Gait & Posture 36 (2012) 667–671

Review

Basic gait analysis based on continuous wave radar

Jun Zhang *

Department of Electronic Engineering, Tianjin University of Technology and Education, Dagunan Road, Tianjin 300222, People’s Republic of China

A R T I C L E I N F O

Article history:

Received 14 June 2011

Received in revised form 17 April 2012

Accepted 30 April 2012

Keywords:

Gait

CW radar

Time–frequency analysis

Doppler

Spectrogram

A B S T R A C T

A gait analysis method based on continuous wave (CW) radar is proposed in this paper. Time–frequency

analysis is used to analyze the radar micro-Doppler echo from walking humans, and the relationships

between the time–frequency spectrogram and human biological gait are discussed. The methods for

extracting the gait parameters from the spectrogram are studied in depth and experiments on more than

twenty subjects have been performed to acquire the radar gait data. The gait parameters are calculated

and compared. The gait difference between men and women are presented based on the experimental

data and extracted features. Gait analysis based on CW radar will provide a new method for clinical

diagnosis and therapy.

� 2012 Elsevier B.V. All rights reserved.

Contents lists available at SciVerse ScienceDirect

Gait & Posture

jo u rn al h om ep age: ww w.els evier .c o m/lo c ate /g ai tp os t

1. Introduction

Gait is one of the most basic human movements. The currentmethods of gait analysis are mostly based on camera systems [1],for example, using infrared camera with infrared ray transmitterand several markers which can reflect infrared light. Duringexperiments, cameras are set at different positions laboratory, andreflective markers are stuck on the different parts of the humanbody such as the pelvis, knees, ankles, and the camera records themotion trajectory of the markers on the human body, and thosedata will be used to perform an analysis of the gait. Some other gaitanalysis methods use cameras to get the image of human walkingor using acceleration sensors on a human body to measure gaitmotion parameters [2–4]. The main problems of current gaitmeasurement methods include: (1) for a camera system, theirregular shape and color changes in the video makes it difficult totrack the human body, the video processing algorithms arerelatively computationally intensive, and relatively high cost ofthe systems. (2) The sensors attached to the human body mayaffect the normal walking behavior.

This paper introduces a low-cost all-weather CW radar systemfor gait analysis. The gait analysis is realized through detecting themicro-Doppler frequency signal caused by a human moving [5].Gait radar is getting more attention by military and securitydepartments since radar can detect a human target at a distancefrom hundreds meters to several kilometers in all weather

* Tel.: +86 13207634016; fax: +86 02228181027.

E-mail address: junandzhang@126.com.

0966-6362/$ – see front matter � 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.gaitpost.2012.04.020

condition. This paper will focus on the possibility of the medicalapplication of gait analysis based on CW radar. For observinghumans, radar has advantages over other sensors: the radartransmitted electromagnetic wave signal is insensitive to day andnight, while smoke, dust and fog only slightly reduce the signal.Radar signals can also penetrate most clothing, preventingdisguises from being effective. It is possible to obtain the gaitsignal and measure the gait parameters of a person in his/hernatural walking state without him/her being aware of it, and wecan obtain some gait parameters such as stride time and speed oftorso directly.

The aim of this investigation was twofold. First, a new systemfor gait analysis is introduced and the methods for measuring thegait parameters are discussed. Second, different gait states andparameters are investigated by CW radar.

2. Method

2.1. The principle of gait analysis based on CW radar

Radar transmits an electromagnetic wave to an object, the object reflects the

wave back to the radar receiver, and the return signal contains information that

represents some kinds of the features of the object. If the object or some parts of it

have some kind of slow rotation or vibration, each moving part will result in a

modulation of the Doppler frequency shift, this phenomenon is called the micro-

Doppler effect, and we can extract certain kinds of features of the observed object

from the micro-Doppler signal. When radar illuminates the human body, the

different echo signals contain micro-Doppler feature caused by irregular movement

of the limbs and torso. Those Doppler features reflect the human gait motion

characteristics [6].

The CW radar system used for this experiment works with a single antenna, and

transmits a stable continuous wave signal and directly converts the echo signal to

base band. The basic principle of the system is shown in Fig. 1(a). Fig. 1(b) shows the

operating state of radar. The base-band output frequency of the system is the

Fig. 1. The principle of the system (a) and the operating diagram of the gait CW radar (b).

J. Zhang / Gait & Posture 36 (2012) 667–671668

Doppler frequency corresponding to the speed of moving targets. The Doppler

frequency of an object which moves with angle u to the radial direction of the radar

can be written as:

f d ¼ 2 f 0vðtÞ

Ccos u (1)

where f0 = 10.525 GHz is the operating frequency of the radar, v(t) is the velocity of

the human motion, so the Doppler frequency and velocity of objects are directly

related. In this experiment we used a commercial data sampling card to convert the

base band analog signal to a digital signal and stored the converted data on to a

computer. The base-band digital signal was Short-time Fourier Transform (STFT)

analyzed and parameters were extracted in the computer.

Suppose that the transmitter signal of the radar is

ST ðtÞ ¼ A cosð2p f 0tÞ (2)

When scattering from the total human body is considered, the radar return

becomes a summation of the different moving parts: torso, arms, legs and feet. Each

part has a different velocity and acceleration, if K different parts of the body are

considered, the received echo signals from different parts of human body can be

written as:

SRðtÞ ¼XK

i¼1

Ai cosð2p f 0ðt � tiÞÞ

¼XK

i¼1

Ai cosð2pð f 0 þ f diðtÞÞtÞ(3)

where ti = 2Ri(t)/C is the two-way transmission time delay from the radar antenna

to the object, C is the speed of light, Ri(t) is the distance variation between the radar

and the different parts of the human body, fdi(t) is the Doppler frequency caused by

ith part of the body. Fig. 2(a) shows a radar echo signal from a man who walked back

and forth two times in the radial direction of the radar.

2.2. The Short-time Fourier transform of gait radar signal

Normally for analyzing a time-stationary signal, the most useful method is the

Fourier Transform (FT). Using a FT we can obtain the frequency spectrum which

reflects the signal features in the frequency domain. But for a walking human, the

Fig. 2. The time wave (a) of and time-frequency

torso and limbs have different motion velocity and acceleration, and will cause

time-varied Doppler frequency shifts, so radar echoes from walking human are

non time-stationary in the time domain. Therefore if we use a FT for analyzing gait

radar signals, we will lose the time-varying Doppler frequency information. Time–

frequency signal representation techniques are good tool for revealing the

features of non-stationary signal in the time frequency domain [6]. In order to

introduce time dependency in the Fourier transform, a simple and intuitive

solution consists of pre-windowing the signal S(t) around a particular time t,

calculating its FT, and doing that for each time instant t. The resulting transform is

called the Short-time Fourier Transform (STFT) [7]. The spectrogram, i.e. a

representation of the frequency content of the signal as a function of time, can be

represented as the power of STFT.

Here we use STFT to get the time–frequency distribution of a radar gait signal.

The STFT of a signal SR(t) can be defined as:

Fsðt; f Þ ¼Z þ1�1

SRðuÞh�ðu � tÞe� j2p fu du (4)

where h is the short-time analysis window function. Here we choose a small

Hamming window to time–frequency analyze the real radar gait signal. The radar

signal is digitized at 1500 samples per second. The length of the Hamming window

is 128 samples. We perform a FT on the echo Doppler signal in the time window for

each time instant t to obtain the time–frequency spectrogram. An example time–

frequency spectrogram of gait signal is shown in Fig. 2(b), the horizontal axis

represents the time in the figure and the vertical axis represents the Doppler

frequency caused by body motion. From the figure we can see the Doppler

frequency change caused by the human arms, legs and torso movement. Since the

different parts of the human body do not move with constant radial velocity, the

small micro-Doppler signatures of the human body are time-varying and therefore

STFT analysis techniques are a good tool to reveal more gait characteristics from

time-varying gait signals.

2.3. Data analysis

2.3.1. The envelope of time–frequency spectrogram

The envelope of the time–frequency spectrogram is very useful for analyzing the

feature of time frequency features of gait signals [8]. The highest Doppler frequency

at each time bin makes up a high-frequency envelope. Since there may be noise

spectrogram (b) of human gait radar echo.

Fig. 3. The time–frequency spectrogram envelope (a) and (b) parameters of the spectrogram envelope.

J. Zhang / Gait & Posture 36 (2012) 667–671 669

existing and spectrum leakage from the windowed Fourier transform, before we

choose the highest Doppler frequency at each time, we should have a limit:

jFsðt; f Þj � T (5)

T is chosen so that the frequency component from small parts of the human body

such as the hands can be retained in the spectrogram. It can be chosen by comparing

the radar cross section (RCS) between the hand and human body. In our experiment,

T is chosen to be 1/100 the strength of the body torso echo. Fig. 3(a) shows the

envelope of the STFT spectrogram with a dotted line. We also have a solid line

representing the torso Doppler frequency versus time in this figure. The vertical axis

Fig. 3 is converted to motion speed instead of Doppler frequency according to

expression (1).

The dotted line represents the envelopes of the STFT spectrogram in Fig. 3(b), and

the two envelopes correspond to two contiguous steps. We define several

parameters which represent the features of envelop. K1, K2, K3, and K4 represent

respectively the slope of the four lines which are used to fit the shape of the

envelope, we will give further explanation about them later. ftorso is the Doppler

frequency of the torso. T1 and T2 represent the time width of two contiguous

envelopes; Tw is the human stride time period and Ts is the double supporting time.

The solid line in Fig. 3 represents the torso speed versus time.

2.3.2. The extraction of gait parameters

We can find some parameters representing the features of gait from spectrogram

envelopes. Such as torso velocity, stride period, cadence, the acceleration of leg in

initial swing, the deceleration of leg in terminal swing, supporting time, the time of

the three swing phase, and the measure of the symmetry between the motions of

two legs.

(1) The speed of torso: vt

The speed of torso vt is related to the Doppler frequency of the torso, the

Doppler frequency of the torso can be extracted from the frequency

distribution F(v) which is the power of Fourier transform of the gait radar

signal. vt can be calculated as the expression (6).

vt ¼p f dtersoC

v0(6)

where fdterso corresponds to the frequency that the frequency

distribution F(2pfdterso) is largest, because the torso echo is the

most powerful among the different parts of human body.(2) The gait cycle: Tw

In Fig. 3(b) we have the gait cycle parameter Tw, to get a high resolution

time period of gait cycle, we choose the time interval between the two vertices

of the contiguous envelope of the spectrogram. The time–frequency

coordinates of a vertex are calculated by a curve fitting method as follows.

There are four steps to perform: firstly, the maximum Doppler point is found in

the analyzed envelope of the spectrogram, secondly, four points on each side of

a vertex on spectrogram envelope are chosen and we can get eight points

coordinates {(fi,ti), i = 1, . . ., 8}; thirdly, the polynomial curve fitting is

performed, a 4-order polynomial is defined as:

f ðtÞ ¼ at4 þ bt3 þ ct2 þ dt þ e (7)

Substituting the eight points coordinates into the polynomial, the optimum

curve parameters {a,b,c,d,e} can be calculated through the least squares

method. Finally, the vertex coordinates can be calculated by derivation of the

polynomial equation. The gait cycle Tw is the time difference between the two

consecutive vertexes. The average gait cycle can be acquired by calculating the

average between of several consecutive Tw values, although single frequency

CW Doppler radar cannot measure the distance of object, we can estimate the

stride length Rs through torso speed and the gait cycle Tw.

(3) The acceleration and deceleration of limbs

The Polygon approximation method, which is used to estimate the

silhouette of an object in image processing, is used here to give the definition of

four parameters K1, K2, K3, K4. The curve envelope of a time–frequency

spectrogram can be considered as a silhouette of an object, the vertex of

envelope (point A in Fig. 3(b)) is set as a start point. Points C and E in Fig. 3(b)

are at the two sides of the bottom of the envelope curve. We define the

approximation error Eabc according to the expression (8):

Eabc ¼ ðSAB þ SBCÞ (8)

where SAB is the area formed by curve AB and line AB, and SBC is

the area formed by curve BC and line BC, point B is chosen in

curve AC which minimizes the approximation error Eabc, the

slopes of line AB and BC is defined as K2 and K1. At the same

time, we define the approximation error Eade according to the

expression (9):

Eade ¼ ðSAD þ SDEÞ (9)

where SAD is the area formed by curve AD and line AD, and SDE is

the area formed by curve DE and line DE, point D is chosen in

curve AE which minimizes the approximation error Eade, the

slope of line AD and DE is defined as K3 and K4.

Since Fig. 3 shows the variation of velocity of human body with time, the

four parameters K1, K2, K3, and K4 represent the slopes of lines in time–

frequency plane, so the parameters also represent the acceleration and

deceleration of limbs during human walking.

(4) The period of double standing phase: Ts

The parameter Ts represents the period of double standing phase. This

parameter can be obtained through calculating the time interval between two

contiguous step envelopes defined as in Fig. 3(b).

(5) The symmetry of the two legs swing while walking Dg

This parameter represents the unbalanced motion of human body. We

define this parameter as the difference between contiguous steps of two legs.

Dg is defined as:

Dg ¼T1

T2(10)

Fig. 4. The typical time–frequency envelope of different persons. (a) Men, (b) women, (c) Parkinson disease sufferer, (d) hemiplegics.

J. Zhang / Gait & Posture 36 (2012) 667–671670

where T1 and T2 are defined in Fig. 3(b), Dg = 1 means a well

symmetric gait while walking.(6) The time of the three swing phase

In Fig. 3(b), the time of initial swing is represented as Tu, the time of mid

swing is represented as T1, and the time of terminal swing is calculated by

Tt = (Tw � Tu � T1 � Ts).

(7) The maximum limb swing speed

The maximum limb swing speed Vmax can be calculated from the

spectrogram.

3. Results

3.1. Walking test on healthy persons

To test the capability of gait analysis of radar, more than twentyyoung men and women were asked to walk in a free state along theradial direction of the radar. The computer recorded and analyzedthe acquired data. The spectrogram envelopes of a typical man anda woman are shown in Fig. 4(a) and (b). From Fig. 4(a) and (b), wecan find some common features and also some differencesbetween men and women. For common features, first, themovement of torso is relatively stationary in swing phase andhas a small speed change during double supporting time; second,there are regular swing phase with the legs accelerating anddecelerating; third, the two legs swing in almost symmetric state.For differences, first, women have longer double supporting timethan man. Second, in the terminal phase, women have more rapiddeceleration process than man. Third, women walk in moresymmetric motion of two legs than man since normally women

walk in an elegant way. Table 1 demonstrates some typical gaitparameters of ten men and ten women and proves the gaitdifference between men and women.

3.2. Walking test on disabled individuals

We have carried out tests on a man suffering from Parkinson’ssyndrome and on a man with hemiplegics disease. The spectro-grams are shown in Fig. 4(c) and (d) respectively.

From Fig. 4, we can see there are many difference betweenhealthy persons and disabled persons. First, a disabled personwalks at a very slow speed. Secondly, the torso of a disabled personshakes more while walking than a healthy person. The torso line inFig. 4(c) and (d) shows that the speed of torso motion is largelyvaried. Third, there is considerable asymmetry between themotions of two legs in stride time, acceleration and velocity rangeand so on. Fourth, the double support time is much longer than fora healthy person.

4. Discussions

In Table 1, Vmax is the actual measurement value. During humanwalking from support phase to the mid of swing phase, feet have arapidly accelerating process and reach the largest speed. Based onour data, normally the time of from support phase to the mid ofswing phase is about 0.25 s (for example), and the walking rangeduring this time interval is about 0.6 m, so the maximum velocityof feet can be calculated as 4.8 m/s.

Today gait analysis has been applied in medical diagnosis andthe evaluation of treatment [9], and also for patients’ recovery

Table 1The features extracted from data of young men and young women.

vtorso (m/s) Tw (s) Tu (s) T1 (s) Tt (s) Ts (s) Dg Vmax (m/s)

Man

1 1.47 0.49 0.15 0.27 0.037 0.03 0.88 4.6

2 1.76 0.52 0.16 0.30 0.027 0.04 0.89 5.5

3 1.26 0.57 0.14 0.38 0.017 0.023 0.7 4.5

4 1.51 0.50 0.13 0.27 0.055 0.045 0.76 4.5

5 1.76 0.45 0.15 0.27 0.014 0.04 0.8 5.3

6 1.59 0.53 0.14 0.35 0.027 0.02 0.8 5.0

7 1.76 0.47 0.13 0.28 0.067 0.03 0.88 4.5

8 1.51 0.48 0.15 0.26 0.02 0.04 0.91 4.6

9 1.21 0.49 0.12 0.33 0.02 0.02 0.75 4.1

10 1.67 0.46 0.12 0.31 0.02 0.02 0.88 5.3

Average 1.55 0.5 0.14 0.3 0.03 0.031 0.83 4.79

Woman

1 1.59 0.47 0.06 0.33 0.007 0.08 0.98 5.2

2 1.76 0.50 0.07 0.36 0.002 0.06 1 5.1

3 1.51 0.48 0.08 0.35 0.007 0.06 0.92 5.2

4 1.47 0.48 0.07 0.37 0.006 0.05 0.95 5.5

5 1.76 0.45 0.13 0.26 0.01 0.05 1 5.3

6 1.42 0.48 0.09 0.38 0.002 0.07 0.96 4.7

7 1.38 0.52 0.07 0.37 0.001 0.08 0.86 4.7

8 1.42 0.50 0.08 0.35 0.01 0.06 0.96 4.1

9 1.50 0.47 0.09 0.32 0.001 0.06 0.98 5.5

10 1.50 0.50 0.09 0.35 0.002 0.06 0.93 4.7

Average 1.53 0.49 0.08 0.34 0.005 0.06 0.95 5

J. Zhang / Gait & Posture 36 (2012) 667–671 671

[10,11]. CW gait radar can provide continuous real-timemonitoring and measurement of patient’s gait without the patientsbeing aware, and can obtain the basic gait data in a natural gaitstate. From the experiments we can find the gait differencebetween the young men and women, and we can obtain the gaitdata from disabled individuals to help physicians to performcorrect diagnosis and evaluation of the condition of patient. Theexperiments show that gait radar system is a valid instrument forrecording basic gait parameters. In future work, the correspondingrelationship between radar gait signal and various diseases will bestudied and the database will be built.

5. Conclusions

A CW radar gait analysis system can provide the capability ofobtaining the gait data in human instinctive walking state andperforming gait analysis in real time, it can also provide some gaitparameters more precisely than a video camera system. Those dataand parameters may indicate how to perform rehabilitationtraining in different stages of rehabilitation. The radar gait analysissystem therefore has the potential to become a valuable new toolfor clinical diagnosis and therapy.

Acknowledgment

This work is supported by the National Nature ScienceFoundation of Tianjin, China (grants 09JCYBJC27300).

Conflict of interest statementThe authors have no financial and personal relationships with

other people or organizations that could in appropriately influence(bias) their work.

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