# Precise Position Estimation Using Smartphone Raw GNSS Data Based on Two-Step Optimization

## Abstract

**:**

## 1. Introduction

## 2. Related Researches

## 3. GSDC 2022 Overview

#### 3.1. Dataset

#### 3.2. Score Metric

#### 3.3. Baseline Position

## 4. Strategy

## 5. Preprocessing

#### 5.1. Initial State Estimation

- 1
- Convert to the east-north-up (ENU) coordinate system and detect large jumps in the altitude.
- 2
- Delete the epoch detected in Step 1 as an outlier.
- 3
- Interpolate the 3D position of missing epochs from the previous and next data.

#### 5.2. Selection of GNSS Observations

`MultipathIndicator`) in the smartphone log is turned on, the observations for that satellite are rejected. The following is a description of the process for each observation.

#### 5.2.1. Pseudorange Selection

#### 5.2.2. Doppler Selection

#### 5.2.3. Carrier Phase Selection

#### 5.2.4. Example of Observation Selection

## 6. Velocity-Estimation Step

#### 6.1. Doppler Factor

#### 6.2. Motion Factor

#### 6.3. Optimization

#### 6.4. Outlier Removal and Interpolation

## 7. Position-Estimation Step

#### 7.1. Velocity/Clock Drift Factor

#### 7.2. Pseudorange Factor

#### 7.3. TDCP Factor

#### 7.4. Optimization

## 8. Evaluation and Discussion

#### 8.1. Evaluation Using Training Data

#### 8.1.1. Evaluation of Positioning Accuracy

- 1
- Exclude runs for which the ground truth does not include altitude. Although the final score is determined by the horizontal positioning error, runs without ground truth for altitude were excluded. This is because we cannot compute position and velocity references in the ECEF coordinates.
- 2
- Exclude runs for which the carrier phase has not been obtained. The
`HardwareClockDiscontinue`flag in the log is only reported on Google Pixel 4, which includes some runs for which the carrier phase has not been obtained correctly. Because TDCP cannot be used in these cases, they were excluded from the evaluation. - 3
- During the competition, a participant pointed out that the ground truth for some runs was not sufficiently accurate. The competition host then made an announcement and published a list of the inaccurate ground truths. The runs containing these inaccurate ground truths were eliminated.

#### 8.1.2. Evaluation of Two-Step Optimization

#### 8.2. Evaluation Using Test Data

#### 8.3. Discussion

## 9. Conclusions

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

## References

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**Figure 1.**Driving trajectories included in test data provided at GSDC 2022. In total, 36 runs were provided and divided into two parts: one run in the San Francisco area and another in the Los Angeles area.

**Figure 2.**Los Angeles vehicle driving trajectory included in GSDC 2022. (

**a**) Stops under elevated tracks and (

**b**) runs through long tunnels where GNSS signals are completely blocked.

**Figure 3.**Flow of the proposed method comprising two optimization steps: velocity estimation and position estimation via factor graph optimization (FGO).

**Figure 4.**TDCP residual of L1 signals computed by Equation (4). The Doppler observation is used to detect and exclude cycle slips in the carrier-phase observation.

**Figure 5.**Selection of GNSS observations by preprocessing. Compared to the carrier phase, Doppler is highly available.

**Figure 6.**Graph structure of proposed method in velocity-estimation step. The Doppler and motion factors are adopted to estimate the velocity.

**Figure 7.**Graph structure of proposed method in position-estimation step. Pseudorange, TDCP, and velocity/clock drift factors were adopted.

**Figure 8.**Driving trajectory of three vehicles extracted from the training dataset for evaluation (

**a**) highway environment, (

**b**) street driving, and (

**c**) driving with GNSS blockage for a long period of time.

**Figure 9.**Comparison of horizontal positioning error between baseline (blue line) and proposed method (red line).

**Figure 10.**Comparison of horizontal cumulative distribution function (CDF) for each run and the entire evaluation dataset. The blue and red lines represent the baseline and proposed method, respectively.

Course Type | Highway | Street | All |
---|---|---|---|

Score (50%) m | 2.296 | 2.772 | 2.599 |

Score (95%) m | 4.943 | 6.431 | 5.890 |

Mean m | 3.620 | 4.602 | 4.245 |

Course Phone | 2021-03-16-US-MTV-3 GooglePixel5 | 2021-03-16-US-MTV-1 SamsungGalaxyS20Ultra | 2021-12-07-US-LAX-1 GooglePixel6Pro | All | ||||
---|---|---|---|---|---|---|---|---|

Baseline | Two-Step | Baseline | Two-Step | Baseline | Two-Step | Baseline | Two-Step | |

Score (50%) m | 2.322 | 0.225 | 3.963 | 0.782 | 2.494 | 0.648 | 2.599 | 0.749 |

Score (95%) m | 4.697 | 0.520 | 9.072 | 1.450 | 4.777 | 1.230 | 5.890 | 1.297 |

Mean m | 3.510 | 0.372 | 6.517 | 1.116 | 3.635 | 0.939 | 4.245 | 1.023 |

Course | All | |
---|---|---|

One-Step | Two-Step | |

Score (50%) m | 0.801 | 0.749 |

Score (95%) m | 1.442 | 1.297 |

Mean m | 1.122 | 1.023 |

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**MDPI and ACS Style**

Suzuki, T.
Precise Position Estimation Using Smartphone Raw GNSS Data Based on Two-Step Optimization. *Sensors* **2023**, *23*, 1205.
https://doi.org/10.3390/s23031205

**AMA Style**

Suzuki T.
Precise Position Estimation Using Smartphone Raw GNSS Data Based on Two-Step Optimization. *Sensors*. 2023; 23(3):1205.
https://doi.org/10.3390/s23031205

**Chicago/Turabian Style**

Suzuki, Taro.
2023. "Precise Position Estimation Using Smartphone Raw GNSS Data Based on Two-Step Optimization" *Sensors* 23, no. 3: 1205.
https://doi.org/10.3390/s23031205