# Towards the Crowdsourcing of Massive Smartphone Assisted-GPS Sensor Ground Observations for the Production of Digital Terrain Models

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Research

## 3. Methodology

#### 3.1. Data Collection

#### 3.2. Pre-Processing

_{x}, c

_{y}, c

_{z}] are the coordinates value of reference point in the Cartesian system, s is the scale factor, [r

_{x}, r

_{y}, r

_{z}] are the rotation angles, and [N, E, U] are the coordinates value transformation results in ITM.

#### 3.3. Grid Construction

#### 3.4. Kalman Filter

#### 3.4.1. Boundary Conditions

#### 3.4.2. State Vector

_{x}(i, j) is the first derivative along the X-axis, and H

_{y}(i, j) is the first derivative along the Y-axis:

_{x}and S

_{y}, depicted in Equation (3), one for each axis:

_{sx}(i, j) and V

_{sy}(i, j) are white noise vectors, and dx and dy are the grid resolutions in X and Y-axis, respectively.

#### 3.4.3. A-Priori State Vector

^{+}(i − 1, j), S

^{+}(i, j − 1), and its co-variances P

^{+}(i − 1, j), P

^{+}(i, j −1). With this, the following can be calculated: (1) the a-priori state vectors S

^{−}

_{x}(i, j) and S

^{−}

_{y}(i, j) for each of the axis; (2) the a-priori state co-variance matrix P

^{−}

_{x}(i, j) and P

^{−}

_{y}(i, j) using a pre-determined model co-variance matrices, Q

_{x}(i, j) and Q

_{y}(i, j), respectively; and thus, (3) the a-priori state vector S

^{−}(i, j) with its co-variance matrix P

^{−}(i, j), depicted in Equation (4).

#### 3.4.4. Model’s Accuracy

_{x}(i, j) and Q

_{y}(i, j), were included. These are the co-variances matrices of the model used in the Kalman filter process, representing the estimated accuracy of the model. The model used here relies on the Euler method, and thus, its accuracy can be determined accordingly. The accuracy estimation is depicted in Equation (5) for the X-axis, and in Equation (6) for the Y-axis:

_{xx}is the second derivative alongside the X-axis, H

_{yy}is the second derivative alongside the Y-axis, H

_{xy}and H

_{yx}are the second derivatives alongside both axes, dx and dy are the resolutions alongside X and Y-axis, respectively, and b and c represent the (i − 1) and (j − 1) point heights, respectively. These equations show that the accuracy of the model is determined by the estimated accuracy of the second derivatives and the grid resolution. Thus, for example, if the second derivative accuracy is estimated at 0.08 (1/m) and the grid resolution is 5 m, then the estimated accuracy will be 1 m, while the X and Y derivatives estimated accuracies will be 0.4 (1/m). The equations also show that the higher the grid resolution is (i.e., smaller interval), the more accurate the model becomes when using the Kalman filter.

#### 3.4.5. Updated State Vector

^{+}(i, j) is the updated state vector, and P

^{+}(i, j) is the covariance of the updated state vector.

#### 3.4.6. Outlier Detection

^{−}(i, j) and the measurement Z(i, j) are calculated, depicted in Equation (8).

_{L(i,j)}is calculated from the elevation accuracy of the model σ

^{2}

_{H}

^{−}

_{(i,j)}and the measurement accuracy R(i, j), depicted in Equation (9).

_{α}, depicted in Equation (10). If the test result is true, then only the model result value (the a-priori state vector) will be used, and if the result is false, the updated state vector result value will be used. This value is determined depending on the value of α (normal distribution); for example, if α is 0.05 (5% significant level) then ξ

_{α}will be 1.96, and if α is 0.01 then ξ

_{α}will be 2.58, and so forth.

#### 3.4.7. Smoothing

#### 3.5. Elevation Conversion

## 4. Experimental Results

- Environmental diversity—the idea is to collect data from different areas composed of diverse environmental settings. These include roads, walking paths, open areas, concealed areas near buildings and trees. The rationale is that these might have a different effect on the reliability of the observations (e.g., multipath and occlusions), thus allowing a broader examination and evaluation. Accordingly, collection means, i.e., walking and driving, might also have an effect.
- Organization of observations—different areas impose constraints on the ability to collect field data and thus presenting varying point densities. Built areas, for example, are relatively uniform and homogenous in structure with building arrangements, thus allowing the collection of more ordered and controlled observations. This is opposite to open areas, mainly around woodland and extreme topography, which are harder to access, relying only on sparse paths, thus presenting more heterogeneous observation density and data-holes. Since interpolation is implemented on the raw observation data to generate a grid, this factor is important to analyze.

#### 4.1. Residential Area

#### 4.2. Open Area

#### 4.3. Technion Area

#### 4.4. Diverse Large Area

#### 4.5. Summary

## 5. Conclusions and Future Work

## Author Contributions

## Conflicts of Interest

## References

- Monteiro, E.; Fonte, C.C.; Lima, J.L. Assessing positional accuracy of drainage networks extracted from ASTER, SRTM and OpenStreetMap. In Proceedings of the 18th AGILE International Conference on Geographic Information Science, Lisboa, Portugal, 9–12 June 2015. [Google Scholar]
- Neis, P.; Zielstra, D. Recent developments and future trends in volunteered geographic information research: The case of OpenStreetMap. Future Internet
**2014**, 6, 76–106. [Google Scholar] [CrossRef][Green Version] - Zandbergen, P.A.; Barbeau, S.J. Positional accuracy of assisted GPS data from high-sensitivity GPS-enabled mobile phones. J. Navig.
**2011**, 64, 381–399. [Google Scholar] [CrossRef] - Senaratne, H.; Mobasheri, A.; Ali, A.L.; Capineri, C.; Haklay, M. A review of volunteered geographic information quality assessment methods. Int. J. Geogr. Inf. Sci.
**2017**, 31, 139–167. [Google Scholar] [CrossRef] - Hyyppä, H.; Yu, X.; Hyyppä, J.; Kaartinen, H.; Kaasalainen, S.; Honkavaara, E.; Rönnholm, P. Factors affecting the quality of DTM generation in forested areas. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2005**, 36, 85–90. [Google Scholar] - Chen, Q.; Wang, H.; Zhang, H.; Sun, M.; Liu, X. A point cloud filtering approach to generating DTMs for steep mountainous areas and adjacent residential areas. Remote Sens.
**2016**, 8, 71. [Google Scholar] [CrossRef] - Zandbergen, P.A. Accuracy of iPhone locations: A comparison of assisted GPS, WiFi and cellular positioning. Trans. GIS
**2009**, 13, 5–25. [Google Scholar] [CrossRef] - Garnett, R.; Stewart, R. Comparison of GPS units and mobile Apple GPS capabilities in an urban landscape. Cartogr. Geogr. Inf. Sci.
**2015**, 42, 1–8. [Google Scholar] [CrossRef] - Over, M.; Schilling, A.; Neubauer, S.; Zipf, A. Generating web-based 3D City Models from OpenStreetMap: The current situation in Germany. Comput. Environ. Urban Syst.
**2010**, 34, 496–507. [Google Scholar] [CrossRef] - Goetz, M.; Zipf, A. The evolution of geo-crowdsourcing: Bringing volunteered geographic information to the third dimension. In Crowdsourcing Geographic Knowledge; Springer: Dordrecht, The Netherlands, 2013; pp. 139–159. [Google Scholar]
- Klimaszewski-Patterson, A. Smartphones in the field: Preliminary study comparing GPS capabilities between a smartphone and dedicated GPS device. Appl. Geogr. Conf.
**2010**, 33, 270–279. [Google Scholar] - Retscher, G.; Hecht, T. Investigation of location capabilities of four different smartphones for LBS navigation applications. In Proceedings of the 2012 International Conference on Indoor Positioning and Indoor Navigation (IPIN), Sydney, Australia, 13–15 November 2012; pp. 1–6. [Google Scholar]
- Hwang, S.; Yu, D. GPS localization improvement of smartphones using built-in sensors. Int. J. Smart Home
**2012**, 6, 1–8. [Google Scholar] - Mok, E.; Retscher, G.; Wen, C. Initial test on the use of GPS and sensor data of modern smartphones for vehicle tracking in dense high rise environments. In Proceedings of the Ubiquitous Positioning, Indoor Navigation, and Location Based Service (UPINLBS), Helsinki, Finland, 3–4 October 2012; pp. 1–7. [Google Scholar]
- Boroujeni, B.Y.; Frey, H.C.; Sandhu, G.S. Road grade measurement using in-vehicle, stand-alone GPS with barometric altimeter. J. Transp. Eng.
**2013**, 139, 605–611. [Google Scholar] [CrossRef] - Bell, S.; Jung, W.R.; Krishnakumar, V. WiFi-based enhanced positioning systems: Accuracy through mapping, calibration, and classification. In Proceedings of the 2nd ACM SIGSPATIAL International Workshop on Indoor Spatial Awareness, San Jose, CA, USA, 2 November 2010; pp. 3–9. [Google Scholar]
- Chu, H.; Gallagher, A.; Chen, T. GPS refinement and camera orientation estimation from a single image and a 2D map. In Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), Columbus, OH, USA, 23–28 Jun 2014; pp. 171–178. [Google Scholar]
- Del Rosario, M.B.; Redmond, S.J.; Lovell, N.H. Tracking the evolution of smartphone sensing for monitoring human movement. Sensors
**2015**, 15, 18901–18933. [Google Scholar] [CrossRef] [PubMed] - Neuhold, R.; Haberl, M.; Fellendorf, M.; Pucher, G.; Dolancic, M.; Rudigier, M.; Pfister, J. Generating a lane-specific transportation network based on floating-car data. In Advances in Human Aspects of Transportation; Springer: Cham, Switzerland, 2017; pp. 1025–1037. [Google Scholar]
- Nour, A.; Casello, J.; Hellinga, B. Developing and optimizing a transportation mode inference model utilizing data from GPS embedded smartphones. In Proceedings of the Transportation Research Board 94th Annual Meeting, Washington, DC, USA, 11–15 January 2015. [Google Scholar]
- Zhang, L.; Dalyot, S.; Sester, M. Travel-mode classification for optimizing vehicular travel route planning. In Progress in Location-Based Services; Springer: Berlin/Heidelberg, Germany, 2013; pp. 277–295. [Google Scholar]
- Li, X.; Goldberg, D.W. Toward a mobile crowdsensing system for road surface assessment. Comput. Environ. Urban Syst.
**2018**. [Google Scholar] [CrossRef] - Gong, Y.; Zhu, Y.; Yu, J. DEEL: Detecting elevation of urban roads with smartphones on wheels. In Proceedings of the 2015 12th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON), Seattle, WA, USA, 22–25 June 2015; pp. 363–371. [Google Scholar]
- Li, Z. Sampling Strategy and Accuracy Assessment for Digital Terrain Modelling. Ph.D. Thesis, University of Glasgow, Glasgow, UK, 1990. [Google Scholar]
- Yan, X.; Su, X. Linear Regression Analysis: Theory and Computing; World Scientific: Singapore, 2009. [Google Scholar]
- Khorbotly, S.; Hassan, F. A modified approximation of 2D Gaussian smoothing filters for fixed-point platforms. In Proceedings of the 2011 IEEE 43rd Southeastern Symposium on System Theory (SSST), Auburn, AL, USA, 14–16 March 2011; pp. 151–159. [Google Scholar]
- Knudsen, T.; Andersen, R.C. Gradient based filtering of digital elevation models. In Proceedings of the 6th Geomatic Week Conference, Barcelona, Spain, 8–11 February 2005. [Google Scholar]
- Golyandina, N.; Florinsky, I.; Usevich, K. Filtering of digital terrain models by 2D singular spectrum analysis. Int. J. Ecol. Dev.
**2007**, 8, 81–94. [Google Scholar] - Gallant, J. Multiscale methods in terrain analysis. In Proceedings of the International Symposium on Terrain Analysis and Digital Terrain Modelling, Nanjing, China, 23–25 November 2006; pp. 23–25. [Google Scholar]
- Wang, P. Applying two dimensional Kalman filtering for digital terrain modelling. In International Archives of Photogrammetry, Remote Sensing, and Spatial Information Sciences; Fritsch, D., Englich, M., Sester, M., Eds.; Copernicus GmbH: Göttingen, Germany, 1998; Volume 31. [Google Scholar]
- Wang, P.; Trinder, J.C.; Han, S. Two-dimensional Kalman smoothing for digital terrain modelling. Int. Arch. Photogramm. Remote Sens.
**2000**, 33 Pt 4, 1157–1164. [Google Scholar] - Li, Z.; Zhu, C.; Gold, C. Digital Terrain Modeling: Principles and Methodology; CRC Press: Boca Raton, FL, USA, 2004. [Google Scholar]
- Arun, P.V. A comparative analysis of different DEM interpolation methods. Egypt. J. Remote Sens. Space Sci.
**2013**, 16, 133–139. [Google Scholar] - Burrough, P.A.; McDonnell, R.A. Principles of GIS; Oxford University Press: London, UK, 1998. [Google Scholar]
- Steinberg, G.; Even-Tzur, G. Official GNSS-derived Vertical Orthometric Height Control Network. Surv. Land Inf. Sci.
**2008**, 68, 29–34. [Google Scholar] - Höhle, J.; Höhle, M. Accuracy assessment of digital elevation models by means of robust statistical methods. ISPRS J. Photogramm. Remote Sens.
**2009**, 64, 398–406. [Google Scholar] [CrossRef] - Bland, J.M.; Altman, D.G. Statistics notes: Measurement error proportional to the mean. BMJ
**1996**, 313, 106. [Google Scholar] [CrossRef] [PubMed] - Hamill, T.M. Hypothesis tests for evaluating numerical precipitation forecasts. Weather Forecast.
**1999**, 14, 155–167. [Google Scholar] [CrossRef]

**Figure 1.**Smartphone model’s accuracy test results: grey bars depict the horizontal accuracy; black bars depict the vertical accuracy.

**Figure 3.**1D (

**top**) and 2D (

**bottom**) set of measurements (in white), and their corresponding boundary conditions (in grey).

**Figure 4.**The four simultaneous Kalman filter processes implemented under four different boundary conditions.

**Figure 5.**The area analyzed with the complete observation database (red dots). Purple depicts the residential area, red depicts the open area, orange depicts the Technion area, and yellow depicts the diverse area.

**Figure 6.**3D visualization of the 10 m resolution DTM for the residential area: pre-Kalman filter (

**top**), and post-Kalman filter (

**bottom**) (all values in meters).

**Figure 7.**3D visualization of the 10 m resolution DTM for Technion area: pre-Kalman filter (

**top**), and post-Kalman filter (

**bottom**) (all values in meters).

**Figure 8.**3D visualization of the 10 m resolution DTM for the entire area: pre-Kalman filter (

**top**), and post-Kalman filter (

**bottom**) (all values in meters).

**Table 1.**Statistical evaluation of elevation differences in respect to the photogrammetric reference DTM: 10 m pre- and post-Kalman filter DTM (2356 grid-points).

Pre-Kalman Filter | Post-Kalman Filter | Improvement | |
---|---|---|---|

Abs Max Difference | 10.3 m | 7.9 m | 23% |

MAD | 2.6 m | 2.4 m | 8% |

STDEV | 1.9 m | 1.7 m | 11% |

**Table 2.**Statistical evaluation of elevation differences in respect to the photogrammetric reference DTM: 10 m pre- and post-Kalman filter DTM (1056 grid-points).

Pre-Kalman Filter | Post-Kalman Filter | Improvement | |
---|---|---|---|

Abs Max Difference | 23.1 m | 17.1 m | 26% |

MAD | 5.1 m | 4.6 m | 10% |

STDEV | 4.2 m | 3.5 m | 17% |

**Table 3.**Statistical evaluation of elevation differences in respect to the photogrammetric reference DTM: 10 m pre- and post-Kalman filter DTM (5092 grid-points) and 30 m SRTM (575 grid-points).

Pre-Kalman Filter | Post-Kalman Filter | Improvement | SRTM | |
---|---|---|---|---|

Abs Max Difference | 55.0 m | 25.5 m | 55% | 33.4 m |

MAD | 6.4 m | 6.3 m | 2% | 5.1 m |

STDEV | 5.1 m | 4.5 m | 12% | 3.5 m |

**Table 4.**Statistical evaluation of elevation differences in respect to the photogrammetric reference DTM: 10 m pre- and post-Kalman filter DTM (60,000 grid-points) and SRTM (7200 points).

Pre-Kalman Filter | Post-Kalman Filter | Improvement | SRTM | |
---|---|---|---|---|

Abs Max Difference | 85.9 m | 57.1 m | 34% | 47.6 m |

MAD | 8.7 m | 8.6 m | 1% | 4.9 m |

STDEV | 7.8 m | 7.7 m | 1% | 4.0 m |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Massad, I.; Dalyot, S. Towards the Crowdsourcing of Massive Smartphone Assisted-GPS Sensor Ground Observations for the Production of Digital Terrain Models. *Sensors* **2018**, *18*, 898.
https://doi.org/10.3390/s18030898

**AMA Style**

Massad I, Dalyot S. Towards the Crowdsourcing of Massive Smartphone Assisted-GPS Sensor Ground Observations for the Production of Digital Terrain Models. *Sensors*. 2018; 18(3):898.
https://doi.org/10.3390/s18030898

**Chicago/Turabian Style**

Massad, Ido, and Sagi Dalyot. 2018. "Towards the Crowdsourcing of Massive Smartphone Assisted-GPS Sensor Ground Observations for the Production of Digital Terrain Models" *Sensors* 18, no. 3: 898.
https://doi.org/10.3390/s18030898