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Ultrasonic distance and velocity measurement using a pair of LPM signals for cross-correlation method: Improvement of Doppler-shift compensation and examination of Doppler velocity estimation
Ultrasonics 52 (2012) 873–879
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Ultrasonic distance and velocity measurement using a pair of LPM signals for cross-correlation method: Improvement of Doppler-shift compensation and examination of Doppler velocity estimation Shinnosuke Hirata a,⇑, Minoru Kuribayashi Kurosawa b a Department of Mechanical Engineering and Intelligent Systems, Graduate School of Informatics and Engineering, The University of Electro-Communications, E4-329, 1-5-1, Chofugaoka, Chofu, Tokyo 182-8585, Japan b Department of Information Processing, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, G2-32, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8502, Japan
a r t i c l e
i n f o
Article history: Received 30 August 2011 Received in revised form 10 February 2012 Accepted 13 February 2012 Available online 27 February 2012 Keywords: Ultrasonic distance and velocity measurement Pulse-echo method Over-sampling signal processing Doppler velocity estimation Doppler-shift compensation
a b s t r a c t Real-time distance measurement of a moving object with high accuracy and high resolution using an ultrasonic wave is difficult due to the influence of the Doppler effect or the limit of the calculation cost of signal processing. An over-sampling signal processing method using a pair of LPM signals has been proposed for ultrasonic distance and velocity measurement of moving objects with high accuracy and high resolution. The proposed method consists of cross correlation by single-bit signal processing, high-resolution Doppler velocity estimation with wide measurement range and low-calculation-cost Doppler-shift compensation. The over-sampling cross-correlation function is obtained from cross correlation by singlebit signal processing with low calculation cost. The Doppler velocity and distance of the object are determined from the peak interval and peak form in the cross-correlation function by the proposed method of Doppler velocity estimation and Doppler-shift compensation. In this paper, the proposed method of Doppler-shift compensation is improved. Accuracy of the determined distance was improved from approximately within ±140 lm in the previous method to approximately within ±10 lm in computer simulations. Then, the proposed method of Doppler velocity estimation is evaluated. In computer simulations, accuracy of the determined Doppler velocity and distance were demonstrated within ±8.471 mm/s and ±13.87 lm. In experiments, Doppler velocities of the motorized stage could be determined within ±27.9 mm/s. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Acoustic sensing is used in many industrial applications due to advantages of acoustic sensors, the low purchase cost, small size, and simple hardware. Furthermore, measurement methods of distance, displacement, and velocity have been studied for environment recognition in mobile devices. The pulse-echo method is one of the typical methods of ultrasonic distance measurement. The pulse-echo method is based on determination of the time of flight (TOF) of an echo reflected from an object [1–3]. For improvement of the signal-to-noise ratio (SNR) of the reflected echo and distance resolution, pulse compression has been introduced to the pulse-echo method. Frequencymodulated (FM) signals or signals being coded by pseudo-random sequences are typically transmitted in the pulse-echo method with pulse compression, which is called the cross-correlation method [4–10]. In the case of a linear-frequency-modulated (LFM) signal,
⇑ Corresponding author. E-mail address: [email protected] (S. Hirata). 0041-624X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2012.02.007
a received signal is correlated with a reference signal, which is the transmitted LFM signal. The TOF of the received LFM signal is estimated from the maximum peak time, which is same as the envelope’s peak time, in the cross-correlation function between the received signal and the reference signal. The signal processing for cross correlation consists of huge iterations of multiplications and accumulations. Real-time ultrasonic distance measurement by the cross-correlation method is difficult because of the highcost digital signal processing. To reduce the calculation cost of cross correlation without decreasing the sampling frequency, a signal processing method using a delta-sigma modulated single-bit digital signal has been proposed [11–13]. Cross correlation by single-bit signal processing consists of a recursive cross-correlation operation of single-bit signals and a smoothing operation accomplished by a FIR low-pass filter. The calculation cost of cross correlation is reduced by the recursive cross-correlation operation. The SNR of the cross-correlation function is improved by the high sampling frequency and the smoothing operation. Therefore, cross correlation by single-bit signal processing can realize real-time ultrasonic distance measurement and improve the accuracy of distance measurement in a noisy environment [14].
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In the case of a moving object, the reflected echo is modulated due to the Doppler effect caused by the object’s motion. The Doppler effect on the reflected echo brings about decrease or increase in the signal period in proportion to the Doppler velocity of the object. Therefore, the Doppler effect on the reflected echo is used for Doppler velocity estimation of the object [15–17]. Furthermore, ultrasonic distance and velocity measurement based on the Doppler effect have been studied [18–22]. In the cross-correlation method, a Doppler-shift LFM signal cannot be correlated with a reference LFM signal. Cross correlation using a linear-period-modulated (LPM) signal has been therefore proposed for ultrasonic distance measurement of a moving object: a Doppler-shift LPM signal can be correlated with a reference LPM signal [20–22]. However, the cross-correlation function between the Doppler-shift LPM signal and the reference LPM signal is also modulated, so that the maximum peak time may not be same as the envelope’s peak time in the modulated cross correlation function. In the typical method of Doppler-shift compensation, the TOF of the Dopplershift LPM signal is typically estimated from the envelope’s peak time in the modulated cross-correlation function and the Doppler velocity of the object. The envelope of the cross-correlation function can be approximated with the absolute amplitude of the complex cross-correlation function, which is obtained from cross correlation with a complex reference signal. Therefore, the typical method of Doppler-shift compensation increases the calculation cost of the digital signal processing. In another method of Doppler-shift compensation, a pair of LPM signals, which includes an up-chirp LPM signal and a down-chirp LPM signal, is transmitted [22]. The obtained cross-correlation function has two peaks, which are the peak by the up-chirp LPM signal and the peak by the downchirp LPM signal. Because the center of two peaks is independent of the object’s motion, the TOF of the Doppler-shift LPM signal can be estimated from the center of two peaks. However, the received signal must be correlated with the up-chirp LPM signal and the down-chirp LPM signal. In case this method is introduced to an over-sampling cross-correlation function, therefore, the high calculation cost is required for digital signal processing. An oversampling signal processing method of ultrasonic distance and velocity measurement using a pair of LPM signals, which includes two down-chirp LPM signals, has been proposed [23]. The signal processing method consists of cross correlation by single-bit signal processing, high-resolution Doppler velocity estimation with wide measurement range, and low-calculation-cost Doppler-shift compensation. The over-sampling cross-correlation function between the pair of received LPM signals and the single reference LPM signal also has two peaks. The Doppler velocity and distance of the object are determined from the peak interval and peak form in the modulated cross-correlation function by numerical calculation alone. In this paper, estimation of the envelope’s peak time from the Doppler velocity of the object is proposed to improve low-calculation-cost Doppler-shift compensation. Then, performances of the proposed method of ultrasonic distance and velocity measurement are examined. The Doppler velocity error and distance error are brought about by the proposed signal processing method or fluctuations in air. Therefore, the determined Doppler velocities and distances of the object were evaluated based on computer simulations and the experimental results.
2. An over-sampling signal processing method of ultrasonic distance and velocity measurement The over-sampling signal processing method of ultrasonic distance and velocity measurement is consists of cross correlation by single-bit signal processing, high-resolution Doppler velocity
estimation with wide measurement range and low-calculationcost Doppler-shift compensation. In this method, a pair of two LPM signals is transmitted with a loudspeaker. An echo reflected from a moving object is received with a microphone. The received signal is converted into a single-bit received signal by a delta-sigma modulator. The single LPM signal is converted into a single-bit reference signal by a digital comparator. The cross-correlation function between the received signal and the reference signal is obtained from cross correlation by single-bit signal processing. In the case of typical cross correlation, signal processing by DSP software is suitable. In the case of cross correlation by single-bit signal processing, however, signal processing by FPGA hardware is suitable. In the case of the typical method, multiplication and summation of 40,925 multi-bit samples is required when the length of single LPM signal and the sampling frequency of signal processing are 3.274 ms and 12.5 MHz. On the other hand, the calculation cost of the proposed method is a summation of 200 single-bit samples, then, 2-times subtractions and 3-times integrations. Furthermore, cross correlation by single-bit signal processing was implemented by approximately 1000 FPGA logic elements and 40,000-bit RAM. The over-sampling cross-correlation function between the pair of received LPM signals and the single reference LPM signal has two peaks. The interval of two peaks decreases or increases in proportion to the Doppler velocity of the object. The Doppler velocity can be determined from the peak interval by numerical calculation alone. In high-resolution Doppler velocity estimation with wide measurement range, the resolution of the estimated Doppler velocity can be improved by the high sampling frequency. The TOF of the received LPM signal is typically estimated from the maximum peak time, which is same as the envelope’s peak time, in the cross-correlation function. In the case of a moving object, however, the maximum peak time may not be same as the envelope’s peak time in the modulated cross-correlation function, as illustrated in Fig. 1. Therefore, the envelope’s peak time is required in Doppler-shift compensation. Simulation results of the maximum peak time, the minimum peak time and the envelope’s peak time, which are differences from the TOF, are illustrated in Fig. 2. In the simulation, the period of the single LPM signal linearly swept from 20 ls to 50 ls. The length of the single LPM signal was 3.274 ms. When the LPM signals is transmitted, the distance to the wall was 1 m. The propagation velocity of an ultrasonic wave in air was approximately 346.2 m/s at 24.2 °C. The sampling frequency of
Envelope of cross-correlation function Modulated cross-correlation function
te pmax
pmin tmax tmin Fig. 1. Modulated cross-correlation function and its envelope.
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0.08
tmax Maximum peak time Minimum peak time
0.06
Envelope’s peak time
0.04
Envelope’s peak time
Difference of peak time from TOF [ms]
0.1
0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1 -10
-5
5
0
tmin
10
v(e-p /l -1) b 0
Doppler velocity [m/s] Fig. 2. Simulation results: differences of maximum peak time, minimum peak time, and envelope’s peak time from TOF of received LPM signal.
signal processing was 12.5 MHz. The envelope’s peak time is between the maximum peak time and the minimum peak time. Furthermore, the maximum peak amplitude and the minimum peak amplitude are periodically shifted, as illustrated in Fig. 3. Therefore, the envelope’s peak time is approximated from the maximum peak times, the minimum peak time and the rate of peak amplitudes in the previous method [23]. Then, the distance to the object is determined from the Doppler velocity and the envelope’s peak time. In low-calculation-cost Doppler-shift compensation, the calculation cost of distance measurement of the object can be suppressed to a similar degree of cross correlation by single-bit signal processing. 3. Improvement of Doppler-shift compensation
v(e p /l -1) 0 Doppler velocity b 0
Fig. 4. Envelope’s peak time which shuttles with Doppler velocity of object between maximum peak time and minimum peak time.
The differences of maximum peak time and minimum peak time from the envelope’s peak time are also periodically shifted with the Doppler velocity of the object, as illustrated in Fig. 4. The envelope’s peak time shuttles between the maximum peak time and the minimum peak time with the Doppler velocity of the object. Therefore, the envelope’s peak time can be estimated from the peak times and the Doppler velocity. The single LPM signal is expressed as,
l0 p l0 l0 p l0 2p ln s ; f ðtÞ ¼ sin 2p ln t þ s pb pb pb pb
ð1Þ
the phase of the single LPM signal is additionally expressed as,
hðtÞ ¼ 2p
l0 p l0 p l0 ln s : ln t þ s pb pb pb
ð2Þ
Therefore, the period pLPM(n) of the sine waves in the single LPM signal are expressed as,
The previous method of Doppler-shift compensation is includes distance errors larger than the typical method. Therefore, improvement of Doppler-shift compensation is required for the proposed method of ultrasonic distance and velocity measurement.
! ) ps l0 p l0 ln s ¼ 2p n; pb pb i¼1 p p b b ðn1Þ p l0 e l0 1 e l0 : pLPM ðnÞ ¼ s pb
2p
l0 pb
(
ln
n X
pLPM ðiÞ þ
ð3Þ ð4Þ
If the Doppler shift v þvv is the integral multiple of the period rate of d
pmax pmin
pmin pmax
pb m
the sine waves e l0 , the phase shift of the modulated cross-correlation function from the non-Doppler-effect cross-correlation function is null. Therefore, the envelope’s peak time is same as the maximum peak time in the modulated cross-correlation function. If the Doppler shift v þvv is the half-integer multiple of the period d pb 2mþ1 ð Þ rate of the sine waves e l0 2 , the phase shift of the modulated cross-correlation function from the non-Doppler-effect cross-correlation function is 180°. Therefore, the envelope’s peak time is same as the maximum peak time in the modulated cross-correlation function. The envelope’s peak time thus shuttles with the Doppler velocity between the maximum peak time and the minimum peak time, as illustrated in Fig. 4. Therefore, the compensated peak time can be estimated from the peak times and the coefficient, which depends on the Doppler velocity. The compensated peak time is ex p p b m b ðmþ1Þ pressed as, if v e l0 1 6 v d < v e l0 1 ,
Rate of peak amplitudes
1.5
1 -10
-5
0
5
10
Doppler velocity [m/s] Fig. 3. Simulation results: rate of maximum peak amplitude and minimum peak amplitude in same parameters as Fig. 2.
2l0 v ð2m þ 1Þ; r ¼ ln p v þv
ð5Þ
tc ¼ r tmax þ ð1 rÞ tmin :
ð6Þ
b
d
S. Hirata, M.K. Kurosawa / Ultrasonics 52 (2012) 873–879
v d ps l0 : v þ v d pb
ð7Þ
Simulation results of distance error determined by the previous method, the typical method and the improved method of Doppler-shift compensation are illustrated in Fig. 5. In case the sampling frequency of signal processing is 12.5 MHz, the least significant distance (LSD) is 13.87 lm. The distance error determined by the previous method of Doppler-shift compensation, which is distance estimation from the envelope’s peak time approximated from the peak form, is indicated in Fig. 5a. Accuracy of the distance determined by the previous method was approximately within ±140 lm. The error of the previous method is brought about by approximation of the envelope’s peak time. For comparison, the distance error determined by the typical method of Doppler-shift compensation, which is distance estimation from the envelope approximated with the absolute amplitude of the complex crosscorrelation function, is also indicated in Fig. 5b. Accuracy of the distance determined by the typical method was approximately within ±80 lm. The error of the typical method is brought about by the envelope approximation with the absolute amplitude of the complex cross-correlation function. In the case of a finite-length LPM signal, the envelope of the complex cross-correlation function cannot be exactly approximated due to the pulse edge of the LPM signal. To reduce the distance error by the typical method, therefore, a long-length LPM signal or amplitude modulation of the LPM signal with a window function is required. The distance error determined by the improved method of Doppler-shift compensation, which is distance estimation from the compensated peak time, is also illustrated in Fig. 5c. Accuracy of the distance determined by the improved method was approximately within ±10 lm. The error of the improved method is brought about by the velocity error of the proposed method of Doppler velocity estimation, which was ±10 mm/s. Low-calculation-cost Doppler-shift compensation is thus improved by estimation of the compensated peak time from the Doppler velocity of the object.
4. Evaluation of the proposed signal processing method 4.1. Simulation parameter Ultrasonic distance and velocity measurement by high-resolution Doppler velocity estimation with wide measurement range and low-calculation-cost Doppler-shift compensation was evaluated with computer simulations using MATLAB. Simulation parameters were same as previous parameters. The pair of two LPM signals is transmitted by a loudspeaker, and then the echo reflected from the wall was detected by a microphone. In the simulation, the SNR of the reflected echo was approximately 20 dB by adding normally distributed random noises as environmental noise to the received signal. The received signal of the microphone was converted into a single-bit receive signal by the 7th-order deltasigma modulator. The single-bit received signal was correlated with the single-bit reference signal, which was the transmitted LPM signal converted into a single-bit digital signal by a digital comparator. The oversampling cross-correlation function between the single-bit received signal and the single-bit reference signal was obtained from the recursive cross-correlation operation of single-bit signals and the smoothing operation accomplished by the triangular weighted
Errors of determinedd distance [µm]
TOF ¼ t c
(a) 150 100
50
0
-50
-100
-150 -10
-5
0
5
10
Doppler velocity [m/s]
(b) 150 Errors of determinedd distance [µm]
where r is the coefficient, tc is the compensated peak time, tmax is the maximum peak time, and tmin is the minimum peak time. Therefore, the TOF of the received LPM signal is expressed as
100
50
0
-50
-100
-150 -10
-5
0
5
10
Doppler velocity [m/s]
(c) 150 Errors of determined distance [µm]
876
100
50
0
-50
-100
-150 -10
-5
0
5
10
Doppler velocity [m/s] Fig. 5. Simulation results: distance errors determined by previous method, typical method and improved method of Doppler-shift compensation in same parameters as Fig. 2: (a) distance determined by approximation of envelope’s peak time from peak form, (b) distance determined by approximation of envelope of modulated cross-correlation function, (c) distance determined by estimation of compensated peak time from Doppler velocity of object.
moving average filter. The length of the weighted moving average filter for the smoothing operation was 141 taps. The weights of the filter were given by the triangular function. The Doppler velocity was determined from the interval between the first peak and second peak in the cross-correlation function, which shows the
S. Hirata, M.K. Kurosawa / Ultrasonics 52 (2012) 873–879
Doppler-shift length of the single LPM signal. The compensated peak time was estimated from the maximum peak time, the minimum peak time, and the determined Doppler velocity. Then, the distance to the object was determined from the compensated peak time and the determined Doppler velocity. 4.2. Simulation result The Doppler velocity and distance determined by the proposed signal processing method were evaluated by computer simulation. In the simulation, the Doppler velocity of the moving object was changed from 0.2 m/s to 0.2 m/s. In the case of each Doppler velocity, the Doppler velocity and distance to the object were determined from 500 simulations. The probability distributions of the determined Doppler velocities and the distances of the object are illustrated in Fig. 6. The Doppler velocities were determined from the peak interval. In case the sampling frequency is 12.5 MHz, the LSV of the proposed method of Doppler velocity estimation is 8.471 mm/s. The velocity errors by the proposed signal processing method are +1 or 1 LSV. The distances are determined from the compensated peak time and the Doppler velocity. In this simulation, the actual distance to the wall decreases or increases in proportion to the Doppler velocity when the transmitted signal reaches the wall. In case the Doppler velocities are 0.2 m/s, 0.1 m/s, 0.1 m/s, 0.2 m/s, the differences of distances from 1 m are 578.0 lm, 288.9 lm, 288.8 lm, 577.4 lm. In case the sampling frequency is 12.5 MHz, the LSD of the proposed method of Doppler-shift compensation is 13.87 lm. The distance errors by the proposed signal processing are within ±1 LSD. The proposed method of Doppler velocity estimation and Doppler-shift compensation can realize high accuracy and resolution with low-calculation cost by numerical calculation alone.
Probability [%]
100
50
877
5. Evaluation of fluctuations in air for Doppler velocity estimation 5.1. Experimental setup High-resolution Doppler velocity estimation with wide measurement range and low-calculation-cost Doppler-shift compensation was evaluated by experiments in ultrasonic distance and velocity measurement. The experimental setup for ultrasonic distance and velocity measurement is illustrated in Fig. 7. In the experiment, the period of the single LPM signal linearly swept from 20 ls to 50 ls. The length of the single LPM signal was 3.274 ms, and the length of two-cycles LPM signals were 6.548 ms. A pair of two LPM signals was generated from the function generator and amplified by the amplifier. The pair of two LPM signals is transmitted with the loudspeaker, and then the echo reflected from the wall was detected with the microphone. The distance d0 between the loudspeaker and the microphone was 0.100 m. The propagation velocity of an ultrasonic wave in air was approximately 346.2 m/s at 24.2 °C. The SNR of the reflected echo was approximately 20 dB by environmental noise in the experiment. The received signal of the microphone is converted into a singlebit receive signal by the 7th-order delta-sigma modulator. The sampling frequency of the 7th-order delta-sigma modulator was 12.5 MHz. In the computer using MATLAB, the single-bit received signal was correlated with the single-bit reference signal, which was the transmitted LPM signal converted into the single-bit digital signal by the digital comparator. The cross-correlation function between the single-bit received signal and the single-bit reference signal was obtained from the recursive cross-correlation operation of single-bit signals and the smoothing operation accomplished by the triangular weighted moving average filter. The length of the weighted moving average filter for the smoothing operation was 141 taps. The weights of the filter were given by the triangular function. The Doppler velocity was determined from the interval between the first maximum peak and the second maximum peak in the cross-correlation function, which shows the Doppler-shift length of the single LPM signal. The compensated peak time was estimated from the maximum peak time, the minimum peak time, and the determined Doppler velocity. Then, the distance to the object was determined from the compensated peak time and the determined Doppler velocity.
5.2. Experimental result 0 -0.3
-0.2
-0.1
0
0.1
0.2
0.3
Doppler velocity [m/s]
Probability [%]
100
50
0 0.999
0.9995
1.000
1.0005
1.001
Distance [m] Fig. 6. Simulation results: probability distributions of determined Doppler velocities and distances of object.
The velocity determined by the proposed method of Doppler velocity estimation was evaluated by the experimental result. The position of the moving motorized stage could not be measured in the experimental setup in Fig. 7. Therefore, the distance determined by the proposed method of Doppler-shift compensation cannot be evaluated from these experiments. In the experiments, the velocity of the motorized stage was changed from 0.200 m/s to 0.200 m/s. In the case of each Doppler velocity, the velocity of the motorized stage was determined from 500 experiments. The probability distributions of the velocities determined from the peak interval are illustrated in Fig. 8. Furthermore, Averages and standard deviations of the determined velocities are indicated in Table 1. In case the sampling frequency is 12.5 MHz, the LSV of the proposed method is 8.47 mm/s. Standard deviations r of the velocity errors by fluctuations in air were from 3.88 mm/s to 9.31 mm/s. In case accuracy of Doppler velocity estimation is defined as ±3r, accuracy of the determined velocities was less than ±27.9 mm/s in the experiments. The proposed method of Doppler velocity estimation can demonstrate
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Wall
Pair of two LPM signals Function generator (Tektronix AFG3252)
oudspeaker Loudspeaker (Pioneer PT-R4)
Amplifier (NF HSA4014)
Ultrasonic pulse d0
Pre-amp (B&K 5935L) Delta-sigma modulator (Analog Devices AD7720)
-vd
d1 Reflected echo
ophon ne ne Microphone 8) (B&K 4138)
+vd Motorized stage (SIGMA KOKI SGMA46-300)
1-bit DSM signal Fig. 7. Experimental setup of ultrasonic distance and velocity measurement.
100
Determined distance and velocity
Doppler velocity [m/s]
Probability [%]
0.2
50
0 -0.3
-0.2
-0.1
0
0.1
0.2
0.1
0
-0.1
0.3
Doppler velocity [m/s] -0.2 Fig. 8. Experimental results: probability distributions of determined velocities of motorized stage.
0.9
1.0
1.1
Distance [m] Table 1 Averages and standard deviations of determined velocities of motorized stage in experiments. Velocity of stage (m/s)
Average of velocity (m/s)
r of velocity (m/s)
0.200 0.100 0 0.100 0.200
0.201 9.74 102 1.55 103 0.102 0.192
6.06 5.54 3.88 5.45 9.31
high resolution from experiments in ultrasonic velocity measurement. The distance to the wall was 0.900 m, when the motorized stage started to move. The motorized stage was accelerated to 0.200 m/s in a second, and then the motorized stage was decelerated to 0 m/s in a second. The motorized stage thus moved to the distance of 1.100 m in 2 s. The motorized stage was accelerated to 0.200 m/s in a second, and then the motorized stage was decelerated to 0 m/s in a second. The motorized stage thus backed to the distance of 0.900 m in 2 s. The velocities and distances determined by the proposed method of Doppler velocity estimation and Doppler-shift compensation are illustrated in Fig. 9. The velocity of the motorized stage and the distance to the wall can be concurrently
Fig. 9. Experimental results: velocities of motorized stage and distances to wall determined by proposed method of ultrasonic distance and velocity measurement.
determined by the proposed method of ultrasonic distance and velocity measurement.
6. Conclusions An over-sampling signal processing method of ultrasonic distance and velocity measurement using a pair of LPM signals has been proposed. The proposed method consists of cross correlation by single-bit signal processing, high-resolution Doppler velocity estimation with wide measurement range, and low-calculationcost Doppler-shift compensation. In this paper, accuracy of lowcalculation-cost Doppler-shift compensation was improved by estimation of the envelope’s peak time from the Doppler velocity of the object. Furthermore, the Doppler velocities and distances determined by the proposed method were evaluated with computer simulations and experiments in ultrasonic distance and velocity measurement. In the computer simulations, accuracies of the proposed method of Doppler velocity estimation were demonstrated as 8.471 mm/s and +1 or 1 LSV. Meanwhile, accuracies of
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the proposed method of Doppler-shift compensation were demonstrated as 13.87 lm and ±1 LSD. In the experiments, the Doppler velocities could be determined within ±27.9 mm/s by the proposed method of Doppler velocity estimation.
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Ultrasonic distance and velocity measurement using a pair of LPM signals for cross-correlation method: Improvement of Doppler-shift compensation and examination of Doppler velocity estimation Shinnosuke Hirata a,⇑, Minoru Kuribayashi Kurosawa b a Department of Mechanical Engineering and Intelligent Systems, Graduate School of Informatics and Engineering, The University of Electro-Communications, E4-329, 1-5-1, Chofugaoka, Chofu, Tokyo 182-8585, Japan b Department of Information Processing, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, G2-32, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8502, Japan
a r t i c l e
i n f o
Article history: Received 30 August 2011 Received in revised form 10 February 2012 Accepted 13 February 2012 Available online 27 February 2012 Keywords: Ultrasonic distance and velocity measurement Pulse-echo method Over-sampling signal processing Doppler velocity estimation Doppler-shift compensation
a b s t r a c t Real-time distance measurement of a moving object with high accuracy and high resolution using an ultrasonic wave is difficult due to the influence of the Doppler effect or the limit of the calculation cost of signal processing. An over-sampling signal processing method using a pair of LPM signals has been proposed for ultrasonic distance and velocity measurement of moving objects with high accuracy and high resolution. The proposed method consists of cross correlation by single-bit signal processing, high-resolution Doppler velocity estimation with wide measurement range and low-calculation-cost Doppler-shift compensation. The over-sampling cross-correlation function is obtained from cross correlation by singlebit signal processing with low calculation cost. The Doppler velocity and distance of the object are determined from the peak interval and peak form in the cross-correlation function by the proposed method of Doppler velocity estimation and Doppler-shift compensation. In this paper, the proposed method of Doppler-shift compensation is improved. Accuracy of the determined distance was improved from approximately within ±140 lm in the previous method to approximately within ±10 lm in computer simulations. Then, the proposed method of Doppler velocity estimation is evaluated. In computer simulations, accuracy of the determined Doppler velocity and distance were demonstrated within ±8.471 mm/s and ±13.87 lm. In experiments, Doppler velocities of the motorized stage could be determined within ±27.9 mm/s. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Acoustic sensing is used in many industrial applications due to advantages of acoustic sensors, the low purchase cost, small size, and simple hardware. Furthermore, measurement methods of distance, displacement, and velocity have been studied for environment recognition in mobile devices. The pulse-echo method is one of the typical methods of ultrasonic distance measurement. The pulse-echo method is based on determination of the time of flight (TOF) of an echo reflected from an object [1–3]. For improvement of the signal-to-noise ratio (SNR) of the reflected echo and distance resolution, pulse compression has been introduced to the pulse-echo method. Frequencymodulated (FM) signals or signals being coded by pseudo-random sequences are typically transmitted in the pulse-echo method with pulse compression, which is called the cross-correlation method [4–10]. In the case of a linear-frequency-modulated (LFM) signal,
⇑ Corresponding author. E-mail address: [email protected] (S. Hirata). 0041-624X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2012.02.007
a received signal is correlated with a reference signal, which is the transmitted LFM signal. The TOF of the received LFM signal is estimated from the maximum peak time, which is same as the envelope’s peak time, in the cross-correlation function between the received signal and the reference signal. The signal processing for cross correlation consists of huge iterations of multiplications and accumulations. Real-time ultrasonic distance measurement by the cross-correlation method is difficult because of the highcost digital signal processing. To reduce the calculation cost of cross correlation without decreasing the sampling frequency, a signal processing method using a delta-sigma modulated single-bit digital signal has been proposed [11–13]. Cross correlation by single-bit signal processing consists of a recursive cross-correlation operation of single-bit signals and a smoothing operation accomplished by a FIR low-pass filter. The calculation cost of cross correlation is reduced by the recursive cross-correlation operation. The SNR of the cross-correlation function is improved by the high sampling frequency and the smoothing operation. Therefore, cross correlation by single-bit signal processing can realize real-time ultrasonic distance measurement and improve the accuracy of distance measurement in a noisy environment [14].
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In the case of a moving object, the reflected echo is modulated due to the Doppler effect caused by the object’s motion. The Doppler effect on the reflected echo brings about decrease or increase in the signal period in proportion to the Doppler velocity of the object. Therefore, the Doppler effect on the reflected echo is used for Doppler velocity estimation of the object [15–17]. Furthermore, ultrasonic distance and velocity measurement based on the Doppler effect have been studied [18–22]. In the cross-correlation method, a Doppler-shift LFM signal cannot be correlated with a reference LFM signal. Cross correlation using a linear-period-modulated (LPM) signal has been therefore proposed for ultrasonic distance measurement of a moving object: a Doppler-shift LPM signal can be correlated with a reference LPM signal [20–22]. However, the cross-correlation function between the Doppler-shift LPM signal and the reference LPM signal is also modulated, so that the maximum peak time may not be same as the envelope’s peak time in the modulated cross correlation function. In the typical method of Doppler-shift compensation, the TOF of the Dopplershift LPM signal is typically estimated from the envelope’s peak time in the modulated cross-correlation function and the Doppler velocity of the object. The envelope of the cross-correlation function can be approximated with the absolute amplitude of the complex cross-correlation function, which is obtained from cross correlation with a complex reference signal. Therefore, the typical method of Doppler-shift compensation increases the calculation cost of the digital signal processing. In another method of Doppler-shift compensation, a pair of LPM signals, which includes an up-chirp LPM signal and a down-chirp LPM signal, is transmitted [22]. The obtained cross-correlation function has two peaks, which are the peak by the up-chirp LPM signal and the peak by the downchirp LPM signal. Because the center of two peaks is independent of the object’s motion, the TOF of the Doppler-shift LPM signal can be estimated from the center of two peaks. However, the received signal must be correlated with the up-chirp LPM signal and the down-chirp LPM signal. In case this method is introduced to an over-sampling cross-correlation function, therefore, the high calculation cost is required for digital signal processing. An oversampling signal processing method of ultrasonic distance and velocity measurement using a pair of LPM signals, which includes two down-chirp LPM signals, has been proposed [23]. The signal processing method consists of cross correlation by single-bit signal processing, high-resolution Doppler velocity estimation with wide measurement range, and low-calculation-cost Doppler-shift compensation. The over-sampling cross-correlation function between the pair of received LPM signals and the single reference LPM signal also has two peaks. The Doppler velocity and distance of the object are determined from the peak interval and peak form in the modulated cross-correlation function by numerical calculation alone. In this paper, estimation of the envelope’s peak time from the Doppler velocity of the object is proposed to improve low-calculation-cost Doppler-shift compensation. Then, performances of the proposed method of ultrasonic distance and velocity measurement are examined. The Doppler velocity error and distance error are brought about by the proposed signal processing method or fluctuations in air. Therefore, the determined Doppler velocities and distances of the object were evaluated based on computer simulations and the experimental results.
2. An over-sampling signal processing method of ultrasonic distance and velocity measurement The over-sampling signal processing method of ultrasonic distance and velocity measurement is consists of cross correlation by single-bit signal processing, high-resolution Doppler velocity
estimation with wide measurement range and low-calculationcost Doppler-shift compensation. In this method, a pair of two LPM signals is transmitted with a loudspeaker. An echo reflected from a moving object is received with a microphone. The received signal is converted into a single-bit received signal by a delta-sigma modulator. The single LPM signal is converted into a single-bit reference signal by a digital comparator. The cross-correlation function between the received signal and the reference signal is obtained from cross correlation by single-bit signal processing. In the case of typical cross correlation, signal processing by DSP software is suitable. In the case of cross correlation by single-bit signal processing, however, signal processing by FPGA hardware is suitable. In the case of the typical method, multiplication and summation of 40,925 multi-bit samples is required when the length of single LPM signal and the sampling frequency of signal processing are 3.274 ms and 12.5 MHz. On the other hand, the calculation cost of the proposed method is a summation of 200 single-bit samples, then, 2-times subtractions and 3-times integrations. Furthermore, cross correlation by single-bit signal processing was implemented by approximately 1000 FPGA logic elements and 40,000-bit RAM. The over-sampling cross-correlation function between the pair of received LPM signals and the single reference LPM signal has two peaks. The interval of two peaks decreases or increases in proportion to the Doppler velocity of the object. The Doppler velocity can be determined from the peak interval by numerical calculation alone. In high-resolution Doppler velocity estimation with wide measurement range, the resolution of the estimated Doppler velocity can be improved by the high sampling frequency. The TOF of the received LPM signal is typically estimated from the maximum peak time, which is same as the envelope’s peak time, in the cross-correlation function. In the case of a moving object, however, the maximum peak time may not be same as the envelope’s peak time in the modulated cross-correlation function, as illustrated in Fig. 1. Therefore, the envelope’s peak time is required in Doppler-shift compensation. Simulation results of the maximum peak time, the minimum peak time and the envelope’s peak time, which are differences from the TOF, are illustrated in Fig. 2. In the simulation, the period of the single LPM signal linearly swept from 20 ls to 50 ls. The length of the single LPM signal was 3.274 ms. When the LPM signals is transmitted, the distance to the wall was 1 m. The propagation velocity of an ultrasonic wave in air was approximately 346.2 m/s at 24.2 °C. The sampling frequency of
Envelope of cross-correlation function Modulated cross-correlation function
te pmax
pmin tmax tmin Fig. 1. Modulated cross-correlation function and its envelope.
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0.08
tmax Maximum peak time Minimum peak time
0.06
Envelope’s peak time
0.04
Envelope’s peak time
Difference of peak time from TOF [ms]
0.1
0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1 -10
-5
5
0
tmin
10
v(e-p /l -1) b 0
Doppler velocity [m/s] Fig. 2. Simulation results: differences of maximum peak time, minimum peak time, and envelope’s peak time from TOF of received LPM signal.
signal processing was 12.5 MHz. The envelope’s peak time is between the maximum peak time and the minimum peak time. Furthermore, the maximum peak amplitude and the minimum peak amplitude are periodically shifted, as illustrated in Fig. 3. Therefore, the envelope’s peak time is approximated from the maximum peak times, the minimum peak time and the rate of peak amplitudes in the previous method [23]. Then, the distance to the object is determined from the Doppler velocity and the envelope’s peak time. In low-calculation-cost Doppler-shift compensation, the calculation cost of distance measurement of the object can be suppressed to a similar degree of cross correlation by single-bit signal processing. 3. Improvement of Doppler-shift compensation
v(e p /l -1) 0 Doppler velocity b 0
Fig. 4. Envelope’s peak time which shuttles with Doppler velocity of object between maximum peak time and minimum peak time.
The differences of maximum peak time and minimum peak time from the envelope’s peak time are also periodically shifted with the Doppler velocity of the object, as illustrated in Fig. 4. The envelope’s peak time shuttles between the maximum peak time and the minimum peak time with the Doppler velocity of the object. Therefore, the envelope’s peak time can be estimated from the peak times and the Doppler velocity. The single LPM signal is expressed as,
l0 p l0 l0 p l0 2p ln s ; f ðtÞ ¼ sin 2p ln t þ s pb pb pb pb
ð1Þ
the phase of the single LPM signal is additionally expressed as,
hðtÞ ¼ 2p
l0 p l0 p l0 ln s : ln t þ s pb pb pb
ð2Þ
Therefore, the period pLPM(n) of the sine waves in the single LPM signal are expressed as,
The previous method of Doppler-shift compensation is includes distance errors larger than the typical method. Therefore, improvement of Doppler-shift compensation is required for the proposed method of ultrasonic distance and velocity measurement.
! ) ps l0 p l0 ln s ¼ 2p n; pb pb i¼1 p p b b ðn1Þ p l0 e l0 1 e l0 : pLPM ðnÞ ¼ s pb
2p
l0 pb
(
ln
n X
pLPM ðiÞ þ
ð3Þ ð4Þ
If the Doppler shift v þvv is the integral multiple of the period rate of d
pmax pmin
pmin pmax
pb m
the sine waves e l0 , the phase shift of the modulated cross-correlation function from the non-Doppler-effect cross-correlation function is null. Therefore, the envelope’s peak time is same as the maximum peak time in the modulated cross-correlation function. If the Doppler shift v þvv is the half-integer multiple of the period d pb 2mþ1 ð Þ rate of the sine waves e l0 2 , the phase shift of the modulated cross-correlation function from the non-Doppler-effect cross-correlation function is 180°. Therefore, the envelope’s peak time is same as the maximum peak time in the modulated cross-correlation function. The envelope’s peak time thus shuttles with the Doppler velocity between the maximum peak time and the minimum peak time, as illustrated in Fig. 4. Therefore, the compensated peak time can be estimated from the peak times and the coefficient, which depends on the Doppler velocity. The compensated peak time is ex p p b m b ðmþ1Þ pressed as, if v e l0 1 6 v d < v e l0 1 ,
Rate of peak amplitudes
1.5
1 -10
-5
0
5
10
Doppler velocity [m/s] Fig. 3. Simulation results: rate of maximum peak amplitude and minimum peak amplitude in same parameters as Fig. 2.
2l0 v ð2m þ 1Þ; r ¼ ln p v þv
ð5Þ
tc ¼ r tmax þ ð1 rÞ tmin :
ð6Þ
b
d
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v d ps l0 : v þ v d pb
ð7Þ
Simulation results of distance error determined by the previous method, the typical method and the improved method of Doppler-shift compensation are illustrated in Fig. 5. In case the sampling frequency of signal processing is 12.5 MHz, the least significant distance (LSD) is 13.87 lm. The distance error determined by the previous method of Doppler-shift compensation, which is distance estimation from the envelope’s peak time approximated from the peak form, is indicated in Fig. 5a. Accuracy of the distance determined by the previous method was approximately within ±140 lm. The error of the previous method is brought about by approximation of the envelope’s peak time. For comparison, the distance error determined by the typical method of Doppler-shift compensation, which is distance estimation from the envelope approximated with the absolute amplitude of the complex crosscorrelation function, is also indicated in Fig. 5b. Accuracy of the distance determined by the typical method was approximately within ±80 lm. The error of the typical method is brought about by the envelope approximation with the absolute amplitude of the complex cross-correlation function. In the case of a finite-length LPM signal, the envelope of the complex cross-correlation function cannot be exactly approximated due to the pulse edge of the LPM signal. To reduce the distance error by the typical method, therefore, a long-length LPM signal or amplitude modulation of the LPM signal with a window function is required. The distance error determined by the improved method of Doppler-shift compensation, which is distance estimation from the compensated peak time, is also illustrated in Fig. 5c. Accuracy of the distance determined by the improved method was approximately within ±10 lm. The error of the improved method is brought about by the velocity error of the proposed method of Doppler velocity estimation, which was ±10 mm/s. Low-calculation-cost Doppler-shift compensation is thus improved by estimation of the compensated peak time from the Doppler velocity of the object.
4. Evaluation of the proposed signal processing method 4.1. Simulation parameter Ultrasonic distance and velocity measurement by high-resolution Doppler velocity estimation with wide measurement range and low-calculation-cost Doppler-shift compensation was evaluated with computer simulations using MATLAB. Simulation parameters were same as previous parameters. The pair of two LPM signals is transmitted by a loudspeaker, and then the echo reflected from the wall was detected by a microphone. In the simulation, the SNR of the reflected echo was approximately 20 dB by adding normally distributed random noises as environmental noise to the received signal. The received signal of the microphone was converted into a single-bit receive signal by the 7th-order deltasigma modulator. The single-bit received signal was correlated with the single-bit reference signal, which was the transmitted LPM signal converted into a single-bit digital signal by a digital comparator. The oversampling cross-correlation function between the single-bit received signal and the single-bit reference signal was obtained from the recursive cross-correlation operation of single-bit signals and the smoothing operation accomplished by the triangular weighted
Errors of determinedd distance [µm]
TOF ¼ t c
(a) 150 100
50
0
-50
-100
-150 -10
-5
0
5
10
Doppler velocity [m/s]
(b) 150 Errors of determinedd distance [µm]
where r is the coefficient, tc is the compensated peak time, tmax is the maximum peak time, and tmin is the minimum peak time. Therefore, the TOF of the received LPM signal is expressed as
100
50
0
-50
-100
-150 -10
-5
0
5
10
Doppler velocity [m/s]
(c) 150 Errors of determined distance [µm]
876
100
50
0
-50
-100
-150 -10
-5
0
5
10
Doppler velocity [m/s] Fig. 5. Simulation results: distance errors determined by previous method, typical method and improved method of Doppler-shift compensation in same parameters as Fig. 2: (a) distance determined by approximation of envelope’s peak time from peak form, (b) distance determined by approximation of envelope of modulated cross-correlation function, (c) distance determined by estimation of compensated peak time from Doppler velocity of object.
moving average filter. The length of the weighted moving average filter for the smoothing operation was 141 taps. The weights of the filter were given by the triangular function. The Doppler velocity was determined from the interval between the first peak and second peak in the cross-correlation function, which shows the
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Doppler-shift length of the single LPM signal. The compensated peak time was estimated from the maximum peak time, the minimum peak time, and the determined Doppler velocity. Then, the distance to the object was determined from the compensated peak time and the determined Doppler velocity. 4.2. Simulation result The Doppler velocity and distance determined by the proposed signal processing method were evaluated by computer simulation. In the simulation, the Doppler velocity of the moving object was changed from 0.2 m/s to 0.2 m/s. In the case of each Doppler velocity, the Doppler velocity and distance to the object were determined from 500 simulations. The probability distributions of the determined Doppler velocities and the distances of the object are illustrated in Fig. 6. The Doppler velocities were determined from the peak interval. In case the sampling frequency is 12.5 MHz, the LSV of the proposed method of Doppler velocity estimation is 8.471 mm/s. The velocity errors by the proposed signal processing method are +1 or 1 LSV. The distances are determined from the compensated peak time and the Doppler velocity. In this simulation, the actual distance to the wall decreases or increases in proportion to the Doppler velocity when the transmitted signal reaches the wall. In case the Doppler velocities are 0.2 m/s, 0.1 m/s, 0.1 m/s, 0.2 m/s, the differences of distances from 1 m are 578.0 lm, 288.9 lm, 288.8 lm, 577.4 lm. In case the sampling frequency is 12.5 MHz, the LSD of the proposed method of Doppler-shift compensation is 13.87 lm. The distance errors by the proposed signal processing are within ±1 LSD. The proposed method of Doppler velocity estimation and Doppler-shift compensation can realize high accuracy and resolution with low-calculation cost by numerical calculation alone.
Probability [%]
100
50
877
5. Evaluation of fluctuations in air for Doppler velocity estimation 5.1. Experimental setup High-resolution Doppler velocity estimation with wide measurement range and low-calculation-cost Doppler-shift compensation was evaluated by experiments in ultrasonic distance and velocity measurement. The experimental setup for ultrasonic distance and velocity measurement is illustrated in Fig. 7. In the experiment, the period of the single LPM signal linearly swept from 20 ls to 50 ls. The length of the single LPM signal was 3.274 ms, and the length of two-cycles LPM signals were 6.548 ms. A pair of two LPM signals was generated from the function generator and amplified by the amplifier. The pair of two LPM signals is transmitted with the loudspeaker, and then the echo reflected from the wall was detected with the microphone. The distance d0 between the loudspeaker and the microphone was 0.100 m. The propagation velocity of an ultrasonic wave in air was approximately 346.2 m/s at 24.2 °C. The SNR of the reflected echo was approximately 20 dB by environmental noise in the experiment. The received signal of the microphone is converted into a singlebit receive signal by the 7th-order delta-sigma modulator. The sampling frequency of the 7th-order delta-sigma modulator was 12.5 MHz. In the computer using MATLAB, the single-bit received signal was correlated with the single-bit reference signal, which was the transmitted LPM signal converted into the single-bit digital signal by the digital comparator. The cross-correlation function between the single-bit received signal and the single-bit reference signal was obtained from the recursive cross-correlation operation of single-bit signals and the smoothing operation accomplished by the triangular weighted moving average filter. The length of the weighted moving average filter for the smoothing operation was 141 taps. The weights of the filter were given by the triangular function. The Doppler velocity was determined from the interval between the first maximum peak and the second maximum peak in the cross-correlation function, which shows the Doppler-shift length of the single LPM signal. The compensated peak time was estimated from the maximum peak time, the minimum peak time, and the determined Doppler velocity. Then, the distance to the object was determined from the compensated peak time and the determined Doppler velocity.
5.2. Experimental result 0 -0.3
-0.2
-0.1
0
0.1
0.2
0.3
Doppler velocity [m/s]
Probability [%]
100
50
0 0.999
0.9995
1.000
1.0005
1.001
Distance [m] Fig. 6. Simulation results: probability distributions of determined Doppler velocities and distances of object.
The velocity determined by the proposed method of Doppler velocity estimation was evaluated by the experimental result. The position of the moving motorized stage could not be measured in the experimental setup in Fig. 7. Therefore, the distance determined by the proposed method of Doppler-shift compensation cannot be evaluated from these experiments. In the experiments, the velocity of the motorized stage was changed from 0.200 m/s to 0.200 m/s. In the case of each Doppler velocity, the velocity of the motorized stage was determined from 500 experiments. The probability distributions of the velocities determined from the peak interval are illustrated in Fig. 8. Furthermore, Averages and standard deviations of the determined velocities are indicated in Table 1. In case the sampling frequency is 12.5 MHz, the LSV of the proposed method is 8.47 mm/s. Standard deviations r of the velocity errors by fluctuations in air were from 3.88 mm/s to 9.31 mm/s. In case accuracy of Doppler velocity estimation is defined as ±3r, accuracy of the determined velocities was less than ±27.9 mm/s in the experiments. The proposed method of Doppler velocity estimation can demonstrate
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Wall
Pair of two LPM signals Function generator (Tektronix AFG3252)
oudspeaker Loudspeaker (Pioneer PT-R4)
Amplifier (NF HSA4014)
Ultrasonic pulse d0
Pre-amp (B&K 5935L) Delta-sigma modulator (Analog Devices AD7720)
-vd
d1 Reflected echo
ophon ne ne Microphone 8) (B&K 4138)
+vd Motorized stage (SIGMA KOKI SGMA46-300)
1-bit DSM signal Fig. 7. Experimental setup of ultrasonic distance and velocity measurement.
100
Determined distance and velocity
Doppler velocity [m/s]
Probability [%]
0.2
50
0 -0.3
-0.2
-0.1
0
0.1
0.2
0.1
0
-0.1
0.3
Doppler velocity [m/s] -0.2 Fig. 8. Experimental results: probability distributions of determined velocities of motorized stage.
0.9
1.0
1.1
Distance [m] Table 1 Averages and standard deviations of determined velocities of motorized stage in experiments. Velocity of stage (m/s)
Average of velocity (m/s)
r of velocity (m/s)
0.200 0.100 0 0.100 0.200
0.201 9.74 102 1.55 103 0.102 0.192
6.06 5.54 3.88 5.45 9.31
high resolution from experiments in ultrasonic velocity measurement. The distance to the wall was 0.900 m, when the motorized stage started to move. The motorized stage was accelerated to 0.200 m/s in a second, and then the motorized stage was decelerated to 0 m/s in a second. The motorized stage thus moved to the distance of 1.100 m in 2 s. The motorized stage was accelerated to 0.200 m/s in a second, and then the motorized stage was decelerated to 0 m/s in a second. The motorized stage thus backed to the distance of 0.900 m in 2 s. The velocities and distances determined by the proposed method of Doppler velocity estimation and Doppler-shift compensation are illustrated in Fig. 9. The velocity of the motorized stage and the distance to the wall can be concurrently
Fig. 9. Experimental results: velocities of motorized stage and distances to wall determined by proposed method of ultrasonic distance and velocity measurement.
determined by the proposed method of ultrasonic distance and velocity measurement.
6. Conclusions An over-sampling signal processing method of ultrasonic distance and velocity measurement using a pair of LPM signals has been proposed. The proposed method consists of cross correlation by single-bit signal processing, high-resolution Doppler velocity estimation with wide measurement range, and low-calculationcost Doppler-shift compensation. In this paper, accuracy of lowcalculation-cost Doppler-shift compensation was improved by estimation of the envelope’s peak time from the Doppler velocity of the object. Furthermore, the Doppler velocities and distances determined by the proposed method were evaluated with computer simulations and experiments in ultrasonic distance and velocity measurement. In the computer simulations, accuracies of the proposed method of Doppler velocity estimation were demonstrated as 8.471 mm/s and +1 or 1 LSV. Meanwhile, accuracies of
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the proposed method of Doppler-shift compensation were demonstrated as 13.87 lm and ±1 LSD. In the experiments, the Doppler velocities could be determined within ±27.9 mm/s by the proposed method of Doppler velocity estimation.
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