# Convolutional Neural Network Based Multipath Detection Method for Static and Kinematic GPS High Precision Positioning

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## Abstract

**:**

## 1. Introduction

#### 1.1. Introduction of GPS Multipath Error and Its Mitigation

_{i}denotes a factor consisting of the carrier loop noise bandwidth and a conversion term from cycle

^{2}to millimetres

^{2}, which includes the L

_{i}wavelength. CNR is the measured CNR from the GPS data. Some receiver and antenna designs can mitigate multipath effects. Special hardware designs such as vision correlator [16] and Multipath Estimating Delay-Lock-Loop [17] have been used by some receiver manufacturers to mitigate multipath error. Lau and Cross [18] use multiple closely spaced antennas to model multipath error based on the multipath phase differences of antenna pairs.

#### 1.2. Introduction of Relevant Machine Learning Algorithms

## 2. Proposed Convolutional Neural Network Based Multipath Detection Method

- Pre-process each ${\mathrm{MP}}_{\mathrm{i}}$ in the time window (i.e. Table 1) to ${\mathrm{MP}}_{\mathrm{i}}^{0}$ by:$${\mathrm{MP}}_{\mathrm{i}}^{0}={\mathrm{MP}}_{\mathrm{i}}-{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{MP}}_{\mathrm{i}}/\mathrm{n}.$$
- Scale the ${\mathrm{MP}}_{\mathrm{i}}^{0}$ and ${\mathrm{CNR}}_{\mathrm{i}}$ to [0.1] using the following two equations:$${\mathrm{CNR}}_{\mathrm{i}}^{\mathrm{s}}=0.8\left[\frac{{\mathrm{CNR}}_{\mathrm{i}}-{\mathrm{CNR}}_{\mathrm{max}}}{{\mathrm{CNR}}_{\mathrm{max}}-{\mathrm{CNR}}_{\mathrm{min}}}\right]+0.1$$$${\mathrm{MP}}_{\mathrm{i}}^{\mathrm{s}}=\mathsf{\sigma}([\frac{{\mathrm{MP}}_{\mathrm{i}}^{0}}{|{\mathrm{MP}}_{\mathrm{i}}^{0}|}]\mathrm{log}(|{\mathrm{MP}}_{\mathrm{i}}^{0}|+1))$$
- If the detector is untrained, convolution filters are trained for MP and CNR by SAE, respectively. The training is implemented in minFunc, developed by Schmidt [30]. After tuning, the parameters for convolution filters used in this work are: the number of filters = 4, the length of each filter = 5, which proved to give best performance (more detail is presented in Section 5).
- Using Equations (3) and (4) to compute the feature activations of each filter throughout the network in the convolution layer.
- In the pooling layer, the feature maps are subsampled to reduce data resolution. The determination of subsampling factor is presented in Section 5.

## 3. Validation Methodologies of the Proposed Method

- The proposed method aims to detect multipath errors in carrier phase measurements (not signals). The multipath errors in measurements are the output of processed signals from receiver hardware. Therefore, the multipath errors to be detected in carrier-phase measurements are the results of the combination of antenna architecture and receiver signal processing architecture (including correlator design). Characteristics of multipath errors in carrier phase measurements of combinations of antennas and receivers are very similar. Factors affecting the phases and magnitudes of carrier phase multipath errors can be found in [3].
- The proposed method aims to detect multipath errors. The definition of multipath errors is described in Section 1.1 and [3]. Non-line-of-sight only measurements are not multipath contaminated measurements; therefore, the non-line-of-sight only problem is outside the scope of this investigation.
- The proposed method doesn’t rely on the repeated multipath characteristics in sidereal days, and doesn’t need multipath pattern/signature to build up in the previous consecutive measurement epochs in real-time implementation of the multipath detection. A machine learning classifier can learn the characteristics of multipath errors in carrier phase measurements from CNR and MP data in the training datasets as described in Section 2.

## 4. Data Description

#### 4.1. Description of Data Simulation and Collection

#### 4.2. Description of Real Data Collection

## 5. Tuning of Parameters and Comparison between Classifiers

## 6. Test Results

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geometry of multipath signals, a reflector, and an antenna (adapted from [13]).

**Figure 6.**Images show the environments for the collection of (

**a**) Dataset STR1; (

**b**) Datasets STR2; STU, STE; (

**c**) Dataset KTR1; (

**d**) Datasets KTR2, KTU, KTE1; (

**e**) Dataset KTE2; and (

**f**) Dataset KTE3.

**Figure 8.**Detection results using feature of MP, SNR and their combination when changing the length of input time window with Dataset SIMTU (

**a**); STU (

**b**); and KTU (

**c**).

**Figure 9.**Detection results when changing the subsampling factor of the pooling layer with Dataset STU (blue squares) and KTU (red triangles).

**Figure 10.**‘True’ double-differenced carrier phase residuals of detected multipath measuremetns (red dots) and direct-signal only measurements (blue dots) in Dataset KTR1 (GPS L1 C/A data). Red dots in the squared areas represent mulitpath errors with small magnitudes.

Satellite | Observation 1 | Observation 2 | … | Observation n − 1 | Observation n |
---|---|---|---|---|---|

PRN k | CNR_{1} | CNR_{2} | … | CNR_{n−1} | CNR_{n} |

MP_{1} | MP_{2} | … | MP_{n−1} | MP_{n} |

Simulated/Real Data | Label | ||
---|---|---|---|

Multipath | Direct-Signal Only | ||

Detection | Multipath | N_{11} | N_{12} |

Direct-signal only | N_{21} | N_{22} | |

Recall | N_{11}/(N_{11} + N_{21}) | ||

Rate of false detection (on multipath) | N_{12}/(N_{11} + N_{12}) | ||

Accuracy | (N_{11} + N_{22})/(N_{11} + N_{12} + N_{21} + N_{22}) |

Tests | Tuning Dataset | Training Dataset | Test Dataset | Remarks |
---|---|---|---|---|

1 | SIMTU | SIMTR | SIMTE | Simulated data |

2 | STU | STR1+STR2 | STE | Real static data |

3 | KTU | KTR1+KTR2 | KTE1 | Real kinematic data |

4 | KTU | KTR1+KTR2 | KTE2 | Real kinematic data |

**Table 4.**List of data collected with a GNSS simulator; GDOP denotes Geometric Dilution of Precision.

Datasets | Date | Time (GPST) | No. of available Satellites | Average GDOP |
---|---|---|---|---|

SIMTR | 18 June 2015 | 00:00:00–03:59:59 | 2–7 | 8.8 (1.8–50+) |

SIMTU | 18 June 2015 | 04:00:00–11:59:59 | 3–8 | 4.6 (1.5–50+) |

SIMTE | 18 June 2015 | 12:00:00–23:59:59 | 2–8 | 6.3 (1.5–50+) |

Datasets | Date | Time (GPST) | No. of Available Satellites | Average GDOP | Environment of Data Collection |
---|---|---|---|---|---|

STR1 | 18 January 2017 | 00:00:00–03:59:59 | 6–9 | 2.9 (1.3–4.0) | Open clear area |

STR2 | 21 January 2017 | 04:00:00–07:59:59 | 4–9 | 3.3 (1.8–5.5) | Near to a wall |

STU | 21 January 2017 | 08:00:00–11:59:59 | 5–11 | 3.6 (1.2–17.1) | Near to a wall |

STE | 21 January 2017 | 12:00:00–23:59:59 | 6–9 | 2.8 (1.3–3.4) | Near to a wall |

Datasets | Date | Time (GPST) | Tangential Speed of Rotation | Environment of Data Collection |
---|---|---|---|---|

KTR1 | 27 July 2015 | 03:25:01–03:50:00 | 0.73 m/s | Open clear area |

KTR2 | 3 June 2015 | 07:42:01–08:07:00 | 0.14 m/s | Near a wall |

KTU | 3 June 2015 | 08:07:01–08:32:00 | 0.14 m/s | Near a wall |

KTE1 | 4 June 2015 | 08:09:01–09:09:00 | 0.10 m/s | Near a wall |

KTE2 | 16 August 2016 | 08:39:04–09:07:47 | N/A | Near a building |

**Table 7.**Detection results of changing the number of filters and length of each filter with Dataset KTU.

Detection Accuracy (%) | Length of Each Filter | ||||
---|---|---|---|---|---|

3 | 4 | 5 | 6 | ||

Number of filters | 3 | 58.99 | 58.91 | 58.92 | 58.86 |

4 | 58.80 | 59.03 | 59.38 | 58.71 | |

5 | 58.67 | 59.21 | 58.90 | 58.57 | |

6 | 59.31 | 59.09 | 58.62 | 58.60 |

Datasets | Classifers | Recall (%) | Rate of False Detection (%) | Accuracy (%) |
---|---|---|---|---|

SIMTU | Softmax | 70.1 | 13.5 | 79.6 |

SIMTU | Random forest | 81.2 | 10.1 | 86.0 |

STU | Softmax | 92.3 | 28.3 | 77.9 |

STU | Random forest | 87.4 | 28.5 | 76.2 |

KTU | Softmax | 59.8 | 34.9 | 63.9 |

KTU | Random forest | 74.4 | 37.1 | 65.2 |

SIMTE | Softmax | 78.5 | 30.1 | 72.4 |

SIMTE | Random forest | 80.4 | 16.4 | 82.3 |

STE | Softmax | 81.5 | 28.4 | 74.6 |

STE | Random forest | 78.1 | 29.0 | 73.1 |

KTE | Softmax | 69.7 | 37.1 | 64.3 |

KTE | Random forest | 75.5 | 36.8 | 65.8 |

Tests | Signal | Recall (%) | Rate of False Detection (%) | Accuracy (%) |
---|---|---|---|---|

1 | L1 C/A | 79.8 | 16.2 | 82.2 |

1 | L2P(Y) | 77.7 | 16.4 | 81.2 |

1 | L2 C | 82.2 | 25.8 | 76.8 |

1 | L5 | 86.8 | 13.6 | 86.6 |

2 | L1 C/A | 81.5 | 28.4 | 74.6 |

2 | L2P(Y) | 80.2 | 34.4 | 69.1 |

2 | L2 C | 74.5 | 34.4 | 67.7 |

2 | L5 | 66.2 | 37.7 | 63.0 |

3 | L1 C/A | 75.7 | 35.9 | 66.7 |

3 | L2P(Y) | 81.9 | 35.0 | 68.9 |

4 | L1 C/A | 73.8 | 31.1 | 61.5 |

4 | L2P(Y) | 69.4 | 37.5 | 55.2 |

**Table 10.**RMS errors in horizontal and height components and their percentage improvement (when comparing with the results of other stochastic models) of the tested stochastic models based on the proposed method in Dataset KTE1.

RMS Error [mm] | Standard Least Square Solution | Elevation Model | SIGMA-ε Model | Proposed Method |
---|---|---|---|---|

Horizontal | 10.2 | 8.3 | 6.2 | 6.7 |

Vertical | 27.0 | 28.8 | 21.5 | 18.9 |

3D | 28.8 | 30.0 | 22.4 | 20.1 |

%improvement | ||||

Horizontal | - | 18.5 | 39.5 | 34.4 |

Vertical | - | −6.8 | 20.2 | 29.8 |

3D | - | −3.9 | 22.4 | 30.4 |

**Table 11.**RMS errors in horizontal and height components and their percentage improvement (when comparing with the results of other stochastic models) of the tested stochastic models based on the proposed method in Dataset KTE3.

RMS Error [mm] | Standard Least Square Solution | Elevation Model | SIGMA-ε Model | Proposed Method |
---|---|---|---|---|

Horizontal | 13.8 | 11.7 | 11.8 | 11.7 |

Vertical | 27.2 | 22.1 | 24.2 | 22.1 |

3D | 30.5 | 25.1 | 26.9 | 25.0 |

%improvement | ||||

Horizontal | - | 14.6 | 14.1 | 15.0 |

Vertical | - | 18.7 | 11.3 | 18.9 |

3D | - | −3.9 | 22.4 | 30.4 |

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## Share and Cite

**MDPI and ACS Style**

Quan, Y.; Lau, L.; Roberts, G.W.; Meng, X.; Zhang, C.
Convolutional Neural Network Based Multipath Detection Method for Static and Kinematic GPS High Precision Positioning. *Remote Sens.* **2018**, *10*, 2052.
https://doi.org/10.3390/rs10122052

**AMA Style**

Quan Y, Lau L, Roberts GW, Meng X, Zhang C.
Convolutional Neural Network Based Multipath Detection Method for Static and Kinematic GPS High Precision Positioning. *Remote Sensing*. 2018; 10(12):2052.
https://doi.org/10.3390/rs10122052

**Chicago/Turabian Style**

Quan, Yiming, Lawrence Lau, Gethin Wyn Roberts, Xiaolin Meng, and Chao Zhang.
2018. "Convolutional Neural Network Based Multipath Detection Method for Static and Kinematic GPS High Precision Positioning" *Remote Sensing* 10, no. 12: 2052.
https://doi.org/10.3390/rs10122052