a novel approach to improve vehicle speed estimation using ... · – 10 sec.) is present in the x...

A Novel Approach To Improve Vehicle Speed

Estimation Using Smartphone’s INS/GPS Sensors

Arijit Chowdhury

TCS Innovation Labs

Tata Consultancy Services

Kolkata,India

[email protected]

Tapas Chakravarty TCS Innovation Labs

Tata Consultancy Services

Kolkata,India

tapas.chakravarty @tcs.com

P. Balamuralidhar Tata Consultancy Services

TCS Innovation Labs

Bangalore,India

[email protected]

Abstract—In recent times, number of researchers have

investigated vehicle tracking applications by fusing the

measurements done by accelerometers, as part of inertial

navigation system (INS), and GPS (Global Positioning System).

However, the sensors in recreational devices like mobile phone

have limitations in measurement accuracy and reliability.

Usually, sudden changes in vehicle speed are not always captured

well by GPS. Accelerometers, on the other hand, suffer from

multiple noise sources. In this paper, we investigate the noise

performance of accelerometers, available in a few smartphones.

Then, we apply the noise analysis for the purpose of estimating

the moving vehicle speed. A number of experiments were carried

out to capture the vehicle’s position & speed from OBD2, GPS as

well as 3-axes accelerometer. We demonstrate a method by which

the phone’s orientation is compensated for while calculating

speed from the measured acceleration. Further, a new method of

INS/GPS fusion is proposed which enhances the accuracy of

speed estimation. It is envisaged that with increasing estimation

accuracy, the application of multi-sensor fusion in autonomous

vehicles will be greatly enhanced

Keywords-component; GPS; Allan Variance; OBD2; speed

correction; accelerometer

I. INTRODUCTION

A vehicle navigational framework that combines GPS measurements and inertial navigation system (INS) are gaining much importance and is becoming an important field of study. The performance of low cost GPS receiver together with low cost INS (or alternatively, inertial measurement unit) is therefore very important from navigational perspective [1-2]. Detailed performance analyses of such generally available sensors are likely to throw up new approaches that will greatly enhance the estimation accuracy in futuristic vehicles including autonomous ones. Personally owned Smartphones are becoming the most popular choice in deploying sensors like accelerometers; gyroscopes etc. not only for the purpose of navigation but also for the purpose of introducing driving related applications. If personal phones can be utilized to accurately estimate the speed of the moving vehicles, new solutions can be introduced to serve the consumers better. Also such data can be used to send control signal for control and guidance of vehicle [3]. Accelerometers are generally used to identify aggressiveness in driving [4-5]. On the other hand,

Smartphones have an added advantage in being able to process the captured data and transmit them over communication network [6]. Two recent works on similar lines are related to the smartphone based sensing for identifying aggressive driving behavior [7-8]. Keeping the above stated synergy in mind, we decided to utilize the Smartphones and commercially available applications, to carry out extensive experiments in moving vehicles, for the purpose of investigating the accuracy and reliability of vehicle speed estimation. It is envisaged that an increased accuracy in estimating the vehicle speed under varying conditions, particularly for congested city drive, will make autonomous vehicles more reliable

In this paper, we propose an approach to mitigate the issue of estimating the true speed of a moving vehicle using primarily smartphone accelerometers. It is known that the accelerometers suffer from multiple noise effects. The noise level and the type may vary from phone to phone. In order to test the variability, authors have used Allan Variance method [9-10] to estimate and compensate for the noise present in accelerometers. Authors compare different smartphones for noise performance of their integrated accelerometers. After suitable compensation, the measured acceleration values are integrated to obtain the speed of the moving vehicle.

Further, a method of GPS and accelerometer data fusion is investigated for improving the accuracy of speed estimation. For such, GPS based measurements at 5sec interval are used to correct the speed estimation from acceleration measurements. A new method of forward and backward speed estimation is proposed. It is seen that the proposed approach significantly improves the speed estimation. For comparison purposes, we have utilized the OBD2 based speed measurement as the true measure of the vehicle speed.

II. ACCELEROMETER NOISE MEASUREMENT

In this section, the different types of noise errors impacting an accelerometer measurement are investigated. An important concern regarding the noise effect is that they impact the speed evaluating vide the integration process.

A. Constant bias

Offset of the output value from the true value is called bias of an accelerometer, in 2/ sm . A constant bias error of ε, when

Proceedings of the 8th International Conference on Sensing Technology, Sep. 2-4, 2014, Liverpool, UK

441

integrated to get speed, causes an error which grows proportionally with time.

The total error in speed estimation is e(t) = 0.5.ε.t, where t is the time of integration. [10]

B. White Noise / Velocity Random Walk

Accelerometer output generally contains some amount of white noise. Integration of the white noise produces a random walk with variance proportional to √t. Hence, white noise creates a velocity random walk [10]. This is measured in m/s/√s.

C. Rate Ramp

This is a deterministic error. Slow monotonic change of output over time is Rate ramp. It can be described as: w(t)=R.t , where R is the slope of the ramp. This creates a line of slope +1 in AD plot [9-10]. R is the value of Allan Deviation at time = √2.

Other errors are briefly summarized in table I.

TABLE I. SUMMARY OF DIFFERENT ERRORS

Error Type Description

Result of

Double

Integration

Temperature

Effects

Temperature dependent residual

bias

Any residual bias

causes an error in

speed which

grows linearly

with time

Calibration

Deterministic errors in scale

factors, alignments and

accelerometer linearities

Speed changes proportional to

the time rate and

duration of acceleration

Bias Instability Bias fluctuations, usually

modeled as a bias random walk

A second-order

random walk in

speed

III. ALLAN DEVIATION RESULTS FOR DIFFERENT PHONES

In this section we present the results on Allan variance method applied to different phones. These phones have different accelerometer makes; in addition, they may be embedded differently in each smartphone. Thus, the Allan variance method is applied on different phones to measure their noise characteristics.

Allan Variance is a time domain signal analysis technique that can be used on any signal to determine the character of noise in the system. Allan Variance is measured as a function of averaging time. Hence Allan variance calculation gives (t,AD(t)) pair where t = averaging time. AD(t) is the value of Allan deviation = √Allan variance. We mention briefly the technique to calculate AD [9-10].

1. Divide a sequence of data it into sequence of length t. There must be enough data for at least 10 such sequences.

2. The data in each bin is averaged to obtain a series of averages (a(t)1, a(t)2, ..., a(t)n), where n is the number of bins.

3. The Allan Variance is then calculated using (1)

2i1 i )a(t) - a(t)(

)1(*2

1)( ∑

−= +

intAVAR (1)

Allan Deviation, denoted by AD(t) is given in (2)

AVAR(t))()( == ttAD σ . (2)

Then in log-log scale plot of (t, AD(t)) different slope sections identifies different types of noise which are orthogonal in nature. After identifying a process it is possible to obtain its numerical parameters directly from the AD plot [9-10]. A typical plot of Allan deviation shows different errors in different zone of t. The slope of the line indicates type of noise and parameters of different noise can be computed from the AD curve. Value of different noise parameters can be calculated using table 2 of reference [10].

The error modeling, discussed as above, is now tested on different smartphones (iphone5, google nexus, LG nexus and Samsung note 2). Results and plot for these 4 types of smartphones are presented in fig. 2-5 and table II and III respectively.

Figure 1. Allan deviation plot for Samsung google nexus for all 3 axes

The analysis of the Samsung google nexus AD plot (as shown in figure 1) displays the presence of white noise for all three axes and additionally a bias instability for X axis. The value of white noise variance is the value at t = 1 on the approximate line with slope -1/2. Clearly for x, y, z axis the value of σ at t = 1 are 0.019, 0.018, 0.02 respectively. Hence, these are the standard deviation of white noises for the given axis. The values of different types of error coefficient can be calculated as indicated in table II. Only for the X axis, the Allan deviation curve shows a flat portion from t = 7 to 25s. Hence bias instability for X axis BX = 0.0065/0.664 = 0.0098

2/ sm .


442

Figure 2. Allan deviation plot for Samsung galaxy note 2.

For Samsung note 2, the Allan deviation plot is shown in figure 2. Bias instability (portion with slope = 0 in time zone 7 – 10 sec.) is present in the X axis only with value Bx =

0.0006/0.664 = 0.0009 2/ sm , which is 10 times smaller than

Samsung google nexus (refer figure 2). Thus, it is seen that the accelerometer performance in Samsung note 2 is better than Samsung google nexus phone. Similar comparisons can be made from Allan deviation plots to obtain noise characteristics and determine different noise coefficients (as listed in table III and 4).

Allan deviation plot for iPhone 5 is given in figure 3. The plot shows the presence of white noise and bias instability (flat region in the AD curve) on each the axis. The curve of Z-axial accelerometer in iphone plot (fig. 3) indicates a correlated noise and/or sinusoidal noise in time interval 10 – 36 s. All the noise parameters found with method described in this note using table II are summarized in table III.

Figure 3. Allan deviation plot for iPhone 5

AD curve for LG nexus in figure 4 shows presence of white noise for all 3 axis, bias instability for X axis only. Presence of Rate Ramp is observed only in case of LG nexus (figure 4) for Z axis in the region t= 5 – 40 s.( slope of AD curve in fig. 4 is +1 ) and measurement for this noise can be measured by fitting

a straight line through the slope and reading value at t = 2 .

Hence for that Rate ramp RZ = )2(σ = 0.0004 2// ssm .

White noise parameters for LG nexus are summarized in table III.

Figure 4. Allan deviation plot for LG nexus.

Now from the presented AD figures the white noise

parameter ( ssm // ) of these 4 phones are given in table II.

TABLE II. WHITE NOISE VARIANCE FOR DIFFERENT PHONES

Accelerometers x axis y axis z axis

GOOGLE NEXUS 0.019 0.018 0.02

IPHONE 5 0.0029 0.0031 0.003

LG NEXUS .002 .0018 .0031

NOTE 2 .0016 .0017 .0025

In table III bias instability (in 2/ sm ) for different phones is

consolidated.

TABLE III. BIAS INSTABILITY FOR DIFFERENT PHONES

Accelerometers x axis y axis z axis

GOOGLE NEXUS 0.0098 NA NA

IPHONE 5 0.0012 0.0012 0.0018

LG NEXUS .0012 NA NA

NOTE 2 .0009 NA NA


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TABLE IV. ACCELERATION MEASUREMENT AT STEADY STATE

IV. VELOCITY CALCULATION

Figure 5 displays the experimental set-up. In this case, the OBD2 based speed of vehicle is collected at 1 Hz sampling rate and the accelerations are also logged using the smartphone at 1Hz sampling rate. Along with these, the GPS data (position, speed) are logged at 5 s time gap (0.2 Hz). The speed calculation method, using both accelerometers and GPS data is outlined in subsequent sections. The data are collected using Kiwi Bluetooth OBD2 device [11], Samsung Note 2 and Torque application. The accelerometer readings are calibrated to eliminate errors mentioned in table II and III.

A. Acceleration integration method

Trapezoid rule is used to integrate samples of acceleration to obtain speed given a current speed. Let the consecutive

samples for accelerations be ,...,, 321 aaa and the speed

samples are given by ,...,, 321 vvv Then we compute

intermediate speeds as given in (3).

11 vv =)

)(5.0 11 iiii aavv ++= −−

)) (3)

Results obtained using that are shown in details in results section.

Figure 5. Photograph of the experimental set-up displaying Bluetooth

OBDII device and Tab as data logger

V. RESULTS

In this section, we present results of the application of INS/GPS fusion in vehicle navigation. Fig. 6 presents accelerometer data collected in steady state from the phone, with car at rest (but engine was kept on). One can see from fig. 6 that the longitudinal acceleration has a mean acceleration of approximately 1.03 m/s

2. This indicates that the phone

mounting is not perfectly vertical. We measured this phenomenon for all the rest periods in a given trip. The same is presented in table IV.

Time Sequence (sec)

0 5 10 15 20 25 30 35 40 45 50

Accele

ration

(m

/s2)

0.2

0.6

1.0

1.4

8.4

8.8

9.2

9.6

10.0

Vertical Acceleration

Longitudinal Acceleration

Figure 6. Longitudinal & vertical accelerations for vehicle at rest (engine

kept running)

In table IV, the tilt angle of the phone in the Y-Z plane is calculated for three instances of measurement. (the vehicle is moving along Y-axis in the X-Y plane and vertical acceleration is along Z axis). Tilt angle is the rotation relative to phone orientation. Then from the trip data we calibrate the measured acceleration to get longitudinal acceleration using (4).

b - )sin( * θii acca = (4)

Where, the tilt angle is θ and fixed bias is b. In our case 06≅θ and b = 0.11. Thus we perform tilt adjustment on

acquired data to get actual forward acceleration.

Time

(sec)

Lateral Acceleration

(m/s2)

Vertical Acceleration

(m/s2)

Longitudinal

Acceleration (m/s2)

Calibrated Longitudinal

Acceleration (m/s2)

Tilt Angle (in

Y-Z plane) in

deg

µ σ µ σ Μ σ µ Σ

47 -0.0169 0.4921 9.2666 0.33213 1.0389 0.2223 0.11025 0.0232 6.08

73 -0.2061 0.6679 9.3141 0.35055 0.9583 0.2530 0.09362 0.0247 5.61

103 0.03914 0.1808 9.2722 0.17347 0.9759 0.3922 0.09710 0.0390 5.71


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From the calibrated longitudinal acceleration, we calculate the vehicle speed using (3). Fig. 7 shows the plot of OBD speed data with the computed speed for approx. 3 min. interval. It is seen that the computed speed diverges from true speed as time progresses. This is indicated by Allan variance analysis also. The result depicted by fig. 7 is a known phenomenon and that is why, in many cases, accelerometer data is fused with intermittent GPS measurements as a measure of error correction. In our case, available GPS measurement at 5s interval can be utilized. To make fusion of accelerometer data with GPS we need to correct vehicle speed found using the integration (3).

Time Sequence (sec)

0 20 40 60 80 100 120 140 160 180 200

Ve

hic

le S

pe

ed

(K

m/h

)

0

10

20

30

40

50

60

70

OBD II measurement

Derived from Accelerometer (longitudinal)

Figure 7. Computed speed from (3) with corresponding GPS and OBD

speed..

At every 5 s time interval, we correct the current speed of vehicle using (4a-4b) instead of (3). This is called forward correction and speed calculated is called F- speed (we use this notation for simplification of representation only)

mod(5) 1 ifor == ii vv)

(4a)

)(5.0 11 iiii aavv ++= −−

))Otherwise (4b)

Error is measured by i v- ii OBDve = , where iOBDv the

speed is measured from OBD2. Using (4a-4b) at 5 second interval, we correct the estimated speed of the moving vehicle by forcing that value to calculated speed. Using this method, the error becomes smaller; the accumulated error is corrected after 5 seconds by use of GPS measured speed. Plot of the forward speed as compared with OBD2 speed is given in fig. 8. From fig. 8, it is clear that the error reduces but still error lies in the range (-13, 7) km/hr with r.m.s. error 3.444 km/hr. Hence, the approach requires further improvement.

We propose a new estimation improvement method called hereafter as Forward-Backward correction (F-B correction) which computes past speed from known present speed. These speeds are referred as F-B speed.

mod(5) 1 ifor == ii vv))

(5a)

)(5.0 11 iiii aavv +−= −−

))))Otherwise (5b)

Time Sequences (sec)

0 20 40 60 80 100 120 140 160 180 200

Veh

icle

Speed (

Km

/h)

0

10

20

30

40

50

60

70

OBD2 measured

Accelerometer & GPS fused-Forward Calculation

Figure 8. Calculated F-speed is compared with OBD2 speed.

We can further estimate our speed as an average of F-speed and F-B speed to obtain a better estimate of speed from inertial measurements. In fig (9) we present the computed speeds from forward and forward-backward correction method as compared with OBD2 speed. It is observed that the true speed is a weighted average of the two proposed correction methods.

) (5.0 iii vvV)))

+= Where iV is the estimated speed (6)

Equation (6) estimates speeds ( iV ) using INS/GPS fusion

and these calculations can be used effectively to get proper speed estimation. Fig. 10 presents the final estimated speed as compared with OBD2 speed.

Time Sequence (sec)

0 5 10 15 20 25 30 35 40 45 50

Ve

hic

le S

pe

ed

(K

m/h

)

10

20

30

40

50

60

OBD2 measured

Accelerometer + GPS - Forward

Accelerometer + GPS - Backward

Figure 9. Calculated F and FB speed relative to OBD2 speed .


445

Time Sequence (sec)

0 20 40 60 80 100 120 140 160 180 200

Vehicle S

peed (Km/h)

0

10

20

30

40

50

60

70

OBD2 measured

Average of Forward & Backward fusion(Accelero

Figure 10. Estimeted speed using INS/GPS fusion and compared with OBD2 speed.

Fig. 10 shows clearly that the estimated speed is very close to true speed (measured from OBD2). The estimated speed errors are in the range (-6, 5.5) km/hr and r.m.s. error = 1.84 km/hr. Hence combination of F-B speed and F-speed offers 50% improvement over standard INS/GPS fusion.

VI. CONCLUSION

The usage of Smartphones in large scale sensor deployment

and analysis is gaining prominence. Phone based sensors like accelerometers & GPS offer an attractive opportunity to

deploy vehicle tracking solutions; however, such solutions

are affected by the professed lack of measurement accuracy

as compared to professional grade units. A GPS based speed

estimation method requires high sampling rate, to obtain

accuracy. Thus, for a typical long duration vehicle trip, the

power consumption will be heavy. Accelerometer based

speed estimation can become a much preferred method

provided the sensor errors are properly compensated for. In

this paper, we attempt to analyze a few categories of

smartphones (as sensor & computation units) from the

perspective of noise. Further, we apply an innovative fusion algorithm to get a much better estimate of vehicle speed

using primarily accelerometer measurements. Further tests

are required to validate the proposed approach by fusing

GPS measurements at still lower sampling rate. It is

envisaged that with increasing estimation accuracy, the application of multi-sensor fusion in autonomous vehicles

will be greatly enhanced

REFERENCES

[1] M. S. Grewal, L. R. Weill and A. P. Andrews, Global Positioning Systems, Inertial Navigation and Integration, 2nd Ed., Wiley-Interscience, 2007, New Jersey

[2] V. Gupta, “Vehicle Localization using low-accuracy GPS, IMU and Map Aided vision”, Doctoral Thesis. The Pennsylvania State University, 2009.

[3] R. D. Martini, “GPS/INS sensing coordination for vehicle state identification and road grade positioning”. Doctoral thesis. The Pennsylvania State University, 2006.

[4] T.Chakravarty, A. Ghose, C. Bhaumik & A. Chowdhury, “MobiDriveScore-A system for mobile sensor based driving analyis: a risk assessment model for improving one’s driving”, Sensing Technology (ICST), 2013, 7th Intl. Conf. on, pp 338 - 344

[5] T. Toledo, O. Musicant, and T. Lotan. In-vehicle data recorders for monitoring and feedback on drivers behavior. Transportation Research Part C: Emerging Technologies, 16(3):320–331, 2008.

[6] A. Ghose, P. Biswas, C. Bhaumik, M. Sharma, A. Pal, and A. Jha, “Road condition monitoring and alert application: Using in-vehicle smartphone as internet-connected sensor”, In Pervasive Computing and Communications Workshops (PERCOM Workshops), 2012 IEEE International Conference on, pages 489–491, 2012.

[7] J. H. Hong, B. Margines, A. K. Dey, “A Smartphone-based Sensing Platform to Model Aggressive Driving Behaviors”, ACM Conf. Human-Computer Interaction (CHI), April 2014, Toronto Canada.

[8] R. Vaiana, T. Iuele, V. Astarita, M. V. Caruso1, A. Tassitani, C. Zaffino & V. P. Giofrè, “Driving Behavior and Traffic Safety: An Acceleration-Based Safety Evaluation Procedure for Smartphones”, Modern Applied Science; Vol. 8, No. 1; 2014, pp-88-96

[9] J. O. Woodman, "An introduction to inertial navigation." University of Cambridge, Computer Laboratory, Tech. Rep. UCAMCL-TR-696 14 (2007): 15. http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-696.pdf

[10] X. Zhang, Y. Li, P. Mumford, C. Rizos, “Allan Variance Analysis on Error Characters of MEMS Inertial Sensors for an FPGA-based GPS/INS System”, Proceedings of the International Symposium on GPS/GNNS. 2008.

[11] http://www.plxdevices.com/.


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