Abstract. 1 Introduction

Transcription

1 A Low Sample Rae Real Time Advanced Sonar Ring Saeid Fazli and Lindsay Kleeman ARC Cenre for Percepive and Inelligen Machines in Complex Environmens (PIMCE) Inelligen Roboics Research Cenre(IRRC) Monash Universiy, Ausralia Absrac This paper describes an advanced sonar ring ha employs a low receiver sample rae o achieve processing of 48 receiver channels a near real ime repeiion raes of 5 Hz. The sonar ring sensing covers 36 degrees around he robo wih simulaneously firing of 4 ransmiers. The receiver sampling frequency is 5 khz, compared o previous work a MHz, firsly o maximize he speed of processing and secondly o avoid memory limiaions of he DSPs. The processing o produce accurae disance and bearing measuremens is performed on 6 DSPs using emplae maching of echoes wih shor duraion. This paper presens a summary of he hardware archiecure, sofware archiecure and sensing heory of he advanced sonar ring. The use of a reference poin and offse able is inroduced and experimenally verified o improve he sensor accuracy and robusness. The problem and soluion o cycle hopping, caused by he low sampling rae, are described in he paper. Inroducion A fas, accurae and robus environmen sensor is always a criical par of roboic asks such as map building, localizaion, arge racking and collision avoidance. As research in his area increases, he accuracy of sonar sensors has improved [Peremans, Audenaer e al. 993; Kleeman and Kuc 995; Joerg and Berg 998; Kleeman 999; Yaa, Ohya e al. 999; Yaa, Ohya e al. ]. Meanwhile, Digial Signal Processor (DSP) sysems have enabled he ulrasonic echo o be sampled a bi ampliude resoluion and MHz sample rae and hen processed in near real ime o measure range o. mm and bearing o. degrees [Heale and Kleeman ]. This approach is fas and accurae bu operaes only wihin he beamwidh of he ransducers. Mechanical scanning and many measuremens aken in sequence are needed o cover a full 36 degrees. Figure. Advanced sonar ring mouned on an AcivMedia Pioneer 3 DX mobile robo. The sonar ring makes possible rapid navigaion of a mobile robo wihou he complicaion of mechanical scanning and delays associaed wih scanning sensors, such as scanning laser or sonar [Vlasimil MASEK 998; Vlasimil MASEK 999]. Researchers have developed a sonar ring ha allows simulaneous firing of ransmiers and hresholding of echo signals o measure reflecors wih a bearing accuracy of around degree [Yaa, Ohya e al. 999; Yaa, Ohya e al. ]. Furhermore, inerference can be rejeced [Borensein and Koren 995; Joerg and Berg 998; Kleeman 999], making possible he operaion of muliple sonars in he same acousic space, or in noisy spaces. This is imporan for cooperaive roboics, swarm roboics or any ime wo sonar equipped mobile robos ha need o work in he same area. The increasing performance of DSPs makes i possible o perform inensive sonar echo processing around an enire ring of 48 ransducers from a single simulaneous se of ransmissions in near real ime. Thus he sequenial scanning of he individual sonar sensors has been condensed ino one measuremen cycle. The new real ime muli-dsp advanced sonar ring is firs repored in [Fazli and Kleeman 4] and his paper discusses low sample rae issues and soluions o cycle hopping.

2 The sample rae of he advanced sonar ring is as low as 5 KHz, allowing each DSP o process all echoes of 8 receivers in near real ime and save all processed informaion in he memory of each DSP which is 9 KB. A low sample rae gives rise o problems, such as lower accuracy and cycle hopping ha may cause saionary arges o appear o shif in bearing and hop a wavelengh in range. The nex secion briefly inroduces hardware componens of he advanced sonar ring. The sensing heory, known as mached filering, is presened in secion 3. This secion shows ha he maximum likelihood esimaor of he arrival ime of he echo corruped by addiive whie Gaussian noise is he bes esimaor [P.M.Woodward 964]. This heory is imporan for undersanding and solving he problem of cycle hopping discussed laer. Secion 4 briefly inroduces he advanced sonar ring sofware archiecure and he implemenaion of pulse capuring and soring wihin a DSP conex. Experimenal resuls are presened in secion 5 o show he effeciveness of he proposed sysem. In his secion he concep of cycle hopping rejecion is explained. Conclusions are presened in he las secion. The Advanced Sonar Ring Hardware Archiecure in Brief Figure shows he advanced sonar ring mouned on an AcivMedia Pioneer 3 DX mobile robo. I conains a 48- ransducer sonar ring, each group of eigh Polaroid 7 series ransducers, arranged in four pairs, conrolled by a digial slave DSP board and an associaed analogue board. Each pair consiss of a ransceiver and a receiver 4 mm and 5 degrees apar. The sensor is capable of covering a full 36 degrees around robo when he effecive beamwidh of each pair of ransducers is a leas 5 degrees and his occurs for highly reflecive specular arges a ranges closer han.8 m. The advanced sonar ring has six analogue slave PCBs which are responsible for simulaneous firing of all ransmiers and daa acquisiion process. Each of hem is conrolled by a digial slave board conaining a DSP. The receiver channels are amplified and low pass filered before sampling wih ADCs a 5 khz. The ransmission elecronics allow a programmable digial pulse rain o be sen o he ransducer wihou he need for preloaded memory buffers. Insead he digial slave DSP direcly conrols he ransmi logic every microsecond under inerrup service rouine. Variable gain amplifiers conrol he ampliude of he received echoes from differen ranges. Also each board conains a high volage DC-DC converer o produce a 3 V bias on he 8 ransducers (Figure ). Afer pulses are ransmied and echoes are capured by analog slave, he echoes are digiized by Analog o Digial Converers (ADC) of digial slave boards. The sensor has six digial slave PCBs, each one conains a DSP which conrols an associaed analog slave and connecs o i using a ribbon cable. The DSP is responsible for generaing he ransmi pulses for he four ransceivers and processing he echoes colleced by he eigh ransducers. Two -bi ADS786 ADCs are configured o allow pairwise synchronised sampling of 8 inpu channels a 5 khz sample rae. An Analog Devices 89M DSP was chosen due o he single clock cycle access o on-chip RAM of 9 k byes, allowing echoes o be exraced, sored and processed wihin he DSP chip. The speed of he on-chip memory allows he processor o fech wo operands (one from daa memory and one from program memory) and an insrucion (from program memory) in a single cycle (Figure 3). A maser PCB conrols all six digial slaves and connecs he sensor o a hos compuer. The maser board conains a Ribbon connecor 4-ch ADC 4-ch ADC DSP Pulse Generaor + Echo Processor PC4 Type Connecor CONTROL +3v FET Transmier Drive Circui +LP Filer +Variable Gain Amplifier Rx Trx Rx Trx Rx Trx Rx 3 Trx 3 Sonar Ring A ransducer pair Figure. A Sonar Ring and an Analogue Slave PCB Block Diagram Figure 3. A Digial Slave PCB

3 Cenral Compuer High Speed Buffer ed UAR T PC4 Type Connecor Buffer DSP 75MHz ADSP 89M Figure 4. A Maser PCB 89M DSP, flash memory and a high speed buffered UART (Figure 4). I communicaes wih a cenral compuer via he high speed serial link and wih all he digial slave boards via a PC4 ype connecor using he Inernal Direc Memory Access (IDMA) por. The DSPs conain wo DMA pors, Inernal DMA por and Bye DMA por. The IDMA por provides an efficien means of access he on-chip program memory and daa memory of he DSP wih only one cycle per word of overhead. The IDMA por has a 6-bi muliplexed address and daa bus and suppors 4-bi program memory. The IDMA por is compleely asynchronous and can be wrien o while he ADSP 89M is operaing a full speed. Also, he maser board conains he sofware in he flash memory, boos all he slave DSPs using BDMA por, sends all user commands and reads he high level daa from slave boards and ransfers hem o a hos compuer using a RS3 serial por. 3 The Advanced Sonar Ring Sensing Theory Power supply Flash Memor y 5KB The basic idea of range finding is o calculae he Time- Of-Fligh (TOF) of capured echoes using mached filering mehod based on he radar recepion heory. In his secion we show ha his mehod is he bes arrival ime esimaor in heory. Equaions (-6) are based on [P.M.Woodward 964] and jusify he opimaliy of he arrival ime esimaion used in he advanced sonar ring. The problem is o exrac he informaion from a noisy received signal. We assume ha he waned informaion in he receiver is x, noise is whie Gaussian and he 3 received signal is denoed by y. The signal y is available and we require he probabiliy disribuion p ( x y), which gives us some informaion abou x from he knowledge of y. The calculaaion of p ( x y) is a problem of inverse probabiliy. The produc law for probabiliies is p ( x, y) = p( x) p( y x) = p( y) p( x y) () and since y is given, he second of hese equaions may be wrien p ( x y) = k p( x) p ( y x) () where k is he normalizing consan of disribuion. In equaion () p (x) is he prior probabiliy of x and p ( x y) is he poserior probabiliy of x. If we denoe u x as a ime-dependen signal represening he informaion x and n as addiive whie Gaussian noise, hen he received waveform is y = ux + n (3) which is available in he receiver and he recepion mehod should deermine p ( x y). The Likelihood Funcion is wrien as p ( y x) = k exp( E / N) = k exp{ ( y u ) d} N x (4) where N is N/W, N is he mean noise power and W is he bandwidh of he signal. The inegral in he equaion is definie and he limis mus correspond o he oal inerval of ime occupied by he signal. The erm y can be absorbed ino k p ( x y) = k p( x) exp{ ux d}exp{ yuxd} (5) N N Equaion (5) shows ha he erm q( x) = yu d (6) is he only erm ha depends on y and using ha we can obain all informaion abou poserior disribuion. Equaion (6) is a cross correlaion beween he received signal, y and a prediced noiseless received signal, u x. In discree form, equaion (5) becomes: p ( x y) = kp( x)exp{ ux }exp{ yux} (7) N N Now le us coninue wih he problem of range finding or TOF esimaion. The pulse shape will be denoed by u (),a delay ofτ occurs in he pulse shape and he goal is o esimae he value ofτ by analysis of he received waveform y (), given by y ( ) = u( τ ) + noise (8) A copy of u (), as a emplae, is available for comparison wih y() a he receiver. I is assumed haτ is independen of ime which means he arge is saionary, and also i will be assumed ha all he noise in he sysem, including ha which is inroduced by he receiver iself while operaing on y (), can be regarded as an addiion o he inpu signal. Equaions (7) can be rewrien as x

4 p ( τ y) = kp( τ )exp{ u ( τ )}exp{ y( ) u( τ )} (9) N N Equaion (9) shows ha o esimae he delay, i is sufficien o calculae he convoluion of y() and u( ) - ha is a cross correlaion. None of he remaining erms involve y (). The imporance and effeciveness of cross correlaion is shown in Figure 5. Figure 5 (a) shows a ypical sample of Gaussian noise. The noise was consruced using a random funcion. The signal chosen is shown in Figure 5 (b) which is real daa capured by advanced sonar ring. As shown in he figure, u() is delayed by an amoun τ which represens he TOF for he arge. The sum of noise and signal, y (), is shown in Figure 5 (c). u() and y() are available a he receiver, bu u ( τ ) as shown if Figure 5 (b), is no. The problem is o esimae where u() is locaed in he noise. Esimaion process sars wih q ( τ ) = y( ) u( τ ) () N q(τ ) has been compued over as wide range as possible, as shown in Figure 5 (d). I will be seen ha q(τ ) has reduced he bandwidh of he noise so ha i has a similar srucure o ha of he signal. In fac, his is because of cross-correlaion process, which is an effecive filer. a In Figure 5 (e), he exponenial funcion of q(τ ) is ploed againsτ, and if he prior disribuion p(τ ) is uniform, his final graph represens he complee expression (9) for p ( τ y). I will be seen ha all he poserior probabiliy is concenraed in a narrow region of uncerainiy a approximaely he rue value ofτ. Acually, due o sampling effecs and noise, he maximum of p ( τ y) does no fall exacly a he rue value shown in Figure 5 (b). In fac, one of he imporan facors in his process is signal/noise energy raio ha affecs he uncerainiy of he delay esimaion. Now, we describe he applicaion of his mehod in he advanced sonar ring. The sonar ring simulaneously fires all 4 ransmiers of he ring using a very shor squarewave pulse, and analyses simulaneously he waveforms of all 48 receivers using mached filers o accuraely deermine he arrival ime of echoes. The ransmied pulse is cycles of 7.4 khz plus a couner-imed burs o reduce reverberaion in he ransducer. The pulse is generaed by momenarily removing a 3V bias, he same bias as is required o operae he ransducers as receivers. Figure 6 shows he volage waveform used o drive ransmiers, a sample waveform received from a smooh, hard reflecor and he frequency componens of he echoed signal using fas Fourier ransform (FFT). b τ Ampliude (v) a 3 c b Time (µsec) d e c Figure 5. (a) Gaussian noise, (b) signal a = τ, (c) noise + signal, (d) q (τ ), (e) poserior disribuion for τ (Noe: The lengh of he signals d and e are bigger han a,b and c due o he croos correlaion) 4 Figure 6. (a) volage waveform o drive ransmiers (b) an echo (c) frequency componens of he echo

5 A emplae for one mere range and zero bearing was used as a prooype, and physical models used by [Kleeman and Kuc 995] were applied o generae he emplaes shown. The pulse absolue ampliude is normalised o maximum of 7, so he waveforms can be sored in an array of signed byes. Muliple mached filers are required o mainain accuracy because he pulse shape depends grealy on he bearing of he reflecor and is range. Due o differen elecronic circuis applying o ransceivers and receivers of he advanced sonar ring, he echo pulse shapes of he same arge are slighly differen and herefore i is necessary o make paricular ses of emplaes for each of hem o gain he highes cross correlaion. Because pulse shape depends on range and angle of arrival, several filers are generaed. The emplaes are pre-compued and saved in he DSPs. Finally 3 emplaes for each se are generaed for varying ranges and angles ha includes for one mere range, one, four, seven and en degrees bearing, for wo mere range, one, four and eigh degrees bearing, for hree mere range, wo and six degrees bearing, for four mere range, wo and six degrees bearing and for five mere range, wo and six degrees bearing. Based on above menioned heory, he maximum likelihood esimaor for he arrival TOF wih addiive whie Gaussian noise is he imeτ ha maximizes he cross-correlaion, Cor (τ ), beween he received pulse p() and an anicipaed pulse shape an (). p( ) an( τ ) Cor( τ ) = T () p ( ) an ( ) T The anicipaed pulse shape an() is one of he emplaes capured from a plane in one mere range and one degree bearing. The received echo is ried agains all available emplaes for several differen angles a he given range, and he one which gives he highes correlaion coefficien is seleced o esimae he arrival ime. A sonar pulse is regisered if is maximum cross-correlaion is greaer han 8% oherwise is discarded. There are some reasons why a pulse may be rejeced including environmenal noise, anoher sonar sensor using a differen pulse shape, anoher ransmier in he same sonar ring using differen pulse shape or overlapping pulses from differen sources, resuling a disored pulse. To esimae he TOF o sub-sample accuracy (less han 4 microseconds in he advanced sonar ring), parabolic inerpolaion is performed on he maximum hree adjacen samples of Cor (τ ). If he hree maxima y, y, and y occur a ineger sample numbers, and, he parabolic esimae of he posiion of he maximum is y 4 3 _ max max_ y + y new pos = prev pos + () ( y y + y ) T where prev _ max_ pos is he posiion of y and new_ max_ pos is he new maximum posiion wih subsample resoluion. TOF is deermined by applying mached filering o he echoes idenified by hresholding and pulse spliing. Filering is performed by firs choosing a se of appropriae emplaes using he sar sample number of he echo and finding he approximae range of he echo, hen cross correlaing he received echo wih all seleced emplaes. For example if he sar sample number of he echo shows an approximae range of cm, he firs four emplaes are chosen by sofware. The alignmen beween he echo and each emplae are adjused by 3 samples which means alignmen of he peaks on each oher and six shifs o each side. This is less comprehensive han a full convoluion implemenaion bu is advanageous as i can run faser and because each DSP processes all echoes of eigh receivers, he process is compuaionally inensive. Afer finding a reliable echo, exceeding he correlaion hreshold, which is 8%, he quesion is how o calculae he TOF. In fac, he TOF is he sar poin of he echo pulse, bu noise can change he sar poin of he echo and more imporanly in pracice he hresholding and spliing process, as are explained laer, relies on groups of eigh samples ha a leas one of hem exceeds he hreshold level, herefore he regisered sar poin of he echo varies wih ime and canno be considered as a reliable TOF. The mehod used in he advanced sonar ring is o find he sar poin of he emplae when he alignmen of emplae and pulse resuls in he maximum correlaion. Sar Sample Peak Shif (+) Peak Echo pulse Templae Cross Correlaion Assumed Maximum Cross Correlaion Siuaion Before Inerpolaion Figure 7. Alignmen of a Received Echo and a Templae when Maximum Correlaion Occurs 5

6 Figure 7 shows an example of filering, which is assumed ha maximum correlaion happens in he shown condiion,, herefore he TOF is TOF = 4µ sec( pulse _ peak _ no emplae _ peak _ no shif) (3) where pulse _ peak _ no is sample number of he pulse peak and emplae _ peak _ no is he sample number of he emplae peak, and in he calculaion of he shif, sub sample resoluion is considered using equaion (). y 4 3 _ ( y + y shif = peak dif + ) (4) ( y y + y ) where peak _ dif is difference beween pulse _ peak and emplae _ peak when maximum correlaion occurs (Figure 7). 4 The Advanced Sonar Ring Sofware Archiecure in Brief The sofware consiss of hree pars, a hos program, a maser program and a slave program. The hos program is developed using C++ under Linux which provides a graphical user inerface o communicae wih he sensor using a serial por, and o save he resuls while showing hem in he screen. A user is able o send differen commands o he sensor, such as upload and download of daa memory and program memory of maser DSP and slave DSPs, firing of ransducers, reading and wriing of he flash memory and ransferring he high level daa o he hos, shown in he graphical environmen. The maser and slave programs are sored in he flash memory. Afer urning on he sensor, he maser is booed via he bye DMA mehod of ADSP-89M. This sofware is a command parser capable of communicaion wih he hos compuer and all digial slave boards, allowing he cenral compuer o conrol all pars of he advanced sonar ring. By sending a command o he maser, i can boo all digial slave boards using inernal DMA por. A fire command is issued o all slaves simulaneously, hus synchronizing he firing of all ransceivers o wihin a clock cycle or 3 nanoseconds. The sofware of each slave can communicae wih he maser by a command parser conaining some commands o access low level daa. The mos imporan par of his sofware is an echo processor ha is organised ino wo sages. During he firs sage, assembly code performs on-he-fly processing of he samples from he eigh receivers o exrac discree pulses ha exceed he noise floor. On-he-fly processing is essenial no only o have a real ime sensor bu also o conserve he on-chip daa memory of he DSP. The second sage processes he exraced pulses wih C code o exrac arrival imes and bearing informaion using emplae maching mehod. The pulse capuring program consiss of opimised assembly code o exrac pulses from eigh receiver channels and save hem ino pulse buffers. This real ime program enables approximaely 8k words of raw receiver daa o be processed in a ransmi cycle o yield pulse resuls wihin he 48k words of daa memory. The sofware is run while receiving echoes and processes all eigh channels wihin 5 insrucion cycles or wo microseconds. The eigh channels are processed independenly hrough four sages conaining DC bias removal, hresholding, aggregaion and soring ino a pulse buffer. A block processing echnique is used for hresholding. Each block of eigh samples conaining a leas one sample wih ampliude greaer han he hreshold are deemed o be par of an echo. When here are wo or more consecuive blocks exceeding he hreshold level, he sofware merges hem and if here is jus a block of 8 samples, he sofware discards hem because each echo mus have a leas 6 samples (Figure 8). Also, an adapive hreshold level is applied o allow for differen ime varying gains in he receiver preamplifiers resuling in differen noise levels. Sage wo processing occurs in he DSP afer all receiver channels have been logged and sored simulaneously in he pulse buffers. N Group8_Couner == Y Group8_Couner - = (To Remove he Las Group8 ) Group8_Couner = Pu_Sign = STOP N START Group8_Couner = Pu_Sign = Pu_Sign== Wrie Sar Sign & Sample Number In he Pulse Buffer Wrie 8 samples o Pulse Buffer and Check Threshold > Threshold Updae he Poiner of Pulse Buffer To Curren Pos Group8_Couner ++ Pu_Sign = Figure 8. A Flow Char of an On-The-Fly Thresholding, Aggregaion and Soring Assembly Code Running in 5 Insrucion Cycles Y Y N 6

7 The processing ime in his sage occurs in addiion o he ime of fligh beween ransmiing and receiving he furhes echo approximaely 3 milliseconds. This processing ime hen direcly impacs on he real ime performance of he sensor since i akes place sequenially wih respec o he capure ime. To deermine he echo pulse arrival imes, he above menioned mached filering echnique is performed on he echo pulses exraced during sage one of he processing. Afer all arrival imes are esimaed, he bearing esimaion is performed for all arges seen by boh receivers of each pair using a riangulaion mehod. If a arge is seen by jus one of he receivers i is deemed o be an unreliable arge. A he end of he calculaion, he slave boards are waiing o be read by he maser board and afer he high level daa of all slave boards are read and sen o he cenral compuer, he maser board sends anoher fire command simulaneously o all he slave boards. 5 Experimenal Resuls 5. Reference Poin and Offse Table Concep and Resuls Choosing a reference emplae amongs all precompued emplaes is an imporan issue, which resuls he exclusive indicaion of he sar poin of an echo, mached wih varying emplaes, ha is he same TOF when maximum correlaion occurs in differen emplaes. The imporance is due o varying sizes and asymmeric pulse shapes of emplaes used in mached filering. In oher words, he TOF of a saionary arge or a very slow objec, when maximum correlaion occurs wih differen emplaes in mached filering, in he emplaes of he same range or differen ranges, is varying because of he differen sar poins of emplaes. In he advanced sonar ring, o solve his problem and avoid jumping TOFs, he emplae for one mere range and one degree bearing is seleced as reference emplae and he sar poin of ha is considered as he reference poin of echoes. Objec Posiion Before Applying The Offse Zoom In Offse Reference Templae Reference Poin Anoher Templae Final Posiion afer Applying The Offse Cross Correlaio Advanced Sonar Ring Wall Assumed Maximum Cross Correlaion posiion Figure 9. The Concep of he Offse and Calculaion Mehod Figure. Experimenal Resul of a Wall posiion befor and afer Applying he Offse 7

8 The sofware uses a lookup able called offse able ha conains offse values beween he reference emplae and all ohers. To calculae he offse value, correlaion beween each emplae and he reference emplae is calculaed and when maximum correlaion occurs, he difference beween wo sar poins is calculaed and considered as he offse value of ha emplae ( Figure 9). To ge sub-sample resoluion he above menioned inerpolaion mehod is also used in offse values compuaion. The offse able is pre-compued and saved wih emplaes. Using offse values he equaion (3) can be rewrien as a b Cycle Hopping Real Peak TOF = 4µ sec( pulse _ peak _ no emplae _ peak _ no shif offse) () when he offses are no applied, he resul of range esimaion for a saionary arge such as a wall is no consisen and differen ranges are calculaed when he maximum correlaion occurs wih differen emplaes. The experimenal resuls, before and afer applying his facor are shown in Figure. This problem also occurs when a calculaion process of a moviing plaform or moving arge uses differen emplaes due o change in he given range, for example when i uses mere emplaes and hen changes o wo meer emplaes. Therefore he offse able increases he robusness of he advanced sonar ring. 5. Cycle Hopping Rejecion Concep and Resuls The mached filering is performed using a 3-poin cross correlaion, explained in secion 3, beween a deermined echo and each of he relaed emplaes for a given range. If he maximum correlaion is greaer han 8% hen he echo is considered as a reliable echo, hen he arrival ime of he echo is esimaed using equaion (3). During experimens, we found he posiion of a saionary objec someimes jumps beween wo differen posiions. More invesigaion of he echoes showed ha he maximum value of he cross correlaion, which is sampled a he same rae of he echo, occurs in differen locaions wihin cross correlaion vecor, resuling a varying TOF value caused by a changing shif, described in equaion (3). This problem is called cycle hopping since he error in shif is usually approximaely one wavelengh and deails are shown in Figure. The problem arises firsly due o a low sample rae of 5 khz missing he real peak in he sampling process, and also due o he noise level in he capured echo, which makes local maxima very close o each oher and indisinguishable in some condiions. Cycle hopping occurs when he ampliude of an adjacen local maximum is greaer han ha of he samples calculaed around he real peak posiion. c Figure. (a) A cross correlaion a 5 khz and he cycle hopping problem (b) he real shape of cross Correlaiom (c) real peak locaion using he inerpolaion mehod To solve he problem and o find a genuine peak posiion wihin he cross correlaion marix, an inerpolaion process is employed afer he cross correlaion calculaion. This process compues a real peak value of he local maxima using a parabolic inerpolaion over hree adjacen samples. Then, he maximum is chosen amongs he resuls of his process. Figure (a) shows a real cross correlaion vecor which has a peak in he wrong posiion, comparing o he oher echoes capured from he same arge and he same receiver. Figure (b) shows he real correlaion waveform and he resul of he inerpolaion process on he local maxima is shown in Figure (c). As can be seen, his mehod can provide a beer esimae of he real maximum and avoid he varying TOF. Also, experimenal resuls are shown in Figure. This figure shows he effeciveness of he applied mehod in he real environmen. The compued posiion of each objec is considered a he end of each line. The cycle hopping causes a difference of abou 4 samples i.e. 6 microseconds in he arrival ime of he echo, herefore abou 6*.343/=.75 mm difference in he range. As can be seen in Figure, his variaion effecs he bearing esimaion markedly when one of he ranges obained from a receiver of each pair is flucuaing. 8

9 cm Figure. Experimenal Daa Showing he Effeciveness of The Cycle Hopping Rejecion Mehod 6 Conclusions Cycle Hopping Resuls Advanced Sonar Ring Zoom In Wall Real Resuls afer Applying The Cycle Hopping Rejecion Mehod The paper has presened a new approach o a low sample rae muli DSP real ime sonar-ring echo processing based on he emplae mached arrival ime esimaor. The concep of a reference poin, an offse able and he problem of cycle hopping a he low sample raes has been discussed and he effeciveness of he inerpolaion soluion has been demonsraed wih experimenal daa. Fuure work will be performed wih high speed accurae sonar sensing applicaions on a mobile robo such as localizaion, SLAM, obsacle deecion, environmenal change deecion and pah-planning. Acknowledgemens We graefully acknowledge Mr. Seven Armsrong for his assisance in he design and consrucion of he hardware and basic communicaion infrasrucure of he sonar ring and funding from he ARC Cenre for Percepive and Inelligen Machines in Complex Environmens. References [Borensein, J. and Y. Koren 995]. "Error eliminaing rapid ulrasonic firing for mobile robo obsacle avoidance." IEEE Transacions on Roboics and Auomaion (): [Fazli, S. and L. Kleeman 4]. A Real Time Advanced Sonar Ring wih Simulaneous Firing. 4 IEEE/RSJ Inernaional Conference on Inelligen Robos and Sysems, , Sendai, Japan. [Heale, A. and L. Kleeman ]. A real ime DSP sonar echo processor. IEEE/RSJ Inernaional Conference on Inelligen Robos and Sysems, Oc 3-Nov 5, 6-66, Takamasu, Insiue of Elecrical and Elecronics Engineers Inc. [Joerg, K.-W. and M. Berg 998]. Mobile robo sonar sensing wih pseudo-random codes. Proceedings of he 998 IEEE Inernaional Conference on Roboics and Auomaion. Par 4 (of 4), May 6-998, 87-8, Leuven, Belgium, IEEE, Piscaaway, NJ, USA. [Kleeman, L. 999]. Fas and accurae sonar rackers using double pulse coding. 999 IEEE/RSJ Inernaional Conference on Inelligen Robos and Sysems (IROS'99): Human and Environmen Friendly Robos whih High Inelligence and Emoional Quoiens', Oc 7-Oc 999, 85-9, Kyongju, Souh Korea, IEEE, Piscaaway, NJ, USA. [Kleeman, L. and R. Kuc 995]. "Mobile robo sonar for arge localizaion and classificaion." Inernaional Journal of Roboics Research 4(4): [P.M.Woodward 964]. Probabiliy and Informaion Theory wih Applicaion o Radar, Oxford:Pergamon Press. [Peremans, H., K. Audenaer, e al. 993]. "High-resoluion sensor based on ri-aural percepion." IEEE Transacions on Roboics and Auomaion 9(): [Vlasimil MASEK, M. K., Aiguo MING and Ljubisa VLACIC 998]. "Fas Mobile Robo Obsacle Deecion Using Simulaneous Firing of Sonar Ring Sensors." [Vlasimil MASEK, M. K., Aiguo MING and Ljubisa VLACIC 999]. "A New Mehod o Improve Obsacle Deecion Accuracy Using Simulaneous Firing of Sonar Ring Sensors." The Japan Sociey for Precision Engineering 33(N.): [Yaa, T., A. Ohya, e al. 999]. "Fas and accurae sonar-ring sensor for a mobile robo." Proceedings - IEEE Inernaional Conference on Roboics and Auomaion Proceedings of he 999 IEEE Inernaional Conference on Roboics and Auomaion, ICRA99, May -May : [Yaa, T., A. Ohya, e al. ]. Using one bi wave memory for mobile robos' new sonar-ring sensors. IEEE Inernaional Conference on Sysems, Man and Cyberneics, Oc 8-Oc, , Nashville, TN, USA, Insiue of Elecrical and Elecronics Engineers Inc., Piscaaway, NJ, USA. 9