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Pulsed laser ranging techniques based on digital signal processing methods for automobile anti collision application Zhihui SUN Jiahao DENG School of Aerospace Science and Engineering Beijing Institute of Technology No 5 Zhongguancun South Street Beijing China 100081 ABSTRACT A 1 55 m digital laser radar system is designed and implemented for automobile anti collision application In order to reduce the influence of foggy rainy and snowy weather on laser detection digital signal processing methods are adopted Multi pulse coherent average algorithm is used to improve the signal to noise ratio of echo by N times The correlation detection algorithm is adopted to estimate the time of flight Multi time delayed correlating method is used to improve the time of flight estimation resolution Experimental results indicate that the digital signal processing methods in this paper can reduce the influence of bad weather conditions and obtain high range accuracy Keywords automobile anti collision distance measurement laser ranging laser radar time of flight estimation digital signal processing weak signal detection correlation detection 1 INTRODUCTION Traffic accidents take place frequently with the increase of automobile number and speed Driving safely draws more and more attention and the research on automobile anti collision system becomes hot Automobile anti collision systems adopt mm wave radar or laser radar to detect proceeding vehicles obstacles pedestrians and measure the distance of objects When the distance is less than the safety distance the systems alert the driver or brake automatically Therefore drive safety in poor weather condition such as rainy snowy foggy is enhanced and traffic accidents can be avoided Compared with mm wave radar the main advantages of laser radar are more mature reliable and cheaper However the disadvantages of laser radar are its inability to penetrate rain and fog and also there is the question of eye safety regarding using high power pulse lasers so laser radar doesn t encounter the favorable opinion of car makers for a long time Recently along with the progress in manufacture technology of laser diode photodetector and also signal processing techniques the weakness of automobile laser radar is overcome Some companies such as IBEO Omron automotive electronics Daihatsu have developed advanced automobile laser radars and their performances are as good as mm wave radar 1 3 In this paper a 1 55 m digital laser radar system is designed and implemented for automobile anti collision application By comparing 1 55 m laser with 0 9 m laser the 1 55 m laser is safe to eyes and its capabilities in detection and penetrating fog are stronger The system adopts high speed analog to digital converter ADC to sample the pulse echo signal and then digital signal processing methods are used for signal preprocessing and time of flight estimation Experimental results show that the detection capability of weak echo signal is enhanced and the ranging accuracy of the system is improved Thus the performance of digital laser radar system in poor weather conditions is improved 2 OVERVIEW OF AUTOMOBILE LASER RADAR SYSTEM 2 1 Working principle The working principle of automobile laser radar system is illustrated in Fig 1 When the range to a preceding vehicle R is less than S1 alarming range the system alerts the driver to slow down when the range R is less than S2 braking range the system alerts the driver to brake or brake automatically Fig 1 Working principle of automobile laser radar system The range to a preceding vehicle R is calculated on the basis of elapsed time between transmission of a laser pulse and reception of reflected light 4 Knowing the laser pulse travels at the velocity of the light c m s and measuring the time of flight of the laser pulse t the range R m is given by R c t 2 1 The laser radar range equation is the foundation for designing the system and evaluating the performance of the system Given that the target is larger than the beam and has a Lambertian reflectance distribution the equation is 5 Pr 2 WherePr power received in wattsPt power transmitted in watts t transmitting optics efficiency r receiving optics efficiency reflectanceD entrance pupil diameter in meters a atmospheric transmission factor one way exp R where atmospheric attenuation coefficient in km 1 R range in meters As can be seen from Eq 2 several factors influence the performance of laser radar system Generally when do research on the performance the laser radar range equation is often expressed in the form of signal to noise ratio power SNR t 2 t 2 th t 2 3 where NEP is noise equivalent power in watts and it is interpreted as the standard deviation for the Gaussian distribution of the additive noise NEP is combined together by the noise in detector and preamplifier NEP t t h h 4 WhereNEPdetector noise equivalent power of detector NEPpreamplifier noise equivalent power of preamplifier Eq 3 relates the signal to noise ratio SNR to range for given hardware parameters weather conditions and target characteristics SNR is an important parameter in evaluating the performance of the laser radar system Probability of detection is another important parameter based on pulse detection in white noise using a matched filter the probability of detection is Pd erf 5 WherePd probability of detectionerf x unilateral error function TNR threshold to noise ratio is expressed as follows TNR t t 6 Where pulse width FAR average false alarm rate Pfa PRF and Pfa single pulse false alarm rate PRF laser pulse repetition frequency 2 2 Comparison between 0 9 m and 1 55 m laser radars Generally 0 9 m laser radars exhibit good performance only with cooperative obstacles in good visibility conditions in order to detect non cooperative obstacles and improve performances in poor weather conditions devices outside Class I are required 6 and the problem of eye safety is caused Compared with 0 9 m laser 1 55 m laser is safe to eye and the capability of penetrating fog is stronger consequently the allowed transmitted laser pulse energy is increased and the detection capability in low visibility is improved As can be seen from Eq 2 the atmospheric effects limit the performance of the laser radar system Two way atmospheric transmission factor Tais Ta exp 2 R 7 where atmospheric attenuation coefficient is 7 th thh q 8 where laser wavelength in mRv visibility distance in km q the size distribution of the scattering particles 1 6for high visibility R v 50 km 1 3for average visibility 6 km R v 50 km 0 585 V 1 3 for low visibility R v 6 km Fig 2 shows a plot of two way atmospheric transmission factor versus range for 0 9 and 1 55 m lasers as the visibility distance Rvis 0 5 km which stands for moderate foggy weather condition As can be seen from Fig 2 1 55 m laser is stronger in the capability of penetrating fog than 0 9 m laser Comparison between 0 9 and 1 55 m laser radars in detection capabilities is made to detect a low reflecting pedestrian with a high probability Pd 0 999 Pfa 10 13 in moderate foggy weather condition visibility distance Rv 0 5 km As laser pulse width 100 ns laser pulse repetition frequency PRF 10 KHz from Eq 5 and Eq 6 the required SNR is calculated SNR 12 dB As is shown in Fig 3 the horizontal line is the required SNR to achieve the high probability Si APD and InGaAs APD are used as detectors respectively by 0 9 and 1 55 m laser radars The noise equivalent power of APD NEPdetector is 8 NEPdetector NEPHZ 9 where NEPHzis noise equivalent power of APD in watts perHz and B is noise bandwidth in hertz The noise equivalent power of preamplifier NEPpreampl is 9 NEPpreampl t 10 where k Boltzmann s constantT the temperature in degrees Kelvin N noise factor of the preamplifier Res the responsivity of APD RL the load resistor 1 2 BC and B noise bandwidth in hertz C capacitance of the APD From Eq 3 4 8 9 10 the SNR of 0 9 and 1 55 m laser radar system can be obtained with following parameters Pt 50 W t r 0 6 0 15 0 9 m or 0 25 1 55 m based on pedestrian as target D 0 04 m R v 0 5 km k 1 38 10 23 J K T 295 K 22 C N 2 C 1 pF B 35 MHz NEPHz 10 14 W Hz Si APD or 0 15 10 15 W Hz InGaAs APD Res 9 4 A W Si APD or 9 A W InGaAs APD Fig 3 shows a graph of SNR versus range for 0 9 and 1 55 m laser radar systems as the visibility distance R v 0 5 km With the probability Pd 0 999 Pfa 10 13 required SNR 12 dB as can be seen from the graph the maximum detection range of 0 9 m laser radar system is about 150 m while 200 m for 1 55 m laser radar system The theoretical comparison results show that the detection capability of 1 55 m laser radar is stronger in poor weather conditions So development of 1 55 m laser radar can improve performance in low visibility such as fog conditions and if advanced signal processing methods are adopted the performance can be improved further more 2 3 1 55 m digital laser radar system construction As shown in Fig 4 1 55 m digital laser radar system consists of following three components transmitter that drives pulse reference signal and emits pulsed laser light receiver that condenses the reflected light undergoes photoelectric conversation and weak pulse signal amplification signal processing system that samples the pulse echo signal by high speed ADC and undergoes signal preprocessing and time of flight estimation by digital signal processing methods The signal processing system is based on field programmable gate arrays FPGA and digital signal processor DSP FPGA is used to complete time sequence control functions such as laser pulse reference signal generation high speed ADC sampling data buffering and interrupt signal generation DSP is used to implement signal preprocessing and time of flight estimation algorithm Working principles of the 1 55 m digital laser radar system are as follows DSP starts FPGA to generate a pulse reference signal with 100 ns pulse width and 10 KHz repetition frequency and laser driving circuit amplifies the pulse reference signal to control the diode laser to emit pulsed laser light then transmitting optics shape the laser light into narrow beam and transmit forward Receiving optics condense the light reflected back from the reflecting object and the photodetector converts it to an electrical current pulse signal then transimpedance amplifier converts the weak current pulse signal to a voltage pulse signal the variable gain amplifier further amplifies the voltage pulse signal suitable for the input voltage range of ADC At the same time of generating the laser pulse reference signal the ADC samples the pulse echo signal at 200 MHz equivalent frequency under the control of FPGA and FPGA stores the data in its inner random access memory RAM when required data have been sampled FPGA interrupts DSP DSP responses the interruption and reads the data in and implements multi pulse coherent average algorithm to increase the SNR of pulse echo signal then adopts correlation detection method to estimate time of flight and further improves the resolution of time of flight estimation by multi time delayed correlating method 3 PULSE ECHO SIGNAL SAMPLING Dual channel ADC with 10 bit resolution and 100 MHz sampling frequency is adopted The pulse echo signal is sampled alternately by channel A and B under the control of reversed clocks and the equivalent sampling frequency is doubled to 200 MHz The working principle is shown in Fig 5 Alternate sampling is strict with the time sequence of clocks and the reversed clock signal of alternate sampling is generated by FPGA Then the data sampled are stored in inner RAM of FPGA Principle of sampling control and data buffering by FPGA is shown in Fig 6 and the process is implemented by Verilog HDL language programming As shown in Fig 6 input clock frequency of FPGA is 50 MHz two 100 MHz reversed clocks are generated by on chip phased lock loop PLL The clocks and data of dual channel ADC are connected to ADCLOCKA ADCLOCKB DBA and DBB respectively The data sampled are stored in two RAMs of FPGA Because dual channel ADC operates alternatively the sampling data should be recombined by the Bus Controller When the bus address is even the data of channel A are output when the bus address is odd the data of channel B are output 4 MULTI PULSE COHERENT AVERAGE As can be seen from Fig 2 and Fig 3 despite performance of 1 55 m laser radar in foggy weather is better than that of 0 9 m laser radar as the range increase atmosphere attenuation becomes severe pulse echo signal is weak and sometimes even submerged in noise In order to increase the SNR of pulse echo signal multi pulse coherent average algorithm is adopted Basic principle of multi pulse coherent average algorithm is multiple pulse echoes are sampled by high speed ADC and then the sampling values are accumulated corresponding to their relative positions The pulse echo signal can be expressed as follows X t A s t w t 11 where s t normalized pulse signalA the amplitude of pulse echo signal w t zero mean Gaussian white noise and its root mean square value is N pulse echoes are sampled if there are M sampling points in each echo and sampling interval is t then the value of sampling point j j 0 1 M 1 in pulse echo i i 0 1 N 1 is x t A s t w j t 12 Where tiis sampling start time of pulse echo i and the sampling start time of different pulse echoes is required as the same Eq 12 can be abbreviated as xij A sij wij 13 M sampling value of a pulse echo is stored and summed respectively with M sampling value of last pulse echo when N pulse echoes have been sampled and accumulated the coherent average value of point j is t t t 14 Eq 14 can be further arranged as t t t tt ht Input SNR powert is define as SNRi t 6t Then output SNR powert is SNR N SNRi 7t As can be seen from Eqt 7t the SNR of pulse echo signal is improved by N time after processed by multi pulse coherent average algorithmt Experimental results of multi pulse coherent average algorithm are shown in Fig 7 at is a plot of pulse echo signal sampled by high speed ADC and the noise is high bt ct and dt are the processing results when coherent average times N h t As can be seen from Fig 7 the SNR of pulse echo signal is improved gradually as the coherent average times increaset However the processing time becomes longer as the coherent times increaset So the choose of coherent average times is the tradeoff between SNR improvement and processing timet ht ht TIME OF FLIGHTTIME OF FLIGHT ESTIMATIONESTIMATION ht ht CorrelationCorrelation detectiondetection As can be seen from Eqt t Target range is calculated on the basis of time of flight estimationt And the ranging accuracy mainly depends on the time of flight estimation accuracyt There are several time of flight estimation methods leading edge detection zero crossing detection peak detection constant fraction detection and correlation detection t Compared with other detection methods correlation detection is the best in performance and less affected by the noise t In this paper correlation detection method is used to estimate time of flightt The mathematical model of pulse echo signal can be expressed as X nt A s n t w nt 8t where n is the sampling point at time delay M is the sampling length and other parameters are the same as Eqt tt The correlation detection method uses the position of peak of cross correlation function r kt as the estimated argmaxr ktr kt t tt t ht The range is calculated by R t where t is time of flight estimated is the sampling intervalt As can be seen from Eqt t the ranging resolution by correlation detection method depends on the sampling frequency of ADC and high sampling frequency provides better range resolutiont In this paper MHz ADC is used the time of flight estimation resolution is h ns and the ranging resolution is t7h mt In order to improve ranging resolution further adopting ADC with higher sampling frequency is a choice but the problem is that the circuit becomes complicated and hard to implemented also the cost is hight So this paper presents multi time delayed correlating method to improve ranging resolution without using higher sampling frequency ADCt ht ht Multi timeMulti time delayeddelayed correlatingcorrelating methodmethod Time of flight estimation by correlation detection method is to calculate the position of cross correlation peakt When time of flight is integer times of sampling interval the cross correlation peak can be sampled otherwise the neighbor of the peak is sampled and time of flight estimation error is producedt If the cross correlation peak delays a certain time so that the peak can be sampled then the certain time delayed can modify the time of flight estimation error caused by samplingt The delayed cross correlation function is r k dt t t t t t t where d is a certain time delayed and it is less than the sampling intervalt As can be seen from Eqt t to calculate delayed cross correlation function just need to delay the reference signal for a certain time d and then calculate cross correlationt If let sd n s n d and rd kt r k dt then Eqt tcan be expressed as follows rd kt t t t when d the delayed reference signal is t t t t as shown in Fig 8t The delayed cross correlation functions are t t t t t t t If the maximum of delayed cross correlation functions is t i t then the time of flight estimated t is t a t As can be seen from Eqt t the time of flight estimation resolution is improved by K times on the basis of correlation detection methodt In this paper five delayed reference signals are used and the time of flight estimation resolution is improved by h timest When sampling frequency of ADC is MHz the sampling interval h ns then time of flight estimation resolution improved by multi time delayed correlating method is ns and the ranging resolution is improved to t h m correspondinglyt 6t 6t CURRENTCURRENT EXPERIMENTEXPERIMENT RESULTSRESULTS Currently indoor short range measurement experiments have been done to verify the multi pulse coher