Airborne Ultrasonic Position and Velocity Measurement Using Two Cycles of Linear-Period-Modulated Signal

Transcription

1 Airborne Utrasonic Position and Veocity Measurement Using Two Cyces of Linear-Period-Moduated Signa Shinya Saito 1, Minoru Kuribayashi Kurosawa 1, Yuichiro Orino 1, and Shinnosuke Hirata 2 1 Department of Information Processing, Interdiscipinary Graduate Schoo of Science and Engineering, Tokyo Institute of Technoogy, Tokyo, Japan saitou.s.aa@m.titech.ac.jp, mkur@ip.titech.ac.jp, orino.y.aa@m.titech.ac.jp 2 The University of Eectro-Communications, Tokyo, Japan hirata@mce.uec.ac.jp Abstract. Rea-time position and veocity measurement of a moving object with high accuracy and resoution using an airborne utrasonic wave is difficut due to the infuence of the Dopper effect or the imit of the cacuation cost of signa processing. The cacuation cost had been reduced by singe-bit processing and puse compression using two cyces of inear-period-moduated (LPM) signa. In this paper, accuracy of the utrasonic two-dimensiona position and veocity vector measurement of the proposed method using two microphones is evauated by experiments. Keywords: utrasonic position and veocity measurement, puse compression, inear-period-moduation, singe-bit signa. 1 Introduction Acoustic sensing systems are used in many industria appications due to advantages of acoustic sensors, their ow-purchase cost, sma size, and simpe hardware. Method of airborne utrasonic measurement are widey researched [4][5]. The puse-echo method is one of the typica methods of utrasonic distance measurement. The puse-echo method is based on determination of the time-of-fight (TOF) of an echo refected from an object [8]. Puse compression has been introduced in the puse-echo method for improvement of the signa-to-noise ratio (SNR) of the refected echo and distance resoution [7]. A inear-frequency-moduated (LFM) signa is used in the puse-echo method. The frequency of LFM signa ineary sweeps with time. A received signa is correated with a reference signa which is the transmitted LFM signa. The TOF of the transmitted signa is estimated by the maximum peak in the crosscorreation function of received signa and reference signa. The signa processing for cross-correation consists of huge iterations of mutipications and accumuations. Therefore, rea-time utrasonic measurement is difficut because of the high cost in digita signa process. R. Groß et a. (Eds.): TAROS 211, LNAI 6856, pp , 211. c Springer-Verag Berin Heideberg 211

2 Airborne Utrasonic Position and Veocity Measurement 47 So a signa process method using a deta-sigma moduated singe-bit digita signa has been proposed to reduce the cacuation cost of cross-correation. The proposed signa processing consists of a recursive cross-correation by singe-bit signas of and smoothing operation by a moving average fiter. The cacuation cost of cross correation is reduced by the recursive cross-correation operation of singe-bit signas [2]. In the case of a moving object, the refected signa is moduated due to the Dopper effect caused by the object motion. The inear shift of the signa period means the hyperboic shift of the frequency. Therefore, a Dopper-shift LFM signa cannot be correated with a reference LFM signa. So puse compression using a inear-period-moduated (LPM) signa has been introduced for utrasonic measurement of a moving object [6][1]. The signa period of the LPM signa ineary sweeps with time. Thus, a Dopper-shift LPM signa can be correated with a reference LPM signa. However, the cross-correation function of the Dopper-shift LPM signa and a reference LPM signa is aso moduated due to Dopper effect. The method of typica Dopper-shift compensation is high cost using the enveop but Dopper-shift compensation is required. A ow-cacuation-cost method of utrasonic measurement by puse compression using two cyces of LPM signa and Dopper-shift compensation has been aready proposed [3]. Utrasonic distance and veocity measurement have been aready achieved by using one microphone[3]. In this paper, method of two-dimensiona position and veocity vector measurement are considered by using two microphones, and accuracy of the two-dimensiona position and veocity vector measurement are evauated by experiments. 2 Cross Correation by Singe-Bit Processing The proposed method of utrasonic distance and veocity measurement by puse compression using two cyces of LPM signa is iustrated in Fig. 1 [2]. In the proposed method, two cyces of LPM signa are transmitted by a oudspeaker. The received signa of one microphone is converted into a singe-bit received signa by a deta-sigma moduator. The singe reference LPM signa is converted into a singe-bit reference signa of N sampes by a digita comparator. The cross-correation function c 1 (t) of the received signa x 1 (t) and the reference signa h 1 (i) is expressed as c 1 (t) = N 1 i= h 1 (N i) x 1 (t i) (1) The cacuation of the cross-correation operation of Eq. (1)requires huge numbers N of mutipica-tions and accumuations of singe-bit sampes. The difference of the cross-correation function, C 1 (t) C 1 (t 1), is expressed as c 1 (t) c 1 (t 1) = h 1 (N) x 1 (t) h 1 (1) x 1 (t N)

3 48 S. Saito et a. Pair of LPM signas Utrasonic puse -v d Object +v d d d 1 Refected echo Microphone TOF Deta-sigma Recursive cross-correation operation Cross correation moduator Received signa by singe-bit signa processing DS Smoothing operation -1 c 1 (t) c S (t) + -2 S z -1 FIR Low-pass fiter Summation of bit sampes Digita comparator Reference signa d Fig. 1. The singa processing of utrasonic position and veocity measurement by puse compression using two cyces of LPM signa {h 1 (N i) h 1 (N i +1)} x 1 (t i) (2) N 1 + i=1 The vaues of h 1 (1) and h 1 (N) are 1 and -1 respectivey. Furthermore, h 1 (i) has severa hundreded zero-cross points Z i.thevauesofh 1 (N 1) h 1 (N i +1) are expressed as 2, N i = Z 2m 1. h 1 (N i) h 1 (N i 1) = 2, N i = Z 2m. (3), N i Z i. where m is a natura number. The cacuation of the recursive cross-correation operation, which is performed by integrating the difference of the cross-correation function, is expressed as c 1 (t) =c 1 (t 1) x 1 (t N)+2 x 1 (t N + Z 1 ) 2 x 1 (t N + Z 2 )+ x 1 (t) (4) The cacuation cost of the recursive cross-correation operation is integration and summations of singe-bit sampes. The number of summations Z i +2 ony depends on the number of zero-cross points in the transmitted LPM signa. 3 The Method of Position and Veocity Measurement 3.1 Two-Dimensiona Position Measurement The TOF of an echo is estimated from the cross-correation function. The arrangement of microphones, the oudspeaker, and the object is shown in Fig. 2. In

4 Airborne Utrasonic Position and Veocity Measurement 49 Fig. 2, d is a distance from the oudspeaker to the object, θ is an ange between the oudspeaker and the object, and L is a distance from the oudspeaker to microphones. The TOF of the microphone-1 and the microphone-2 have usuay different vaues of TOF 1 and TOF 2 respectivey. When d is much arger than 2L, θ is θ = sin 1 (TOF 1 TOF 2 )c (5) 2L where c is the propagation veocity of an utrasonic wave. Using the ange θ, the distance d is simpy derivated by geometric cacuation. 3.2 Two-Dimensiona Veocity Vector Measurement The method of the veocity vector measurement is iustrated in Fig. 3 and Fig. 4. In this method, the dopper veocity can be estimated from the signa ength of the transmitted signa and the echo. The signa ength difference is in proportion to the veocity of the object as shown in Fig. 3. The signa ength is detected from the interva of the cross-correation function peaks by two cyces LPM signas. The measured veocities are the vector components of the utrasonic propagation direction, which is v 1 and v 2 in Fig. 4, in the proposed method of utrasonic measurement by puse compression using two cyces of LPM signa. The measured veocity v 1 is a component of the object veocity v; the direction of v 1 is estimated from the geometrica reation between the distance d, the ange θ and the space L. Namey, from the measurement using the microphone-1, one veocity component of v is obtained correspondence to the direction of v 1. Simiary, Microphone-2 Microphone-1 2L θ d v object Fig. 2. The method of utrasonic position measurement Transmitted signa Cross-correation function Transmitted signa -V Received signa +V Fig. 3. The change of the signa ength

5 5 S. Saito et a. another veocity component of the object veocity v, nameyv 2,isacquiredby using the microphone-2. Now, taken the vectors which is norma to the v 1 and v 2 respectivey, the vectors intersect at one point. The veocity v is estimated from intersection point drawn in Fig Experiment 4.1 Experimenta Setup The experimenta setup for the utrasonic two-dimensiona position and veocity vector measurement is iustrated in Fig. 5. In the experiment, the period of the transmitted LPM signa ineary swept from 2 μs to5μs. The ength of the transmitted LPM signa was ms, the driving votage of the oudspeaker was 2V p p. The LPM signa was generated from the function generator and ampified by an ampifier. Two cyces of the LPM signa were transmitted by the oudspeaker, and the echo from the object was detected by two microphones. The distance from the oudspeaker to the microphones were.9 m. The propagation veocity of an utrasonic wave in the air was approximatey m/s at 27. C. The received signas by the microphones were convertedinto the singe-bit detasigma moduated signas. The samping frequency of the deta-sigma moduator was 12.5 MHz. The received signas were correated with the singe reference signa using MATLAB on the computer. The reference signa was simpy converted into a singe-bit signa by the digita comparator. The cross-correation function of the received signa and the reference signa was obtained from a recursive cross-correation operation of singe-bit signas and a smoothing operation by a weighted moving average fiter. The ength of the fiter was 141 taps. Microphone-1 Microphone-2 v object v 1 v 2 ange bisector L Microphone-2 θ d object v 2 ange bisector Fig. 4. The method of utrasonic veocity measurement

6 V Airborne Utrasonic Position and Veocity Measurement 51 Functiion generator (Textronix AFG3252) Microphone (B&K 4138) +v v Pair of two LPM signas (Pioneer PT-R4) Ampifer (NF HSA414) Oscioscope (LeCroy LT364L) ΔΣ Deta-Sigma moduator (Anaog Devices AD772) Motorized stage (SIGMA KOKI SGAM46-3) Microphone1 Pre-amp (B&K 5935A) Microphone2 θ v object Φ Fig. 5. Experimenta setup of utrasonic position and veocity measurement Accuracy of the position and veocity measurement was evauated by experiments. The object was a pastic ba whose diameter was 17 cm. The object distance d was 1.5 m and the ange θ was 2 to the object when two cyces of the LPM signa was transmitted. The veocity of the object was.4 m/s, the direction of movement was norma to a straight ine that inks the microphones and the oudspeaker, Φ = 18 in Fig. 5. The measurement was executed 15 times. 4.2 Experimenta Resut The cross-correation function was obtained by experiments as shown in Fig. 6. The first two peaks of cross-correation function were caused by the waves which the microphone received from the oudspeaker directy. The second two peaks of cross-correation function were caused by the echo from the object. The peak of the cross-correation function was detected by imiting the time range of crosscorreation function and cacuating the maximum point in the imited time range. The probabiity distribution of the distance and the ange are iustrated in Fig. 7. Average and standard deviation of the distance and ange were 1.66 m and 73.8 μm, 19.5 and.9 respectivey. The average of distance and ange were a itte different from the setup vaue, but it is inevitabe that errors are observedabout2to3cmand1to2 when the object s position was set. Given that, it can be said that high accuracy of the distance and ange by the proposed method is demonstrated by experiments of the utrasonic two-dimensiona position measurement.

7 52 S. Saito et a. 1 Cross-correation function.5.5 peaks of the echo Time[ms] Fig. 6. Cross-correation function Probabiity[%] 6 4 Probabiity[%] Distance[m] Ange[deg] Fig. 7. The probabity distributions of the position, distance(eft) and ange(right) Probabiity[%] Probabiity[%] Dopper veocity[m/s] Ange[deg] Fig. 8. The probabity distributions of the veocity(eft) and direction ange(right)

8 Airborne Utrasonic Position and Veocity Measurement 53 The probabiity distribution of veocity is aso iustrated in Fig. 8. Average and standard deviation of the veocity and the direction ange of movement were.43 m/s and.38 m/s, and 1.9 respectivey. Average of the veocity and direction of movement were near to setup vaue, but standard deviations of the veocity and the ange were a itte arge. The approximate vaue of the object s veocity vector can beestimated,butthemeasuring accuracy needs to be improved sighty. 5 Concusion Accuracy of airborne utrasonic two-dimensiona position and veocity vector measurement using two microphones with two cyces of LPM signa was examined by experiments. Experiments were executed using a recursive cross-correation by singe-bit signas and a ow-cacuation-cost method of Dopper-shift compensation. High accuracy regarding the utrasonic position measurement was obtained. On the other hand, there was room for improvement regarding veocity vector measurement but the approximate vaue of the object s veocity can be estimated. Now a recursive cross-correation is being impemented in FPGA because utrasonic two-dimensiona position and veocity measurement was not rea-time in these experiments. For the future work, muti moving object in the area wi be considered. References 1. Ates, R.A., Skinner, D.P.: Sonar-veocity resoution with a inear-period-moduated puse. J. Acoust. Soc. Am. 61(4), (1977) 2. Hirata, S., Kurosawa, M.K., Katagiri, T.: Cross-correation by singe-bit signa processing for utrasonic distance measurement. IEICE Trans. Fundam. E91(A), (28) 3. Hirata, S., Kurosawa, M.K., Katagiri, T.: Utrasonic distance and veocity measurement by ow-cacuation-cost dopper-shift compensation and high-resoution dopper veocity estimation with wide measurement range. Acoustica Science and Technoogy 3(3), (29) 4. Jorg, K.W., Berg, M.: Sophisticated mobie robot sonar sensing with pseudo-random codes. Robotics and Autonomous Systems 25(3), (1998) 5. Kahod, J., Rautenberg, J., Ruckert, U.: Continuous sonar sensing for mobie minirobots. In: Proc. the 22 IEEE Internationa Conference on Robotics and Automation, vo. 1, pp (22) 6. Kroszczynski, J.J.: Puse compression by means of inear-period moduation. Proc. of the IEEE 57(7), (1969) 7. Marioi, D., Narduzzi, C., Offei, C., Petri, D., Sardini, E., Taroni, A.: Digita timeof-fight measurement for utrasonic sensors. IEEE Trans. Instrumentation and Measurement 41(1), (1992) 8. Marioi, D., Sardini, E., Taroni, A.: Utrasonic distance measurement for inear and anguar position contro. IEEE Trans. Instrumentation and Measurement 37(4), (1988)