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### 生理颤抖从加速度计估计方法及其在实时应用中的重要性 #### 一、引言生理颤抖是指人体某一部分出现的一种有节奏的、不自主的运动[1,2]。这种颤抖在每个人身上都会以很小的幅度存在，通常被称为生理颤抖。然而，在某些情况下，这种颤抖可能会因病理因素而加剧。对于机器人辅助手术器械和过程而言，准确地过滤掉生理颤抖至关重要。 #### 二、研究背景与意义本文着重于开发单阶段的鲁棒算法，以便通过加速度计实现对生理颤抖的精确过滤，并应用于实时场景中。现有的方法大多基于一个假设，即颤抖具有单一的主导频率。然而，通过对生理颤抖数据进行时频分析后发现，颤抖在整个持续时间内包含多个主导频率，而非单一的频率。基于这一发现，本文回顾了现有的颤抖过滤方法，并提出了两种改进算法。 #### 三、现有方法回顾当前用于颤抖过滤的方法主要包括： 1. **经典频域分析法**：这种方法依赖于频谱分析技术来识别颤抖的主导频率。然而，这种方法的一个主要局限性在于它假定了颤抖具有单一的主导频率。 2. **Kalman滤波器**：Kalman滤波器是一种有效的状态估计方法，可以处理系统噪声和测量噪声。它被广泛应用于多种动态系统的状态估计中。在颤抖过滤领域，Kalman滤波器能够较好地跟踪颤抖的变化，但在多频率颤抖的情况下效果有限。 3. **自适应滤波器**：这类滤波器可以根据输入信号的变化自动调整参数。在处理颤抖时，自适应滤波器可以更好地适应颤抖频率的变化，提高滤波性能。 #### 四、新改进算法介绍本研究提出了两种改进算法： 1. **基于时间-频率分析的改进算法**：该算法利用时频分析技术来识别颤抖的不同频率成分，并对其进行分离。相比于传统方法，该算法能够更准确地捕捉到颤抖的多个主导频率。 2. **基于模型的自适应滤波器**（Model-Based Adaptive Filter）：该滤波器结合了Kalman滤波器和自适应滤波器的优点，不仅可以跟踪颤抖的变化，还能根据颤抖的频率变化自动调整滤波参数，从而提高了滤波的精度和鲁棒性。 #### 五、实验结果与分析为了验证新算法的有效性，研究者进行了大量的实验，包括从微外科医生和新手受试者那里收集的颤抖数据。实验结果显示，新的改进算法在颤抖估计方面表现优于现有的算法。此外，研究还提出了一种将预期运动/漂移与颤抖成分分离的程序，进一步提高了系统的准确性和实用性。 #### 六、结论与展望准确地过滤生理颤抖对于提高机器人辅助手术器械的性能具有重要意义。通过对现有方法的改进，本文提出的两种新算法在颤抖过滤方面取得了更好的效果。未来的研究方向可能包括进一步优化算法性能，以及探索更多应用场景下的颤抖过滤技术。 ### 参考文献 1. **[1]** 未知作者. "Physiological Tremor." [在线]. 可用: [链接未提供]. 2. **[2]** 未知作者. "Tremor Disorders." [在线]. 可用: [链接未提供]. 以上总结概述了文章的主要内容和技术细节，强调了准确过滤生理颤抖的重要性，并介绍了新算法的具体改进之处。

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Sensors 2011, 11, 3020-3036; doi:10.3390/s110303020

OPEN ACCESS

sensors

ISSN 1424-8220

www.mdpi.com/journal/sensors

Article

Estimation of Physiological Tremor from Accelerometers for

Real-Time Applications

Kalyana C. Veluvolu

1,⋆

and Wei Tech Ang

School of Electronics Engineering, Kyungpook National University, Daegu, Korea

School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore;

E-Mail: wtang@ntu.edu.sg

⋆

Author to whom correspondence should be addressed; E-Mail: veluvolu@ee.knu.ac.kr;

Tel.: +82-53-9507232; Fax: +82-53-9505505.

Received: 10 January 2011; in revised form: 28 February 2011 / Accepted: 4 March 2011 /

Published: 7 March 2011

Abstract: Accurate ﬁltering of physiological tremor is extremely important in robotics

assisted surgical instruments and procedures. This paper focuses on developing single stage

robust algorithms for accurate tremor ﬁltering with accelerometers for real-time applications.

Existing methods rely on estimating the tremor under the assumption that it has a single

dominant frequency. Our time-frequency analysis on physiological tremor data revealed that

tremor contains multiple dominant frequencies over the entire duration rather than a single

dominant frequency. In this paper, the existing methods for tremor ﬁltering are reviewed

and two improved algorithms are presented. A comparative study is conducted on all the

estimation methods with tremor data from microsurgeons and novice subjects under different

conditions. Our results showed that the new improved algorithms performed better than the

existing algorithms for tremor estimation. A procedure to separate the intended motion/drift

from the tremor component is formulated.

Keywords: tremor; inertial sensors; BMFLC; Kalman ﬁlter; real-time estimation

1. Introduction

Tremor is deﬁned as “a rhythmic, involuntary movement of a body part” [1,2]. Tremor exists in all

humans in small magnitude and is considered as physiological tremor. However, there exists pathologies

Sensors 2011, 11 3021

with very disabling forms of tremor caused by movement disorders called as pathological tremors. They

are classiﬁed by position/motor behavior. Accordingly, pathological tremor can be classiﬁed into three

categories: rest, postural and kinetic tremor [2]. Physiological tremor has different aetiology compared

to pathological tremor and manifests differently in terms of amplitude and frequency [3–5].

The general assumption is that tremor has a single dominant frequency [3,5]. Pathological

tremor (patients with essential tremor and Parkinson disease) tend to display tremor with a dominant

frequency [5–8 ]. The frequency of the pathological tremor tends to remain constant with slight

variations [5]. The amplitude of the physiological tremor is much lower than the pathological tremor and

has different frequency bands. Recent results [9] for subjects with physiological tremor contradict the

general assumption and suggest that tremor parameters (like amplitude, frequency, bandwidth) largely

vary from subject to subject. In [9], it was shown that for physiological tremor has multiple dominant

frequencies with 3–4 Hz bandwidth.

Physiological hand tremor lies in the band of 8–12 Hz with an amplitude of 50 µm and can

be approximated by a sinusoidal movement [1,3]. Physiological tremor leads to an intolerable

imprecision of the surgical procedure (e.g., vitreoretinal surgery) which require a positioning accuracy

of about 10 µm [10]. To compensate physiological tremor, robotics assisted surgical procedures have

received signiﬁcant attention [11–13]. In [11,12] a robotic handheld instrument to cancel physiological

tremor of surgeon in vitreoretinal microsurgery was implemented. The robotic instrument has to estimate

the tremor motion and generate an out-of-phase movement to cancel it in the real-time. The tip of the

micron will be unaffected by the tremor motion of the surgeon. MEMS accelerometers constitutes the

most common for tremor sensing in robotics assisted procedures [14,15].

Physiological tremor presents a technical challenge because of the high frequency band and its

application in real-time. The error compensation control loop has to be executed in real-time. The system

has to sense the tremor motion, distinguish between voluntary and undesired components, and generate

an out-of-phase movement of the effector (hardware or software) to nullify the erroneous part, all in one

sampling cycle. This approach will only work when there is a distinctive and accurate separation between

the desired and unwanted motion. For example, dominant frequency of physiological hand tremor lies

in the band of 6–15 Hz while hand movement of surgeon during microsurgery is almost always less

than 0.5–1 Hz. Due to presence of accelerometers in tremor sensing equipment, physiological

tremor ﬁltering is more challenging with the presence of drift, noise and gravity in acceleration

measurements [14].

Although linear ﬁlters [16,17] are successful in compensating tremor, the inherent time delay [18]

is a major drawback where zero-phase ﬁltering is required. In [19], it was shown that delay as small

as 30 ms may degrade performance in human-machine control applications. Effective tremor

compensation requires zero-phase lag in the ﬁltering process so that the ﬁltered tremor signal can be used

to generate an opposing motion to tremor in real-time. To overcome the problems with delays, adaptive

algorithms like Weighted-frequency Fourier linear combiner (WFLC) and Band limited multiple Fourier

linear combiner (BMFLC) are developed. Weighted-frequency Fourier linear combiner (WFLC) [20]

is an adaptive algorithm which models any quasi-periodic signal as a modulating sinusoid, and tracks

its frequency, amplitude and phase. WFLC incorporates frequency adaptation procedure into Fourier

Linear Combiner (FLC) [21]. Main drawback of WFLC lies in tracking signals with multiple dominant

Sensors 2011, 11 3022

frequencies, for example physiological tremor display multiple dominant frequencies [9]. Any presence

of low-frequency component or high frequency noise affects the frequency adaptation, and compels the

use of pre-ﬁltering (band-pass ﬁlter) that introduces delay into the ﬁltering process. In [4], pre-ﬁltering

state was employed to eliminate voluntary motion and tremor was modeled with WFLC for data sensed

from gyroscopes for joint rotation. Recently, a two stage algorithm was developed for tremor estimation

with WFLC and Kalman Filter for pathological tremor [7] with gyroscopes. Most of the techniques

discussed are not ideal for robotics related tremor cancellation due to involvement of accelerometers that

only provide acceleration of the tremor motion.

Band limited multiple Fourier linear combiner (BMFLC) [9,22] is also an adaptive algorithm

developed to track multiple dominant frequencies in tremor for accurate tremor ﬁltering. The adaption

process is achieved using least mean square (LMS) optimization similar to WFLC and FLC. As

physiological tremor has multiple dominant frequencies [9], BMFLC-based algorithms should perform

better than WFLC-based algorithms. As the frequency components in BMFLC are constant, analytical

integration can be employed to obtain the displacement from acceleration. In a single stage, BMFLC can

also separate voluntary and involuntary motion and can provide the tremor signal in the displacement

domain. Due to this reason, it becomes an ideal choice for tremor ﬁltering when data is sensed

with accelerometers.

In this paper, a study is conducted on 6 micro surgeons and 6 healthy subjects to analyze

time-frequency tremor characteristics. Existing methods on tremor estimation are ﬁrst reviewed and

the two improved methods are discussed. We improve the existing BMFLC algorithm by modifying

the adaption procedure. Instead of relying on LMS for adaptation, we combine BMFLC with recursive

least squares (RLS) and Kalman Filter to develop two new methods for accurate tremor estimation. All

the existing and proposed methods are reviewed for performance on the data collected. The estimation

accuracy is validated over several trails of data to show the effectiveness of the proposed methods.

2. Tremor Data and Characteristics

Tremor recordings are performed through the Micro Motion Sensing System (M

) [23,24]. The

consists of a pair of orthogonally placed position sensitive detectors (PSD) and an infra-red (IR)

diode to track the 3D displacement of the tip of microsurgical instrument in real-time. The IR diode is

used to illuminate the workspace. A ball is attached to the tip of an intraocular shaft to reﬂect IR rays

onto the PSDs. Experimental setup is shown in Figure 1. Instrument tip position is then calculated from

the centroid position of the light falling on the PSDs. The resolution, minimum accuracy and sampling

rate of the M

are 0.7 µm, 98%, and 250 Hz respectively [23].

The tremor data recorded from 6 healthy subjects and 6 microsurgeons is considered for analysis in

this paper. All subjects gave informed consent prior to the test and reported no physical or cognitive

impairments. The subjects had their wrists rested on a small platform of the (M

) and were asked to

take a comfortable seating position. They had to hold the stylus between their index ﬁnger and thumb in

order to ensure that all subjects have similar grip across trials. The tip of the stylus was pointed near the

center of the M

workspace. Two types of tasks are performed by the subjects:

Sensors 2011, 11 3023

(1) Stationary Task: In this task, subjects are instructed to point the laser light at the center point of

the platform with the stylus provided for 30 s duration.

(2) Tracing Task: In this task, subjects trace the circumference of a circular path on the platform

for 30s, with the speed that is realistic for surgical micro manipulation tasks.

The subjects performed two trials for each task with approximately one minute break between

each trail.

Figure 1. Micro Motion Sensing System (M

) setup.

2.1. Time-Frequency Characteristics of Tremor

In [9], it was shown that the physiological tremor characteristics varied between groups of surgeons

and novice subjects. Results showed that existence of several dominant tremor frequencies in the tremor

band of healthy subjects. The awareness of the tests and procedures likely affect the tremor band as

surgeons were able to control the tremor amplitude. It was further quantitatively shown in [9], that the

tremor amplitude of surgeons is lower than for the novices.

The analysis of tremor frequency characteristics can be performed with the single sided amplitude

spectrum. Using the amplitude spectra, the dominant frequencies and the bandwidth of the tremor

can be identiﬁed. However, the time-frequency characteristics of the tremor cannot be quantiﬁed with

the amplitude spectrum. Existence of multiple peaks in amplitude spectrum of healthy subjects can

also be related to dynamic changes in tremor frequency in the given band. It was not clear whether

the single dominant frequency changes or there exists multiple dominant frequencies at any given

time instant. To further analyze the tremor characteristics, we employ the BMFLC [9,25] to obtain

the time-frequency map. By construction, BMFLC divides the time domain signal into individual

time-frequency components there by providing a high-resolution time-frequency map of the signal in

a given band of interest.

To study the time-frequency characteristics of tremor, the data of 6 microsurgeons and 6 healthy

subjects are analyzed with BMFLC. For illustration, time-frequency mapping, FFT spectrum analyzer

and spectrogram for surgeon #1 and novice subject #1 are shown in the Figure 2. Observation

of tremor amplitude spectrum and BMFLC time-frequency map reveals that existence of multiple

dominant frequencies through out the tremor period. BMFLC requires an initial period of 1 s for

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