Remote Gait Analysis Using Ultra-Wideband Radar Technology Based on Joint Range-Doppler-Time Representation

Objective: In recent years, radar technology has been extensively utilized in contactless human behavior monitoring systems. The unique capabilities of ultra-wideband (UWB) radars compared to conventional radar technologies, due to time-of-flight measurements, present new untapped opportunities for in-depth monitoring of human movement during overground locomotion. This study aims to investigate the deployability of UWB radars in accurately capturing the gait patterns of healthy individuals with no known walking impairments. Methods: A novel algorithm was developed that can extract ten clinical spatiotemporal gait features using the Doppler information captured from three monostatic UWB radar sensors during a 6-meter walking task. Key gait events are detected from lower-extremity movements based on the joint range-Doppler-time representation of recorded radar data. The estimated gait parameters were validated against a gold-standard optical motion tracking system using 12 healthy volunteers. Results: On average, nine gait parameters can be consistently estimated with 90-98% accuracy, while capturing 94.5% of participants' gait variability and 90.8% of inter-limb symmetry. Correlation and Bland-Altman analysis revealed a strong correlation between radar-based parameters and the ground-truth values, with average discrepancies consistently close to 0. Conclusion: Results prove that radar sensing can provide accurate biomarkers to supplement clinical human gait analysis, with quality similar to gold standard assessment. Significance: Radars can potentially allow a transition from expensive and cumbersome lab-based gait analysis tools toward a completely unobtrusive and affordable solution for in-home deployment, enabling continuous long-term monitoring of individuals for research and healthcare applications.


I. INTRODUCTION
G AIT, the coordinated biomechanical pattern of human walking motion, serves as a unique biometric identifier, reflecting one's physical capabilities and neuromuscular function.Analysis of gait patterns not only yields a deeper understanding of musculoskeletal dynamics for biomechanical research, but also provides valuable insights into the health status of an individual.Research efforts are progressively directed towards developing new home-based gait analysis solutions, allowing individuals to undergo comprehensive gait assessments within the comfort of their own homes, away from clinical settings.This advancement offers benefits, not only to healthy individuals aiming to optimize their performance or monitor changes in their gait mechanics over time, but also to patients with chronic musculoskeletal disorders (e.g.osteoarthritis and back pain), acquired brain injuries (e.g.stroke and traumatic brain injury) and neurodegenerative diseases (e.g.Parkinson's and Alzheimer's disease) [1], [2].Continuous and long-term monitoring of gait patterns of individuals can enable healthcare professionals and researchers to: 1) understand better walking mechanics; 2) identify pathologies impacting gait [3]; 3) track injury/disease progression; 4) identify frailty [4]; 5) evaluate balance function (e.g.fall risk [5]); 6) evaluate medication or treatment (e.g.Deep Brain stimulation [6]) efficacy; 7) assess the impact of orthopedic footwear or orthotics; and 8) design rehabilitation exercises to restore patient mobility (e.g.stroke recovery) [7].
Generally, gait analysis technologies are classified into: 1) wearable (direct), and 2) non-wearable (remote) [8].Wearable systems are inconvenient for long-term monitoring of individuals, especially the elderly, mainly due to user non-compliance.Marker-based motion capture (MOCAP) technologies, the current gold standard remote gait assessment method [9], are impractical for in-home use, due to the space and high-cost requirements.Thus, non-wearable markerless technologies are more desirable.Among these, electromagnetic radars emerge as a highly promising technology for in-home gait analysis.Unlike existing systems (Table I), such as imaging technologies [10], ultrasonic sensors [11] and LIDAR sensors [12], radar systems pose no privacy concerns (no visual data captured), have better penetration capacity (e.g. through clothing) and higher sensitivity to subtle movements, and are less affected by ambient environmental conditions.Despite the portability of pressure-sensitive floor mats [13], radar sensors are more suitable for home settings, since they offer wider coverage, enable uninterrupted data collection, and have the potential to capture full-body kinematics, thereby widening the scope of future applications.Moreover, pressure mats typically require flat and hard surfaces, restricting their application in homes with carpets or uneven surfaces, and entail high costs to achieve comparable spatial resolution to radars.
A commonly used radar technology is ultra-wideband (UWB) radar, which transmits low-power and high-bandwidth pulses, making it ideal for safe indoor long-term healthcare applications.Operating in the unlicensed frequency band and implementable in CMOS technology, UWB radar sensors provide the opportunity for cost-effective and compact monitoring systems.Unlike narrowband radars, UWB radars enable multi-target discrimination and enhanced detection of micro-movement features from human targets with high spatial resolution.Compared to frequency-modulated continuous wave (FMCW) radars, pulsed UWB sensors exhibit simpler time-domain characteristics and typically offer higher range resolution, lower power consumption, reduced susceptibility to interference from other wireless devices, and higher penetration capabilities through walls or furniture, making them more suitable for indoor environments.Various studies have successfully employed UWB radars in health-related applications, including vital sign analysis [14], sleep stage classification [15], cardiovascular system monitoring [16], daily life activity recognition [17], and fall detection [18], demonstrating the capability these systems have in extracting both physiological and behavioral biomarkers.
Pulsed UWB radar systems have also been used for analyzing walking patterns and quantifying gait parameters of human targets.For the extraction of gait features, most studies use Doppler frequency information of back-scattered radar signals, resulting from the relative motion between the walking target and radar.Unlike conventional radars, Doppler frequency components in UWB systems, caused by the target's radial velocity, are measured based on phase shifts instead of frequency shifts in the received signals and are sometimes referred to as phasebased or spatial Doppler components [19].The captured Doppler pattern (micro-Doppler signature), generated by the translational motion of the torso and the oscillatory movements of limbs, can be used to uniquely characterize an individual's movement pattern [20].
Various studies have explored the use of learned walking characteristics derived from Doppler patterns in radar data, employing principal component analysis or deep learning methods for motion classification [21], [22], [23] and person identification [24] tasks.The extracted features in these studies, however, do not necessarily have a human-understandable interpretation.Our study focuses mainly on the extraction of spatiotemporal gait parameters (STGPs) with high clinical significance, which are commonly used by healthcare experts for assessing gait performance in healthy individuals [25], [26] and patients with gait impairments [27], [28].There are currently limited studies investigating and validating the performance of UWB radar systems in spatiotemporal gait analysis.Related prior work in this field includes the study in [29], where a method is proposed for extracting walking speed and step-time instances from micro-Doppler spectrograms (Doppler-time representation) generated from UWB radar data of walking participants.A similar approach was developed in [30], where average and variability values for walking speed and stride time were extracted for healthy young and elderly participants, as well as stroke and Parkinson's patients.The heuristic spherical trigonometrical approach proposed in [31], enabled extraction of additional gait parameters, including step/stride length, cadence, and lower-limb orientation, from Doppler signatures, given participant's limb dimensions.Other studies [32] have utilized Doppler spectrogram representations of FMCW radar signals during treadmill-based trials to extract additional parameters including stance/swing time and maximum foot/ankle/knee velocities.
The majority of these analysis methods, however, rely primarily on the Doppler spectrogram representation which retains only temporal gait information, unless information about the participant or the setup is provided for spatial parameter extraction.This limits their application to purely treadmill-based and single-participant tasks.For this reason, we propose the use of the joint range-Doppler-time (RDT) representation [33], [34], originally employed for FMCW radars, that captures both temporal and spatial walking information.This can allow a transition to overground walking experiments, which better resemble real-world in-home scenarios for assessing an individual's functional mobility.Additionally, this representation can be potentially useful in applications involving multiple people detection, identification, or tracking.
Within this context, we have developed a novel, computationally efficient algorithm to extract clinical STGPs using the joint RDT representation of recorded data from three independent commercially available monostatic UWB radar sensors.A method for detecting gait events, such as toe-off and heel strike times, from the joint RDT map of each UWB radar data is introduced.Features extracted from the three independent sensors are integrated through a weighted average and a multilateration approach, which is more computationally efficient than signal-level data fusion.The proposed method can successfully extract gait parameters including step/stride time, cadence, step/stride length, walk ratio, and swing/stance/double-support phase duration, which have not been collectively reported in any UWB radar-based gait analysis study.Our approach further allows us to quantify gait variability and asymmetry based on the instantaneous values of gait parameters, which are key indicators of gait and balance abnormalities.The method's accuracy was assessed in this preliminary study using marker-based MOCAP data from 12 healthy participants, during 6-meter walking trials, as an initial step to establish baseline gait measurements and demonstrate proof of concept.Finally, the study investigates and quantifies how the number of radars employed affects the algorithm's performance in extracting gait features.

A. Experimental Setup
The experimental setup used for data collection during the 6-meter walking trials is illustrated in Fig. 1.Radar data were recorded simultaneously using three independentlyoperating monostatic impulse-radio ultra-wideband (IR-UWB) transceiver radars (XeThru X4M03, Novelda AS, Oslo, Norway), which were positioned as shown in Fig. 1(a).All three radars were oriented such that their line of sight crossed the center of the walking pathway at a height of about 1 m.This configuration, although not necessarily optimal, was informed by simulation analysis to minimize radar blind areas, maximize coverage, and ensure overlapping fields of view.All radar sensors were configured with the same settings to transmit simultaneously pulses with a carrier frequency of 7.29 GHz, at a pulse repetition frequency of 15.19 MHz, allowing a maximum unambiguous range of 9.87 m [35].Radar data were recorded at a high sampling rate of 500 Hz, allowing radial velocities up to 5.15 m/s to be detected from the captured Doppler frequencies in the received data.This empirically selected sampling rate value ensures that all body part velocities can be unambiguously detected for walking speeds up to 1.70 m/s, while maximizing the signal-to-noise ratio (SNR) of the received radar signals and minimizing the data transfer rates and storage requirements.
The ground truth kinematic motion data were recorded using a marker-based 3D MOCAP system consisting of 28 optical high-resolution infrared cameras (16 Vantage v8 and 12 Vero v2.2, Vicon Motion Systems, Oxford, U.K.).The system tracked the 3D position of body segments of interest, at 200 Hz, from 27 passive reflective markers (Fig. 1(c)) attached to the following body landmarks: feet (1st and 5th metatarsal bones and calcaneus (heel bone)), shanks (cluster), thighs (cluster), torso (clavicle, 7th cervical spine bone, and 10th thoracic spine bone), and hands.Additional markers were attached to each radar (Fig. 1(d)), to define the global coordinate system in the recorded data.Both recording systems were also synchronized to ensure that they acquired the same walking information from each participant.

B. Participant Information and Experimental Protocol
Twelve healthy participants with no known walking impairments or abnormalities were recruited in this study (6 males and 6 females), aged 24.4 ± 3.1 years (ranging from 20 to 30 years) with height 1.71 ± 0.10 m and weight 67.08 ± 13.53 kg.Informed signed consent was obtained from all participants before data collection.The experimental procedure, which was approved by the Imperial College London institutional ethics committee (SETREC approval ref: 21IC6761), was conducted in the Biodynamics Laboratory of the MSk Lab in the Department of Surgery and Cancer at Imperial College London, U.K.. Participants were asked to walk along the midline of the designated pathway at their normal walking speed for a total of six times.The first and last 0.5 m in the recordings were neglected to ensure only steady-state walking is considered in the analysis.Along with each participant measurement, a 30-second empty room recording was obtained to assist in radar data pre-processing (See Section III-B).

III. PROPOSED METHOD
The details of the proposed algorithm are provided in the following subsections, for MOCAP (Section III-A) and radar Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.(Sections III-B to III-F) systems.An overview of the proposed processing pipeline is provided in Figs. 2 and 3.

A. Motion Capture Data Analysis
MOCAP data were pre-processed in the Vicon Nexus software to ensure correct marker labeling, and fill gaps in marker trajectories based on spline or pattern-fill interpolation methods.The kinematic trajectories were then low-pass (LP) filtered in MATLAB using a 4th-order zero-lag Butterworth filter with a cutoff frequency at 7 Hz, as proposed in [36], since the bandwidth of normal gait kinematics is typically within 4-6 Hz [37].Heel-strike (HS) and toe-off (TO) event times were extracted from the left and right foot marker trajectories using the Foot-Velocity algorithm (FVA) proposed in [36].Torso marker trajectories were used for quantifying walking velocity.Examples of detected events for both feet are shown in Fig. 2. The values of STGPs, and their associated variability/asymmetry, using MOCAP data are extracted using the methods described in Sections III-D and III-F.

B. Radar Signal Pre-Processing
1) Clutter and Noise Suppression: Recorded radar signals are commonly corrupted by noise and clutter artifacts, due to the extremely low transmitted power and unwanted reflections from background targets or interference from surroundings, especially in indoor settings.Thus, artifact suppression steps are essential before any analysis of the received radar signals.
The clutter removal stage is based on the adaptive clutter suppression method proposed in [38], which achieves higher signalto-clutter ratios when compared to conventional empty-room or background subtraction algorithms.This approach utilizes an adaptive exponential moving average (EMA) filter to construct the stationary clutter map (C) that is then subtracted from the received data (P ) to produce the clutter-suppressed data (R).
The iterative filtering process can be expressed as where m = 0, . .., M − 1 is the discrete slow-time index with M being the total recorded time samples and n = 0, . .., N − 1 is the discrete fast-time (range) index with N being the number of range samples.The parameters λ max and λ min are the upper and lower bounds for EMA filter parameter λ, P [m, n] and R[m, n] are the normalized upper envelopes of the received radar signal and clutter-suppressed signal respectively, and d[m, n] is a variable controlling the dynamics of λ.The constructed clutter map in this study is initialized using the average empty-room recorded signal.
Noise artifacts are suppressed from the received signals using the matched filtering technique, which involves the convolution of the received signal with the time-reversed waveform of the transmitted radar pulse.The resulting noise-suppressed signal (S) is given by where symbol denotes the convolution operation and x is the template of the transmitted pulse.
2) Quadrature Demodulation: A digital quadrature demodulation step was performed to recover the original baseband signal from the received amplitude-and angle-modulated radiofrequency signal, caused by the target's walking motion.The demodulated baseband signal (S b ) is given by where f 0 is the transmitted pulse carrier frequency.The resulting signal is then LP filtered with a 26-tap Hamming-windowbased filter, to remove high-frequency component artifacts.
The complex-value nature of the baseband signal results in the Doppler spectrum being non-conjugate symmetric, thereby capturing both the target's radial speed and direction.

1) Range-Doppler-Time Map Extraction:
The RDT representation of all three radar signals is extracted by computing the discrete short-time Fourier Transform (STFT) of the radar return of each range sample across the slow-time dimension.This produces a 3D array that retains both temporal and spatial information from radar signals, at the expense of increased memory requirements.The obtained RDT map is described by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where m is the new downsampled discrete slow-time index variable, k is the discrete Doppler frequency index and w is the window function used in the STFT computation, of length L samples.A 0.2s-long (100 samples) window was employed in this study, with 95% overlap, giving effectively a time resolution of 0.01 s.The selected window length provides a balance between the trade-off of time and frequency resolution in the STFT computation, while also ensuring that all spectral components remain stationary within this time duration.In literature, STFT window lengths employed for the extraction of gait-related features from Doppler representations range between 0.1-0.4s [23], [29].A Kaiser window, with a roll-off coefficient of 15, was chosen over a rectangular window for the STFT computation, since it offers better spectral leakage control with improved side-lobe attenuation.The parameter values were determined empirically as they provide sufficient time and frequency resolution (0.5 Hz) for the subsequent processing steps.
A contrast enhancement technique is then applied to each RDT frame, based on the Naka-Rushton equation [39], which amplifies the weaker Doppler shifts generated by the limbs and suppresses noise components.The contrast-enhanced RDT frames are obtained by where μ represents the average magnitude of each RDT frame.Given that the selected contrast enhancement approach constrains the RDT frame values within the range [0,1], an empirically derived fixed threshold of 0.7 is subsequently applied to each RDT frame to further eliminate noise and minor body movement artifacts.
2) Torso Tracking: The relative distance, or range, of the participant's torso from each radar is obtained by tracking the average of the five highest-intensity Doppler shift components in each RDT frame, similar to the approach in [29].The human torso has the largest surface area compared to other body parts and thus produces the strongest radar return signal.The sign of the Doppler shift generated by the human torso is also used to determine the participant's walking direction.
3) Envelope Extraction: The upper and lower envelopes of each RDT map frame are extracted, which capture the maximum and minimum Doppler frequency components for all ranges.The envelope extraction method employed in this study is the percentile method, originally proposed by Van Dorp and Groen [40] for Doppler spectrogram analysis.This method has been extensively used in literature for the extraction of lower-limb Doppler envelopes during walking [41], due to its low noise sensitivity and low computational cost.The percentile method is based on the normalized cumulative amplitude distribution of each RDT frame, which is computed by where K is the Doppler frequency axis length.In each frame m, the upper envelope is extracted by detecting when P [ m, k, n] = 0.975 (97.5 th percentile), and the lower envelope when P [ m, k, n] = 0.025 (2.5 th percentile), for each range sample n.By varying the percentile values, the shank or thigh envelope signals can be theoretically extracted [32], however, this was not investigated in this study.Additionally, to eliminate Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.multipath propagation artifacts, the extracted envelopes are only non-zero within ±0.75 m from the estimated torso's range.

4) Peak Envelope Value Extraction:
For each frame, the extrema of the upper and lower envelopes are extracted for each radar sensor, along with the range location at which they occur, which correspond to the summed range-Doppler trajectory of the body's lower extremities [42], and predominantly feet.The maximum upper envelope values are considered for a target moving toward the radar and the minimum lower envelope values for a receding target.The trajectories of the envelope extrema are referred to, in this paper, as peak envelope value (PEV) trajectories.

5) Detection of Gait Cycle Events:
The PEV trajectories captured by each radar individually are used for the detection of gait cycle events, including HS and TO times.Identifying HS and TO times directly from the PEV trajectory is non-trivial, since the time-varying Doppler trajectory of feet is usually masked by the trajectory of other lower limbs, especially during the aforementioned gait events.Therefore, HS and TO times are estimated based on empirical observations from simulated PEV trajectories.For PEV trajectory simulation, the publicly available MOCAP database recorded in the Multidisciplinary Motor Centre of the University of Antwerp [43] was used, consisting of data captured from 138 healthy individuals (ages 21-83).The local minima in the simulated PEV trajectory (t min ) are used to estimate HS times (t hs ), and the succeeding local maxima (t max ) to estimate TO times (t to ).These local maxima correspond to the time instants of maximum thigh velocity (t thigh ) that occur at the onset of the swing phase [32].Through analysis of PEV trajectories from all individuals, it was determined that t hs = t min + Δt hs and t to = t max + Δt to , where average Δt hs = 0.04 s and average Δt to = −0.03s.Fig. 4 shows an example of a simulated PEV trajectory for one radar sensor with the corresponding estimated and true HS and TO times.
The estimated HS and TO times from each radar are integrated to yield unified values using a weighted average approach.The weight w i (t i event ) for each radar i, where i ∈ {1, 2, 3}, is given by where t i event denotes the estimated HS or TO times and R(t i event ) the estimated torso's range from each radar at the detected HS or TO times.This compensates for signal attenuation that occurs with increasing range from each radar.

6)
Step and Torso Spatial Position Estimation: The torso and PEV trajectories from all three radar sensors are then used to obtain the true spatial position of the torso and lower limbs.For this, the Algebraic 3D Multilateration technique [44] is used, which uses the 3D position of radar sensors to fuse radar range estimates to obtain unique target positions in 3D space.The global coordinate system used in this study, illustrated in Fig. 1(a), is defined such that x is the direction of travel, y is the medial-lateral (side-to-side) direction and z is the vertical direction.Assuming that the target of interest (torso or lower limbs) is located at position (x t , y t , z t ) and each radar is located at positions (x i , y i , z i ), where i ∈ {1, 2, 3}, the range r i between each radar and the target is given by This set of equations can be expressed in the matrix form Ax = b, as a non-homogeneous linear system, given by where s t = x 2 t + y 2 t + z 2 t .The general solution to this 3D multilateration problem can be obtained by combining the particular and homogeneous solutions to the non-homogeneous system (further details in [44]).The selected radar positions and the geometrical constraint that the target's motion is restricted between the radars, ensure that a unique solution for the target's 3D position x can be obtained.
The obtained torso's 3D position is filtered using a linearvelocity Kalman filter, since the participant is walking along a straight path.The lower limbs' 3D position is also LP filtered using a 4th-order Butterworth filter with a cutoff frequency at 7 Hz, replicating the filtering approach employed in MOCAP data analysis (Section III-A).Filtering is essential since range estimates are highly sensitive to resolution and measurement noise.Additionally, the spatial positions of walking steps are determined based on the estimated positions of lower limbs at HS times, as done in a typical gait analysis procedure.

D. Extraction of Spatiotemporal Gait Parameters
The proposed method was designed to extract ten spatiotemporal gait parameters from radar data.The same principles apply to the extraction of MOCAP gait parameters, which are used as ground truth measures for the method's validation.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

1)
Step Time: Defined as the time required for a single step and is estimated by the time duration between two successive detected steps, i.e. between the HS times of the opposite feet.
2) Stride Time: Describes the time duration required for the completion of a full gait cycle and is estimated as the time between two consecutive HS of the same foot.
3) Cadence: Captures the rhythmical aspect of walking and typically denotes the number of steps completed per minute.This is estimated as the reciprocal of the step time.

4)
Step Length: Describes the distance along the direction of motion that is covered by one foot in a single step.This is computed as the difference in the x-dimensional position between the HS event of one foot and the HS event of the other foot.
5) Stride Length: Defined as the distance along the direction of motion covered by both feet during a single complete gait cycle.This feature is estimated by the difference in the x-dimensional position between two successive HS events of the same foot.
6) Walk Ratio: Defined as step length divided by cadence.7) Walking Speed: Typically defined as the time a participant takes to walk a specific distance on a flat surface.In our method, however, it is calculated as the time derivative of the torso's trajectory along the direction of travel.
8) Swing Time: Describes the time duration of the swing phase of the gait cycle, i.e. the period during walking when one foot is not in contact with the ground.This is estimated as the time between a TO event and its subsequent HS event of the same foot.It is equivalent to the single-support (SS) duration of the contra-lateral leg.9) Stance Time: Describes the time duration of the stance phase of the gait cycle, i.e. the period during walking in which only one foot is in contact with the ground.This is estimated as the time between an HS event and its subsequent TO event of the same foot.
10) Double-Support Time: Describes the time duration of the double-support (DS) phase of the gait cycle, i.e. the period during walking in which both feet are in contact with the ground.This is estimated as the time between an HS event of one foot and the subsequent TO event of the other foot.

E. Quantifying Multilateration Resolution Based on Range Errors
The relationship between the range estimate errors (Δr i ) for each radar and the multilateration errors in x-dimension (δx), y-dimension (δy), and z-dimension (δz), based on the global coordinate system described in Section III-C6, is Δr i (x, y, z) = r i (x + δx, y + δy, z + δz) − r i (x, y, z) (10) where r i (x, y, z) is given in (8)  where the least-squares solution for the multilateration errors δx can be obtained from By assuming that the range estimates errors for all radars are twice the radars' range resolution of 0.051 m, the worst-case errors (δx) for the current experimental setup, on the pathway floor, are shown in Fig. 5.The static error analysis results indicate that, with the current setup, the method's resolution is > 0.1 m for y-dimension and > 0.2 m for z-dimension in the majority of the pathway's area.This effectively suggests that y-dimensional gait parameters, such as step or stride width, or z-dimensional features cannot be reliably and accurately captured with the current setup, due to small displacements in these dimensions, and thus will not be reported in this study.

F. Gait Parameter Variability and Inter-Limb Asymmetry
The temporal variability and inter-limb asymmetry of gait parameters are key biomarkers of balance and mobility deficiencies [25].In this study, variability is quantified using the Gait Variability Index (GVI) proposed in [45] and asymmetry using the symmetry ratio discussed in [25].
The GVI score combines the mean and standard deviation values of 9 gait parameters which are commonly used for gait instability analysis (step/stride length, step/stride time, swing/stance time, single/double support time, and velocity), weighted by principal component analysis of data from 250 subjects.This score offers a more holistic view of the gait dynamics, as variability measures of single STGPs may not provide a comprehensive representation of the gait variability [46].The GVI values for both radar and MOCAP systems were calculated using the supplementary material provided in [45].
The symmetry ratio is computed for step time/length and swing/stance times, where a value of 1 denotes perfect symmetry.Due to low resolution in the y-dimension (Section III-E), our method, with the current setup, cannot distinguish between the left and right sides of the human body, thus Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.this metric is calculated based on the assumption that detected steps are alternating.The symmetry ratio is given by min(V Leg1 , V Leg2 )/max(V Leg1 , V Leg2 ), where V Leg1 and V Leg2 are the mean parameter values for each leg in each unidirectional walking segment.

A. Radar-Based Spatiotemporal Parameter Accuracy
The values of the STGPs extracted from the radar sensors were compared to their ground truth values from the MOCAP system.Fig. 6 provides a comparison of the estimated and true average gait features, for each participant in this study.Standard deviation values are also shown as shaded areas around the mean values, to provide an indication of variability of STGPs for both systems.The boxplots in Fig. 6 present the radar system's accuracy for each gait parameter, which is quantified as 1 minus the mean absolute percentage error (MAPE) between radar-and MOCAP-based parameters.The mean accuracy values for each parameter over all participants are also shown in Fig. 7.As shown in the obtained results, the proposed method can accurately capture the majority (nine out of ten) of gait features.Step time, stride time, cadence, stride length, and walking speed are extracted with more than 95.1% mean accuracy, while step length and walk ratio achieve at least 89.9% mean accuracy.Stance and swing times are captured with 94.3% and 90.8% mean accuracy respectively.The method's performance is sub-optimal when it comes to double-support duration, yielding only 66.8% mean accuracy.
The small inaccuracies in most gait parameters arise mainly due to the system's spatiotemporal resolution.Although the radar settings chosen were empirically derived to yield satisfactory results, no rigorous analysis was conducted to find the optimal settings that maximize the accuracy of all estimated STGPs.The primary factor causing the difference in accuracy between step/stride length and step/stride time is the limited spatial resolution of the radar system.While both step/stride times and step/stride times exhibit comparable magnitudes, the former have a higher value-to-resolution ratio.The decrease in accuracy for step compared to stride features, i.e., step time/length against stride time/length, can be also attributed to the system's fixed limited spatial and temporal resolution.For smaller (i.e., step) values, the discrepancy between the estimated and true values becomes more significant as a proportion of the resolution, impacting accuracy more than with larger (i.e., stride) values.Additionally, step features are determined by tracking both feet and any variations in heel strike definitions between the feet can result in higher measurement errors.
Inaccuracies in parameters associated with the gait cycle phases are mainly due to random estimation errors in detecting HS and TO events.These events are detected based on the estimated lower-limb (PEV) trajectories, which are also subject Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.to uncertainties.The stance phase typically occupies 60% of the gait cycle, while the swing phase occupies the remaining 40% on average [25], thus uncertainties in gait event detection are more pronounced in estimating swing time.Double support durations are very brief (20% of the gait cycle [25]) and are significantly affected by both the gait event detection inaccuracies and the system's temporal resolution.
Spearman correlation and Bland-Altman analysis were performed for the extracted features and the results are shown in Figs. 8 and 9 respectively.The correlation coefficients (r), p-values, two-way absolute intra-class correlation coefficients (ICC 2,1 ), and 95% prediction and confidence intervals are reported for each gait feature in Fig. 8.The reproducibility coefficients (RPC), coefficients of variation (CV), and 95% limits of Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.agreement (mean ± 1.96 standard deviation), between radar and MOCAP-derived features are also noted in the Bland-Altman plots in Fig. 9. Results show high correlation and consistency between radar-based gait parameters and their ground truth values, for most parameters of interest, except double-support durations.Moreover, Bland-Altman plots show that on average the difference between radar and MOCAP features is roughly centered around zero.

B. Performance for Different Radar Configurations
The experimental setup used in this study allows for comparisons to be made when different number of radar sensors are used.Although the developed method is designed for three radars, it can be easily adapted for one or two sensors.The algorithm can be validated for a two-radar configuration using radars 1 and 2 (see Fig. 1(a)), and a single-radar configuration using any radar.For the latter, radar 3 can be used to validate the method when the radar's beam axis is parallel to the walking pathway (PR), while radar 1 or 2 when the radar's beam axis is not parallel to the walking pathway (nPR).For the three-radar configuration, the 3D, 2D, and 1D position of radars is used for multilateration, while for the two-radar configuration only 2D and 1D positions are used.For the single-radar configuration, the range information is used for defining spatial gait features.
The comparison results for the different radar configurations are shown in Fig. 7, where performance is assessed based on the average accuracy for each STGP over all participants.As anticipated, the results obtained demonstrate that the overall accuracy of the method increases with the utilization of more radars.Interestingly, for the three-radar configuration, the 1D multilateration exhibits a slightly better performance for spatial feature extraction than 2D or 3D scenarios.This can be explained by considering that the displacements defining these spatial characteristics predominantly occur along the x-dimension, i.e. the walking direction of participants.Despite this drawback, both 2D and 3D approaches are expected to outperform the 1D case in scenarios where the participant walks freely in space, and can potentially allow extraction of y-dimensional or even z-dimensional gait features.On the other hand, in the case of the two-radar configuration, the 1D multilateration technique exhibits sub-optimal performance, primarily because both radars have the same x-dimensional coordinates.In the single-radar setup, the PR configuration outperforms the nPR configuration.In this context, the radar range estimates serve as approximations for the x-dimensional position of the target.The accuracy of this approximation degrades as the radar's beam axis moves farther away from the pathway's mid-line, which explains the higher error observed in the nPR configuration.

C. Variability and Symmetry Analysis
The gait variability of each participant was quantified using the GVI score that is originally extracted using nine gait parameters (Section III-F).As shown in Fig. 10(a), when all nine features are used, the estimated and true values of GVI vary significantly, mainly due to the method's inaccuracy for the extraction of some of these features and their associated variability.For this reason, a modified version of the GVI score Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.was computed using five (stride length, step/stride time, stance time, velocity), three (stride time/length, velocity), two (stride time, velocity), and one (velocity) features, with results shown in Fig. 10(a).The choice and ranking of these gait features were based on evaluating the mean absolute error in their coefficients of variation.The mean accuracy for the estimated GVI score over all participants with all nine features was 79.2% (68.7-84.4%),89.3% (79.5-94.3%)for 5 features, 94.5% (84.4-98.1%)for three features, 95.8% (86.5-99.6%)for two features, and 97.3% (93.6-99.4%)for one feature.Results indicate that using fewer features results in a more accurate modified GVI score, due to lower compounded uncertainty in the mean and standard deviation values of the included features.However, with fewer features used, the modified GVI score may not be able to capture the true gait variability in individuals with gait impairments [46].
The obtained symmetry ratios per participant for step time, step length, swing time, and stance time are shown in Fig. 10(b).Despite the method being unable, at the current stage, to distinguish between left-right body sides, the inter-limb symmetry of each participant can be captured by most gait features, except for step length which performs sub-optimally for some participants.In fact, the step time and stance time for each participant capture most of the gait symmetry using our method.A combined symmetry ratio metric is also provided, shown in Fig. 10(b), computed as the average of all extracted symmetry ratio scores.This combined metric captures 84.2-94.4% of inter-limb symmetry of all participants, with a mean accuracy over all participants of 90.8%.If the step sequence is known, the combined ratio captures on average 95.4% (87.8-98.8%) of the gait symmetry.

D. Study Limitations and Future Work
While the proposed radar-based gait analysis algorithm holds significant promise in accurately quantifying various gait parameters, there exist a few limitations that should be addressed in future studies.Firstly, the sample size for the validation of the method was small and involved only healthy young participants.This was mainly done to establish a baseline for designing and improving the proposed methodology using an easily accessible participant cohort, before progressing to more complex elderly patient cohorts.Therefore, to comprehensively assess the symmetry and variability metrics, the sample size should be expanded by incorporating individuals from various age groups and patients with neurological or musculoskeletal disorders [2].This will also validate whether the proposed method can capture the differences in gait parameters and their associated variability/asymmetry, between participants with and without gait impairments.It is worth noting that feature accuracies may vary significantly between different pathologies, necessitating customization and, potentially, a more specific selection of metrics, as not all conditions will require all the metrics under consideration.To achieve this, our future studies will verify the method's performance using data collected by UWB radar sensors from both patients with neurological/neurodegenerative disorders and healthy elderly controls during a 4-meter walk task, which is part of the Living Lab study [47] conducted at Imperial College London, U.K..This study will allow us to further assess whether the proposed radar-based method can capture functional biomarkers from elderly patients in a home-like environment, which can potentially provide clinicians with a rapidly deployable and automated way of monitoring disease progression, measuring patient frailty, and evaluating treatment effectiveness.
Another limitation is the proposed method's incapacity to capture 3D gait parameters, despite its capability to achieve this.Parameters such as step/stride width and foot progression angle will provide further insights into an individual's balance control and risk of falls [25].In future iterations, a simulated brute-force approach based on the multilateration error analysis method (Section III-E) should be used to identify the optimal radar layout that minimizes estimation errors, particularly in the medial-lateral and vertical dimensions.Additionally, it should be investigated whether the employment of additional monostatic, or possibly multistatic, radar sensors improves the accuracy of the proposed method for all considered gait features.Finally, further studies should investigate different spatiotemporal resolution settings for the radar sensors to maximize the accuracy of detected gait parameters.

V. CONCLUSION
This article investigated whether UWB radars are capable of extracting clinically important STGPs with comparable quality to the parameters estimated from marker-based MOCAP technology.A novel and computationally efficient approach was developed to detect toe-off and heel-strike events from the captured Doppler information, based on the range-Doppler-time representations of radar signals recorded from commercially available radar sensors.The proposed method can extract ten gait parameters, along with variability and symmetry scores.The Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.performance of the algorithm was validated using overground walking data recorded from 12 healthy participants during 6meter walking tasks.The results demonstrate that, on average, nine out of ten gait parameters can be estimated with consistently high accuracy, while capturing an individual's gait variability and inter-limb symmetry.In conclusion, radar technology shows promise as an unobtrusive, cost-effective, and reliable solution for remote long-term in-home gait analysis, offering potential benefits for both biomechanical research and healthcare.While our study demonstrates favorable results, further research is required to understand the system's performance in real-world applications with patients who suffer from gait abnormalities.

Fig. 1 .
Fig. 1.The experimental setup employed in this study: (a) Radar sensor positions, (b) Participant walking along the specified pathway, (c) Position of the 27 reflective markers on the subject, and (d) Position of the three reflective markers attached to each radar.

Fig. 2 .
Fig. 2. (a) MOCAP data analysis pipeline.(b) Examples of vertical and horizontal trajectories for left (L) and right (R) feet for MOCAP data.The detected heel strike (HS) and toe-off (TO) events, together with extracted spatiotemporal parameters, are indicated (SS: single-support, DS: double-support).

Fig. 4 .
Fig.4.Example of a PEV trajectory for one radar sensor, generated using MOCAP data.The radial velocities of the left (L) and right (R) feet, shanks, and thighs are generated based on the derivative of the relative position of each body part to the radar.The estimated and true heel-strike (HS) and toe-off (TO) events are marked for both feet.

Fig. 5 .
Fig. 5. Multilateration error analysis for our experimental setup, in all dimensions, based on first-order Taylor series, at a height of 0 m.The maximum error for each radar was set as twice the range resolution.

Fig. 6 .
Fig. 6. (First row) Comparison of average spatiotemporal gait features extracted using the proposed radar method and MOCAP system for each participant.Shaded areas correspond to one standard deviation from the mean value.(Second row) Box plot representation of accuracy values for all radar-based features for each participant.Blue circles denote outliers, which are identified using the interquartile range (IQR) method.

Fig. 7 .
Fig. 7. Comparison of the accuracy results for different radar configurations and multilateration approaches over all participants.Black markers indicate the mean accuracy for each feature.

Fig. 8 .
Fig. 8. Correlation plots for all extracted spatiotemporal features, with best-fit lines, perfect-correlation lines, and 95% prediction/confidence intervals shown.The correlation coefficients (r), p-values, and intra-class correlation coefficients (ICC) are also reported for each gait feature.

Fig. 9 .
Fig. 9. Bland-Altman plots for all extracted spatiotemporal features.Plots illustrate the difference between radar and MOCAP data against the average values of the two systems for all participants.The solid horizontal lines indicate the mean difference and dashed lines the upper/lower 95% limits of agreement (SD: standard deviation).The reproducibility coefficient (RPC) and coefficient of variation (CV) are also indicated for each gait feature.

Fig. 10 .
Fig. 10.(a) GVI score for each participant for radar and MOCAP gait features when all required 9 features are used.Comparison results are also shown when 5 features (stride length, step/stride time, stance time, velocity), 3 features (stride time/length, velocity), 2 features (stride time, velocity), and 1 feature (velocity) are used.(b) Estimated and true symmetry ratio values for each participant using step time/length and swing/stance time.The combined ratio using all 4 features is also shown.
. Using the first-order Taylor series expansion, this can be linearly approximated as ⎡ (11)1)