A Novel Approach To Improve Vehicle Speed Estimation Using Smartphone s INS/GPS Sensors

Transcription

1 A Novel Approach To Improve Vehcle Speed Estmaton Usng Smartphone s INS/GPS Sensors Arjt Chowdhury TCS Innovaton Labs Tata Consultancy Servces Kolkata,Inda arjt.chowdhury@tcs.com Tapas Chakravarty TCS Innovaton Labs Tata Consultancy Servces Kolkata,Inda P. Balamuraldhar Tata Consultancy Servces TCS Innovaton Labs Bangalore,Inda balamural.p@tcs.com Abstract In recent tmes, number of researchers have nvestgated vehcle trackng applcatons by fusng the measurements done by accelerometers, as part of nertal navgaton system (INS), and GPS (Global Postonng System). However, the sensors n recreatonal devces lke moble phone have lmtatons n measurement accuracy and relablty. Usually, sudden changes n vehcle speed are not always captured well by GPS. Accelerometers, on the other hand, suffer from multple nose sources. In ths paper, we nvestgate the nose performance of accelerometers, avalable n a few smartphones. Then, we apply the nose analyss for the purpose of estmatng the movng vehcle speed. A number of experments were carred out to capture the vehcle s poston & speed from OBD, GPS as well as 3-axes accelerometer. We demonstrate a method by whch the phone s orentaton s compensated for whle calculatng speed from the measured acceleraton. Further, a new method of INS/GPS fuson s proposed whch enhances the accuracy of speed estmaton. It s envsaged that wth ncreasng estmaton accuracy, the applcaton of mult-sensor fuson n autonomous vehcles wll be greatly enhanced Keywords-component; GPS; Allan Varance; OBD; speed correcton; accelerometer I. INTRODUCTION A vehcle navgatonal framework that combnes GPS measurements and nertal navgaton system (INS) are ganng much mportance and s becomng an mportant feld of study. The performance of low cost GPS recever together wth low cost INS (or alternatvely, nertal measurement unt) s therefore very mportant from navgatonal perspectve [1-]. Detaled performance analyses of such generally avalable sensors are lkely to throw up new approaches that wll greatly enhance the estmaton accuracy n futurstc vehcles ncludng autonomous ones. Personally owned Smartphones are becomng the most popular choce n deployng sensors lke accelerometers; gyroscopes etc. not only for the purpose of navgaton but also for the purpose of ntroducng drvng related applcatons. If personal phones can be utlzed to accurately estmate the speed of the movng vehcles, new solutons can be ntroduced to serve the consumers better. Also such data can be used to send control sgnal for control and gudance of vehcle [3]. Accelerometers are generally used to dentfy aggressveness n drvng [4-5]. On the other hand, Smartphones have an added advantage n beng able to process the captured data and transmt them over communcaton network [6]. Two recent works on smlar lnes are related to the smartphone based sensng for dentfyng aggressve drvng behavor [7-8]. Keepng the above stated synergy n mnd, we decded to utlze the Smartphones and commercally avalable applcatons, to carry out extensve experments n movng vehcles, for the purpose of nvestgatng the accuracy and relablty of vehcle speed estmaton. It s envsaged that an ncreased accuracy n estmatng the vehcle speed under varyng condtons, partcularly for congested cty drve, wll make autonomous vehcles more relable In ths paper, we propose an approach to mtgate the ssue of estmatng the true speed of a movng vehcle usng prmarly smartphone accelerometers. It s known that the accelerometers suffer from multple nose effects. The nose level and the type may vary from phone to phone. In order to test the varablty, authors have used Allan Varance method [9-] to estmate and compensate for the nose present n accelerometers. Authors compare dfferent smartphones for nose performance of ther ntegrated accelerometers. After sutable compensaton, the measured acceleraton values are ntegrated to obtan the speed of the movng vehcle. Further, a method of GPS and accelerometer data fuson s nvestgated for mprovng the accuracy of speed estmaton. For such, GPS based measurements at 5sec nterval are used to correct the speed estmaton from acceleraton measurements. A new method of forward and backward speed estmaton s proposed. It s seen that the proposed approach sgnfcantly mproves the speed estmaton. For comparson purposes, we have utlzed the OBD based speed measurement as the true measure of the vehcle speed. II. ACCELEROMETER NOISE MEASUREMENT In ths secton, the dfferent types of nose errors mpactng an accelerometer measurement are nvestgated. An mportant concern regardng the nose effect s that they mpact the speed evaluatng vde the ntegraton process. A. Constant bas Offset of the output value from the true value s called bas of an accelerometer, n m / s. A constant bas error of ε, when 441

2 ntegrated to get speed, causes an error whch grows proportonally wth tme. The total error n speed estmaton s e(t) =.5.ε.t, where t s the tme of ntegraton. [] B. Whte Nose / Velocty Random Walk Accelerometer output generally contans some amount of whte nose. Integraton of the whte nose produces a random walk wth varance proportonal to t. Hence, whte nose creates a velocty random walk []. Ths s measured n m/s/ s. C. Rate Ramp Ths s a determnstc error. Slow monotonc change of output over tme s Rate ramp. It can be descrbed as: w(t)=r.t, where R s the slope of the ramp. Ths creates a lne of slope +1 n AD plot [9-]. R s the value of Allan Devaton at tme =. Other errors are brefly summarzed n table I. Error Type Temperature Effects Calbraton Bas Instablty III. TABLE I. SUMMARY OF DIFFERENT ERRORS Descrpton Temperature dependent resdual bas Determnstc errors n scale factors, algnments and accelerometer lneartes Bas fluctuatons, usually modeled as a bas random walk Result of Double Integraton Any resdual bas causes an error n speed whch grows lnearly wth tme Speed changes proportonal to the tme rate and duraton of acceleraton A second-order random walk n speed ALLAN DEVIATION RESULTS FOR DIFFERENT PHONES In ths secton we present the results on Allan varance method appled to dfferent phones. These phones have dfferent accelerometer makes; n addton, they may be embedded dfferently n each smartphone. Thus, the Allan varance method s appled on dfferent phones to measure ther nose characterstcs. Allan Varance s a tme doman sgnal analyss technque that can be used on any sgnal to determne the character of nose n the system. Allan Varance s measured as a functon of averagng tme. Hence Allan varance calculaton gves (t,ad(t)) par where t = averagng tme. AD(t) s the value of Allan devaton = Allan varance. We menton brefly the technque to calculate AD [9-]. 1. Dvde a sequence of data t nto sequence of length t. There must be enough data for at least such sequences.. The data n each bn s averaged to obtan a seres of averages (a(t) 1, a(t),..., a(t) n ), where n s the number of bns. 3. The Allan Varance s then calculated usng (1) 1 AVAR ( t) = (a(t) 1 - a(t) ) * ( n 1) + (1) Allan Devaton, denoted by AD(t) s gven n () AD( t) = σ ( t) = AVAR(t). () Then n log-log scale plot of (t, AD(t)) dfferent slope sectons dentfes dfferent types of nose whch are orthogonal n nature. After dentfyng a process t s possble to obtan ts numercal parameters drectly from the AD plot [9-]. A typcal plot of Allan devaton shows dfferent errors n dfferent zone of t. The slope of the lne ndcates type of nose and parameters of dfferent nose can be computed from the AD curve. Value of dfferent nose parameters can be calculated usng table of reference []. The error modelng, dscussed as above, s now tested on dfferent smartphones (phone5, google nexus, LG nexus and Samsung note ). Results and plot for these 4 types of smartphones are presented n fg. -5 and table II and III respectvely. Fgure 1. Allan devaton plot for Samsung google nexus for all 3 axes The analyss of the Samsung google nexus AD plot (as shown n fgure 1) dsplays the presence of whte nose for all three axes and addtonally a bas nstablty for X axs. The value of whte nose varance s the value at t = 1 on the approxmate lne wth slope -1/. Clearly for x, y, z axs the value of σ at t = 1 are.19,.18,. respectvely. Hence, these are the standard devaton of whte noses for the gven axs. The values of dfferent types of error coeffcent can be calculated as ndcated n table II. Only for the X axs, the Allan devaton curve shows a flat porton from t = 7 to 5s. Hence bas nstablty for X axs B X =.65/.664 =.98 m / s. 44

3 a straght lne through the slope and readng value at t =. Hence for that Rate ramp RZ = σ ( ) =.4 m / s/ s. Whte nose parameters for LG nexus are summarzed n table III. Fgure. Allan devaton plot for Samsung galaxy note. For Samsung note, the Allan devaton plot s shown n fgure. Bas nstablty (porton wth slope = n tme zone 7 sec.) s present n the X axs only wth value B x =.6/.664 =.9 m / s, whch s tmes smaller than Samsung google nexus (refer fgure ). Thus, t s seen that the accelerometer performance n Samsung note s better than Samsung google nexus phone. Smlar comparsons can be made from Allan devaton plots to obtan nose characterstcs and determne dfferent nose coeffcents (as lsted n table III and 4). Allan devaton plot for Phone 5 s gven n fgure 3. The plot shows the presence of whte nose and bas nstablty (flat regon n the AD curve) on each the axs. The curve of Z-axal accelerometer n phone plot (fg. 3) ndcates a correlated nose and/or snusodal nose n tme nterval 36 s. All the nose parameters found wth method descrbed n ths note usng table II are summarzed n table III. Fgure 4. Allan devaton plot for LG nexus. Now from the presented AD fgures the whte nose parameter ( m / s / s ) of these 4 phones are gven n table II. TABLE II. WHITE NOISE VARIANCE FOR DIFFERENT PHONES Accelerometers x axs y axs z axs GOOGLE NEXUS IPHONE LG NEXUS NOTE In table III bas nstablty (n m / s ) for dfferent phones s consoldated. TABLE III. BIAS INSTABILITY FOR DIFFERENT PHONES Accelerometers x axs y axs z axs GOOGLE NEXUS.98 NA NA IPHONE Fgure 3. Allan devaton plot for Phone 5 AD curve for LG nexus n fgure 4 shows presence of whte nose for all 3 axs, bas nstablty for X axs only. Presence of Rate Ramp s observed only n case of LG nexus (fgure 4) for Z axs n the regon t= 5 4 s.( slope of AD curve n fg. 4 s +1 ) and measurement for ths nose can be measured by fttng LG NEXUS.1 NA NA NOTE.9 NA NA 443

4 TABLE IV. Tme (sec) ACCELERATION MEASUREMENT AT STEADY STATE Lateral Acceleraton (m/s) Vertcal Acceleraton (m/s) Longtudnal Acceleraton (m/s) Calbrated Longtudnal Acceleraton (m/s) µ σ µ σ Μ σ µ Σ Tlt Angle (n Y-Z plane) n deg IV. VELOCITY CALCULATION Fgure 5 dsplays the expermental set-up. In ths case, the OBD based speed of vehcle s collected at 1 Hz samplng rate and the acceleratons are also logged usng the smartphone at 1Hz samplng rate. Along wth these, the GPS data (poston, speed) are logged at 5 s tme gap (. Hz). The speed calculaton method, usng both accelerometers and GPS data s outlned n subsequent sectons. The data are collected usng Kw Bluetooth OBD devce [11], Samsung Note and Torque applcaton. The accelerometer readngs are calbrated to elmnate errors mentoned n table II and III. A. Acceleraton ntegraton method Trapezod rule s used to ntegrate samples of acceleraton to obtan speed gven a current speed. Let the consecutve samples for acceleratons be a1, a, a3,... and the speed samples are gven by v1, v, v3,... Then we compute ntermedate speeds as gven n (3). ) v 1 = v 1 v v +.5( a + a ) (3) = 1 1 Results obtaned usng that are shown n detals n results secton. V. RESULTS In ths secton, we present results of the applcaton of INS/GPS fuson n vehcle navgaton. Fg. 6 presents accelerometer data collected n steady state from the phone, wth car at rest (but engne was kept on). One can see from fg. 6 that the longtudnal acceleraton has a mean acceleraton of approxmately 1.3 m/s. Ths ndcates that the phone mountng s not perfectly vertcal. We measured ths phenomenon for all the rest perods n a gven trp. The same s presented n table IV. Acceleraton (m/s ) Tme Sequence (sec) Vertcal Acceleraton Longtudnal Acceleraton Fgure 6. Longtudnal & vertcal acceleratons for vehcle at rest (engne kept runnng) Fgure 5. Photograph of the expermental set-up dsplayng Bluetooth OBDII devce and Tab as data logger In table IV, the tlt angle of the phone n the Y-Z plane s calculated for three nstances of measurement. (the vehcle s movng along Y-axs n the X-Y plane and vertcal acceleraton s along Z axs). Tlt angle s the rotaton relatve to phone orentaton. Then from the trp data we calbrate the measured acceleraton to get longtudnal acceleraton usng (4). a = acc * sn( θ ) - b (4) Where, the tlt angle s θ and fxed bas s b. In our case θ 6 and b =.11. Thus we perform tlt adjustment on acqured data to get actual forward acceleraton. 444

5 From the calbrated longtudnal acceleraton, we calculate the vehcle speed usng (3). Fg. 7 shows the plot of OBD speed data wth the computed speed for approx. 3 mn. nterval. It s seen that the computed speed dverges from true speed as tme progresses. Ths s ndcated by Allan varance analyss also. The result depcted by fg. 7 s a known phenomenon and that s why, n many cases, accelerometer data s fused wth ntermttent GPS measurements as a measure of error correcton. In our case, avalable GPS measurement at 5s nterval can be utlzed. To make fuson of accelerometer data wth GPS we need to correct vehcle speed found usng the ntegraton (3). 7 6 OBD II measurement Derved from Accelerometer (longtudnal) Vehcle Speed (Km/h) OBD measured Accelerometer & GPS fused-forward Calculaton Tme Sequences (sec) Vehcle Speed (Km/h) Tme Sequence (sec) Fgure 7. Computed speed from (3) wth correspondng GPS and OBD speed.. At every 5 s tme nterval, we correct the current speed of vehcle usng (4a-4b) nstead of (3). Ths s called forward correcton and speed calculated s called F- speed (we use ths notaton for smplfcaton of representaton only) v ) = v for = 1mod(5) (4a) v v +.5( a + a ) Otherwse (4b) = 1 1 Error s measured by e = OBDv - v, where OBDv the speed s measured from OBD. Usng (4a-4b) at 5 second nterval, we correct the estmated speed of the movng vehcle by forcng that value to calculated speed. Usng ths method, the error becomes smaller; the accumulated error s corrected after 5 seconds by use of GPS measured speed. Plot of the forward speed as compared wth OBD speed s gven n fg. 8. From fg. 8, t s clear that the error reduces but stll error les n the range (-13, 7) km/hr wth r.m.s. error km/hr. Hence, the approach requres further mprovement. We propose a new estmaton mprovement method called hereafter as Forward-Backward correcton (F-B correcton) whch computes past speed from known present speed. These speeds are referred as F-B speed. Fgure 8. Calculated F-speed s compared wth OBD speed. We can further estmate our speed as an average of F-speed and F-B speed to obtan a better estmate of speed from nertal measurements. In fg (9) we present the computed speeds from forward and forward-backward correcton method as compared wth OBD speed. It s observed that the true speed s a weghted average of the two proposed correcton methods. V =.5( v + v ) Where V s the estmated speed (6) Equaton (6) estmates speeds ( V ) usng INS/GPS fuson and these calculatons can be used effectvely to get proper speed estmaton. Fg. presents the fnal estmated speed as compared wth OBD speed. V e h c le S p e e d (K m /h ) Tme Sequence (sec) OBD measured Accelerometer + GPS - Forward Accelerometer + GPS - Backward v ) = v for = 1mod(5) v v.5( a + a ) 1 = 1 Otherwse (5a) (5b) Fgure 9. Calculated F and FB speed relatve to OBD speed. 445

6 7 OBD measured Average of Forward & Backward fuson (Accelero 6 Vehcle Speed (Km/h) Tme Sequence (sec) Fgure. Estmeted speed usng INS/GPS fuson and compared wth OBD speed. Fg. shows clearly that the estmated speed s very close to true speed (measured from OBD). The estmated speed errors are n the range (-6, 5.5) km/hr and r.m.s. error = 1.84 km/hr. Hence combnaton of F-B speed and F-speed offers 5% mprovement over standard INS/GPS fuson. VI. CONCLUSION The usage of Smartphones n large scale sensor deployment and analyss s ganng promnence. Phone based sensors lke accelerometers & GPS offer an attractve opportunty to deploy vehcle trackng solutons; however, such solutons are affected by the professed lack of measurement accuracy as compared to professonal grade unts. A GPS based speed estmaton method requres hgh samplng rate, to obtan accuracy. Thus, for a typcal long duraton vehcle trp, the power consumpton wll be heavy. Accelerometer based speed estmaton can become a much preferred method provded the sensor errors are properly compensated for. In ths paper, we attempt to analyze a few categores of smartphones (as sensor & computaton unts) from the perspectve of nose. Further, we apply an nnovatve fuson algorthm to get a much better estmate of vehcle speed usng prmarly accelerometer measurements. Further tests are requred to valdate the proposed approach by fusng GPS measurements at stll lower samplng rate. It s envsaged that wth ncreasng estmaton accuracy, the applcaton of mult-sensor fuson n autonomous vehcles wll be greatly enhanced REFERENCES [1] M. S. Grewal, L. R. Well and A. P. Andrews, Global Postonng Systems, Inertal Navgaton and Integraton, nd Ed., Wley- Interscence, 7, New Jersey [] V. Gupta, Vehcle Localzaton usng low-accuracy GPS, IMU and Map Aded vson, Doctoral Thess. The Pennsylvana State Unversty, 9. [3] R. D. Martn, GPS/INS sensng coordnaton for vehcle state dentfcaton and road grade postonng. Doctoral thess. The Pennsylvana State Unversty, 6. [4] T.Chakravarty, A. Ghose, C. Bhaumk & A. Chowdhury, MobDrveScore-A system for moble sensor based drvng analys: a rsk assessment model for mprovng one s drvng, Sensng Technology (ICST), 13, 7 th Intl. Conf. on, pp [5] T. Toledo, O. Muscant, and T. Lotan. In-vehcle data recorders for montorng and feedback on drvers behavor. Transportaton Research Part C: Emergng Technologes, 16(3): 331, 8. [6] A. Ghose, P. Bswas, C. Bhaumk, M. Sharma, A. Pal, and A. Jha, Road condton montorng and alert applcaton: Usng n-vehcle smartphone as nternet-connected sensor, In Pervasve Computng and Communcatons Workshops (PERCOM Workshops), 1 IEEE Internatonal Conference on, pages , 1. [7] J. H. Hong, B. Margnes, A. K. Dey, A Smartphone-based Sensng Platform to Model Aggressve Drvng Behavors, ACM Conf. Human-Computer Interacton (CHI), Aprl 14, Toronto Canada. [8] R. Vaana, T. Iuele, V. Astarta, M. V. Caruso1, A. Tasstan, C. Zaffno & V. P. Gofrè, Drvng Behavor and Traffc Safety: An Acceleraton-Based Safety Evaluaton Procedure for Smartphones, Modern Appled Scence; Vol. 8, No. 1; 14, pp [9] J. O. Woodman, "An ntroducton to nertal navgaton." Unversty of Cambrdge, Computer Laboratory, Tech. Rep. UCAMCL-TR (7): pdf [] X. Zhang, Y. L, P. Mumford, C. Rzos, Allan Varance Analyss on Error Characters of MEMS Inertal Sensors for an FPGA-based GPS/INS System, Proceedngs of the Internatonal Symposum on GPS/GNNS. 8. [11] 446