Ultrasonic distance and velocity measurement

by low-calculation-cost Doppler-shift compensation

and high-resolution Doppler velocity estimation

with wide measurement range

Shinnosuke Hirata1;�, Minoru Kuribayashi Kurosawa1 and Takashi Katagiri2

1Department of Information Processing,Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology,G2–32, 4259 Nagatsuta, Midori-ku, Yokohama, 226–8502 Japan2Sutekina Inc., Komagane, 1134–12 Akaho, Komagane, 399–4117 Japan

(Received 27 November 2008, Accepted for publication 17 December 2008 )

Keywords: Ultrasonic distance and velocity measurement, Pulse compression,Linear-period modulation, Doppler-shift compensation

PACS number: 43.35.Yb, 43.63.Vx [doi:10.1250/ast.30.220]

1. IntroductionUltrasonic sensing systems have been studied for meas-

urement of distance or velocity [1–3]. The pulse-echo methodis one of the typical methods of ultrasonic distance measure-ment. The pulse-echo method is based on determination ofthe time of flight (TOF) of an echo reflected from an object.For improvement of the signal-to-noise ratio (SNR) of thereflected echo and distance resolution, pulse compression hasbeen introduced in the pulse-echo method [1]. However, real-time distance measurement by pulse compression is difficultbecause of the high-calculation-cost digital signal processingfor cross-correlation of the received signal and the referencesignal. To reduce the calculation cost of cross correlation, asensor signal processing method using a delta-sigma modu-lated single-bit digital signal has been proposed [4]. Theproposed recursive cross-correlation operation of single-bitsignals can reduce the calculation cost of cross-correlation.

In the case of a moving object, the reflected echo ismodulated due to the Doppler effect. The Doppler effect onthe reflected echo brings about decrease or increase in thesignal period in proportion to the Doppler velocity of theobject. Pulse compression using a linear-period-modulated(LPM) signal has been proposed for distance measurement ofa moving object [2]. The cross-correlation function of theDoppler-shift LPM signal and the reference LPM signal isalso modulated due to the Doppler effect. Therefore, thedistance of the moving object is estimated from the envelopeof the cross-correlation function. However, cross correlationwith a complex reference signal to obtain an envelope of thecross-correlation function increases the calculation cost of thedigital signal processing. The distance and velocity measure-ment of a moving object using a pair of LPM signals, whichincludes an up-chirp LPM signal and a down-chirp LPMsignal, has been proposed [3]. However, cross correlation withtwo reference LPM signals also increases the calculation cost.Furthermore, the velocity of a moving object is estimatedfrom the phase of the peaks in the cross-correlation function.

Therefore, measurement range of the velocity is limited due tothe transmitted LPM signal.

In this paper, low-calculation-cost Doppler-shift compen-sation and high-resolution Doppler velocity estimation withwide measurement range are proposed. A pair of LPM signals,which includes two down-chirp LPM signals, is transmitted inthe proposed method. The received signal is correlated withthe single reference LPM signal using cross-correlation bysingle-bit signal processing. The distance and the Dopplervelocity of the object are estimated from the modulated cross-correlation function with the low calculation cost.

2. Doppler-shift compensationIn the case of a non-Doppler effect, the TOF of the

received LPM signal is typically estimated from the max-imum peak time in the cross-correlation function. In the caseof a moving object, however, the cross-correlation functionfor estimation of the TOF of the received LPM signal ismodulated due to the Doppler effect, as illustrated in Fig. 1.

The Doppler effect on the wave form of the modulatedcross-correlation function is caused by the phase shift of thereceived LPM signal. Therefore, the maximum peak time inthe modulated cross-correlation function does not show theTOF of the received LPM signal. The peak time in theenvelope of the cross-correlation function is required toestimate the TOF of the received LPM signal. In the proposedmethod, the peak time tp in the envelope of the cross-correlation function can be estimated from the maximum peaktime tmax, the minimum peak time tmin, and their absoluteamplitudes jpmaxj and jpminj in the modulated cross-correla-tion function obtained from single-bit signal processing. If thephase shift of the cross-correlation function is null, the ratio ofjpmaxj to jpminj is 1.4285 and the peak time tp in the envelopeof the cross-correlation function is tmax. If the phase shift ofthe cross-correlation function is �90�, the ratio of jpmaxj tojpminj is 1 and the peak time tp in the envelope of the cross-correlation function is the halfway point between tmax and tmin.If the phase shift of the cross-correlation function is �180�,the ratio of jpmaxj to jpminj is 1/1.4285 and the peak time tp in�e-mail: hirata.s.ab@m.titech.ac.jp

220

Acoust. Sci. & Tech. 30, 3 (2009) #2009 The Acoustical Society of Japan

the envelope of the cross-correlation function is tmin. Bya first-order approximation of the ratio shift of absoluteamplitudes, the peak time tp in the envelope of the cross-correlation function can be expressed as, if jpmaxj > jpminj,

rmax ¼ 0:5 �

����pmax

pmin

����� 1

1:4285� 1þ 0:5

rmin ¼ 1� rmax

8>><>>:

; ð1Þ

and if jpmaxj < jpminj,

rmax ¼ 1� rmin

rmin ¼ 0:5 �

����pmin

pmax

����� 1

1:4285� 1þ 0:5

8>><>>:

; ð2Þ

tp ¼ rmax � tmax þ rmin � tmin; ð3Þ

where rmax is the coefficient value of tmax, and rmin is thecoefficient value of tmin.

The peak time tp in the envelope of the cross-correlationfunction is shifted from the TOF of the received LPM signal.The Doppler effect on the peak time in the envelope of themodulated cross-correlation function is caused by the sweepperiod shift of the received LPM signal. The Doppler-shifttime td of the peak time tp can be expressed as

td ¼p0 � p0d

pb� l0

¼vd

vþ vd�p0

pb� l0; ð4Þ

where p0 is the starting period of the reference LPM signal,p0d is the starting period of the Doppler-shift LPM signal, andpb is the sweep period band of the reference LPM signal.Meanwhile, vd is the Doppler velocity of the object, v is thepropagation velocity of an ultrasonic wave in air, and l0 is thelength of the reference LPM signal. The TOF of the receivedLPM signal can be estimated by subtraction of the Doppler-shift time td estimated in Eq. (4) from the peak time tpestimated in Eq. (3). The proposed Doppler-shift compensa-tion can thus determine the distance of the moving object withlow-calculation-cost by numerical calculation alone.

3. Doppler velocity estimationDoppler velocity estimation of a moving object is required

for the proposed Doppler-shift compensation. The pulsedDoppler method is one of the typical methods of Dopplervelocity estimation. In the pulsed Doppler method, theDoppler velocity is estimated from the Doppler-shift fre-quency, which is given by the Fourier transform of the echoreflected from the moving object. Velocity resolution by theFourier transform is not sufficient for the proposed Doppler-shift compensation, however, because of the short length ofthe ultrasonic pulse. In case the period of the transmitted LPMsignal sweeps from 20 ms to 50 ms in 3.274ms, resolution ofthe Doppler velocity is approximately 2.12m/s.

Furthermore, measurement range of Doppler velocityestimation from the phase of the peaks in the cross-correlationfunction is limited because the measurement range of thephase is �180�. In case the period of the transmittedLPM signal sweeps from 20 ms to 50 ms in 3.274ms, meas-urement range of the Doppler velocity is approximately�1:58m/s.

The length of the received LPM signal is linearlydecreased or increased due to the Doppler effect. When apair of LPM signals is transmitted, the cross-correlationfunction of the pair of LPM signals and the single referenceLPM signal has two peaks. The interval of the first peak andthe second peak of the cross-correlation function showsthe length of the single LPM signal. The cross-correlationfunction of the pair of Doppler-shift LPM signals and thesingle reference LPM signal also has two peaks. The intervalof the first maximum peak and the second maximum peak inthe modulated cross-correlation function shows the Doppler-shift length of the single LPM signal. The Doppler-shiftlength of the single LPM signal is expressed as

ld ¼vd

vþ vd� l0; ð5Þ

where ld is the Doppler-shift length of the single LPM signal,l0 is the length of the single LPM signal, vd is the Dopplervelocity, and v is the propagation velocity of an ultrasonicwave in air.

Time resolution of the Doppler-shift length of the singleLPM signal estimated from the cross-correlation functionobtained by single-bit signal processing is improved by high-sampling-frequency signal processing. Therefore, the Dopplervelocity can be estimated with sufficient velocity resolution.In case the length of the single LPM signal is 3.274ms andsampling frequency is 50MHz, resolution of the Dopplervelocity is approximately 0.0085m/s with wide measurementrange.

4. Distance and velocity measurementThe proposed method of distance and velocity measure-

ment by pulse compression using a pair of LPM signals andDoppler-shift compensation is illustrated in Fig. 2. In theproposed method, a pair of LPM signals is transmitted by aloudspeaker. The received signal of a microphone is con-verted into a single-bit received signal by a delta-sigmamodulator. The single reference LPM signal is converted intoa single-bit reference signal by a digital comparator. Thecross-correlation function of the received signal and the

Received LPM signal Cross-correlation function

TOF ofreceived LPM signal

-vd

+vd

Sweep period ofreference LPM signal

Phase ofreceived LPM signal

Fig. 1 Doppler effect on the received LPM signal andcross-correlation function.

S. HIRATA et al.: ULTRASONIC DISTANCE AND VELOCITY MEASUREMENT

221

reference signal is obtained from a recursive cross-correlationoperation of single-bit signals and a smoothing operationaccomplished by a weighted moving average filter [4]. Thedistance and velocity of the object is determined by theproposed method.

The proposed method was evaluated by a computersimulation using MATLAB. In the simulation, the period ofthe single LPM signal linearly swept from 20 ms to 50 ms. Thelength of the single LPM signal was 3.274ms, and the lengthof the pair of LPM signals was 6.548ms. The distance to theobject was 1.000m, when the pair of LPM signals wastransmitted. The propagation velocity of an ultrasonic wave inair is 346.7m/s at 25�C. The sampling frequency of delta-sigma modulator was 50MHz. The length of the weightedmoving average filter for the smoothing operation was 217taps. The weights of the filter are given by the triangularfunction.

In the proposed Doppler velocity estimation, the Dopplervelocity was estimated from the interval of the first maximumpeak and the second maximum peak in the modulated cross-correlation function, as illustrated in Fig. 3(a). For compar-ison, the Doppler velocity estimated by the pulsed Dopplermethod, and the Doppler velocity estimated from the phase ofthe peaks in the modulated cross-correlation function are alsoindicated in Fig. 3(a). Velocity error of the proposed Dopplervelocity estimation is illustrated in Fig. 3(b). The Dopplervelocity can be determined with high resolution and widemeasurement range by the proposed Doppler velocity esti-mation.

In the proposed Doppler-shift compensation, the peaktime tp in the envelope of the modulated cross-correlationfunction was estimated by a first-order approximation of theratio shift of absolute amplitudes. The Doppler-shift time tdwas estimated from the estimated Doppler velocity. Thedistance of the object determined by subtraction of theDoppler-shift time td from the peak time tp is illustrated inFig. 4(a). Distance error of the proposed Doppler-shiftcompensation is illustrated in Fig. 4(b). For comparison, thepeak time tp0 in the envelope of the cross-correlation functionwas also estimated by cross correlation with a complex

reference signal. The distance of the object determined bysubtraction of the Doppler-shift time td from the peak time tp0is also indicated in Fig. 4(a). Distance error of the typicalDoppler-shift compensation by cross correlation with acomplex reference signal is illustrated in Fig. 4(b). Thedistance determined by the proposed method includes distanceerror of �0:2mm, however, the distance can be determinedby the proposed Doppler-shift compensation with the lowcalculation cost.

5. ConclusionA low-calculation-cost Doppler-shift compensation and

high-resolution Doppler velocity estimation with wide meas-urement range are proposed. In the proposed method, a pairof LPM signals is transmitted, and then correlated with asingle reference LPM signal. The Doppler velocity of theobject can be estimated from the interval of the first maximumpeak and the second maximum peak in the modulated cross-correlation function with high resolution and wide measure-ment range. The distance can be determined from the peaktime in the envelope of the modulated cross-correlationfunction is estimated by a first-order approximation of theratio shift of absolute amplitudes with the low calculationcost.

Loudspeaker

Reflected echoMicrophone

Object

d0

Ultrasonicpulse

d

Digitalcomparator

Delta-sigmamodulator

Single referenceLPM signal

Pair of twoLPM signals

LPMsignal

-vd+vd

Cross correlationby single-bit signal processing

Max. peaksMin. peaks

vd

Doppler-shiftcompensation

l0

ld

TOF

d∆Σ

Fig. 2 Design of the proposed method of ultrasonicdistance and velocity measurement by pulse compres-sion using a pair of LPM signals and applying Doppler-shift compensation.

-10

-8

-6

-4

-2

0

2

4

6

8

10

-10 -8 -6 -4 -2 0 2 4 6 8 10

Est

imat

ed D

oppl

er v

eloc

ity [

m/s

]

Proposed methodPulsed Doppler methodFrom the phase of peaks in cross-correlation function

-15

-10

-5

0

5

10

15

-10 -8 -6 -4 -2 0 2 4 6 8 10Err

or o

f es

timat

ed D

oppl

er v

eloc

ity [

mm

/s]

Doppler velocity [m/s]

(b)

Doppler velocity [m/s]

(a)

Fig. 3 Simulation results of Doppler velocity compensation.

Proposed methodCross correlation with a complex reference signal

-10 -8 -6 -4 -2 0 2 4 6 8 10

0

Doppler velocity [m/s]

(b)

-0.4

-0.2

0.2

0.4

Err

or o

f es

timat

ed d

ista

nce

[mm

]

-10 -8 -6 -4 -2 0 2 4 6 8 100.96

0.98

1

1.02

1.04

Doppler velocity [m/s]

(a)

Est

imat

ed d

ista

nce

[m]

Fig. 4 Simulation results of Doppler-shift compensation.

Acoust. Sci. & Tech. 30, 3 (2009)

222

AcknowledgmentsThis work was supported by a Grant-in-Aid for Research

Fellowships of the Japan Society for the Promotion of Sciencefor Young Scientists.

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linear-period-modulated pulse,’’ J. Acoust. Soc. Am., 61, 1019–1030 (1977).

[4] S. Hirata, M. K. Kurosawa and T. Katagiri, ‘‘Cross-correlationby single-bit signal processing for ultrasonic distance measure-ment,’’ IEICE Trans. Fundam., E91-A, 1031–1037 (2008).

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