Detection of Human Presence by Irregularity ofDoppler Signal Using Multivariate Autoregressive Model

Masatoshi SekineCorporate R&D Center

Oki Electric Industry Co., Ltd.1-16-8 Chuou, Warabi-shi,Saitama, 335-8510 Japansekine566@oki.com

Kurato MaenoCorporate R&D Center

Oki Electric Industry Co., Ltd.1-16-8 Chuou, Warabi-shi,Saitama, 335-8510 Japanmaeno284@oki.com

Toshinari KamakuraFaculty of Science and

EngineeringChuo Univercity

1-13-27 Kasuga, Bunkyo-ku,Tokyo, 112-8551 Japan

kamakura@indsys.chuo-u.ac.jp

ABSTRACTRecently, there has been a greater need for healthcare appli-cations to monitor daily activities and vital information ofpeople in their homes. A Doppler radar is used as a motionsensor. It is promising for monitoring human daily activ-ities and thus body-attached sensors are not necessary forusers. Traditional algorithms that are used for detecting aperson at home assume well-controlled environments thatdo not allow moving objects in the sensing area. However,these algorithms make errors in determining human pres-ence and do not function in environments that have movingobjects whose velocities overlap with those of a person, suchas electric fans and heaters. In this study, we address thisproblem by detecting irregular motions that characterize thepresence of humans and extract prediction errors in a mul-tivariate autoregressive model (MAR) model from DopplerI/Q signals. Performance evaluation results show that ourproposed algorithm achieves high accuracy in distinguishingbetween a person’s movement and disturbances caused bymotions of electrical appliances. It outperforms the tradi-tional frequency-based method that uses Fourier transformsand power spectra of Doppler signals.

Categories and Subject DescriptorsC.3 [Special-Purpose and Application-Based System]:Signal Processing Systems; G.3 [Probability and Statis-tics]: Multivariate Statistics, Time Series Analysis

General TermsAlgorithm, Design, Experimentation

KeywordsHuman Detection, Doppler Radar, Time Series Analysis,I/Q Signal Processing, Multivariate Autoregressive Model

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.HI-KDD ’12, August 12, 2012, Beijing, ChinaCopyright 2012 ACM 978-1-4503-1548-7/12/08 ...$15.00.

1. INTRODUCTIONToday, the aging population is progressing rapidly in many

countries. Japan, which is now struggling to deal with fallingbirth rates and an aging population [5], had only 11.6% ofits population over 65 years old in 1989. However, in 2010,the rate had risen to 23.1%, and 11.4% of the populationwas 75 and over [12]. The ability to realize the automaticand accurate detection of the presence of a person at homeis very important for several healthcare services, such asmonitoring the elderly, providing remote care, security, andsafety management [8]. (a) The most serious problem facedis that elderly people are left alone at home when they die.(b) Some elderly patients also have the tendency to go forunannounced walks, which may be a cause of concern fortheir caregivers. In this study, we use a low-cost 24 GHzcontinuous wave (CW) microwave Doppler radar for hu-man detection. A Doppler radar outputs a signal whosefrequency is different from that of transmitted waves andreceived waves. The frequency increases as the velocity ofthe target increases. In general, a Doppler radar has thefollowing advantages over an infrared sensor: It is not in-fluenced by thermal noises and can detect minute motionssuch as a person’s heartbeat and breathing [10, 11, 13]. Theremote detection of vital signs without the need for probesthat are attached to the body has many advantages. Someadvanced systems recognize specific activities [14] and fallswhen monitoring the elderly [9]. It is also easier to maintaina person’s privacy using a a Doppler radar as compared toan image or video sensor [15], particularly in bathrooms andrestrooms [7], because it outputs only one-dimensional data,while image sensors output two-dimensional image data. Itcan also monitor people when they are in the same roomor in an adjacent room. Finally, it can also detect a personeven if he or she is behind obstacles through radio signalsvia penetration, whereas images and video sensors cannotthe abovementioned.

On the other hand, the use of Doppler radar has certainproblems. It reacts to any moving objects that reflect mi-crowave energy. Therefore, simple algorithms that deter-mine a human presence using amplitude thresholds do notwork in high-noise environments. In [6], the presence ofhumans is detected by frequency analysis based on a short-time Fourier transform (STFT) using a 24 GHz Dopplerradar. It extracts the peak power at low frequencies anddistinguishes the human presence from human absence us-

Analogfilter,Amplifier

A/D converterSignalprocessing

Dopplerradar

I/Q signals

Electrical appliance as disturbance

Output ofresults

TxRx

Figure 1: Human detection system

ing the threshold of peak levels. However, the problem ofdifferentiating between the motion of an object and that ofa person still persists. Low-velocity motions, such as res-piration, heartbeats, and unconscious shaking of the body,are very similar to those associated with oscillations of elec-tric fans and heaters and rotations within microwave ovensand washing machines. Therefore, these traditional humandetection algorithms that use only frequency-based analysiscannot be used to distinguish these motions.In this study, we propose a human detection algorithm

that detects irregular motions of a person using a statisti-cal model. We adapt a multivariate autoregressive (MAR)model to receive Doppler I/Q signals and evaluate theiradaptabilities. As a result, we see that our proposed al-gorithm can detect the presence of a person in the presenceof motions by electrical appliances, while this is not possiblewith the traditional method.

2. HUMAN DETECTION ALGORITHMFigure 1 shows our proposed human detection system.

A 24 GHz CW Doppler radar outputs the in-phase andquadrature-phase (I/Q) signals whose phase is different by±π/4 radians according to the direction of motion of thetarget. We use analog filters such as low-pass filters (LPFs),high-pass filters (HPFs), and the amplifier to improve thesignal-to-noise ratio and resolution. Next, we convert theminto digital signals and process to output the results of thehuman detection. For the proposed human detection sys-tem, while electrical appliances are running, we assume theentire experiment in the presence or absence of a person. .A Doppler radar is deployed in a fixed location, such as

on a wall or a table, and transmits microwave signals witha frequency of ft. We assume that an object moves towardthe sensor with a velocity of v. Then, the frequency of thereceived wave fr is described as follows:

fr = ft ± fd (1)

where the Doppler frequency is fd, which is the differencebetween the frequency of the transmitted wave and the re-ceived wave. If the object moves toward the sensor on thesame axis, the observed Doppler frequency fd will be higher.On the other hand, if the object moves away from the sen-sor, the observed Doppler frequency fd will be lower. fd is

Time

Ampl

itude

Real value

Predicted value

a1

a2

a3

a4

a5

a6

a7

a8

a9

a10

a11

a12

A12

Interval for estimating coefficients (interval A)Interval for calculating prediction errors (interval B)

Prediction error

Figure 2: Prediction error in periodic signal

d1 d5 d9

Prediction errorPredictedvalue

Real value

b1

b2

b3b4

B4

TimeInterval for estimating coefficients (interval A)Interval for calculating prediction errors (interval B)

Ampl

itude

Figure 3: Prediction error in non-periodic signal

calculated as follows:

|fd| = |fr − ft| = ft(c+ v

c− v− 1) =

2v

c− vft � 2v

cft (2)

where c is the velocity of a radio.Next, we define the signal of the transmitted wave Vt at

time t as:

Vt(t) = Kt sin(2πftt) (3)

where Kt is the amplitude of the transmitted wave. Whenthe delay between the transmission time and reception timeis τ , the received signal at the time t, Vr(t) is as follows:

Vr(t) = Kr sin(2π(ft ± fd)t− 2πftτ) (4)

where Kr is the amplitude of the received wave, and it de-pends on the size of the moving objects and the distancebetween the object and the sensor. The transmission sig-nal and the reception signal are superimposed in the mixer.

Time

Ampl

itude

in-phase (I) signalquadrature (Q) signal

Approaching Going away

Figure 4: Moving object is approaching or goingaway from Doppler radar

(a)Electric fan(Toshiba

F-DLN100)

(b)Halogenheater I

(TEKNOSPH-290)

(c)Halogen heaterII (TEKNOSPH-1211(W))

Figure 5: Electrical appliances as disturbance

Moreover, the beat signal Vd at time t is observed as anoutput signal of the Doppler radar as follows:

Vd(t) = Kd sin(2πfdt− 2πftτ) (5)

where Kd is the amplitude of the signal and it dependsmainly on the signal strength of the received wave. Whenthe reflected waves are received using quadrature detection,the phases of the in-phase (I) signal and the quadrature (Q)signal differ by π/4 radians as follows:

I(t) = Kd sin(2πfdt− 2πftτ) (6)

Q(t) = Kd sin(2πfdt− 2πftτ + π/4) (7)

When v > 0 and fd > 0, the moving object is approachingthe radar, and the phase of Q(t) increases by π/4 as com-pared to I(t), as shown in Figure 4. On the other hand,when v < 0 and fd < 0, the moving object is moving awayfrom the radar, and the phase of I(t) increases by π/4 ascompared to Q(t). The differences in phase are used to de-termine the direction of the velocities of moving objects withrespect to the Doppler radar.The MAR model is used for linear prediction of the time

series signals. When it is adapted for the k dimensionalsignal x, which is a vector of the set of variables, the n

Figure 6: Doppler radar (Innosent IPS-154), datalogger (Contec AIO-160802AY-USB), analog filter,and amplifier

Table 1: Participant status

State ID State DistanceI Participant not present in sensing area N/AII

Sitting still on chair1m

III 3 mIV

Walking1m

V 3 mVI

Typing on keyboard of laptop PC1 m

VII 3 mVIII

Lying on floor1m

IX 3 m

Table 2: Disturbance status

State ID State DistanceA No disturbance in sensing area N/AB Electric fan 1mC (Toshiba, FDLN100) rotation and oscillation 3 mD Halogen heater I 1 mE (TEKNOS, PH-200) oscillation 3 mF Halogen heater II 1 mG (TEKNOS, PH-1211(W)) oscillation 3 m

values of vector x(n) are shown as follows:

x(n) =

M∑m=1

⎡⎢⎣α11(m) · · · α1k(m)

.... . .

...αk1(m) · · · αkk(m)

⎤⎥⎦

⎡⎢⎣x1(n−m)

...xk(n−m)

⎤⎥⎦+

⎡⎢⎣e1(n)

...ek(n)

⎤⎥⎦ (8)

where α represents the MAR coefficients, M is the orderof the MAR model, and e represents the prediction errorsbetween the predicted values and the real values. The MARcoefficients are calculated such that the prediction errors areminimized.

If the signal is periodic and the amplitude caused by themotions are larger than those caused by white noises, theprediction errors become small. On the other hand, if thesignal is non-periodic, they become large. Figure 2 and Fig-ure 3 show examples of prediction errors in periodic andnon-periodic signals in one-variable signal. The AR coeffi-cients are first estimated in interval A. Next, the predictionerrors are calculated in interval B. As shown in Figure 2.The signal patterns in interval A also appear in interval B,such as a1 to a4, a5 to a8, and a9 to a12. The optimized

0 2 4 6 8 1005

10152025

Frequency (Hz)

Pow

er (

Vrm

s )2

(a) Sitting still

0 2 4 6 8 1005

10152025

Frequency (Hz)(b) Walking

0 2 4 6 8 1005

10152025

Frequency (Hz)(c) Typing on laptop PC

0 2 4 6 8 1005

10152025

Frequency (Hz)(d) Lying on floor

0 2 4 6 8 1005

10152025

Frequency (Hz)(e) Electric fan

0 2 4 6 8 1005

10152025

Frequency (Hz)(f) Halogen heater I

0 2 4 6 8 1005

10152025

Frequency (Hz)(g) Halogen heater II

Pow

er (

Vrm

s )2

Pow

er (

Vrm

s )2

Pow

er (

Vrm

s )2

Pow

er (

Vrm

s )2

Pow

er (

Vrm

s )2

Pow

er (

Vrm

s )2

Figure 7: Power spectra of filtered original signal

parameters in interval A also fit in interval B. Therefore,prediction errors, which are the differences between the pre-dicted values and the real values, such as A12 minus a12,become small. On the other hand, as shown in Figure 3,non-periodic signal patterns generated by the motion of aperson in interval A are very different from those in intervalB. Signal patterns such as b1 to b4 do not appear in intervalA. Therefore, prediction errors such as B4 minus b4 becomelarge.We apply the MAR model to receive I/Q signals of the

Doppler radar. In general, the MAR model has been provento be particularly useful while describing the dynamic be-havior of economic and financial time series and for fore-casting. In this study, we use it for the detection of theirregularity of time-series I/Q Doppler signals. To show theadaptability of the model, the mean and variance of Akaike’sInformation Criterion (AIC) are used. AIC is originally usedto evaluate and select static models. In this study, we fix astatic model and use it for evaluating the features of data.If the mean of AIC is low, the adaptability of the model ishigh and therefore there are no signs indicating that a per-son is making irregular motions. On the other hand, if themean of AIC is high, the adaptability of the model is low,and therefore it is a sign indicating irregular motions. Inaddition, when the means of AIC are same, the variances ofAIC in the presence of a person are larger than those in theabsence of a person.The AIC is defined as follows:

AIC = Nk log(2π) +N log(|Vm|) +Nk + 2mk2 + k(k + 1) (9)

where N is the data length, Vm is the variance-covariancematrix of the prediction errors, m is the order of the MARmodel, and k is the number of variables.We fix the parameters of m and k. Therefore, AIC de-

0 10 20 30 40 50 60-0.10-0.050.000.050.10

Time (s)

Ampl

itude

(V)

(a) Sitting still

0 10 20 30 40 50 60Time (s)

Ampl

itude

(V)

(b) Walking

0 10 20 30 40 50 60Time (s)

Ampl

itude

(V)

(c) Typing on laptop PC

0 10 20 30 40 50 60Time (s)

Ampl

itude

(V)

(d) Lying on floor

0 10 20 30 40 50 60Time (s)

Ampl

itude

(V)

(e) Electric fan

0 10 20 30 40 50 60Time (s)

Ampl

itude

(V)

(f) Halogen heater I

0 10 20 30 40 50 60Time (s)

Ampl

itude

(V)

(g) Halogen heater II

-0.10-0.050.000.050.10

-0.10-0.050.000.050.10

-0.10-0.050.000.050.10

-0.10-0.050.000.050.10

-0.10-0.050.000.050.10

-0.10-0.050.000.050.10

I signalQ signal

Figure 8: Filtered and normalized amplitude of I/Qsignal

pends on Vm. We make clusters for each state using two-dimensional features of the means and variances of AIC. Weuse the statistical distance such as the Maharanobis distanceand classify the data in order to make it correspond with thecluster at which the distance becomes shortest.

3. PERFORMANCE EVALUATIONWe evaluated our proposed algorithm with respect to the

traditional method using power spectra. We used the Dopplerradar IPS-154 produced by Innosent [3] and Contec data log-ger [2], as shown in Figure 6. We assumed that the sensingarea was within about 5 meters from the front of the Dopplerradar. The Doppler radar was mounted just below the ceil-ing and was pointed in a direction toward the center of thesensing area. The states and distances of the examinee fromthe setting point of the Doppler radar of the examinee wereset as shown in Table 1. On the other hand, the statesand distances for disturbances due to electrical applianceswere set as shown in Table 2. The electrical appliances wereshown in Figure 5.

We obtained the data for combination of nine states of theexaminee and seven states of disturbances, which resultedin a total of 63 states. Of these 63 states, the examinee wasabsent from the sensing area in seven states (State I andStates A to G). On the other hand, the examinee is presentin 56 states (States II to VX and States A to G).

We estimated the MAR coefficients for the 60 s intervalby incorporating ARfit [1] in MATLAB [4]. The order ofthe MAR model was set to 3. We obtained 151 samplesin each state with a 1 kHz sampling rate and obtained thecomponents for 0 to 0.3 Hz with a 20 Hz sub-sampling rate.The window size of each sample time was set to 60 s (1200data points) and each sample was obtained every 0.2 s. Thetime for calculating the variance in each sample was set to

Table 3: Recogniton rate for each state in traditional frequency-based method(%)

State A B C D E F G MeanI 100 83.4 0 0 84.1 0 80.1 49.7II 100 100 100 100 100 100 100 100III 100 100 100 100 100 100 100 100IV 100 100 100 100 100 100 100 100V 100 100 100 100 100 100 100 100VI 100 100 100 96.0 100 100 100 99.4VII 100 100 100 100 100 100 100 100VIII 100 100 100 100 100 100 100 100VX 100 100 100 100 100 100 100 100Mean 100 98.2 88.9 88.4 98.2 88.9 97.8 94.3

Table 4: Recogniton rate for each state in our proposed method(%)

State A B C D E F G MeanI 100 84.8 100 100 100 100 100 97.8II 100 100 100 100 100 100 100 100III 100 100 100 100 100 100 100 100IV 100 100 100 100 100 100 100 100V 100 100 100 100 100 100 100 100VI 100 100 100 100 100 100 100 100VII 100 100 100 100 100 100 100 100VIII 100 100 100 100 100 100 100 100VX 100 100 100 100 100 100 100 100Mean 100 98.3 100 100 100 100 100 99.8

60 seconds. We first estimated the MAR coefficients for 60s in each state and then calculated the AIC by adapting theMAR model to the Doppler I/Q signals. The samples inthe state are clustered and each sample is classified into astate where the Maharanobis distance between them is theshortest.On the other hand, in the traditional method using power

spectra, we extracted the peak frequency and peak power inthe filtered original signal. Those features were used to clas-sify each sample into a state using the Maharanobis distanceas described above.Figure 7 shows the power spectra of the original signals

in the typical seven states. We observe that the frequenciescaused by the examinee ((a) to (d)) range mainly from 0 to10 Hz, while those caused by the disturbances ((e) to (g))range from 0 to 3 Hz. The power spectra obtained when theexaminee is present overlaps with those of the disturbances.This means that the method based on the power spectracannot distinguish the motions of a person from those ofthe disturbances.Figure 8 shows the filtered amplitudes of I/Q signals in

the seven states. We observe that the amplitudes caused byexaminee ((a) to (d)) are mainly non-periodic and irregular,while those caused by disturbances ((e) to (g)) are periodicand regular signals. This is because of the characteristics ofthe motions and is valid for the detection of a person. Theperiods for one complete oscillation of the electric fan andhalogen heaters I and II are 26.2, 19.5, and 21.6 s, respec-tively.Table 3 and Table 4 show the recognition rates for the tra-

ditional frequency-based method and our proposed method.The average recognition rates of the traditional method inthe states in the absence of a person is 49.7%, while thatin the presence of a person is 99.9%. On the other hand,in our proposed method, they are 97.8% and 100%, respec-tively. This is because the traditional method confuses theoscillations of electric fans and the heaters with those ofthe examinee, while our proposed method can accuratelydistinguish between them based on an analysis of their ir-regularity.

4. CONCLUSIONIn this study, we proposed a human detection algorithm

using a 24 GHz microwave Doppler radar. Our algorithmcan detect the presence of a person in spite of the motion ofelectrical appliances using prediction errors and their vari-ances when adapting the MARmodel to receive Doppler I/Qsignals. The results of our performance evaluation show thatour proposed algorithm can detect a person with an accu-racy of over 90 % on average and can distinguish betweenthe motions of a person from those of electrical appliances.In future, we will extend our algorithm to detect daily activ-ities of people such as walking, sitting, sleeping, and fallingin the presence of multiple moving disturbances and noisesin realistic situations and scenarios.

AcknowledgmentThis research was supported in part by “Adaptable andSeamless Technology Transfer Program through Target-drivenR&D”, Japan Science and Technology Agency.

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