An Unobtrusive Method for Remote Quantification of Parkinson’s and Essential Tremor Using mm-Wave Sensing

Tremor is a primary symptom of common movement disorders such as essential tremor and Parkinson’s disease. People experiencing tremors face difficulty in performing everyday tasks which negatively impacts their independence. Tremor quantification helps clinicians in evaluating disease progression and treatment response. The majority of the existing methods include cameras or motion sensors embedded in wearables and hand-held devices. The continuous wearing of contact sensors can be uneasy for the patients while the cameras cause privacy concerns. This article proposes a novel method for tremor quantification using a frequency-modulated continuous wave (FMCW) radar sensor. In this article, an off-the-shelf, low-cost FMCW radar has been configured to capture vibrations induced in distal limbs, a representative feature of essential and Parkinson’s Tremors. Moreover, a signal processing chain is developed to extract characteristic tremor frequency and amplitude by reconstructing the tremor signal from the radar return signals. For robustness and increased accuracy, static clutter and voluntary body motion are eliminated. Extensive experiments were performed and results were compared to the state-of-the-art methods that use accelerometers and gyroscopes. A strong correlation ( ${R}^{{2}} >0.97$ ) is found between the reference sensor readings and predicted values for both quantified parameters. The mean error for the frequency and amplitude is 0.14 Hz and 0.03 cm, respectively. Results demonstrate a superior accuracy as compared to the existing non-contact techniques, with the added advantage of privacy and integrity preserving for the end-user. Hence, the proposed system can provide reliable long-term objective assessment, aiding clinicians in the evaluation of tremor severity and treatment effectiveness.

. With such high incidence rates, and keeping in view the fact, that these neurological diseases cannot be cured, effective and feasible methods are required for the continuous quantification of these patients living independently.
Disease progression and treatment heavily rely on the quantification of key tremor characteristics. Clinically, tremor severity is assessed using qualitative rating scales such as quality of life in essential tremor (QUEST) [9], essential tremor rating scale (ETRS) [10], and unified PD rating scale (UPDRS) [11]. Though these clinical tests indicate the disease severity, however, they are time-consuming, subjective, and sporadic, which may cause a hindrance in portraying an accurate photograph of disease progression [12]. Continuous monitoring can lead to an early diagnosis of further neurological deterioration, assessment of disease progression, and help clinicians in evaluating treatment effectiveness [13]. Tremor frequency and amplitude are two clinically significant parameters that indicate tremor severity [14], [15], [16], [17]. Both parameters are vital in the differential diagnosis of tremor-related diseases, for example, to rule out PD versus ET, where symptoms might be confusing [18]. Table I demonstrates the characteristic fundamental frequency of PD and ET [19], [20]. However, the amplitude of the tremor depends on multiple factors including age, type of tremor, and the time elapsed since the onset of the disease. In the literature, the typical tremor amplitude ranges have been reported to be between 0.1 cm for mild tremors going up to 4 cm for severe tremors [21], [22].

II. RELATED WORK
Various sensors are used for the quantification of tremor parameters. The sensors measure the limb vibrations induced as a result of tremors. This section details the various sensors and methods that exist in the literature that have been used to quantify tremors.

A. Tremor Quantification Through Wearables
Conventional electroencephalography (EEG) and electromyography (EMG) techniques are used to monitor signals from the central nervous system and muscles for detecting tremor motor dysfunction [23], [24], [25]. Recently, wearable motion sensors such as accelerometers and gyroscopes are widely being adopted for the said purpose. These sensors are either used as stand-alone units worn on the upper and lower limbs [26], [27], [28], [29] or are the ones embedded in daily-use devices such as smartwatches and smartphones [30], [31], [32], [33]. Algorithms are developed to process the raw data collected from the accelerometer and gyroscope axes. The fundamental frequency is calculated by performing the power spectral density analysis. Whereas, the amplitude is calculated by either performing a single integration on the gyroscope data or a double integration on the accelerometer readings [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34]. A gyration computer mouse has also been used to track the stability in drawing tasks to quantify tremors [35]. For the EEG and EMG recordings, specialized lab equipment is required, while the continuous wearing of the contact sensors can result in the patient being uncomfortable. Moreover, patients also suffering from cognitive issues may altogether forget to wear them. Handheld devices such as smartphones or the computer mouse cannot be held for too long. Hence these techniques result in missing tremor episodes throughout the day, hindering the continuous objective monitoring of tremors.

B. Tremor Quantification Through Camera Sensors
In the literature, a handful of non-contact solutions also exist. A recent systematic review [36], cites multiple works that use camera-based sensors for the quantification of hand tremors. Similarly, Alper et al. [37] and Sooklal et al. [38] have used Kinect technology using color and depth cameras for detecting and quantifying tremors. However, the continuous use of cameras and video recording invades the privacy of an individual. Moreover, cameras are light-dependent. Hence, non-contact and privacy-preserving solutions are required for long-term reliable tremor quantification.

C. Tremor Quantification Using Electromagnetic Sensors
Recently electromagnetic (EM) sensors have gained popularity in numerous healthcare applications. This is due to their ability to monitor relevant parameters that are indicative of the health status of an individual such as heartrate detection and gait monitoring [39], [40]. Wi-Fi and radar sensors both fall into this category. Though EM sensors have been used for a variety of healthcare applications, their evaluation for tremor quantification due to ET and PD, specific to carebased scenarios is nonexistent. For example, out of the existing studies in the literature, Blumrosen et al. [41] and Lin et al. [45] have quantified tremors, whereas Yang et al. [43] and Gillani and Arslan [44] only detect action tremors during drinking water. Blumrosen et al. [41] used an ultra-wideband (UWB) radar system to quantify tremor frequency and amplitude. The radar system is based on discrete components and hence is large in size. Moreover, discrete components increase overall system cost and power consumption [42]. Linear minimum mean square error criteria were used with matched filtering. Though the system quantified frequency with sensible accuracy, however, for the tremor amplitude, the accuracy declined with increasing distance from 1 to 1.5 and 2 m of the robotic arm from the radar system. In [43], the change in variance of the subcarrier amplitude from an S-band wireless router and a receiving (Rx) omnidirectional antenna is used to distinguish between tremor and no tremor episodes while a person grabs a glass of water. In [44], a frequencymodulated continuous wave (FMCW) radar has been used to detect action tremors employing time-frequency analysis. In [43] and [44] though tremor has been identified, however, the tremor parameters have not been quantified. More recently, a 2 × 2 array 10 GHz X -band Doppler radar sensor was developed to quantify hand tremors [45]. Tremor quantification is done for digital hand-writing scenarios for PD patients. The system correlated (R 2 > 0.85) three time-domain parameters: zero crossing, Willison amplitude, and waveform length to the tremor frequency. The measurement resolution of the system is 20-40 cm. Hence, the system is limited to quantifying hand tremors at a very small range and is not suitable for continuous monitoring in independent living scenarios. The performance evaluation of the proposed system has been done against an Apple pencil, laptop, and smartphone.
Keeping in view the limitations of the current studies, the aim of this article is to quantify tremors for general carebased scenarios that encompass all the major activities that can trigger tremors throughout the day. This has been done keeping in view the needs of the elderly population who suffer from tremors due to neurological dysfunction such as ET and PD. The main objective of this article is to demonstrate the effectiveness, feasibility, and accuracy of an FMCW radar system to quantify tremor parameters for use cases of independent care while preserving the privacy and integrity of the patient. In contrast to the existing techniques which have been developed to account for hand tremors only, the proposed system is a more general purpose specifically tailored and designed to quantify essential and Parkinson's tremors in real-life-like settings.
The system has been designed to account for tremors that occur throughout the day while performing certain actions or while sitting relaxed in a chair. These include actions such as eating or drinking (action tremors); a front extension of the upper limbs to hold it against gravity (posture tremors) and while the patient is relaxing such as sitting in a chair (rest tremors). Action and posture tremors are characteristic of ET while rest tremors are a key symptom in PD patients. In summary, the key contributions of this work are as follows.
1) This article presents a novel system that quantifies tremors specific to ET and PD patients for general carebased scenarios with a focus on independent living. 2) The chirp parameters of a commercial off-the-shelf CMOS FMCW radar on-chip sensor system, have been designed to tailor the sensor specifically to capture tremors in the distill limbs. The single chip reduces the overall cost and power of the system unlike the discrete component systems used in [41] and [43]. The system is easily portable making it suitable for deployment for continuous remote monitoring of tremor patients in the ease of their homes while preserving their privacy and integrity. 3) An algorithm was developed to quantify two clinically important tremor parameters, frequency, and amplitude. In contrast to the existing studies that quantify tremors using time series data or numerical analysis techniques using radar, this algorithm implements a mathematical vibrational model and utilizes phase preservation from the radar return signals.

4)
Extensive experiments were performed for action, posture, and rest tremors. Results were validated through state-of-the-art conventional methods that use accelerometer and gyroscope data [25], [26], [27], [28], [29], [30], [31], [32], [33]. A detailed statistical analysis is performed on the obtained results. The overall signed errors ±SD for the predicted frequency and amplitude are −0.14 ± 0.4 Hz and −0.03 ± 0.1 cm, respectively. The results demonstrate a superior accuracy as compared to existing unobtrusive methods to accurately quantify tremors. For validation purposes, the accelerometer and gyroscope sensors embedded in the iPhone were used as a reference. The data from these sensors were obtained using a mobile application "TREMOR12 [32]." The choice of this application as a validation tool is based on the following factors.
1) The mobile application is compatible with the current regulatory oversight by the European Union (MEDDEV) guidance and the Food and Drug Administration (FDA) for medical mobile applications [32].
2) The application has been tested and evaluated on ET patients aged 55-71 years [3].
3) The application developer and the first author of [32], is a neurosurgeon and experienced mobile application developer. The coauthors are also associated with the departments of Neurology, Psychiatry, and Neurosurgery at the Medical Centre of Maastricht University, The Netherlands. The subsequent sections of this article are as follows. Section III describes the data acquisition system used for tremor quantification. Section IV details the signal processing chain developed to extract tremor frequency and amplitude from the raw radar data. Section V presents the experimental protocol and detailed results.

III. HARDWARE SYSTEM
This section discusses the motivation behind the use of the FMCW radar and presents the details of the data acquisition hardware. Then, the customized configuration applied to the radar sensor to detect tremors is presented.

A. Motivation for Millimeter Wave FMCW Radar
Radar sensors are excellent EM sensors whose performance is not affected by the atmosphere, clothing of the patient, and light conditions of the room. The radar used in this work is a millimeter Wave (mmWave) sensor, with a wavelength in the mm range. This gives an advantage of the small size of transmitting (Tx) and Rx antennas and hence, a compact form factor for the sensor, facilitating portability, a desired aspect for remote health monitoring. The advent of the new generation of low-cost, compact-size mmWave sensors has paved the way for various medical, military, and industrial applications [46], [47], [48]. FMCW radars are continuous wave (CW) radars that transmit the signal continuously as compared to the periodic pulses in pulse radars. This improves the signal-to-noise ratio (SNR) [49]. Moreover, unlike the simple CW radar, the FMCW transmits a frequency-modulated signal with finite bandwidth (BW). This facilitates clutter isolation and aids in velocity and range measurements of the target in front of the radar [50]. With specialized algorithms, these properties can be used to keep track of the subtle changes in the range of the object thus making the FMCW radar a suitable choice for Tremor quantification.

B. Data Acquisition System
Traditional radar systems have discrete components such as antennas, analog components, e.g., the clock, microcontrollers, analog-to-digital converters (ADC), and digital signal processors (DSP) [50]. However, using these discrete components gives rise to increased energy losses, increased power consumption, and larger system space requirement [42]. The sensor used in the current study is a 77 GHz CMOSbased, linear FMCW radar system on a chip manufactured by Texas Instruments [51]. All the components are integrated on a single chip mitigating the above-mentioned issues. It has a programmable C674x DSP core and an ARM Cortex-R4F Microcontroller [52]. The board is powered by a 5 V adapter. The sensor is provided with real and quadrature mixers. Depending on the target application, the sensor can be programmed to select any mixer. The output of the mixers results in continuous beat signals also known as an intermediate frequency (IF), as shown in Fig. 1.
The IF signals are then digitized by the ADCs. To capture these sampled IF signals a TI data capture board DCA1000 is used [53]. The data is transferred to the DCA1000 through the 60-pin Samtec cable also shown in Fig. 1. These are then sent to the computer via an Ethernet connection.

C. Customizing the Radar Sensor for Tremor Detection
As FMCW radars are used for a variety of sensing applications, the system requirements vary depending on the targeted objective. A sensor configured for autonomous driving assistance will vary as compared to medical sensing application. The sensor has to be programmed according to the range requirements, environmental conditions (indoor versus outdoor), and the desired field of view (FOV). In this work, the radar sensor system was configured for indoor requirements which could detect and monitor small tremor vibrations.
The radar system used provides flexibility in configuring chirp timing parameters. This is done by using the mmWave Studio [54]. Using the mmWave Studio IDE, the digital timing engine, local oscillator, ADC sampler, and processor are programmed to control the chirp start time "T s ," idle time (time taken to restart the synthesizer for the new chirp), chirp slope "S ′′ and chirp end time as shown in Fig. 2. Suppose an object is at a distance "d" from the radar, then the reflected signal is delayed by a time "t d " with respect to the transmitted signal, as indicated in Fig. 1. The time delay is given as t d = 2d/c, where "c" represents the speed of light and 2 accounts for the round trip in the case of the collocated radar. The instantaneous phase ϕ IF and frequency f IF of the IF signal are given by the differences in the corresponding instantaneous values of the transmitted and received signals. The phase is given as Inserting the value of "t d " in (1) gives From (2), it is seen that a small variation in "d" results in a corresponding phase change. This can be leveraged to approximate the range of the target. To resolve the range values, the fast Fourier transform (FFT) is applied to the sampled signals, also called range-FFT. According to FFT theory, the frequency resolution increases if the length of the IF signal is increased [47]. The phase of the range FFT calculated from the reflected signal changes completely by 180 • for every 1 mm of range change [48]. This property is crucial for estimating vibration frequencies and algorithms are required for accurate phase unwrapping [56]. From Figs. 1 and 2, it can be seen that a larger BW will result in a longer IF signal. The property of the radar to distinguish between two near objects is known as Range resolution "R res " and is given by The range resolution for the radar used is 3.74 cm. Hence, two distinct vibrating objects such as dominant and nondominant limbs can easily be distinguished. Tremors experienced in the limbs can be irregular or regular depending on the underlying neurological conditions. For example, in a resting tremor, the amplitude may vary over time making it irregular. This affects the velocity of the limb. To measure the velocity changes, a series of equally spaced chirps are transmitted. To monitor the changing velocity "v," the chirp time "T ch " should be controlled. The chirp time and phase change are related by From Fig. 2, it can be observed that "T ch " depends on the slope of the chirp "S ′′ and BW. However, the synthesizer takes some time to synthesize every new chirp. This time is known as idle time. This limits the overall T ch and the effective BW of the sensor. The measurable maximum velocity increases with the frame time "T Frame " that is, a greater number of chirps per frame. Whereas, the velocity resolution increases with a shorter chirp period also known as fast FMCW [57]. For applications where the frequency is very low such as breathing detection (0.1-0.5 Hz), a low number of chirps per frame is enough to guarantee that no phase rollover occurs. However, a fast chirp period along with a higher number of chirps per second is required for applications such as heart rate variability [50].
In this work, T ch (=BW/S) was programmed to be 0.3 ms, which means 3333.3 chirps/s are transmitted. This ensures the detection of frequency vibrations for tremors (4-12 Hz). Table II summarizes the designed parameters and their values used in this work.

IV. SIGNAL PROCESSING CHAIN
This section explains the signal conditioning and preprocessing steps for the received signal. It discusses the FMCW signal model for tremor vibrations and finally details the algorithm developed to extract tremor frequency and amplitude.

A. Signal Pre-Processing
The relative length of the vibrating limb is considerably smaller as compared to the full body thus affecting the radar cross section (RCS). The reflections from the vibrating limbs are weak as compared to the strong interference signals from the surroundings and bulk body movements. These strong reflections are superimposed on the weak vibrating modulated signal. This problem gets pronounced when the vibration frequency f v is also low [47], as in the case of PD rest tremors.
An important consideration is the use of real (I only) versus quadrature (I and Q) mixtures. The TI radar sensor allows using either [55]. For this work, the sensor was programmed to use a quadrature mixer with complex baseband (BB)  architecture. The received input is mixed with sin and cos versions of the transmitted signal. Real BB signals from real mixers result in a double sideband (DSB) signal whereas, complex BB signals from quadrature mixers give a single sideband (SSB) spectrum [53]. The DSB and SSB receiver signals are given as From (5), it can be seen that at a range "R 0 " from the radar, the received signal is the sine wave function with frequency f IF , with an envelope modulated by limb tremor vibration function D v (t) = D max sin(2π f v t). This is illustrated in Fig. 3. Hence, the IF signal spectrum suffers image band noise foldback, reducing the SNR. In comparison, the tremor vibration in SSB (6), is embedded in the phase part of the received input signal. This, unlike the DSB, eliminates the problem of null points and optimum points. Moreover, in SSB the in-band (where the signal of interest lies) and image-band remain distinguished thus increasing performance gain up to 3 dB in noise figure [55]. For these reasons, the radar sensor was programmed to use a quadrature mixer and complex BB architecture, resulting in SSB received signal.

B. FMCW Signal Model for Vibrating Limb
The transmitted FMCW chirp for a single period "T ch " is where "ϕ" denotes the initial phase, f 0 is the start frequency of the chirp, A T is the transmit power amplitude, "S" indicates the chirp slope, and "t" denotes the fast time within one time period "T ch ."  "R 0 " is the distance of the subject from the radar system and R(τ ) is the time-varying range which incorporates the varying range from the vibrating limbs due to tremors. R(τ ) of the vibrating limb from the radar at any given time will be D max is the maximum vibrational amplitude. The typical maximum value for rest tremors is 2 cm while for action tremors this can increase to 3 or 4 cm [20], [21]. τ is the slow radar time and depends on the total chirps transmitted. The signal that is reflected from the subject is a delayed version of the transmitted signal. Hence, the received signal for a single chirp is "A" is the amplitude of the signal. This is dependent on the RCS and propagation attenuation. The third term in (11) can be ignored because the slope is of the order MHz/s while due to the programmed fast FMCW chirps, t d is in nanoseconds. For slow-moving targets, such as human motion, the range can be considered constant within one time period [56]. This assumption cannot be applied to high-speed targets such as the rotor blades of a quadcopter or helicopter [57]. Mathematically, the change in range in one time period "T ch ," should be less than c/2 f c [58]. In this case, this approximately comes out to be 1.95 mm within 0.3 ms, hence, meeting the condition. Thus, the received signal can be approximated as Inserting the value of t d in (12), the beat frequency f b and the standard slow time phase history come out to be Hence, for accurate extraction of the slow time range profile, phase preservation is the key [57].

C. Signal Processing
After collecting the raw radar data, the signal processing was performed in MATLAB R2022a. The complex ADC sampled signals from the radar are obtained in.bin format. These were converted to.mat files using a MATLAB snippet. This resulted in a column vector. The size of the data vector is dependent on the total number of frames, ADC samples, and the total number of chirps transmitted. From Table II, it can be seen that the size of the column vector turns out to be 6 553 600 × 1. The column vector is then reshaped into a fast versus slow time matrix with a size of 256 × 25 600. Each column represents distinct chirps (fast time) while all the transmitted chirps are stacked together such that the rows represent the slow time. The fast Fourier transform (FFT) is performed on each chirp giving the range profile matrix. Static clutter was removed using a low pass filter, eliminating highfrequency reflections from the surroundings. To identify the target, range gating was performed. This was done by selecting the range bin with maximum amplitude after comparison along the successive range bins. At this stage, the dc offset was also removed for constellation correction as done in [59]. The random body motion was canceled out based on signal energy as the voluntary body movements are not oscillatory and have a comparatively larger amplitude [60]. Hence, the signal was divided into small time frames of one second each. The energy for each time segment was calculated and if the calculated energy was greater than a certain threshold the samples in the segment were discarded. From the identified range bin, a 1-D tremor signal is synthesized by selecting the optimal range bin and summing the absolute of the selected range bin. Arctangent demodulation for phase unwrapping was performed. The demodulated signal was smoothed and passed through a third-order Butterworth bandpass filter. The center frequency is set to 8 Hz while the BW is 4 Hz. This has been chosen per the tremor frequency range of 4-12 Hz. Finally, the spectral analysis of the tremor signal is performed by applying zero padding and using a hamming window and performing FFT. The maximum frequency is extracted which denotes the tremor fundamental frequency. Finally, the tremor amplitude is calculated by using (8) and (9) D max for the rest tremors were taken as 2 cm while for action and posture tremors it was taken as 4 cm, per the existing literature [21], [22]. A flow diagram showing the radar signal processing is given in Fig. 4. Snapshots of signal processing from the radar sensor and reference sensor are provided in Figs. 5 and 6, respectively.

V. EXPERIMENTAL VALIDATION AND RESULTS
Tremors are majorly classified as either resting tremors, which occur while the muscles are relaxed or action tremors. Action tremors are further classified as kinetic and postural tremors [61]. Kinetic tremors occur when an individual performs voluntary tasks such as eating and posture tremors can get triggered when patients extend their arms and hold them in a position against gravity. ET and PD, though both are neurological diseases that cause tremors, however, their presentations are noticeably different. Action tremor is more associated with ET while rest tremor is one of the earliest signs in PD patients [62]. However, as the diseases progress, ET patients might develop rest tremors. While, in the case of PD, as the disease progresses motor dysfunction worsens thus patients experience action tremors as well [18].
A total of 60 experiments were conducted for various tremors. Activities were performed that induce action, postural and rest tremors. For each kind of tremor quantification, a total of 15 experiments were performed. Out of these 15 experiments, five involved no tremor trials and ten experiments involved tremor-induced experiments. Each experiment lasted about 8 s. For a true comparison between the proposed methodology and the base sensor, random movements were excluded that arose when the button for the mobile application is pressed to start and stop data capture for the mobile application. Hence, a longer reading was taken for the mobile application. Table III details the list of experiments performed  for data collection. For this proof-of-concept study, the subjects involved are healthy. They were advised to simulate tremors. The study was approved by the university's School of Engineering ethical review board. Data were collected simultaneously from the radar sensor, placed at position A and iPhone, placed at position B, as shown in Fig. 7. The mobile was securely attached to the distal limbs of the subject using a mobile holder as shown in Fig. 7. The radar is programmed for near-field application which allows a maximum of 9.4 m range detection. However, keeping in view the average room dimensions in homes, the subject was asked to sit at a distance of more than 3 m and less than 9 m from the sensor. From Fig. 5(b), the range of the subject can be observed to be slightly greater than 6 m. A varying distance was advised to check the robustness of the tremor quantification system. The mobile application gives the three axes raw data for the accelerometer, gyroscope, and magnetometer. However, signal processing was performed on the gyroscope and accelerometer readings only. This was done to develop a comparison model as is used in the extant literature. After cleaning and filtering the raw signals, power spectral density analysis was performed to extract frequency while integration was performed on the gyroscope data to calculate amplitude. Algorithms from [17] were adopted for reference amplitude calculation while for reference frequency measurement algorithm described in [3] was implemented. Snapshots of signal processing from both sensors are given in Figs. 5 and 6. The data for a trial of an Action tremor is presented where the frequency calculated for the radar sensor is 6.71 Hz [ Fig. 5(e)], and the reference sensor is 6.92 Hz [ Fig. 6(c)]. Detailed statistical analysis was performed on the results obtained from both sensors. To evaluate the performance agreement between the proposed methodology and reference sensor, Bland-Altman plots for frequency and amplitude are used [63]. The value of the bias (middle line parallel to the x-axis) in the plots indicates the average value by which the reference method measures more than the proposed one. Corresponding correlation plots are also shown to validate the linear relationship between the predicted value and the reference sensor value for tremor frequency as well as amplitude. The errors for frequency and amplitude values have been calculated for each trial as A negative value in the error thus indicates that the predicted value by the radar is smaller than the value quantified by the reference sensor. Moreover, the quantified frequency and amplitude have been compared for each tremor type using mean signed error ± standard deviation (ME ± SD). The results for each tremor type are first presented separately and then an overall assessment of the proposed method has been carried out. For further analysis, the system performance is also evaluated for dominant and nondominant limb tremor quantification. Finally, a comparison of the accuracy between our proposed method and the existing non-contact methods is presented. The following sections explain the experimental protocol and the statistical analysis results.

A. Action Tremors
A total of ten experiments were performed in which the subject was asked to simulate tremors while performing an action, as shown in Fig. 7(c). The subject sat in a chair and acted grabbing an object placed on the table in front of the chair. For the no tremor trials, the subject performed the same action 5 times without simulating tremor. For action tremors, the predicted frequency was found to be in the range of 6-10 Hz while the amplitude was calculated to be between 1 and 2 cm. This can be seen in Fig. 8 which shows the Bland Altman and correlation plots for the ten trials in which the subject simulated tremor. The bias in frequency is −0.18 Hz, which demonstrates that the overall predicted frequency is slightly lower than the base sensor values. Similarly for the amplitude, the bias is −0.036 cm. Table IV presents the mean signed error for the frequency and amplitude. While performing action tremor trials the data were not collected separately for dominant and nondominant limbs. This is because the action is always performed using the dominant limb.

B. Posture Tremors
For posture tremor, the subject was asked to extend both arms and hold them straight against gravity as shown in Fig. 7(b). The same was repeated for no tremor trials 5 times,   where the subject maintained the extended arm posture without simulating tremor. Fig. 9 demonstrates the Bland-Altman and correlation plots for the ten trials performed for the posture tremors in which the tremor was simulated. It can be seen from Fig. 9, that the predicted frequency for posture tremor for eight trials lies between 6-8 Hz while in two trials it was 9 and 9.8 Hz. The amplitude values are between 1.3 and 2 cm. The mean error values (bias) for frequency and amplitude are −0.15 Hz and −0.115 cm. The mean error for the frequency and amplitude of posture tremor trials is given in Table V.

C. Rest Tremors (Upper Limb)
To quantify the rest tremors in the upper limbs, the subject sat relaxed in the chair at resting position as shown in Fig. 7(a). For tremor-induced trials, the subject simulated tremors in the upper limbs while maintaining a sitting position. In the no-tremor trials, the subject kept on sitting relaxed in the chair without simulating tremors. The Bland-Altman plots and the corresponding correlation plots are shown in Fig. 10.   Table VI. The bias in the upper limb tremor frequency is positive indicating that the predicted frequency value is slightly higher than the reference sensor. The predicted frequency values are between 4 and 6 Hz, whereas the amplitude values have been calculated to be between 0.65-1 cm. These ranges are lesser as compared to the action and postural tremor values which shows agreement with the literature as mentioned in Table I.

D. Rest Tremors (Lower Limb)
For the quantification of rest tremors experienced in the lower limbs, the subject was asked to sit in the chair in a relaxed position. The subject induced tremors in the lower limbs. The mobile is attached to the lower limb, as shown in Fig. 7(d). For the no-tremor trials, the subject sat in a relaxed position in the chair without inducing tremors. Fig. 11 illustrates the Bland-Altman and the corresponding correlation graphs for rest lower limb tremors. The frequency and amplitude range for lower limb tremors was found to be between 4-6 Hz and 0.6-1 cm, respectively. Table VII lists the mean errors for the overall lower rest tremor trials.

E. No Tremor Trials
For each type of tremor, experiments were performed where the subject simulated the action without tremor. The frequency and amplitude in no tremor trials are significantly Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  smaller than those in which the tremor was induced. This is evident from the Bland-Altman and correlation plots as demonstrated in Fig. 12. It can be observed that the values for frequency and amplitude are 1-2 Hz and 0.2-0.3 cm, respectively. These indicate the slightest body movements or hand movements have given some measurements. This has also been demonstrated through micro-Doppler calculations in the previous work of Gillani and Arslan [44]. Table VIII presents a summary of the overall mean error and standard deviation for no-tremor trials. It also lists these values for no tremor trials for action, posture, and upper and lower limb tremors.

F. Dominant and Nondominant Limbs
To further evaluate the performance of the proposed method, the mean errors for the dominant and nondominant limbs were calculated separately. Fig. 13 visually demonstrates the distribution of normalized errors for the frequency and amplitude values. The errors were normalized for a fair comparison between the dominant and nondominant sides. From the interquartile ranges (IQR) mentioned in Fig. 13, it can be observed that mostly the overall spread of the errors is the same for both the dominant and nondominant sides. However, the error spread is pronounced for lower limb tremor frequency. Median error bias has also been marked in Similarly, the overall amplitude mean errors for the dominant and nondominant sides are smaller than 0.13 cm. This shows that the algorithm can quantify unilateral and bilateral tremors with sensible accuracy.

G. System Performance Summary
The overall mean error (±SD) for the tremor frequency for all 60 experiments was calculated to be −0.144 ± 0.4 Hz while for amplitude it was −0.03 ± 0.1 cm. From Tables IV-IX, it can be observed that the mean error calculated by (14) and (15), is mostly negative. The predicted frequency is slightly lower than the reference sensor value 70% of the time (42 trials out of the 60 experiments). Similarly, the predicted tremor amplitude was 55% of the times (33 out  of the 60 experiments) marginally less than the reference sensor value. This is evident from Tables IV-IX. From  Tables IV-IX, it is also evident that the mean errors in frequency are smaller than 0.4 Hz in all cases except for upper limb dominant side tremor where the error was 0.59 Hz. For amplitude, the maximum error of 0.13 cm has been observed in the dominant limb Posture tremor. The coefficient of determination was also calculated for both the tremor frequency and amplitude. Overall R 2 > 0.966 for both of the parameters and is shown in Figs. 14 and 15. This indicates a strong correlation between the predicted tremor parameters and the base sensor values.
The box plots in Fig. 16 give a descriptive statistical summary of the frequency and amplitude errors. The overall spread of the errors for both parameters is significantly small, as evident from their small IQR values also mentioned in Fig. 16.

H. Comparison With Existing Non-Contact Methods in the Literature
As mentioned in Section II, the non-contact methods that exist in literature are mostly based on cameras. However, this study aimed to develop a methodology that can quantify tremor continuously in a remote setting without invading the privacy of the patient. Hence, a radar sensor was used for the purpose.  have also been compared on the type of tremors detected, the maximum range at which the experiments were performed and the tremor parameters quantified. From Table X, it is evident that the accuracy achieved by the algorithm developed and the programmed FMCW chirp parameters for the current study is greater than those existing in the literature. Moreover, this study involves extensive experiments performed to quantify various tremors including action, posture, and rest tremors. Whereas, existing studies have only quantified hand tremors. The range selected in the current study is comparable to real-home settings. This is also significantly more than those existing in the literature. A summary comparison of this study and existing literature is provided in Table X.

VI. CONCLUSION
Tremors deteriorate the ability of a patient to perform everyday simple tasks. The severity of tremors affects the independence and confidence of the patient. Continuous remote monitoring can help in evaluating tremor severity, underlying neurological disease progression, and treatment response. This study aimed to develop a system that could unobtrusively quantify tremors while maintaining the integrity and privacy of the patient. For this purpose, the radar was customized to detect tremors and an algorithm was developed to reconstruct tremor trajectories and quantify clinically important parameters pertaining to tremors. The quantified parameters were compared to a reference sensor. Results show a superiority of the proposed methodology with increased accuracy. Moreover, the robustness of the approach is evident from the maximum range at which the tremors can be detected and the comprehensive situations in which tremors are triggered.