# Accuracy Enhancement of Anomaly Localization with Participatory Sensing Vehicles

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Review

#### 1.2. Goals and Objectives

^{®}app and an Android app called PAVVET and RIVET, respectively, which can access all the required sensors on a smartphone [22]. These apps include smart power management, remote sensing, security features, and other modes that were needed for this and other projects. The standard GPS receiver of smartphones updates at a rate of 1 Hz, whereas the accelerometer samples at a rate of more than 90 Hz, depending on the device model. This difference in update rates causes the apps to tag a block of accelerometer samples with the same GPS coordinates. For example, if the accelerometer updates 90 times per second but the GPS receiver updates only once per second, the system will tag all 90 accelerometer samples with the GPS coordinates from its last update. Figure 1 illustrates how the resolution gap creates blocks of accelerometer samples with the same geospatial position. Hence, in addition to errors in the geospatial positions reported, the low update rate of low-cost GPS receivers causes a position resolution gap. Table 1 shows an example of the data collected for a GPS block that contains the peak accelerometer signal Gz highlighted as a g-force value of −1.216 at time instant of 46.768 s. This is called a peak inertial event (PIE).

## 2. Materials and Methods

#### 2.1. Error Model

_{GT}) has three components: (1) a distance error D

_{RES}due to the GPS position resolution gap, (2) the sensor distance offset D

_{AX}from the axle of the vehicle that generates the PIE, and (3) any residual error d

_{ε}, which is currently unknown. Hence, the distance error model is

_{AX}is deterministic. It is possible to determine the distribution of the GPS distance error D

_{GT}and the GPS position resolution gap D

_{RES}with a specially designed experiment. Consequently, the residual error d

_{ε}is a function of those two distributions, such that

_{GT}is the geodesic distance between the ground truth and the GPS tag of the PIE. The geodesic distance is the shortest distance between two points on the surface of an ellipsoid model of Earth. The method of Vincenty (1975) or Karney (2013) can compute the geodesic distance, but the latter guarantees convergence for nearly antipodal points [24]. The authors modified the Karney (2013) method to produce negative distances in the direction of travel for points reported behind the ground truth, and positive distances otherwise.

_{p}is the time instant associated with the PIE, t

_{b}is the time instant of the beginning of the GPS block containing the PIE, T

_{RES}is the associated GPS resolution gap time, and S

_{p}is the average speed of the vehicle during the GPS block containing the PIE.

#### 2.2. Experiment Design

^{®}operating system (HTC and Google Pixel (GP)) and two running the iOS

^{®}operating system (i8 and iX) from Apple, Inc. Unfortunately, the HTC did not record GPS coordinates for any of the traversals; thus, the data were consequently abandoned.

_{n}is the instantaneous speed logged for that sample instant, and Δτ

_{n}is the sample period at that sample instant. The initial position d

_{0}= 0 is the distance interpolated position that was closest to C0. This position was determined by firstly identifying the GPS block located prior to C0 and then interpolating the path distance from the first sample of that GPS block until reaching the signal sample that was closest to C0. The observed misalignment of the PIEs among traversals was due to the position error of the coordinates reported for the GPS block closest to C0.

## 3. Results

^{®}models sampled between 91 and 134 Hz, whereas the GP sampled at approximately 385 Hz. The mean sample rate of the GP differed by approximately 1 Hz among the Paved and Unpaved Road experiments. This is due to the statistical nature of the sampling, as discussed in previous work [23]. The authors plan to publish the collected data in a future journal article [26].

#### 3.1. Error Distribution

_{GT}for each experiment as bar charts. The line graph is the best-fit normal distribution to the histogram.

_{i}of histogram bin i are H

_{i}. The values of the distribution evaluated at interval X

_{i}are D

_{i}where the parameters that minimize the sum-of-squares (SOS) error e are the amplitude α, mean µ, and variance σ

^{2}. A Pearson’s chi-squared test quantified the goodness-of-fit of the solution by computing the chi-squared statistic.

_{GT}distribution for a normal distribution. The null hypothesis is that the distributions follow a normal distribution. None of the tests could reject the hypothesis that the GPS distance error is normally distributed because the p-values for all experiments were greater than the standard significance of 0.05. This suggests that the alternative hypothesis could be accepted. It is difficult to observe visually that some of the distributions follow a normal distribution because of their large negative bias and large skew. The average GPS resolution gap time T

_{RES}was 0.55 s with a standard deviation of 0.05 s. The GPS resolution gap distance was computed from Equation (3), and Figure 7 shows the distribution of those distances for each experiment.

_{RES}distribution for a uniform distribution. The df for this test was the number of histogram bins minus one parameter α needed obtain the best-fit uniform distribution. The hypothesis was that the distributions follow a uniform distribution. Since the p-values for all experiments were greater than the standard significance of 0.05, none of the tests could reject the hypothesis that the GPS resolution gap distance was uniformly distributed with a positive bias.

^{−1}for the MnROAD, Paved/Unpaved, and Park Road experiments, respectively. Although three smartphones were in the same spot for the MnROAD, Paved, and Unpaved Road experiments, the difference in their mean errors ranged from less than 1 m to more than 4 m. Except for the highest and lowest speed traversals, the mean GPS resolution gap distance was consistent among smartphones.

^{®}device models, but the differences were more extreme for the Android device. Except for the lowest-speed traversals of the Park Road experiment, the variance of the GPS resolution gap error was consistent among smartphones for the experiments of each environment.

#### 3.2. Residual Error

^{2}for the regression equation shown in the inset was close to unity. The correlation with speed is intuitive because the length of a GPS block must be directly proportional to the vehicle’s speed since the GPS blocks are all approximately 1 s long. The implication from the regression model is that distance errors in this application can approach 30 m at highway speeds, making it impractical to locate an anomaly within sight distance.

^{2}value was only 0.13. This is evidence that the residual distance error must be due to a source that is not related to the movement of the vehicle. The time associated with the mean residual distance error is t

_{ε}such that

_{ε}calculated for each smartphone. The negative time bias suggests that the smartphone incurred a time latency in tagging accelerometer values with GPS coordinates.

## 4. Discussion

_{i}, Φ

_{i}) of a centroid computed from the geospatial positions of N GPS blocks containing PIEs is

_{GT}. A normal distribution of the GPS distance error suggests that the confidence interval of the centroid position is ever-increasing with traversal volume N. Whereas this method is well suited for participatory sensing vehicles, it is less suitable for situations where only a single or relatively few traversals are available. This participatory sensing approach is robust to GPS errors because it leverages a large volume of traversal data to remove outliers and to continuously increase the precision of estimating a centroid location. For statistical significance and confidence in computing the centroid, the number of traversals used in practice should be at least 30.

_{X}from the centroid, in the direction of travel and along the traversal path such that

_{ε}is the mean time latency of GPS tagging. Both T

_{ε}and T

_{RES}are time delays; thus, they are negative values. Therefore, if D

_{AX}is zero, the estimate will be a positive value, which is a distance ahead of the centroid position. If the mean GPS tagging latency is zero, the estimated position of the anomaly will still be a positive distance away from the centroid position.

_{GPS}is the mean update period of the GPS receiver. All the variables of this equation are deterministic. Table 4 lists the estimated distance D

_{X}from the computed centroid position by using the values of T

_{ε}estimated for each smartphone. The distance C

_{GT}from the centroid to the ground truth was measured. Hence, the error E

_{X}of the distance estimates was determined, and the results are listed in Table 4.

^{−1}. The standard deviation of the distance estimate is proportional to the choice of speed interval from which the system selects traversal data. The recommended practice is to determine the mean traversal speed of a detected anomaly and then select traversal data that is within a few m∙s

^{−1}of the mean to satisfy the confidence interval desired for the application. The confidence interval CI of the distance estimate is

_{α}= 1.96 for a 95% confidence interval, σ

_{X}is the standard deviation of the distance estimate, and N is the number of traversals used. From Equation (11), σ

_{X}depends on the standard deviations of the traversal speed, the time latency of GPS tagging, and the GPS update interval. Hence, the confidence interval of the estimate will increase in proportion to the standard deviation of the speed interval used for data selection and decrease by the square root of the number of traversals used.

## 5. Conclusions

^{−1}(42 mph). A regression of the trend suggested that the error can exceed 27 m at highway speeds of 31.3 m∙s

^{−1}(70 mph). Such a large error will be beyond the human sight distance.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Ragnoli, A.; Blasiis, M.R.D.; Benedetto, A.D. Pavement distress detection methods: A review. Infrastructures
**2018**, 3, 50. [Google Scholar] [CrossRef] [Green Version] - Pierce, L.M.; Weitzel, N.D. Automated Pavement Condition Surveys; Academies Press: Washington, DC, USA, 2019. [Google Scholar]
- Karamihas, S.M.; Gilbert, M.E.; Barnes, M.A.; Perera, R.W. Measuring, Characterizing, and Reporting Pavement Roughness of Low-Speed and Urban Roads; Transportation Research Board: Washington, DC, USA, 2019. [Google Scholar]
- Dennis, E.P.; Hong, Q.; Wallace, R.; Tansil, W.; Smith, M. Pavement Condition Monitoring with Crowdsourced Connected Vehicle Data. Transport Res. Rec.
**2014**, 2460, 31–38. [Google Scholar] [CrossRef] - Bridgelall, R. Connected vehicle approach for pavement roughness evaluation. J. Infrastruct. Syst.
**2014**, 20, 04013001. [Google Scholar] [CrossRef] [Green Version] - Alavi, A.H.; Buttlar, W.G. An overview of smartphone technology for citizen-centered, real-time and scalable civil infrastructure monitoring. Future Gener. Comput. Syst.
**2019**, 93, 651–672. [Google Scholar] [CrossRef] - Salau, H.B.; Onumanyi, A.J.; Aibinu, A.M.; Onwuka, E.N.; Dukiya, J.J.; Ohize, H. A Survey of Accelerometer-Based Techniques for Road Anomalies Detection and Characterization. IJESA
**2019**, 3, 8–20. [Google Scholar] - Sattar, S.; Li, S.; Chapman, M. Road Surface Monitoring Using Smartphone Sensors: A Review. Sensors
**2018**, 18, 3845. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chia, L.; Bhardwaj, B.; Lu, P.; Bridgelall, R. Railroad track condition monitoring using inertial sensors and digital signal processing: A review. IEEE Sensors J.
**2018**, 19, 25–33. [Google Scholar] [CrossRef] - Bernal, E.; Spiryagin, M.; Cole, C. Onboard condition monitoring sensors, systems and techniques for freight railway vehicles: a review. IEEE Sensors J.
**2018**, 19, 4–24. [Google Scholar] [CrossRef] - Paixão, A.; Fortunato, E.; Calçada, R. Smartphone’s sensing capabilities for on-board railway track monitoring: structural performance and geometrical degradation assessment. Adv. Civ. Eng.
**2019**, 2019, 1–13. [Google Scholar] [CrossRef] - Gao, R.; Zhao, M.; Ye, T.; Ye, F.; Wang, Y.; Luo, G. Smartphone-Based Real Time Vehicle Tracking in Indoor Parking Structures. IEEE Trans. Mob. Comput.
**2017**, 16, 2023–2036. [Google Scholar] [CrossRef] - Renfro, B.A.; Stein, M.; Boeker, N.; Reed, E.; Villalba, E. An Analysis of Global Positioning System (GPS) Standard Positioning Service (SPS) Performance for 2018; The University of Texas at Austin: Austin, TX, USA, 2019. [Google Scholar]
- Nguyen, T.; Lechner, B.; Wong, Y.D. Response-based methods to measure road surface irregularity: A state-of-the-art review. Eur. Transp. Res. Rev.
**2019**, 11, 43. [Google Scholar] [CrossRef] [Green Version] - Bisconsini, D.; Núñez, J.Y.; Nicoletti, R.; Júnior, J.L. Pavement roughness evaluation with smartphones. IJSEI
**2018**, 7, 43–52. [Google Scholar] - Múčka, P. International Roughness Index specifications around the world. Road Mater. Pavement
**2017**, 18, 929–965. [Google Scholar] [CrossRef] - Du, Y.; Liu, C.; Wu, D.; Jiang, S. Measurement of International Roughness Index by using z-axis accelerometers and GPS. Math. Probl. Eng.
**2014**, 2014, 1–10. [Google Scholar] - Nunes, D.E.; Mota, V.F. A participatory sensing framework to classify road surface quality. JISA
**2019**, 10, 13. [Google Scholar] [CrossRef] [Green Version] - El-Wakeel, A.S.; Li, J.; Noureldin, A.; Hassanein, H.S.; Zorba, N. Towards a practical crowdsensing system for road surface conditions monitoring. IEEE Internet Things J.
**2018**, 5, 4672–4685. [Google Scholar] [CrossRef] - Hossain, M.I.; Tutumluer, E.; Nikita; Grimm, C. Smart City Infrastructure. In Proceedings of the International Conference on Transportation and Development 2019, Alexandria, VA, USA, 10–12 June 2019; pp. 359–370. [Google Scholar]
- Mooney, S.J.; Sheehan, D.M.; Zulaika, G.; Rundle, A.G.; McGill, K.; Behrooz, M.R.; Lovasi, G.S. Quantifying Distance Overestimation From Global Positioning System in Urban Spaces. AJPH
**2016**, 106, 651–653. [Google Scholar] [CrossRef] [PubMed] - Lu, P.; Bridgelall, R.; Tolliver, D.; Chia, L.; Bhardwaj, B. Intelligent Transportation Systems Approach to Railroad Infrastructure Performance Evaluation: Track Surface Abnormality Identification with Smartphone-Based App; Research Report MPC-19-384; North Dakota State University: Fargo, ND, USA, 2019. [Google Scholar]
- Bridgelall, R.; Chia, L.; Bhardwaj, B.; Lu, P.; Tolliver, D.; Dhingra, N. Enhancement of signals from connected vehicles to detect roadway and railway anomalies. Meas. Sci. Technol.
**2019**, 31, 3. [Google Scholar] [CrossRef] - Karney, C.F.F. Algorithms for geodesics. J Geodesy
**2013**, 87, 43–55. [Google Scholar] [CrossRef] [Green Version] - Agresti, A. Statistical Methods for the Social Sciences, 5th ed.; Pearson: Boston, MA, USA, 2018. [Google Scholar]
- Bridgelall, R. Accelerometer Data for Roadway Anomaly Localization. Manuscript in preparation.

**Figure 4.**(

**a**) Smartphones secured to the sedan floor, and (

**b**) two accelerometer signals with peak inertial event (PIEs).

**Figure 8.**GPS ground truth offset and resolution gaps: (

**a**) mean distances, (

**b**) standard deviations, and (

**c**) chart legend.

**Figure 9.**Correlation with speed for (

**a**) GPS distance error, (

**b**) GPS resolution gap, and (

**c**) residual distance error.

Time | Gz | Speed | Latitude | Longitude |
---|---|---|---|---|

44.142 | −1.057 | 9.586 | 45.263 | −93.711 |

46.768 | −1.216 ^{1} | 9.586 | 45.263 | −93.711 |

50.260 | −1.087 | 9.586 | 45.263 | −93.711 |

62.927 | −0.854 | 9.586 | 45.263 | −93.711 |

73.909 | −0.912 | 9.586 | 45.263 | −93.711 |

86.754 | −0.942 | 9.586 | 45.263 | −93.711 |

95.669 | −1.001 | 9.586 | 45.263 | −93.711 |

110.365 | −1.022 | 9.586 | 45.263 | −93.711 |

118.253 | −1.096 | 9.586 | 45.263 | −93.711 |

128.695 | −1.013 | 9.586 | 45.263 | −93.711 |

^{1}Peak inertial event (PIE).

Road | Environment and Rough Spot | Sensor Label | Phone Model | Speed (m∙s^{−1}) | Vehicle Type and Sensor Mount |
---|---|---|---|---|---|

MnRoad | Concrete panel road, open environment, few trees, slightly overcast, joint bump | i4S1 | iPhone^{®} 4S | 18.8 | 2011 Chevy Traverse minivan; behind the rear axle, taped flat onto the trunk floorboard, near the vehicle center line |

i4S2 | iPhone^{®} 4S | 18.8 | |||

i5 | iPhone^{®} 5 | 18.8 | |||

Unpaved Road | Gravel road, open environment, no trees, snow covered adjacent land, dawn, rail tracks | i8 | iPhone^{®} 8 | 10.9 | 2015 Volkswagen Jetta sedan; midway between the vehicle axles, taped flat onto the floorboard on the passenger side |

iX | iPhone^{®} 10 | 11.2 | |||

GP | Google Pixel | 11.3 | |||

Paved Road | Asphalt road, open environment, few trees, dusk, rail tracks | i8 | Identical smartphones and set-up as for the Unpaved Road | 11.8 | Identical set-up as for the Unpaved Road |

iX | 11.6 | ||||

GP | 11.5 | ||||

Park Road | Asphalt road, tree lined park, clear midday, speed bump | i4_a | iPhone^{®} 4 | 2.5 | 2001 Ford Explorer SUV; behind the front axle, taped flat in a tray between the driver and passenger seats. |

i4_b | iPhone^{®} 4 | 5.0 | |||

i4_c | iPhone^{®} 4 | 7.5 |

Road | Sensor Label | N | µ_{s}(Hz) | S (m∙s ^{−1}) | D_{GT}(m) | D_{AX}(m) | D_{RES}(m) | T_{RES}(s) | t_{ε}(s) | D_{GT}p-value | D_{RES}p-value |
---|---|---|---|---|---|---|---|---|---|---|---|

MnROAD | i4S1 | 17 | 91.2 | 18.8 | −16.5 | −3.6 | 8.84 | 0.47 | −0.22 | 0.94 | 0.96 |

i4S2 | 17 | 91.3 | 18.8 | −16.7 | −3.6 | 10.07 | 0.54 | −0.16 | 0.55 | 0.33 | |

i5 | 17 | 137.4 | 18.8 | −15.7 | −3.6 | 10.03 | 0.53 | −0.11 | 0.80 | 0.61 | |

UnpavedRoad | i8 | 30 | 132.8 | 10.9 | −10.5 | 1.3 | 5.63 | 0.51 | −0.57 | 0.48 | 0.61 |

iX | 34 | 133.8 | 11.2 | −7.0 | 1.3 | 5.93 | 0.55 | −0.21 | 0.11 | 0.35 | |

GP | 31 | 385.4 | 11.3 | −6.2 | 1.3 | 6.30 | 0.59 | −0.11 | 0.60 | 0.42 | |

PavedRoad | i8 | 35 | 132.8 | 11.8 | −11.0 | 1.3 | 6.28 | 0.53 | −0.52 | 0.58 | 0.77 |

iX | 34 | 133.8 | 11.6 | −7.7 | 1.3 | 6.50 | 0.55 | −0.22 | 0.66 | 0.90 | |

GP | 35 | 386.5 | 11.5 | −10.4 | 1.3 | 6.19 | 0.53 | −0.48 | 0.54 | 0.72 | |

ParkRoad | i4_a | 29 | 93.2 | 2.5 | −2.8 | −0.9 | 1.39 | 0.56 | −0.17 | 0.82 | 0.20 |

i4_b | 28 | 93.2 | 5.0 | −6.5 | −0.9 | 3.34 | 0.66 | −0.45 | 0.66 | 0.20 | |

i4_c | 30 | 93.2 | 7.3 | −2.6 | −0.9 | 3.92 | 0.54 | 0.32 | 0.25 | 0.74 | |

Average | 0.55 | −0.24 | 0.58 | 0.57 | |||||||

SD | 0.05 | 0.24 | 0.23 | 0.26 |

Road | Sensor Label | S (m∙s ^{−1}) | C_{GT}(m) | D_{AX}(m) | t_{ε}(s) | D_{X}(m) | E_{X}(m) |
---|---|---|---|---|---|---|---|

MnROADCell 40 | i4S1 | 18.8 | −16.08 | −3.6 | −0.22 | −17.10 | −1.02 |

i4S2 | 18.8 | −16.53 | −3.6 | −0.16 | −15.99 | 0.54 | |

i5 | 18.8 | −15.52 | −3.6 | −0.11 | −15.11 | 0.42 | |

UnpavedRoad | i8 | 10.9 | −10.37 | 1.3 | −0.57 | −10.36 | 0.01 |

iX | 11.2 | −6.35 | 1.3 | −0.21 | −6.65 | −0.30 | |

GP | 11.3 | −5.90 | 1.3 | −0.11 | −5.52 | 0.38 | |

PavedRoad | i8 | 11.8 | −10.96 | 1.3 | −0.52 | −10.64 | 0.32 |

iX | 11.6 | −7.56 | 1.3 | −0.22 | −7.01 | 0.56 | |

GP | 11.5 | −10.10 | 1.3 | −0.48 | −9.93 | 0.18 | |

ParkRoad | i4_a | 2.5 | −3.06 | −0.9 | −0.17 | −2.63 | 0.43 |

i4_b | 5.0 | −6.41 | −0.9 | −0.45 | −5.71 | 0.70 | |

i4_c | 7.3 | −2.59 | −0.9 | 0.00 | −4.57 | −1.98 | |

Average | −0.27 | 0.02 | |||||

SD | 0.19 | 0.78 |

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**MDPI and ACS Style**

Bridgelall, R.; Tolliver, D.
Accuracy Enhancement of Anomaly Localization with Participatory Sensing Vehicles. *Sensors* **2020**, *20*, 409.
https://doi.org/10.3390/s20020409

**AMA Style**

Bridgelall R, Tolliver D.
Accuracy Enhancement of Anomaly Localization with Participatory Sensing Vehicles. *Sensors*. 2020; 20(2):409.
https://doi.org/10.3390/s20020409

**Chicago/Turabian Style**

Bridgelall, Raj, and Denver Tolliver.
2020. "Accuracy Enhancement of Anomaly Localization with Participatory Sensing Vehicles" *Sensors* 20, no. 2: 409.
https://doi.org/10.3390/s20020409