a wide-band will increase the number ofweights in BMFLC to a large number, thereby increasing thecomputational complexity. This can be a problem for real-timeembedded systems where both the memory and computationcomplexity are also limited.

To address these problems, we focus on developing a morerobust and simple method suitable for real-time applicationswhere knowledge of subject-specific characteristics are notknown. In this paper, modeling of the tremor signal is per-formed with Autoregressive (AR) model. The AR model ispopular for modeling various physiological signals like heartbeat in intracardiac surgery [25], respiratory motion [26]and pathological tremor [20]. In [27], [28], AR model wasemployed with least mean squares (LMS) and recursive leastsquares (RLS) to estimate the physiological tremor adaptively.However, the performance of the method was not tested withtremor data in real-time. To improve the performance of ARmodel, KF is employed for updating the filter coefficients. Wefurther explore the application of AR model with KF (AR-KF)for real-time tremor estimation. A study was conducted on theestimation performance with the tremor data of five surgeonsand five novice subjects for order and parameters selection.Further, the computational complexity of all the tremor esti-mation methods is analyzed in this paper. Experimental resultshighlight the suitability of AR-KF for real-time applications.

II. METHODS

In this section, we first discuss about the physiologicaltremor data collection and its characteristics. Following thatthe discussion on the experimental setup employed for evalu-ation of the method is presented. Later, adaptive modeling ofthe physiological tremor with AR model and KF is discussed.

A. Physiological Tremor Data

Tremor recordings are performed through the Micro MotionSensing System (M2 S2). The resolution, minimum accuracyand sampling rate of the M2 S2 are 0.7 μm, 98%, and 250 Hzrespectively [29]. Several surgeons and novice subjects partic-ipated in this study. Subjects performed two tasks: pointingtask and tracing task. For more details, see [30]. Data of5 healthy subjects and 5 surgeons was considered for analysisin this paper. It includes 8 trials (4 trials per task) data persubject. The time-frequency characteristics of surgeons andnovice subjects are analyzed in [23]. It was shown that the

Fig. 1. Block diagram for real-time implementation.

time-frequency tremor characteristics were different betweensurgeons and novice subjects. Surgeons tremor profile is morecomplex with a distributed spectrum and of low amplitudecompared to the novice subjects. In this paper, the analysiswas conducted separately for surgeons and novice subjectsdata. This data will be used for evaluation of the proposedmethod in this paper.

B. Experimental Setup

The block diagram representation for real-time tremorcompensation in robotics based surgical device is shown inFig. 1. Accelerometers (ADXL 203, Analog devices, USA)are employed to sense the motion. Tremor like motion isgenerated using a commercially available nanopositioningstage (P-561.3CD from Physik Instrumente, Germany) onwhich a physiological tremor compensation instrument con-sisting of accelerometers is mounted. For more informa-tion about placing accelerometers in the robotics instrument,see [15], [29].

The nanopositioning stage is driven in one axis to replicatethe tremor motion recorded from a surgeon (Surgeon #1, point-ing task) within 100 nm, the maximum range of the stage. Theorientation and accelerometer along with the direction motionare shown in the schematic diagram, Fig. 1. The voltageoutput from the accelerometer is acquired at 250 Hz usinga 16-bit data acquisition (DAQ) card (PD2-MF-150, UnitedElectronic Industries, Inc, USA). QNX operating system wasemployed for real-time implementation. Before the experi-ment, static calibration of the accelerometer is performed usingthe gravity value of 9.81 m/s2. The sensitivity value of theaccelerometer obtained from the calibration is 980 mV/g.The voltage readings acquired from the accelerometer isconverted to acceleration with a quadratic function. Further,the gravitational component is subtracted from the measuredacceleration.

The obtained motion sensed by the accelerometers consistof both voluntary and tremulous motion. Numerical integrationis performed for converting acceleration to position. After thisstage, to separate the tremulous motion from the voluntarymotion and to remove the unwanted integration drift [31], afifth order Butterworth filter with a pass-band of 2–20 Hz wasemployed as shown in the block diagram. The filter order andcutoff frequency are to be chosen such that the filter removesthe unwanted low-frequency drift significantly. This choicedepends on the sensor noise level and the frequency spectrumof the tremor signal. The output of the bandpass filter stage

TATINATI et al.: PHYSIOLOGICAL TREMOR ESTIMATION WITH AR MODEL AND KALMAN FILTER 4979

Fig. 2. AR(3)-KF for tremor estimation.

is provided as input to the adaptive modeling stage for tremorestimation.

C. Tremor Estimation With AR Model and Kalman Filter

An autoregressive (AR) model is a type of random processwhich is popular for prediction of various types of naturalphenomena. It is also one of the linear prediction methodsdesigned to predict an output of a system based on the previousoutputs. For adaptive estimation of physiological tremor, ARmethod is employed. AR model of order M can be representedas AR(M), described as

xn = −M∑

k=1

wk xn−k + εn, (1)

where wk ; k = 1, . . . , M are the time-varying filter coef-ficients, xn−1, xn−2, . . . , xn−M are the delayed inputs andεn is a white noise process with Gaussian distribution andvariance (σ 2). x̂n is one-step forward predicted value ofxn based on M prior samples.

x̂n = −M∑

k=1

wk xn−k . (2)

For illustration, the layout of AR model with forward pre-diction is shown in Fig. 2. The prediction error en is givenas:

en = xn − x̂n. (3)

By denoting,

wn = [ −w1 −w2 · · · −wM]T (4)

xn = [xn−1 xn−2 · · · xn−M

]T, (5)

AR model described in (1) can be written as:

xn = wTn xn + εn. (6)

The mean square error Eep is given as [32]:

Eep = E[x2

n ] − 2wT � + wT ζw, (7)

TABLE I

ADAPTATION SCHEMES

where � = E[xnxn] is the cross-correlation vector between theoriginal tremor signal and the delayed tremor signal vector,and ζ = E[xnxT

n ] is the tremor signal correlation matrix.In practice, precise estimations of ζ and � are not available.When the input and the desired signals are ergodic, one is ableto use time averages to estimate ζ and �, implicitly performedby adaptive algorithms such as LMS [33] and KF [32].

In LMS, filter coefficients (wn) are iteratively updated bythe estimation error (en) and the adaptive gain parameter (μ).The update equation with LMS is shown in Table I. The timeconstant for convergence of LMS is given by 1

2μ [33]. A properselection of μ is required to achieve convergence and stability.If μ is small, convergence will be slow. A large μ may leadto a faster convergence and instability.

To improve the robustness of the method and accuracy, weemploy KF for updating filter coefficients. A distinctive featureof the KF is that its mathematical formulation is described inthe state-space equations and its solution can be computedrecursively. We employ random walk model [32], [34], tocharacterize the evolution of filter coefficients (state dynamics)as

wn+1 = wn + ηn. (8)

The state-space form for AR model can now be describedby state equation (8) and measurement equation (6). Here ηn

represents state noise, modeled as a zero-mean white-noisewhose covariance is defined as

E[ηnηk] ={

Q, n = k0, n �= k

and εn represents measurement noise, modeled as a zero-meanwhite-noise whose covariance is defined as

E[εnεk] ={

R, n = k0, n �= k.

It is assumed that both state noise and measurement noise arestatistically independent [32].

The update equations for KF [32] are shown in Table I.In the above table, the error covariance matrix (Pn) andthe Kalman gain vector (Kn) are computed recursively. Foraccurate modeling of the tremor signal, a proper initializationof error covariance matrix (P0) and filter coefficients (w0) isrequired. For tremor estimation, KF does not require matrixinversion for computing the Kalman gain vector and thislargely reduces the computational requirement. The AR-KFwill be more suitable for real-time applications especially forembedded systems where memory and computation complex-ity are limited. The computational complexity of all methodswill be analyzed in the Results section.


Fig. 3. Order selection for AR model.

1) Selection of AR Model Parameters: For AR model,selection of the optimal order is crucial for accurate estimation.Modeling with lower order provides inaccurate estimationwhere as higher order may lead to noise modeling. Variousmethods have been developed for optimum order selectionto attain accurate estimation. Akaike information criterion(AIC) [35] is one of the most popular methods for linear andnonlinear model identification. For physiological tremor datacollected in our study, AIC identified the third order of ARmodel as the optimal order.

To further verify the optimal order obtained with AIC, astudy was conducted on tremor data of all subjects and trialsfor various orders with AR-LMS (adaptive gain parameter isselected as μ = 0.5, filter coefficients are initialized withzero). % Accuracy (defined in (10)) obtained for various ordersof AR model is shown in Fig. 3. The result further confirmthat the third-order AR model (AR(3)) is the optimal order formodeling the tremor.

Selection of AR-KF Parameters: For optimal selection ofparameters Q and R for modeling the physiological tremorwith AR-KF, a study was conducted on the tremor data of allsubjects. For tremor modeling, covariance matrices are definedas in [36], i.e, Q = σ 2

w I and R = σ 2e ; where σ 2

w is state noisecovariance coefficient, I is a identity matrix of order threeand σ 2

e is the measurement noise variance. The coefficients ofAR model are initialized with zero. For analysis a wide rangeof values ( 10−6 to 100) were selected for σ 2

w and σ 2e . The

surface map of the average accuracy obtained for all subjectsand all trials is shown in Fig. 4. Fig. 4(a) shows that for awide range of selections, the accuracy remains approximatelyconstant. The estimation accuracy decreases for smaller valuesof σ 2

e (<10−3) and when σ 2w approaches unity. For the rest of

the selections, the modeling remains robust. From the surfacemap, one can select the region 10−6 < σ 2

w < 10−2 and10−4 < σ 2

e < 100 to ensure stability and accuracy. In theselected region the variations are within the range of 98% to99%. For tremor modeling with AR-KF, we select Q = 0.01 Iand R = 0.001, highlighted in the Fig. 4(b) with a circle.

For AR-KF state initialization (filter coefficients), astudy was conducted on AR(3)-model filter coefficients{w1, w2, w3} for all subjects and tasks. For illustration,the filter coefficients of AR-LMS and AR-KF for Surgeon#4 (pointing task) are shown in Fig. 5 (solid line). Theparameters chosen for implementation of AR-KF are providedin Table IV, the filter coefficients are initialized withzero. AR-LMS has slow convergence compared to AR-KF.

Fig. 4. Mean of estimation accuracy for various selections of R and Q forall trials and all subjects. (a) 3D surface plot (temperature representation).(b) Selected parameters are highlighted with a circle in the 2D plot

Further, the results in Fig. 5 show that the filter coefficientssettle to a steady state and provide a good estimation accuracy.The initial adaptation period may cause huge error and affectthe stability of the estimation process. To avoid this initialadaptation period, the algorithm should be initialized with thesteady state values.

In order to identify the appropriate filter coefficients forinitialization, statistical analysis on steady state filter coeffi-cients of AR-KF with zero initialization was performed forall subjects and tasks. Results are tabulated in Table II.

Table II shows that, for all subjects, the filter coefficientsfor a specific task for all trials have small standard deviation.Moreover, the differences across both subject groups (surgeonsand novice subjects) and tasks (pointing task and tracing task)are also not significant. Based on the analysis in Table II, weselect the following filter coefficients as the common set offor optimal performance:

w0 = {wi1, w

i2, w

i3} = {−2.88,−0.94, 2.83} (9)

The order of AR model and sampling frequency influencesthe filter coefficients for AR-KF method. Although, the tableshows similar steady state weights for all subjects and trials,


Fig. 5. Surgeon #4, Pointing task: filter coefficients (a) Tremor signal.(b) AR-LMS. (c) AR-KF; (solid line {w1, w2, w3} are for zero initialization,{wi

1, wi2, wi

3} are with selected initialization in (9)).

TABLE II

SETTLED FILTER COEFFICIENTS (M ± SD) FOR 5 SURGEONS (S)

AND 5 NOVICE SUBJECTS (NS) WITH AR-KF

their variation in time-domain can model different subject’stremor signals. However for the case of AR-LMS, the adapta-tion gain parameter (μ) highly influences the filter coefficients.For a slight change in the initialization, the minimum meansquare criterion provides a different minimum and the filtercoefficients settle to different values under different conditions.Hence the statistical analysis of the filter coefficients forAR-LMS is not shown.

To verify whether the pre-defined common set of filtercoefficients in (9) can improve the accuracy over the zeroinitialization, we performed an analysis for all subjects andtrials. The estimation error with AR-LMS and AR-KF withboth the initializations are shown in Fig. 6(a) and Fig. 6(b)respectively. Compared to the zero initialized filter coefficients,both the methods (AR-LMS and AR-KF) displayed improved

Fig. 6. Surgeon #4, pointing task (a) Estimation error with AR-LMS.(b) Estimation error with AR-KF.

TABLE III

ESTIMATION PERFORMANCE (M ± SD) FOR 5 SURGEONS (S)

AND 5 NOVICE SUBJECTS (NS)

performance. The estimation accuracy (defined in (10)) forall the subjects is analyzed and the results are tabulated inTable III. Results show that with the selected initialization,the estimation performance is improved in both the cases. Fora given sampling period, the pre-defined common set can beused to avoid the initial adaptation period. Hence, the identifiedset of filter coefficients in (9) will be used for AR-KF andAR-LMS methods for analysis in the rest of the paper.

III. RESULTS

In this section, we analyze the performance of theAR based methods for tremor estimation thru simulationsand experiments. Further, a comparison with the methods inthe literature is also presented. To quantify the performance,we employ % Accuracy, defined as

% Accuracy = RM S(s) − RM S(e)

RM S(s)× 100 (10)

where the root mean square (RMS) is obtained as

RM S(s) =√

(∑k=m

k=1 (sk)2/m, where m is the number ofsamples, sk is the input signal at instant k and e is definedin (3).


TABLE IV

METHODS & PARAMETERS

TABLE V

COMPARISON WITH EXISTING METHODS

A. Simulation Results

Recently, a comparative study was conducted on all theexisting methods for adaptive estimation of physiologicaltremor in [23]. BMFLC-KF outperformed all the existingmethods WFLC, WFLC-KF, BMFLC-LMS and BMFLC-RLSfor tremor estimation [23]. To validate the approach, wecompared the estimation accuracy of AR-KF with BMFLC-KFand WFLC-KF methods. Results obtained are tabulated inTable V. The parameters chosen for all methods are providedin Table IV. The filter coefficients are initialized with thepre-defined common set of filter coefficients in (9). Both themethods AR-KF and BMFLC-KF show similar estimationperformance and performed better compared to the WFLC-KFmethod. BMFLC-KF performs marginally better compared toAR-KF.

B. Computational Complexity

For real-time embedded applications with limited memory,computational complexity of the filtering method can affect theaccuracy of the end application. Computational complexity ofan adaptive algorithm mainly relies on dimension of observa-tions (l) and states (n) of the method. In general, KF requiresa matrix inversion of order l×l for the computation of Kalmangain vector, thus the computational complexity to implementwill be in the order of O(N3) [37]. For tremor modelingemployed in this paper, the observation dimension is 1×1 (i.e.,l = 1) and matrix inversion is not required. The computationalcomplexity involved is only for the computation of Kalmangain vector and it only involves multiplication operations(O(3n2)). As error is a scalar quantity, the computationalcomplexity of LMS is given by O(N), where N is the order ofthe filter. A comparative study is conducted on all the existingmethods for computational complexity and the number ofoperations required for methods are tabulated in Table VI.As AR and WFLC require an additional band-pass filter, thenumber of operations shown in the Table VI includes the oper-ations required for the band-pass filter. Table VI shows thatBMFLC-KF requires more number of operations compared toother methods. Whereas the AR methods require minimum

TABLE VI

COMPUTATIONAL COMPLEXITY

number of operations compared to WFLC and BMFLC basedmethods. On the whole, AR-KF method provides a goodestimation accuracy and requires less number of operationsas compared to BMFLC-KF. Comparatively, AR-LMS andAR-KF are more suitable for real-time applications.

C. Experimental Validation

In order to evaluate the real-time performance of ARmethods, data recorded from subject #1 (pointing task), shownin Fig. 8(a), is given as input to the nanopositioning system.The tremor signal obtained after the bandpass filter stage ismodeled with the AR method as discussed earlier in Fig. 1.Parameters and the initial conditions for real-time experimentsare similar to the simulation experiments. The computationtime required for the execution of the algorithms is negligible(<1 ms) with the employed QNX system. The results obtainedin real-time for AR-LMS and AR-KF are shown in Fig. 7 andFig. 8 respectively.

Fig. 8(a) shows the input tremor signal together with theestimated tremor signal for AR-KF. For better visibility, asmall portion of Fig. 8(a) (from 3.5 to 5 sec) is shown inFig. 8(b). With the proper initialization, filter coefficients settleimmediately providing good estimation as shown in Fig. 8(c).The estimation error is shown together with the input tremorsignal in Fig. 8(d) for AR-KF. Comparing Fig. 7 and Fig. 8,it can be clearly seen that AR-KF provides better estimation.Experiments are conducted for three subjects (S#1, S#2, S#4)with two trials per subject. The average estimation accuraciesobtained with AR-KF and AR-LMS methods in real-timeare 88 ± 2% and 81 ± 3% respectively. Results show thatAR-KF is more robust compared to AR-LMS for real-timetremor estimation. Although, AR-LMS is initialization depen-dent, in order to highlight the improvement obtained withAR-KF compared to AR-LMS, the comparison is presented.

IV. DISCUSSION

As part of our continuing research in improving the smartsurgical devices such as Itrem [15] with accelerometers, thealgorithms were developed for cancellation of the tremorin real time with piezoelectric actuators. The device housesthree accerelometers for sensing the tip acceleration of x, yand z axes separately. For more details, see [15]. Although1-DOF cancellation is discussed in the paper, the proposedmethod can be applied for the three axes separately and3-DOF cancellation of tremor can be achieved. For sake of theperformance analysis and testing, 1-DOF motion estimation ispresented in this paper.


Fig. 7. Surgeon #1, pointing task: real-time estimation with AR-LMS (a) Estimation of Tremor. (b) Zoomed portion of estimated tremor. (c) Filter coefficients.(d) Tremor input and estimation error.

Fig. 8. Surgeon #1, pointing task: real-time estimation with AR-KF (a) Estimation of Tremor. (b) Zoomed portion of estimated tremor. (c) Filter coefficients.(d) Tremor input and estimation error.

Although the estimation accuracy is high within the adap-tive filtering stage in real-time, actual tremor compensationdepends the other components such as phase delay, separationof voluntary motion, accelerometer noise and integration driftetc. Of all the issues, phase delay can adversely affect thecancellation accuracy. The accelerometer hardware filter timeconstant calculated from the step-response is approximately3 ms and a phase delay of 5 to 10 ms is caused by theband-pass filter. For compensation of physiological tremor inhand-held instruments piezoelectric actuators are employed togenerate an equal and opposite motion in position domain,it yields an additional 1 ms delay for cancellation. Thus,

a total of 8 to 14 ms delay is unavoidable for real-timetremor compensation applications. To verify the applicationof the method to an end application, phase delay of 8 ms isincorporated into the estimation. Estimation results togetherwith the phase delay are shown in Fig. 9. With the phasedelay, the % Accuracy obtained with AR-LMS and AR-KFmethods are 52% and 63% respectively. This also highlightsthe need to overcome the phase delay in order to improve theaccuracy.

For separation of voluntary motion from the sensed motion,a bandpass filter is employed in this paper. Although abandpass filter introduces delay, it is also required to remove


Fig. 9. Surgeon #1, pointing task. Estimation performance with phase delay.(a) AR-LMS. (b) AR-KF.

the drift caused by the double integration of acceleration datato obtain position. The bandpass filter serves for dual purposein eliminating the voluntary motion and the integration drift.Recently, in [20], a filter based on ARMA model stochasticframe work was proposed for online filtering of pathologicaltremor and voluntary motion. Since, physiological tremoramplitude is very small compared to the pathological tremor,the filter [20] is not suitable for our application. As accelerom-eters employed for sensing only provide the acceleration,the position information obtained via numerical integration isprone to integration drift and the obtained position may not beaccurate. Our future work will focus on developing a methodfor accurate position estimation from acceleration.

With the real-time operating system QNX Neutrinoemployed for the tremor cancellation, the computational com-plexity cannot be an issue for real-time implementation. Forthe case of surgical devices, BMFLC-KF or AR-KF canboth be employed for tremor estimation. Further, the tremorbandwidth must be customized for microsurgery applicationswith BMFLC-KF. However for the optical image stabilizationsystem applications that requires on-board tremor estimation,with limited memory and processing speed, computationalcomplexity can also affect the performance.

Further, the proposed method does not require the knowl-edge of subject’s tremor characteristics as required in BMFLC.This further eliminates the need for employing an additionalbandpass filtering stage for customizing the algorithm accord-ing to subject’s tremor characteristics as required in BMFLC.Comparatively, AR method can provide good accuracy withoutthe knowledge of subject’s tremor characteristics.

Recently, a method to compensate phase delay was devel-oped in [38] for the case of periodic signals. As physiological

tremor is non-periodic with presence of several dominantfrequency components, this method is not suitable for real-time tremor estimation. Future research will focus on theprediction methods to perform multi-step prediction to dealwith the phase delay. Moreover as AR-KF filter coefficientssettle to steady state, updated weights at the current samplecan be employed to predict future samples. Further researchis required and this issue will be discussed elsewhere.

V. CONCLUSION

In this paper, we analyze the performance of the AR modelwith KF for real-time tremor estimation. The proposed methodis simple, provides a good estimation accuracy and doesnot require the knowledge of subject’s tremor characteristics.Analysis was conducted on the tremor data of surgeons andnovice subjects to identify the appropriate tremor model para-meters. Results show that a proper initialization can improvethe tremor estimation accuracy. Further, a common set of filtercoefficients are identified for this purpose. Simulation resultsin comparison with existing methods highlight the advantagesof the proposed method. Experimental results further validatethe suitability of the method for real-time estimation. Anaverage estimation accuracy of 88 ± 2% and 81 ± 3% isobtained for AR-LMS and AR-KF methods respectively.

ACKNOWLEDGMENT

The authors would like to specially thank the anony-mous reviewers for their constructive suggestions that largelyimproved the quality of this paper.

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Sivanagaraja Tatinati received the B.Tech. degreein electronics and communication engineering fromAcharya Nagarjuna University, Guntur, India, in2010, and currently pursuing the Ph.D. degree atKyungpook National University, Daegu, Korea. Hiscurrent research interests include robotics assistedmedical instruments, adaptive filtering, and appli-cation of control and estimation algorithms in bio-medical engineering.

Kalyana C. Veluvolu (S’03–M’06–SM’13) receivedthe B.Tech. degree in electrical and electronic engi-neering from Acharya Nagarjuna University, Guntur,India, in 2002, and the Ph.D. degree in electricalengineering from Nanyang Technological University,Singapore, in 2006. Since 2009, he has been withthe College of IT Engineering, Kyungpook NationalUniversity, Daegu, Korea, where he is currently anAssociate professor. From 2006 to 2009, he wasa Research Fellow with the Biorobotics Group,Robotics Research Center, Nanyang Technological

University. His current research interests include non-linear estimation andfiltering, sliding mode control, brain-computer interface, biomedical signalprocessing, and surgical robotics.

Sun-Mog Hong (S’86–M’89) received the B.S.degree from Korea Aerospace University, Seoul,Korea, in 1978, and the M.S. degree from the KoreaAdvanced Institute of Science and Technology, Dae-jon, Korea, in 1980, both in electronic engineer-ing, and the M.S. and Ph.D. degrees in aerospaceengineering from the University of Michigan, AnnArbor, MI, USA, in 1985 and 1989, respectively.Since 1980, he has been with the School of Electron-ics Engineering, Kyungpook National University,Daegu, Korea, where he is currently a Professor.

His current research interests include motion prediction for robotic surgicalsystems and target tracking/track fusion in radar networks.

Win Tun Latt received the B.E. degree in electron-ics from Yangon Technological University, Yangon,Myanmar, in 2000, and the M.Sc. degree in biomed-ical engineering and the Ph.D. degree from NanyangTechnological University (NTU), Singapore, in 2004and 2010, respectively. Since 2012, he has beenwith Singapore Polytechnic, Singapore, where he iscurrently a Lecturer. His current research interestsinclude sensing systems, control systems, signalprocessing, instrumentation, medical robotics, andmechatronics. He is a recipient of the Gold Medal

in Singapore Robotics Games in 2005. He was a Research Staff Member withNTU from 2005 to 2010.

Wei-Tech Ang (S’98–M’04) received the B.Eng.and M.Eng. degrees in mechanical and productionengineering from Nanyang Technological University,Singapore, in 1997 and 1999, respectively, and thePh.D. degree in robotics from Carnegie MellonUniversity, Pittsburgh, PA, USA, in 2004. Since2004, he has been with the School of Mechanicaland Aerospace Engineering, Nanyang TechnologicalUniversity, where he is currently an Associate Pro-fessor and holds the appointment of Head of Engi-neering Mechanics Division. His current research

interests include robotics technology for biomedical applications, whichinclude surgery, rehabilitation and cell micromanipulation.

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