A LabVIEW Based Experimental Platform for Ultrasonic Range Measurements

Transcription

1 DSP Journal, Volume 6, Issue, February, 007 A LabVIEW Based Experimental Platorm or Ultrasonic Range Measurements Abdallah Hammad, Ashra Haez, Mohamed arek Elewa Benha University - Faculty o Engineering at Shobra - Department o Electrical Engineering 108 Shobra st..cairo.egypt abdallah_hammad@hotmail.com, ashrahaez@hotmail.com, tarek_elewa@yahoo.com Abstract Ranging using ultrasonic waves is applied in several areas such as robotics, industry and medicine. Great eorts have been taken in research to improve the precision o this system. hese eorts developed dierent techniques to attain more accurate result. o evaluate the perormance o these techniques a lexible platorm is needed to implement them and then to analyze and compare their perormances. In this ramework a novel design and implementation o a general purpose ultrasonic ranging system is presented. his system is employed to implement three dierent methods they are; simple threshold, double threshold, and correlation detection. hen we analyze statistically their experimental results. he perormance o these techniques is compared in terms o the change o bias, standard deviation, and total error as a unction o range. he experimental results exhibit the lexibility and simplicity o the proposed system by which it can be easily adapted to support other similar applications. 1 R C C is the propagation speed o the ultrasonic waves in the medium, and is the OF. he range measurement uncertainty depends on the quality o estimation o both C and. he irst quantity depends dominantly on the temperature according to equation () C = / 73 m/s () is the absolute temperature in Kelvin his dependency can be relatively easily compensated or [4], so the critical point o the whole measurement procedure is the OF estimation. Amplitude = (1) relected echo threshold level hreshold based detection Keywords: LabVIEW- time o light - ultrasonic ranging - DSP 1. Introduction Measuring the distance between a known base location and the surace o an object by using ultrasound signal is reerred to as ultrasonic ranging which is very important in wide range o applications, including Sonar Mapping [1], robotic ranging and positioning [], as well as ultrasonic based navigation [3]. One o most dominant ranging systems is the ime-o-light (OF) based system, which measure the round trip time between an energy pulse emission and the return o the pulse echo resulting rom its relection rom an object at distance R rom the ultrasonic sensor. In this case R can be computed using the ollowing equation: 1 his study has been implemented on LabVIEW platorm at electronics lab. Faculty o engineering Shobra. Benha University ime Figure (1) hreshold based detection he basic method is to transmit several cycles at least ive, preerably ten or more [5] o highrequency ultrasound and to use a simple hardware or sotware counter to measure the time it takes or the sound to return. he counter is started when the sound is transmitted and stopped when the relected echo is received. hreshold based detection [6] is the most widely used method or OF estimation, and applies to any type o short duration signal. By this method, the received signal is compared with a preset threshold level, such that the arrival o the wave is acknowledged when the signal reaches this level as shown in igure (1). he threshold level should be set suiciently high to eliminate alse detection due to ground level noise. 1

2 DSP Journal, Volume 6, Issue, February, 007 Applying threshold based detection to ultrasonic ranging is shown in igure (). he detection o the relected echo occurs at t, however the signal actually started at OF so there is a bias error error deined by: error = t (3) Even at t there can be an uncertainty o hal the wavelength. One way to reduce this error is to ind the envelope and comparing it with the threshold as shown in igure (), this gives the detected time t 1. Amplitude threshold level echo envelope Where o is the resonant requency o the transducer, and a (t) represents the envelope with a inite duration. he shape o the echo detected by the receiver can be approximated by the ollowing model [9] [ π ] ( ) Sr() t = a( t )sin o( t ) + w t (6) Where the signal w (t) is a white Gaussian noise having zero mean and varianceσ w. he transmitted signal is a noise ree signal, while the received echo signal is an attenuated and delayed version o St ( t ) plus additive white noise. he envelope at ( ) o the relected echo is given by a1 ( t at ( ) ae = ) ( ) t ut ( ) o OF t 1 t ime Figure hreshold based detection error he bias error in this case is given by: error = t 1 (4) he main problem with the threshold method is that, the OF measurement obtained is larger than the actual OF, which corresponds to the starting point (onset) o the echo signal. his is a consequence o the relatively long rise-time o the echoes produced by low-bandwidth ultrasonic transducers or operation in air. hen, the range inormation obtained by threshold is biased, making the target appear slightly arther than it actually is. he resulting bias error, which is in the range o several millimetres to centimetres is not constant then it can not be avoided and it is diicult to be modelled analytically [7]. wo alternative methods double threshold and correlation detection method are used to reduce the bias error [7]. he paper is organized as ollows: an introduction to ultrasonic signal modeling is proposed in section. he dierent ranging techniques using ultrasonic is analyzed in section 3. In section 4 the experimental work and perormance comparison discussions is illustrated. Section 5 and 6 presents the conclusion and uture work respectively. Ultrasonic signal modelling Since the signal ed to the ultrasonic transducer is a short train o ultrasonic waves, and the electrical equivalent o the transducer is a high quality resonant circuit [8], thereore the signal generated in response to the transmit command can be represented in the orm: S () t = a().sin( t π t) (5) t o (7) Where ut ( ) is a unit step unction delayed by and a o is the amplitude parameter, and a 1 is shape parameters o the signal. Ater envelope detection equation (6) becomes: S() t = a( t ) + n() t (8) the orm o at ( ), given by equation (7) is capable o modelling observed echo envelopes or a wide variety o obstacle types located at dierent locations within the active region o the ultrasonic receiver. he exponential term in equation (7) can be neglected at the start o the envelope where t > and ( t ) is small. A parabola is a good approximation or the onset o at ( ) in the time interval t [, + a1 ], thereore the signal observation model becomes: St () ao( t ) + nt () (9) or t [, + a1 ] Uniorm sampling in time produces the sequence Sk ao( tk ) + nk (10) or t k [, + a1] Where t k are the sample times, and s k and n k are the corresponding signal and noise samples that can be processed by a computer. In the next section, three dierent methods o OF estimation are discussed namely simple threshold method, double threshold and optimal correlation detection. 3. Ultrasonic ranging techniques 3.1. Simple threshold method he simplest way o measuring OF is the threshold method. In which the OF is the time at which the echo amplitude waveorm irst exceeds a preset threshold level (L). his level is set according to the noise level. Assuming Gaussian noise, L is usually set equal to 3 5 times the noise standard deviation σ n [7]. Neglecting noise, the time at which the noiseless

3 DSP Journal, Volume 6, Issue, February, 007 signal envelope irst crosses the threshold L is denoted by t * x. By equating the noiseless st () in (9) to L gives: * tx = + L ao (11) However, the time t x, when the signal plus noise exceeds the threshold or the irst time, is not equal * t x, Further, the observed OF is also aected by the sampling requency.i the sampling interval s, then the estimated OF can take on values that are only discrete multiples o the sampling time s = ks = tx + (1) Where k is an integer, is a random delay uniormly distributed in the interval [0, s ]. he variable is added to continuous-valued t x to produce the clock reading k s. he statistics or this estimator have been driven by Kuc [9] to evaluate its bias and variance which are deined by equations (13), (14) respectively: B [ ] = E [ ] (13) Var[ ] = E[ ] E [ ] (14) E is the expectation operator. he results reported in [7] or the above two equations as L σ n increase yields: L s B = a (15) o s var = (16) 1 Equation (15) illustrates the problem inherent to threshold method. For L > 0, this estimator is biased since the actual echo arrival time occurs beore the time t x where the echo exceeds the threshold. Since a o changes along with the echo amplitude it is clear that the bias will be amplitude dependent, this will be veriied in the experimental work. (3-) Double threshold method A second method or estimation the OF and reduce the bias obtained in the simple threshold is the double threshold method. In which a two-points are it to the rising edge o the ultrasonic echo envelope to an appropriate power law [11]. It was ound that the rising edge was very well approximated by a parabola. he conventional electronics used to detect and process the signal had near negligible additional eect on pulse shape, since the signal s (t) rises parabolically in the orm ao( t ). he time o light can be determined directly rom double threshold measurements L1 = ao( t1 ) (17) L = ao( t ) (18) Eliminating a o then Vt1 t = (19) V 1 his is independent o the signal amplitude. Here V = L /L 1 is the ratio o upper to lower threshold. he accuracy o this estimate will depend on the SNR o the received signal and the setting o these two levels in order to cover the widest possible range o probable signal levels with the least amount o error is examined. It has been reported in [11] that a threshold ratio Vo represents a suitable choice. he double-threshold technique is applicable to any waveorm whose rising edge is o the orm a ( ) x o t t, and it can be seen rom equations (17), and (18) that it is straightorward to generalize rom the x= case to an arbitrary x. he appropriate power law, and whether or not the initial t x rise is o suicient duration or the approximation to remain useul, can be readily determined experimentally or a given system by measurement o the pulse shape. While our work deals with applying and characterizing the parabolic case, it is also valid or general power laws Correlation detection or time o light estimation Digital Signal Processing (DSP) is one o the most powerul technologies that have been widely used in a broad range o ields. It provides high perormance and high precision o signal processing ability, which is impossible to achieve in the conventional Analog signal processing. here are many dierent DSP algorithms used to deal with the range inding signal processing where the main task o DSP is the time o light estimation sometimes reers as time delay estimation DE. In order to obtain OF accurately, DSP has the ability to suppress various kinds o noise, detect and extract the desired echo signal. hose DSP algorithms include correlation [1], adaptive ilter, wavelet analysis and more [13]. his work deals with the study o the correlation application in range inding systems. he digitized versions o the transmitted and received echo signal presented in (5), and (6) that being stored or digital signal processing are expressed as X ( n ), and X E ( n ) respectively: X ( n ) = st( n ) (0) X E( n ) = α st( n ) + w ( n ) (1) Where is the sampling interval,α is the attenuation coeicient, w ( n ) is the additive Gaussian white noise, and is the time delay between the transmitted and received signal (OF), the transmitted digital sequence X ( n ) is also known as a template signal. Correlation is used to reveal the degree o similarity between one sequence o data and the other as a unction o time shit between them, the Crosscorrelation processing is to take the sum o the 3

4 DSP Journal, Volume 6, Issue, February, 007 products o the corresponding data pairs. he Crosscorrelation unction between the transmitted and received sequences is deined as [14]: N 1 C( k ) = x ( n ) x E( n k ) () n = 0 k = 0, 1,, 3, and k is the shited sampling points in respect to the X ( n ), In practice, the delay can be estimated by inding the peak o the cross-correlation unction in equation (), since the amplitude o each sample in the crosscorrelation signal is a measure o how much the received signal resembles the template, at that location. In other words, the value o the crosscorrelation is maximized when the target signal is aligned with the same eatures in the received signal. It reported in [15] that it is possible to estimate the delay rom the cross-correlation o signal envelopes rather than ultrasonic signals with the advantage improved resolution can be expected. Since o the transmitted signal is narrow band signal, the envelope o cross correlation decreases slowly, while the correlation unction itsel is highly oscillatory. he amplitude spectrum o the transmitted signal is shown in Figure (3). (db) Amplitude spectrum requncy (KHz) Figure (3) the amplitude spectrum o the transmitted ultrasonic waves he envelopes o the transmitted and received ultrasonic echo are extracted by digital technique, where the envelopes are the magnitude o the analytic signal obtained via Hilbert transormation (H) o the transmitted and received echo sequences [16]. he complex-valued analytic signal ϕ( t ) is deined as ϕ () t = s() t + js() t = µ () t exp[ π ot] (3) Where the imaginary part o the analytic signal is the Hilbert transorm o the ultrasonic signal s (t) he algorithm that is presented in this work has been implemented with the aim o achieving a resolution o the same order o magnitude as the sampling interval or the estimation o the delay. advantage o this approach is given mostly by the lexibility and very rapid development time oered by this graphical programming sotware. Figure (4) depicts the block diagram o the LabVIEW based data acquisition system. he major hardware components include the data acquisition board (DAQ board- National Instruments PCI-6036E), transmitting unit, receiving unit, ultrasonic transmitter and receiver transducers, and temperature measurement circuit. he system requires three analog inputs (AI) channels. he irst one is used to receive the temperature inormation, the second one is used to acquire the exciting pulses on the ultrasonic transducer, and the last one is to acquire the relected ultrasonic echo signal. he DAQ device has the capability to sample any signal up to a rate o 00 KHz, so we can not sample the three Analog channels at the maximum rate (00 KS/s) but at rate equal to 66.6 KS/s (since all Analog channels are multiplexed) this requency does not satisies Shannon criteria which indicates that a continuous signal can be properly sampled, i its highest requency content does not exceed hal the sampling rate. In this case minimum the sampling requency must be greater than 80 KS/s (twice ultrasonic requency).o solve this problem we irst use one channel to measure the temperature (AI ch3) beore the experiment. hen we use the other two channels or the transmitted and the received signal. In this case we can sample each o the two channels at 100 KS/s ( s =10 µs), this sampling requency gives a poor resolution since the period o the ultrasonic pulses is 5 µs then every complete cycle will be sampled about samples. But experimental work leads to that the DAQ device can sample each o the two channels at maximum sampling requency o 190KS/s he main program starts with measure o the temperature. he temperature data is acquired by means o AD 590 which is a two-terminal integrated circuit temperature transducer that produces an output current proportional to absolute temperature. he interace o temperature circuit with the data acquisition card is the most basic circuit used or interacing the AD590, the circuit acts as current to voltage converter, and the output voltage o this circuit is proportional to temperature. A voltage o 1 mv/k can be adjusted. he output voltage o the interace circuit is measured and is converted to temperature. his temperature is used to calculate the speed o ultrasonic waves in air according to equation (). he second step in the program is to determine the noise statistics o the background noise. 4. Experimental works and results LabVIEW (Laboratory Virtual Instrument Engineering Workbench) [17] developed by National Instrument, is a graphical programming environment suited or high-level or system level design. he 4

5 DSP Journal, Volume 6, Issue, February, 007 LabVIEW platorm with DAQ board received signal rigger emp. measurement Receiving unit ransmitting unit Ultrasonic receiver R40-16 Ultrasonic transmitter R planer relector Figure (4) Experimental system A signal is received rom the receiver unit output in the absence o any received echo; this signal represents the noise. (In our system, the sources o noise include thermal noise in the electronic components and acoustic noise rom sound sources in the environment). his noise signal is analyzed statistically to determine its standard deviation. his value is passed to the program, to set the threshold level or double threshold levels. A trigger signal is generated by the DAQ module that trigger the transmitter unit to generate 10 complete cycles o 40 KHz square wave (center requency o the ultrasonic piezoelectric transducer), the transmitter unit consisting o a microcontroller ollowed by a driver circuit that is used to increase the voltage applied on the ultrasonic transmitter. he system is then acquires both the driving pulses at ultrasonic transmitter end and the relected echo signal ater being ampliied the two signals at rate 194 ks/s per each. It was ound a delay about 300 micro-second between the moment at which the DAQ module triggers the microcontroller and the moment at which the driving signal reaches the transmitter terminal. his delay time t 0 is mainly due to the execution time o the LabVIEW program. We deine this delay time as initialization time (t 0 ) this time must be taken into consideration in the calculation o the time o light. he proposed system uses digital techniques or extracting the envelope o the received echo. his is done by using Hilbert transormation o the incoming signal, where the magnitude o the complex analytic signal is the envelope o the original time signal. According to the selected method the time o light will be calculated. For the case o simple threshold the program search the received echo envelope data array or array index at which its data exceeds the threshold level, and then multiply this index by sampling time which leads to the time t 1. he initialization time t o must be subtracted to get the actual time o light. Consequently the range inormation is obtained by equation (1), 30 trials were stored and the statistical analysis is done obtaining the bias, standard deviation, total error, rom a statistical point o view. It is more realistic to express the overall system accuracy as the root mean square (rms) o the individual element accuracy then the total error ε is calculated using the equation (4): ε = σ + B (4) Where: σ is the standard deviation o the collected 30 range inormation s and B is the bias o the estimated o the range. For double threshold method, in a similar manner, the times t 1, and t are irst determined. Equation (19) is used to obtain the OF and then the range can be calculated. For the correlation detection method it has chosen to digitize the transmitted signal x ( n ) according to the arrangement shown in ig (5). LabVIEW platorm with DAQ board ransmitting unit R40-16 received signal receiver unit Figure (5) Acquisition o the template signal In this scheme the receiver is put to ace the transmitter, both transducers have 40 khz resonant requency. he transmitted signal rom the transducer is picked up by the ultrasonic receiver R Ater ampliication the acquired data is stored. he resulting sequence ( ) x n is delayed by the time o light between the transmitter, and the receiver, however the dierence can be corrected as a result o calibration procedures. he cross correlation virtual instrument tool built in LabVIEW sotware has been used to compute the cross correlation between the template envelope, and received echo envelope, the index at which the value o the cross correlation output array is maximum is then multiplied by the sampling time, this will be the time delay between the two waveorms. Figure (6) presents the low-chart that demonstrates the major unctions o our system. Start emperature measurement and speed o sound estimation n = 0 Noise measurement beore the experiment DAQ triggers micro controller Acquire the two waveorms (transmitted and received) Getting the envelopes o the ultrasonic signals Figure (6) lowchart o the system program Determine the time o light according to the selected method Calculate the distance using R=C*(oF)/ an store this No n=n+1 n=9 Yes Calculate the mean, the bias and the standard deviation end 5

6 DSP Journal, Volume 6, Issue, February, 007 Figure (7) the system ront panel A LabVIEW program is called a virtual instrument (VI). It has two main parts, the ront panel and the block diagram. he ront panel is used or user interactions and display o results. he block diagram is the source code constructed in LabVIEW s graphical programming language, G. his pictorial block diagram is the actual executable program. he ront panel allows the user to enter input such as the number o acquired samples, number o trials that will stored, the ratio between the two threshold levels in the double threshold method. It also displays the outputs such as waveorm graphs o the ultrasonic signal, its envelope, temperature inormation, noise statistics, and cross-correlation output. Figure (7) presents the system ront panel showing all the controls and indicators o ranging system A lat object has been positioned in the ront o the system and its range was varied rom 0.4 m to 3 m. Bias, standard deviation, and total error were recorded. Figure (8-a) shows the bias error dependence on range variation. It is clear that as the range (R) increases the amplitude o the ultrasonic waves decreases due to beam spreading. It can be implied According to equation (7) that the amplitude parameter o the ultrasonic wave's a o will decrease (a o ). Consequently according to equation (15) the bias error or threshold method will increase. On the other hand this bias error can be reduced in the double threshold method, since the estimated OF usually alls to the let o the threshold estimate. Finally the bias error obtained in Correlation detection technique wobbles between 1mm and mm over the whole range. Figure (8-b) shows the standard deviation at regular distance intervals. We observe that or the threshold method the eect o increasing (R) is to degrade the range measurement accuracy. Since the noise level is kept constant, this degradation is mostly caused by the decreasing SNR due to the decrease in signal amplitude with increasing R, or example when the target is moved rom R = 0.4 m to R = 3 m, SNR changes rom 64 to 30 db. We observe also that double threshold method has largest standard deviation which reduces measurement accuracy. his may be due to some sources o errors in the estimation o OF which is estimated rom equation (19 ), these errors include; 1. he estimation o initialize time t o, which may contain random delay, uniormly distributed in the interval 0, S, since t o can take on values that are only a discrete multiples o the sampling time S.. the estimation o t 1 and t may contain random delay, in the interval 0, S 3. he validity o the parabolic assumption o the leading edge o the ultrasonic pulses. All this actors may be combined which leads increasing o the standard deviation o the measured range. For correlation detection the standard deviation seems to be constant about 0.04 cm. his small standard deviation means that all measurements do not spread about the mean value. 5. Conclusions In this work we design and implement a ully integrated system or the measurement o ultrasonic signals. he system is used mainly or range measurement applications. he system has the advantages o lexibility and easy to use. It can be relatively easy adapted to operate also in other similar applications since it has a riendly graphical interace. he designed system has been used to implement three dierent techniques or range measurements and to compare perormances. he comparison is presented in terms o the change o bias, standard deviation, and total error as unction o range. Bias (Cm) hreshold Double threshold Correlation Range (m) (a) 6

7 DSP Journal, Volume 6, Issue, February, 007 Standard deviation (Cm) hreshold Double threshold Correlation Range (m) (b) hreshold Double threshold Correlation In the theoretical study aspect, two interesting areas closely related to the current work can be investigated: he irst case would be the analysis o another curve itting algorithm based on non linear least square curve itting which reduce the standard deviation considerably he second case would be the analysis o phase shit based ultrasonic ranging technique used or small range measurement. In the implementation study aspect, we recommend the study o the implementation o the correlation detection technique on digital signal processing systems at moderate cost otal error (Cm) Range (m) (c) Figure 8 Variation o the bias (a), the standard deviation (b), and the total error (c) with range he double threshold method reduces the bias relative to threshold but on the other hand has the largest standard deviation among the three methods, i.e. in terms o standard deviation; double threshold method is not as good as the simple threshold method and correlation which oers the smallest standard deviation. For the threshold and correlation methods the total error turns out to be dominated by the bias and thereore has a shape which resembles the bias curve. he double threshold method accuracy can be improved by judicious choice o the threshold levels and the threshold ratio (V). Setting these levels too low increase the probability o alse triggering by noise spikes. On the other hand, setting the levels two high limits the useul range obtained by this technique, since at longer distance the signal level decrease (also SNR decrease) which implies that the thresholds correspond to levels closer to the signal peak where pulse shape deviations rom parabolic model are greater. Correlation increases the accuracy o time o light measurements as compared to threshold. However, correlation is obtained through a higher computational load than threshold, which might prevent its use 6. Future work he uture work can be divided into two aspects o the theoretical study or ultrasonic ranging techniques and the implementation o the proposed techniques. 7. Reerences [1] Akihisa OHYA, akayuki OHNO and hin ichi YUA Obstacle Delectability o Ultrasonic Ranging System and Sonar Map Understanding Institute o Inormation Sciences and Electronics, University o sukuba [] Hans W. Wehn and Pierre R. B elanger Ultrasound-Based Robot Position Estimation IEEE transaction on robotics and automation, vol 13,No. 5, October 1997 [3] Muralidharan, Aravind Sonar Based Navigation: Follow he Leader Solution or Bearcat III MS, University o Cincinnati (India), Engineering : Industrial Engineering, 001 [4] C Canali, G. Decicco, B. Morten, M. Prudenziati, and A. aroni, A temperature compensated ultrasonic sensor operating in air or distance and proximity measurements IEEE rans. Ind. Electron., vol. IE-9, no. 4, pp , 198 [5] David Cheeke Fundamentals and applications o ultrasonic waves CRC series in pure and applied physics ISBN (alk. paper) [6] Raphaël Renault Detection o Fast Moving Pulses in a Noisy Environment Msc thesis submitted to Virginia Polytechnic Institute, December 000 [7] B. Barshan, "Fast processing techniques or accurate ultrasonic range measurements," Measurement Science and echnology, vol. 11, pp Jan 000 [8] J. Fraden. Handbook o Modern Sensors, American Institute o Physics, Woodbury, New York, second edition, [9] G. Andria, F. Attivissimo, N. Giaquinto, Digital Signal Processing echniques or Accurate Ultrasonic Sensor Measurement, Measurement Journal o Imeko, vol. 30, September 001, pp [10] B. Barshan and R. Kuc. A bat-like sonar system or obstacle localization. IEEE ransactions on System, Man, and 7

8 DSP Journal, Volume 6, Issue, February, 007 Cybernetics, (4): , July/August 199 [11] McMullan, B., Delanghe, B. and Bird, J.S., A Simple Rising Edge Detector or ime-o- Arrival Estimation, IEEE ransactions on Instrumentation and Measurement, Vol. 45(4), pp 83-87, August 1996 [1] M. Parrila, J.J. Anaya, C. Fritsch, Digital signal processing techniques or high accuracy ultrasonic range measurements IEEE rans. Instr. Meas. IM 40 (4) (1991) 759. [13] Lora G. Weiss Wavelets and wideband correlation processing, IEEE signal processing magazine, January 1994 [14] G Proakis, D.G.Manolakis, Digital signal processing,second edition,199, Macmillan publishing company [15] D. Marioli, C. Narduzzi, C. Oelli, D. Petri, A. E Sardini, aroni, Digital time-o-light measurement o ultrasonic sensor, IEEE rans. Instr. Meas IM 41 (1) (199) [16] G. Andria, F. Attivissimo, N. Giaquinto, Digital Signal Processing echniques or Accurate Ultrasonic Sensor Measurement, Measurement Journal o Imeko, vol. 30, September 001, pp [17] National Instruments Corporation, 8