comparison of gps and mems support for smartphone...
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Comparison of GPS and MEMS Support forSmartphone-Based Driver Behavior Monitoring
Frederick J. Bruwer, Marthinus J. BooysenDepartment of Electrical and Electronic Engineering
Stellenbosch UniversityStellenbosch, South Africa, 7600
Email: [email protected], [email protected],
AbstractβSmartphone-based driver monitoring and otherforms of smartphone-based telematics are fast becoming aprevalent trend, especially in the vehicle insurance industry.Choosing the most appropriate sensor system is a pivotal aspectof any driver behavior monitoring system. This paper evaluatesthe performance of the two sensor systems for smartphone-baseddriver behavior monitoring and telematicsβ GPS and MEMS β interms of the usefulness of data that can be collected for detectingand classifying driving maneuvers as well as the convenienceof use and the effect on battery life. Comparisons are done interms of selected Figures of Merit (FoM) that are commonlyemployed as metrics for classifying driving style. The resultsof comprehensive testing show that the MEMS inertial sensorsoutperform a GPS platform in terms of sampling rate, batterylife and the accuracy with which acceleration, braking, swervingand cornering can be detected.
I. INTRODUCTION
Vehicle Monitoring and Telematics (VMT) is a rapidlygrowing field of interest, especially in the vehicle insuranceindustry. In recent years, various studies have been doneconcerning the migration of VMT from dedicated hardwareto smartphone-based platforms [1]β[3]. The results have beenpromising and smartphone-based VMT (SBVMT) has beenemployed by various automotive insurance companies [4], [5].
One problem inherent to SBVMT, is the sensing platformbeing under the userβs full control and can only be activated bythe user when it is convenient. Various insurance companiesentice users to activate the application by providing incentivesin the form of discounts on monthly premiums and pointssystems that βgameifyβ safe driving [6], [7]. Despite theseefforts, users still use their own discretion to weigh the benefitand inconvenience of activating a SBVMT application. It istherefore important to make these applications as convenient,unobtrusive and transparent as possible. Applications thatrequire a fixed orientation within the vehicle, or consumeexcessive battery power should therefore be avoided, whichadds complexity to the application. Further studies show thatthe accuracy of the information gathered and the concludingfeedback to a driver has a notable effect on a userβs confidencein a system [8]. This further emphasises the need for anaccurate sensing platform.
The options for collecting the information necessary forVMT are essentially limited to GPS and processed data from
various Micro-Electromechanical Systems (MEMS) includinginertial measurement units (IMU) such as gyroscopes andaccelerometers.
A. Contribution
This paper evaluates the performance of the two optionsfor SBVMT β GPS and MEMS β in terms of the usefulnessof data that can be collected for detecting and classifyingdriving maneuvers (with specific relevance to reckless drivingdetection) as well as the convenience of use and the effecton battery life. A novel combination of methods for usingMEMS to estimate the Figures of Merit (FoM) suggestedby Handel et al. are proposed and compared to GPS-basedmethods performing the same estimations [8].
The rest of this paper is organized as follows: Section IIprovides an overview of the literature and state of the artconcerning SBVMT, including a summary of the methodsused, the pros and cons of the two sensor types and a review ofthe best practices to be observed when using MEMS sensorsin this field. Section III describes the testing platform, testscenarios and the specific parameters that will be qualitativelycompared. Section III outlines the results of the tests done andsection V provides the concluding remarks and plans regardingfuture work.
II. STATE OF THE ART
Modern smartphones, despite their widely varying features,typically share a set of standard characteristics that makethem particularly useful for driver and vehicle monitoring.They are battery powered, ubiquitous, permanently connectibleto the Internet, allow effortless acquisition and installationof software through βapp storesβ and provide a platform toacquire GPS and other sensor data. In recent years, the adventof compact and energy efficient MEMS has paved the wayfor smartphones to be equipped with an increasingly diverse,accurate and efficient array of sensors for sensing rotation,acceleration, magnetic field strength, barometric pressure, etc[9]. These sensors have given smartphones the ability to inferlarge amounts of information concerning their immediate andnon-immediate environments.
The Android operating system further facilitates the ex-ploitation of this data by utilizing proprietary algorithms thatprovide βvirtualβ- or βsyntheticβsensors. These sensors include
2015 IEEE Symposium Series on Computational Intelligence
978-1-4799-7560-0/15 $31.00 Β© 2015 IEEE
DOI 10.1109/SSCI.2015.71
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TABLE ISUMMARY OF TECHNIQUES AND SENSORS USED BY SMARTPHONE-BASED
VEHICLE MONITORING SYSTEMS.
Reference Detection technique Sensors usedMohan[1]
pattern matching, orienta-tion calibration
accelerometer, microphone,GPS
Dai [12] pattern matching, orienta-tion calibration accelerometer, gyroscope
Johnson[13]
endpoint detection, dy-namic time warping
accelerometer, gyroscope,magnetometer, GPS
Eren [14]endpoint detection,dynamic time warping,Bayesian classifier
accelerometer, gyroscope,magnetometer
Fazeen[15] pattern recognition accelerometer, GPS
White[16] pattern matching accelerometer, microphone,
GPSWahlstrom[3]
theoretical tire slip thresh-old detection GPS
Handel[8]
multiple figures of merit,threshold detection GPS
Castignani[2] fuzzy logic GPS, accelerometer, magne-
tometer, weather, time of day
(From Android version 2.3 onward): the βLinear Accelerationβsensor, which provides an estimation of the phoneβs acceler-ation with the effect of gravity removed and the βRotationVectorβ sensor, which estimates the rotation of the smartphonerelative to the Earthβs frame of reference, using a combinationof the accelerometer, magnetometer and gyroscope. Thesesynthetic sensors have various limitations for proper operation.The Linear Acceleration sensor, for example, does not functionreliably when the deviceβs orientation changes and the RotationVector sensor is inaccurate when the device is accelerated[10]. Due to their limitations, only the yaw component of theRotation Vector will be considered in this paper, as it operatesindependent of the effects of gravity.
As VMT is such a burgeoning field of study, many initialsystems already exist and compete for market share. Thesesystems achieve monitoring using a variety of sensors, algo-rithms and platforms. The smartphone-based platform can beconsidered the βnew kid on the blockβ, providing numerousadvantages over other hardware platforms as discussed by En-gelbrecht et al. [11]. In this paper, only the relevant smartphonebased systems will be considered.
Despite the variety of methods and sensor combinationsused by the systems listed in table I, only Dai and Eren etal. attempts a system that detects and characterizes drivingevents or driver behavior using only inertial sensors [12], [14].In many cases, a fusion of GPS and Inertial sensor values areused [13], [15]. The use of GPS positioning, however, presentsa few significant obstacles that are not experienced when usinginertial sensors:
1) The sample rate of un-augmented smartphone-basedGPS is at best about 1Hz, which is too slow to detectand classify certain maneuvers accurately, compared toinertial sensors that have update-rates in the order of100Hz.
2) GPS has a high energy consumption. Due to the slow
(50 bps) data throughput of the GPS-system, GPS-antennas are kept active for longer periods than high-speed GSM-antennas. This is contrary to the prevalentobjective of reducing smartphone battery drain wherehigh speed communications are used and the antennasand processor are deactivated periodically to reduce en-ergy consumption. [17]. GPSs average power drain whilesampling at 1Hz is close to 370mW, while the averagepower consumption of sampling three MEMS sensors(gyroscope, accelerometer, magnetometer) at 100Hz iscloser to 60mW (refer to table IV).
3) Un-augmented GPS readings have inaccuracies.Smartphone-based GPS location data is accurateto around 18m, a figure that can increase duringovercast conditions [18]. This considerably reduces theusefulness of GPS-data for characterizing small drivingmaneuvers.
4) Reception of GPS-signal is often inconsistent. Tunnels,forests, high-buildings and incorrect placement withina vehicle can all cause a GPS-device to lose its loca-tional fix. In contrast, inertial sensors are entirely self-contained.
5) Initial acquisition of locational fix can take up to 12minutes (cold start, no A-GPS). This time is drasticallyreduced by Assisted-GPS (A-GPS) technology, but A-GPS requires cellular data, which is not always avail-able and can incur additional data charges. In contrast,MEMS sensors can be sampled on-demand at any time.
The disadvantages of smartphone-based GPS listed in theabove list will be verified in section III-B.
A. Best Practices
Owing to the nature of MEMS sensors, there are some bestpractices to observe when developing a system based on them.
1) Calibration: MEMS accelerometers are not perfect andcan be a scale factor off from the acceleration they measure.Gravity provides an excellent baseline (9.81m.sβ2) withwhich to compare the sensor data and to adjust it accordingly.Gravity also provides a significant problem, as it cannot bedistinguished from vehicle acceleration. This wreaks havocwith inertial navigation algorithms and generally causesincorrect results. Furthermore, as the smartphone is mobile,its orientation is not necessarily known or fixed withinthe vehicle. Bruwer et al. details a method for removinggravitational acceleration from a mobile accelerometer withina vehicle and aligning the sensor axes with the vehicleaxes using an unscented Kalman filter and quaternionmathematics [19]. This system, however, only supports aonce-of calibration of the orientation of the smartphonerelative to the vehicle during initialization. As the smartphonecan be moved within the vehicle at any time, the system mustconstantly be monitored for a smartphone movement withinthe vehicle. This can be done using the MEMS gyroscope, asthe rotation rate of a phone being moved by a person within avehicle is considerably higher than what can be experienced
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z
x
y
zβ²
xβ²
yβ²
lateral
longitu-dinal
Fig. 1. Smartphone and vehicle coordinate system.
by the vehicle itself.For the sake of simplicity during comparisons in this paper,the smartphone is fixed and aligned with the vehicle axes asshown in figure 1.
Raw MEMS data recorded within a vehicle is often noisydue to a combination of engine and road vibrations. Enginevibrations occur at around 14Hz, and road vibration can beanything from 10 to 100Hz. Vehicle maneuvers are typicallymuch lower frequency, since their durations tend to be in theorder of seconds. It can therefore be useful to apply a low passfilter (LPF) to accelerometer and gyroscope data to remove thebulk of the noise. Furthermore, because Android is not a realtime operating system, sensor sampling often does not havethe highest priority in the scheduling system, which leads tovarying sampling frequencies. All data collected must thusin some way be synchronised with respect to their sampletimestamps to avoid drift.
III. EXPERIMENTAL SETUP
In this section, the testing platform and proposed tests arediscussed in detail.
A. Testing Platform:
A smartphone based logging application was developed torecord and store the test data. The application was developedfor the Android operating system (API 18 or newer). The ap-plication allows the simultaneous logging of any combinationof the following sensors to the host-phoneβs memory card:Raw MEMS sensors:β’ Accelerometerβ’ Gyroscopeβ’ Magnetometer
Synthetic or virtual android sensors:β’ Linear Accelerationβ’ Gravityβ’ Rotation Vector
GPS data:β’ Latitudeβ’ Longitudeβ’ Speedβ’ Heading
Battery information (API 21 or later):β’ Instantaneous Current Drawβ’ Average Current Draw
TABLE IISENSOR DATA RECEIVED FROM ANDROID API.
MEMS SensorsAccelerometer:(m.sβ2)
Lateralacceleration(ax)
Longitudinalacceleration(ay)
Verticalacceleration in-cluding gravity(az)
Gyroscope:(Rad.sβ1)
Pitch rate(gx) Roll rate (gy) Yaw rate(gz)
Magnetometer:(Β΅T )
x-axismagneticfield strength(mx)
y-axismagneticfield strength(my)
z-axismagnetic fieldstrength (mz)
Rotation Vector: (Synthetic sensor calculated from MEMS sensor data).x-axis Rotationcomponent qx(xΓ sin(ΞΈ) )
y-axis Rotationcomponent qy(y Γ sin(ΞΈ))
z-axis Rotationcomponentqz(zΓ sin(ΞΈ))
Scalarcomponentqw(cos(ΞΈ))
Global Positioning SystemSpeed(v inm.sβ1)
Heading (h indeg)
Latitude(Cla
in deg)Longitude(Clo
in deg)
The information returned by the GPS and MEMS sensorsrespectively are summarized in table II. Note that these de-scriptions are only applicable if the smartphone is aligned withthe vehicle axes as shown in figure 1 and as discussed in II-A.
The post-processing of sensor data was done using the Rstatistical language. All post-processing was done to emulatethe processing of live data on the smartphone. Therefore, onlycausal filters are applied and data is processed sample bysample.
The Samsung Galaxy S4 smartphone is used as hardwareplatform.
B. Proposed tests
The usefulness of the data for reckless driving detection isevaluated by recording a predefined set of maneuvers with thesmartphone secured in a fixed orientation within the vehicle, sothe phoneβs axes coincide with the vehicleβs axes as illustratedin figure 1. The datasets from the GPS and MEMS arecompared and evaluated with regards to the amount of - andthe accuracy of the information that can be extracted.
To perform this comparison quantitatively, a common set ofvariables that can be used to detect and characterize maneuversmust be generated by both the GPS and MEMS sensors.
As there are multiple ways of classifying reckless driving,there are also various types of data that can be used to do so.Handel et al. identified a set of 12 Figures of Merit (FoMs)and classified them in terms of observability, event stationarity,actuarial relevance, and driver influence [8]. Observability isdefined as the accuracy with which the FoM can be recordedusing GPS, stationarity evaluates for how long a time framethe FoM retains its observability, driver influence qualifies towhat extent the driver has the ability to change the FoM andactuarial relevance reflects the amount of risk caused by theFoM.
Table III shows the characterization of selected FoMs:These FoMs in addition to battery drain and sampling rate
can serve as basis for a comparison of the two systems. The
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TABLE IIICHARACTERIZATION OF FOMS IN INSURANCE TELEMATICS WHEN
CALCULATED USING GNSS-DATA. [8]
FoM Observability Stationarity Driver-Influence
ActuarialRele-vance
Acceleration Medium Low High MediumBraking Medium Low Medium HighSpeeding(Absolute) High High High Medium
Speeding(Relative) Medium High High High
Swerving Low Low Medium LowCornering Medium Medium High MediumLocation High High Low Medium
test setup for each comparison is discussed in the remainderof this section.
1) Battery Drain: To verify the statistics on battery drain,the time it takes for the application to drain a full battery whilelogging GPS-data, logging MEMS data and idle is recorded.All logging is done at maximum sample rate. The screen iskept on for monitoring purposes. The battery drain (in mA)can then be calculated as shown in equation 1.
Iavg =Capacity(mAh)
DrainT ime(h)(1)
2) Sample Rate: Statistics on the sample rate and variancein sample rate of the various sensors are obtained from loggeddriving data.
3) Acceleration: The acceleration FoM is defined byHandel et al. [8] as: βThe number of rapid acceleration eventsand their harshness.β
The positive y-axis value (ay) of the MEMS-accelerometerβsreading indicates longitudinal acceleration. To obtain acceler-ation from the GPS-data, however, the velocity measurementmust be differentiated as shown in equation 2. When thisacceleration exceeds a certain threshold it can be counted asa harsh acceleration. The harshness of the acceleration can bequantified by the magnitude of the acceleration.
a(t) =(v(t) β v(tβ βt))
βt(2)
4) Braking: A similar approach to the one used for the ac-celeration test(III-B3) can be employed here, but the negativey-axis acceleration, βay will be used and compared to thedifferentiated and negated GPS speed.
5) Speeding (absolute): The smartphone-based GPSprovides a location which is typically accurate to withinabout 18 meters [18]. However it also provides a scalar speedaccurate to within 2m.sβ1 calculated with the aid of theDoppler shift in received signals [20]. To estimate the speedof the vehicle using inertial sensors, three different methodsare used in this paper.
a) Integration: Estimating the speed of a vehicle acceler-ating or decelerating in a straight line is done by using equation3.
vest(t) = v(tβ βt) + ay(t) Γ βt (3)
b) Turn speed estimation: When the vehicle is in a turnthe speed can be estimated by using the formula in equation4. Therefore:
vest(t) = ax(t)/gz(t) (4)
If the vertical axis acceleration (az) is below a predefinedthreshold for a number of consecutive samples, indicating alack of road generated vibrations, the vehicle can be assumedto be stationary (vest = 0). The threshold and the numberof samples necessary to avoid false positives is determinedempirically in Section IV.
c) Road irregularity autocorrelation: A final method fordetermining speed using inertial sensors requires a singleGPS velocity reading per vehicle as calibration method. Asdemonstrated by the SenSpeed system developed by Hun etal. A vehicle passing over a road irregularity, such as a speedbump or reflective road studs creates a disturbance in the z-axis acceleration for each wheel passing over the irregularity.If the time between these disturbances ( βtw) is calculatedand the Wheel Base (WB) of the vehicle is known, the speedcan be calculated using equation 5.
v(t) =WB
βtw(5)
The discrete autocorrelation of the z-axis acceleration datacan yield the time between disturbances, as the z-axis accel-eration signature is similar for both wheels.
The wheelbase can be requested from the user, but thisis inconvenient as the wheelbase of their vehicle is notcommon knowledge for most users. Instead, it is proposedthat the system be calibrated by using the GPS speed until aaccurate wheelbase length can be estimated using the reverseof equation 5.
If the detection of speeding is deemed a necessity and theaccuracy of the speed estimated using the inertial sensors isinsufficient, this speed can be used as a trigger, to requesta more accurate GPS-based speed when within a certainthreshold of the maximum legal speed limit. This thresholdcan be determined by quantifying the typical accuracy of theinertial speed estimation.
6) Speeding (relative): To determine if a vehicle is speed-ing, relative to the applicable speed limit in his location. Theroad on which the vehicle is driving must be identified andan external map database with updated speed limit for theapplicable road must be consulted. This typically requiresconstant and fine GPS positioning.
Another method proposed to determine the local speedlimit is a combination of the speed estimation done in sectionIII-B5, a digital speed limit database (an example of a freecommunity-driven one is Wikispeedia [21]) and Geo-fencing.
Geo-fencing is a method of setting a digital perimeterof a specified radius around a specified point and monitoringwhether a device is within or outside of the perimeter. Thismethod of providing location awareness is useful as it allowsthe phone to only use energy consuming GPS-positioning
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when the accuracy is required, when possible more energy-efficient positioning such as, cellular tower triangulation orWiFi-positioning can be used.
In an embodiment of this method, an application can bedesigned to, initially, obtain a fine GPS-location fix and querythe speed limit database to find the current speed limit and theclosest different speed limit. A Geo-fence can now be definedwith a radius equal to the distance to the nearest change inspeed limit. Once the perimeter is crossed, this process canbe repeated, thereby insuring the minimum amount of GPSusage.
The inertial navigation system (INS) discussed in sectionIII-B9 could also be used instead of Andriodβs built in Geo-fencing API.The testing of this method is beyond the scope ofthis paper. The legal aspects of this form of reckless drivingdetection requires further study and anonymous participationdata for testing.
7) Swerving: Swerving is generally defined as βcausingto change direction abruptlyβ. To quantify swerving one canrecord the number of swerves and their harshness. Swervingtypically happens when trying to avoid an object in the pathof the vehicle, performing abrupt lane changes or makingcoarse course corrections. These maneuvers are exceedinglyimportant to detect and classify as they are effective indicatorsof drunk-, fatigued-, distracted- and aggressive driving [12],[13], [22].
Using Inertial sensors, this is easy to identify as a briefspike in either lateral acceleration (ax) or yaw rate(gz), themagnitude of the lateral acceleration is an effective indicatorof the harshness of the swerve as a higher lateral accelerationequates to a higher probability of the vehicle skidding orrolling.
Identifying a swerve via GPS is more challenging. Theyaw rate as shown in equation 6 and the lateral accelerationof equation 7 can be estimated from GPS parameters. Asswerving is often a very brief event and the change ofdirection is typically corrected almost instantly to coincidewith the original heading, GPS, due to its 1Hz update rate,will seldom be able to identify a brief swerve event, muchless the harshness of it.
gz(t) β (h(t) β h(tβ 1))
βt(6)
ax(t) β v(t) Γ sin(h(t) β h(tβ 1))
βt(7)
8) Cornering: The definition used for cornering will, inthis paper, differ from the one given by Handel et al. Handelet al. describes the cornering FoM as: βThe number of eventswhen turning at too high speed and their harshnessβ. As shownby Zeeman et al. and Wahlstrβom et al. [3], [23], the twomain dangers of harsh cornering are tire slip and rollover,both of which are indicated by a large lateral acceleration.The definition of harsh cornering for this paper will therefore
be defined as: βThe number of events when turning above apredefined lateral acceleration threshold and their harshnessβ
Wahlstrβom et al. [3] proposes a method for extrapolatingturn harshness from GPS data. Their method involves aKalman filter algorithm applied to the parameters of the GPSto continuously update an estimate of the ratio between thenormal and horizontal force on the vehicleβs tires. This ratiodetermines the threshold at which the vehicle will slip. Despitethe large amount of processing done on the GPS data, theamount of missed detections and false alarms summed toapproximately 40% of the total number of cornering events.
As with swerving, cornering events and their harshness caneasily be deduced from inertial sensor readings. An extendedincrease in lateral acceleration (ax) and yaw rate (gz) indicatesa cornering event, and the magnitude of the lateral acceleration(ax) is proportional to the harshness of the cornering event.
9) Location: Location data is useful in a SBVMT systemfor three reasons. Firstly, certain geographical areas can beflagged for a higher rate of accidents and thereby increasingthe risk of driving there, secondly, the location of the vehiclecan be useful to transmit for telematics purposes and remotemonitoring and finally, the location of an event on a map is auseful way of providing post-driving feedback to a driver.
A simple and computationally efficient inertial navigationalgorithm is developed below to obtain the 2-dimensionalCartesian coordinate position, heading and speed of the vehiclefrom the Accelerometer, Magnetometer and Gyroscope data.
The inertial navigation algorithm proposed here is based onthe following basic methods, and the algorithms are deliber-ately chosen to be as simple as possible for the purpose ofcomputational efficiency. Heading can be estimated by equa-tion 8 and, if the magnetometer has been deemed calibrated,the proprietary Android rotation vector synthetic sensor canbe used to calculate the heading.
hest(t) = h(tβ βt) + gz(t) Γ βt (8)
Where hest is the estimated heading and βt is the samplingperiod.
hest(t) = atan2(2ΓqyΓqwβ2ΓqxΓqz, 1β2Γq2yβ2Γq2z)(9)
To calculate the coordinate position from MEMS sensordata, an initial point must be defined as the start of the event,the origin (0,0) is defined as the starting point. Given thestarting coordinate C(0) = (Cla(0), Clo(0)) = (0, 0) Thenext coordinate can be calculated as shown in equations 10and 11:
Cla(est)(t) = Cla(est)(tβ βt) + vest(t) Γ βtΓ cos(hest(t))(10)
Clo(est)(t) = Clo(est)(tβ βt) + vest(t) Γ βtΓ sin(hest(t))(11)
The coordinates estimated by equations 10 and 11 are, incontrast to the GPS measurements, in meters, relative to thestart of the event and not in decimal degrees relative to thePrime Meridian at the equator.
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TABLE IVRESULTS OF TESTS ON BATTERY DRAIN FOR THREE MEMS SENSORS
VERSUS GPS.
Idle GPS MEMSDrain time (hh:mm:ss) 04:56:25 04:08:39 04:47:26Current draw (mA) 526 627 542Relative current draw - 101.08 16.44
Histogram Of MEMS Sampling Times
Time(ms)
De
nsity
6 8 10 12 14
0.0
0.1
0.2
0.3
0.4
0.5
Fig. 2. A histogram of the MEMS-sensorsβ sampling period.
For the sake of comparison, the initial GPS coordinatesC(0) are subtracted from each subsequent GPS coordinateand multiplied by an estimation of the earthβs radius at thatposition (6370Γ103m at β33 deg latitude), thereby recordingthe coordinates in meters relative to the origin or C(0).
IV. EXPERIMENTAL RESULTS
In this section, the result of the comparisons between thevarious aspects of GPS and MEMS systems for SBVMTare shown. Quantitative comparisons are done if possible,otherwise, the methods are compared qualitatively in termsof accuracy.
A. Battery Drain
Table IV summarizes the battery drain test statistics for theSamsung Galaxy S4 with a 2600mAh battery:
The current drawn by GPS is therefore more than 5 timesthat of the MEMS sensors.
B. Sample Rate
The highest possible sample rate of the GPS is 1Hz (Ts =1s), while the MEMS sensors are around 100Hz (Ts = 0.01s).This is a significant advantage for the MEMS sensors. Theconsistency of the sample rate is also important however, andhere the MEMS sensors have a slight variation in samplingperiod. Figure 2 shows a histogram of the MEMS samplingperiods.
The GPS is within 10% of its correct sampling period99.81% of the time, while the MEMS-sensors are within 10%of their correct sampling period 88.81% of the time.
C. Acceleration
Figure 3 shows the acceleration of the vehicle over a 25second interval. It is clear that, despite the similarities inacceleration magnitude, the GPS cannot capture the higherfrequency acceleration events. The filtered accelerometer data
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Fig. 3. A plot of the vehicleβs acceleration over a 25 second interval.
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Fig. 4. A plot of the vehicleβs deceleration over a 22 second interval.
shows the higher peak accelerations, that the 1Hz differentiatedGPS-speed fails to detect. From the figure, the gear shifts arealso clearly visible at 4, 10 and 18 seconds. The GPS-data alsohas a delay with respect to the acceleration. Though the erroris small over the long term, the detection of sharp accelerationsand gear shifts are useful for SBVMT and the MEMS-sensorsclearly perform much better.
D. Braking
Figure 4 shows three minor vehicle deceleration events.Similar to the results with acceleration, the GPS cannot recordthe sharp accelerations as effectively as the MEMS sensors,though the average acceleration over the period is similar forboth systems.
E. Speeding(Absolute)
The speed of a GPS is typically accurate to within 2m.sβ1,therefore, in this test, the GPS speed will be used as abenchmark to quantify the accuracy of the speed estimatedwith MEMS. Figure 5 shows the speed estimated by MEMSsensors via accelerometer integration (III-B5a) and turn speedcalculation (III-B5b). This sample has been chosen to illustratethe drift in estimation when there are no fixed reference speedsto work with. The large error in this sample is caused bya variation in road incline, conflicting with the assumptionthat tests are carried out on a level surface. The slight inclinechange causes the accelerometer to measure a component ofthe earthβs gravitational acceleration, thereby causing a driftin the speed estimation. The effect of gravity can be mitigatedusing the methods discussed in II-A. The turn speed estimationwas found to be accurate only for turns with a high yawrate, where the integrated speed can then be corrected. Thosecorrections are shown in green in figure 5. The other method
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ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
0 100 200 300 400
01
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MEMS and GPSβ speed vs time
Time (s)
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GPS MEMS MEMS Turn Speed
Fig. 5. A plot of the speed of a vehicle, estimated via MEMS integration(Red), MEMS turn speed estimation (Green) and GPS-Speed (Blue)
Fig. 6. An extract from a plot of the z-axis (vertical) acceleration measurementversus time. The two impulses in the extract represent the front and rear wheelsrespectively impacting with a speed bump.
for estimating speed through autocorrelation of the z-axisacceleration was found to perform well at low speeds of up to40 km/h. Figure 6 shows a sharp z-axis acceleration caused bydriving over a speed-bump at 20km/h. The two spikes wherethe front and rear wheels hit the bump are clearly visible. Forthis case, the autocorrelation of the extracted data had a localmaximum at 490ms. The vehicle in consideration has a wheelbase of 2.6m, which in turn gives an estimated speed of 19.1km/h while the GPS speed at that point in time is 21.38 km/h.
F. Swerving
As shown by figure 7, the MEMS sensors excel at detectingthe brief lateral accelerations and rotations associated withswerves. GPS, however lacks the update rate necessary fordetecting events shorter than two seconds.
G. Cornering
The lateral acceleration can be recorded directly by theMEMS sensors during cornering as shown in figure 7, avoidingthe necessity for calculating lateral acceleration. The im-plementation of an algorithm for acquiring accurate lateralacceleration data from GPS data is considered beyond thescope of this paper. Suffice it to say that, identifying and ratingthe harshness of cornering events is significantly easier andmore computationally efficient using MEMS than GPS.
H. Location
The comparison of the inertial navigation algorithm with theGPS data showed that, as was expected, integrated noise ofthe accelerometer and gyroscope measurements led to large
0 1 2 3 4 5 6
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Swerve Lateral Acceleration vs time β MEMS
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Swerve Yaw Rate vs time β MEMS
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Swerve Yaw Rate vs time β GPS
Time (s)
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ate
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es/s
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Fig. 7. A series of plots showing the lateral acceleration and yaw ratemeasured by the MEMS sensors and estimated by the GPS over a 7 secondperiod containing a brief lane change and a swerve around an object,respectively.
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ββββββββββββββββββββ
0 50 100 150
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MEMS and GPSβ speed vs time
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GPS MEMS MEMS Turn Speed
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
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Fig. 8. Three plots comparing the speed, heading and coordinates estimatedby the MEMS sensors and measured by the GPS.
errors over time. Furthermore, the assumption that all testswere done on level ground, allowed gravity to cause drift inthe speed as discussed in section II-A1. However, for singlemaneuvers or events, lasting less than a minute, the system didprove accurate at mapping the coordinates as long as the initialvelocity was accurate. Figure 8 shows the drift in speed andcoordinate position calculated by inertial navigation algorithm.
V. CONCLUSIONS
MEMS technology has enabled smartphone based sensorsto grow from strength to strength in recent years and theimprovement of their accuracy, efficiency and size show nosigns of slowing. The information provided by these sensorsare being thoroughly exploited by industries such as fitness,
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TABLE VA SUMMARY OF THE COMPARISON BETWEEN MEMS AND GPS METHODS.
Test: GPS: MEMS:Battery Drain (IV-A) 101.08 mA 16.44 mASample Rate (IV-B) 1 Hz 100 HzAcceleration (IV-C) Misses brief accelera-
tions3
Braking(IV-D)
Misses brief decelera-tions
3
Speeding (IV-E) 3 Inaccurate withoutreference points(turns, bumps)
Swerving (IV-F) 7 3Cornering (IV-G) Lateral Acceleration
requires complexalgorithms
3
Location (IV-H) 3 Only brief events
gaming and lifestyle. In this paper we considered ways toemploy MEMS-sensors instead of GPS in the field of SBVMT.The best practices when using MEMS-sensors were discussedwith reference to the current state of the art. The pros andcons of both systems were listed and then verified throughoutthe rest of the paper. Practical test setups were proposed tothoroughly evaluate and compare both systems in ways theywould typically be used to gather data for SBVMT. TableV provides a brief overview of the results of each test. It isclear from these tests, that MEMS-sensors outperform GPS invarious aspects of SBVMT including the detection of swervingas well as sudden accelerations and decelerations, but there areother areas where GPS is still indispensable, such as providinglocational data. Due to mostly to its lower power consumptionand its independence of unreliable external communicationsit is the view of the author that MEMS-sensors holds theadvantage for use in, for example, reckless driving detectionsystems.
A. Future work
Future work in this area will be focused on acquiringa large and representative set of data for testing purposes.Methods for removing the effect of gravity from readings anddistinguishing between vehicle motion and smartphone motionwithin the vehicle must be perfected. Different techniques forclassifying the MEMS data and detecting driving events willbe investigated, with the final goal of developing a complete,accurate and convenient smartphone based reckless drivingdetection system.
ACKNOWLEDGMENT
The authors would like to thank MiX Telematics and theSouthern African Transport Conference for their continuedfinancial support.
REFERENCES
[1] P. Mohan, V. N. Padmanabhan, and R. Ramjee, βNericell: rich mon-itoring of road and traffic conditions using mobile smartphones,β inProceedings of the 6th ACM conference on Embedded Network SensorSystems. ACM, 2008, pp. 323β336.
[2] G. Castignani, T. Derrmann, R. Frank, and T. Engel, βDriver behaviorprofiling using smartphones: A low-cost platform for driver monitoring,βIntelligent Transportation Systems Magazine, IEEE, vol. 7, no. 1, pp.91β102, Spring 2015.
[3] J. Wahlstrom, I. Skog, and P. Handel, βRisk assessment of vehiclecornering events in gnss data driven insurance telematics,β in IntelligentTransportation Systems (ITSC), 2014 IEEE 17th International Confer-ence on, Oct 2014, pp. 3132β3137.
[4] βDiscovery insure driving challenge,β https://www.discovery.co.za/portal/individual/insure-driving-challenge-campaign, (Visited on09/23/2015).
[5] βDriver feedback mobile app - state farm,β https://www.statefarm.com/customer-care/download-mobile-apps/driver-feedback, (Visited on07/12/2015).
[6] βCar insurance discounts for safer drivers - aviva drive - aviva,β http://www.aviva.co.uk/drive/, (Visited on 07/12/2015).
[7] C. Shi, H. J. Lee, J. Kurczal, and A. Lee, βRoutine driving infotainmentapp: Gamification of performance driving,β in Adjunct Proceedings ofthe 4th International Conference on Automotive User Interfaces andInteractive Vehicular Applications, 2012, pp. 181β183.
[8] P. Handel, I. Skog, J. Wahlstrom, F. Bonawiede, R. Welch, J. Ohlsson,and M. Ohlsson, βInsurance telematics: Opportunities and challengeswith the smartphone solution,β Intelligent Transportation Systems Mag-azine, IEEE, vol. 6, no. 4, pp. 57β70, winter 2014.
[9] Smartphones and tablets drive continued double-digit growthin mems motion sensor market. [Online]. Available: https://technology.ihs.com/421100/smartphones-and-tablets-drive-continued/double-digit-growth-in-mems/motion-sensor-market
[10] βNexus s and gingerbread sensor events which sensor uses whathardware ? - google groups,β https://groups.google.com/forum/#!topic/android-developers/GOm9yhTFZaM, (Visited on 07/12/2015).
[11] J. Engelbrecht, M. J. Booysen, G.-J. van Rooyen, and F. J. Bruwer,βSurvey of smartphone-based sensing in vehicles for intelligent trans-portation system applications,β IET Intelligent Transport Systems, 2015.
[12] J. Dai, J. Teng, X. Bai, Z. Shen, and D. Xuan, βMobile phone baseddrunk driving detection,β in 4th International Conference on PervasiveComputing Technologies for Healthcare (PervasiveHealth). IEEE, 2010,pp. 1β8.
[13] D. A. Johnson and M. M. Trivedi, βDriving style recognition using asmartphone as a sensor platform,β in 14th International Conference onIntelligent Transportation Systems (ITSC). IEEE, 2011, pp. 1609β1615.
[14] H. Eren, S. Makinist, E. Akin, and A. Yilmaz, βEstimating drivingbehavior by a smartphone,β in Intelligent Vehicles Symposium (IV).IEEE, 2012, pp. 234β239.
[15] M. Fazeen, B. Gozick, R. Dantu, M. Bhukhiya, and M. C. Gonzalez,βSafe driving using mobile phones,β IEEE Transactions on IntelligentTransportation Systems, vol. 13, no. 3, pp. 1462β1468, 2012.
[16] J. White, C. Thompson, H. Turner, B. Dougherty, and D. C. Schmidt,βWreckWatch: automatic traffic accident detection and notification withsmartphones,β Mobile Networks and Applications, vol. 16, no. 3, pp.285β303, 2011.
[17] βWhy gps eats so much battery power β itworld,β http://goo.gl/i5JyHu,(Visited on 07/12/2015).
[18] T. W. Jones, L. Marzen, and A. Chappelka, βHorizontal accuracy as-sessment of global positioning system data from common smartphones,βPapers in Applied Geography, vol. 1, no. 1, pp. 59β64, 2015.
[19] F. Bruwer, βVehicle acceleration estimation using smartphone-basedsensors,β in Proceedings of the 35th Annual Southern African TransportConference, 2015.
[20] T. Witte and A. Wilson, βAccuracy of non-differential gps for thedetermination of speed over ground,β Journal of biomechanics, vol. 37,no. 12, pp. 1891β1898, 2004.
[21] βMaps showing posted speed limits in usa cities and towns,β http://www.wikispeedia.org/, (Visited on 07/12/2015).
[22] T. A. Dingus, V. L. Neale, S. G. Klauer, A. D. Petersen, and R. J.Carroll, βThe development of a naturalistic data collection system toperform critical incident analysis: an investigation of safety and fatigueissues in long-haul trucking,β Accident Analysis & Prevention, vol. 38,no. 6, pp. 1127β1136, 2006.
[23] A. Zeeman and M. J. Booysen, βCombining speed and accelerationto detect reckless driving in the informal public transport industry,β inIntelligent Transportation Systems-(ITSC), 2013 16th International IEEEConference on. IEEE, 2013, pp. 756β761.
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