# 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

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**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 |

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**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