# Experimental Assessment of UWB and Vision-Based Car Cooperative Positioning System

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## Abstract

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## 1. Introduction

## 2. Related Works and Objective of the Paper

- UWB ranging performance in general; for example, the success rate of ranging measurements, the ranging accuracy dependence on the range.
- Positioning performance of the platforms using only infrastructure ranging; i.e., V2I-based positioning.
- Assessment on vision and UWB relative positioning; i.e., V2V based relative positioning.
- Cooperative positioning of the platforms based on V2V and V2I ranges.
- Cooperative positioning of the platforms based on V2V and V2I ranges and partial GPS/GNSS data.

## 3. Experiment Setup

#### 3.1. Setting Up the Local Positioning System

#### 3.2. Trajectory

#### 3.3. Platform Setup

- Sensors on the GPSVan: all UWB devices mounted on the vehicle, two GNSS receivers and one GoPro camera (GPR1).
- Sensors on other cars: GNSS receiver, two Pozyx UWB devices (on the right and of the left of each vehicle), and one TimeDomain UWB transceiver.
- Static network of 10 TimeDomain UWB transceivers.

## 4. Data Characterisation

#### 4.1. TimeDomain Static UWB Network

- Average error;
- Median error;
- Standard deviation of the error;
- Median absolute deviation (MAD) = median $\left(\phantom{\rule{3.33333pt}{0ex}}\right|\left\{{e}_{r}\right\}$ − median ($\left\{{e}_{r}\right\}$) $\left|\phantom{\rule{3.33333pt}{0ex}}\right)$;
- Median absolute error = ${\sum}_{i=1}^{n}\left|{e}_{r}\left(i\right)\right|/n$;
- Root mean square (RMS) error = $\sqrt{{\sum}_{i=1}^{n}{e}_{r}{\left(i\right)}^{2}/n}$;
- Percentage of errors larger than 1 m;
- Percentage of unreliable measurements in accordance to the QR criteria, as mentioned above,

#### 4.2. TimeDomain V2V UWB Network

#### 4.3. Pozyx V2V UWB Network

#### 4.4. NLOS Detection and UWB Calibration

#### 4.5. GoPro Video

## 5. Positioning Approaches

**V2I UWB positioning:**vehicle position is estimated by exploiting only UWB range measurements with the static UWB infrastructure (Section 5.1).**Vision + UWB relative positioning:**position of the other vehicles are computed by the GPSVan given the V2V UWB ranges and the visual information provided by the GoPro camera GPR1 (Section 5.2).**Cooperative positioning:**vehicle position is estimated by exploiting V2V UWB range measurements, V2I measurements, visual information, and partial GPS/GNSS data (Section 5.3).

#### 5.1. V2I UWB Positioning

#### 5.2. Relative Positioning with Vision and UWB

- if just one UWB range measurement ${r}_{1}$ is available (assume, without loss of generalization, that ${r}_{1}$ is provided by the right Pozyx network), then the vehicle ${c}_{{i}^{\prime}}$ position is estimated as the intersection between the line passing through the GPR1 optical centre associated with the direction ${\mathbf{u}}_{\alpha}$ (black solid line in Figure 15) and the circumference associated with the ${r}_{1}$ range measurement (light blue dashed circumference in Figure 15);
- if two UWB range measurements ${r}_{1}$, ${r}_{2}$ are available, then the vehicle ${c}_{{i}^{\prime}}$ relative position with respect to the GPSVan is estimated along with the vehicle heading orientation by combining the three measurements. Let ${\mathbf{u}}_{H}^{{c}_{i}}\left({t}_{k}\right)$ be car ${c}_{i}$ heading direction at time ${t}_{k}$, and ${\mathbf{u}}_{T}^{{c}_{i}}\left({t}_{k}\right)$ the corresponding transverse direction, then $({\mathbf{u}}_{T}^{{c}_{i}}\left({t}_{k}\right),{\mathbf{u}}_{H}^{{c}_{i}}\left({t}_{k}\right))$ define a car local reference system (see Figure 16). It is worth noting that ${\mathbf{u}}_{H}^{{c}_{i}}\left({t}_{k}\right)$ can be uniquely identified in the 2D space by an angle $\theta $, and that once ${\mathbf{u}}_{H}^{{c}_{i}}\left({t}_{k}\right)$ is known, then ${\mathbf{u}}_{T}^{{c}_{i}}\left({t}_{k}\right)$ is uniquely determined as well. Assume also that the relative position of the two Pozyx devices is known in the car local reference system. Then, vehicle relative position ${\mathbf{p}}_{r}^{{c}_{{i}^{\prime}}}$ and orientation with respect to the GPSVan are determined by solving the following optimisation problem:$$\{{\widehat{\mathbf{p}}}_{r}^{{c}_{{i}^{\prime}}}\phantom{\rule{3.33333pt}{0ex}},\phantom{\rule{3.33333pt}{0ex}}\widehat{\theta}\}=arg\underset{{\mathbf{p}}_{r}^{{c}_{{i}^{\prime}}},\theta}{min}\left(\frac{{\left({r}_{1}-{\widehat{r}}_{1}\left({\mathbf{p}}_{r}^{{c}_{{i}^{\prime}}},\widehat{\theta}\right)\right)}^{2}}{{\sigma}_{{r}_{1}}^{2}}+\frac{{\left({r}_{2}-{\widehat{r}}_{2}\left({\mathbf{p}}_{r}^{{c}_{{i}^{\prime}}},\widehat{\theta}\right)\right)}^{2}}{{\sigma}_{{r}_{2}}^{2}}+\frac{{\left(\alpha -\widehat{\alpha}\left({\mathbf{p}}_{r}^{{c}_{{i}^{\prime}}},\widehat{\theta}\right)\right)}^{2}}{{\sigma}_{\alpha}^{2}}\right),$$

#### 5.3. Cooperative Positioning

## 6. Results and Discussion

#### 6.1. Positioning with a Static UWB Infrastructure (V2I)

#### 6.2. Relative Positioning with Vision and UWB

#### 6.3. Cooperative Positioning

- V2I: positioning obtained by considering only UWB V2I measurements. Since V2I measurements are available only for the GPSVan (here and in all the cases where they are used), positions of all the other cars inside the main road area are obtained just as Kalman predictions from the last available GNSS measurements, i.e., their trajectories will be straight lines until GNSS updates are available.
- V2I + V2V cooperative approach: cooperative positioning obtained by considering UWB V2I and V2V measurements.
- V2I + V2V + vision cooperative approach: cooperative positioning obtained by considering UWB V2I and V2V measurements and the information coming from the vision based relative positioning system.
- V2I + V2V + partial random GNSS availability: cooperative positioning obtained by considering UWB V2I and V2V measurements and a certain percentage of GNSS measurements randomly available in the main road area (car and time instant of any available measurement are randomly selected). The percentage of available GNSS measurements varies from 0.5% to 4%.
- V2V + GNSS available on certain vehicles: cooperative positioning obtained by considering all UWB V2V measurements and GNSS measurements available on certain cars, varying the number of cars from 1 to 3.

**b**)) and of the V2I + V2V + vision approach (column (

**c**)), compared with the reference (GNSS-based) solution (column (

**a**)). Solid black lines connecting vehicles are shown when the corresponding UWB V2V range measurements are available. Both Figure 20 and Figure 22 confirm the positive impact of vision on the cooperative positioning performance.

- V2I + V2V: GPSVan is provided with UWB V2I measurements, whereas all the other cars can only exploit UWB V2V measurements to determine their positions.
- V2V + (${n}_{G}=1$): GPSVan is provided with GNSS measurements, whereas all the other cars can only exploit UWB V2V measurements to determine their positions.
- V2V + (${n}_{G}=2$): GPSVan and Honda are provided with GNSS measurements, whereas the other cars can only exploit UWB V2V measurements to determine their positions.
- V2V + (${n}_{G}=3$): GPSVan, Honda, and Acura are provided with GNSS measurements, whereas Toyota can only exploit UWB V2V measurements to determine its position.

**b**)) and the V2I + V2V + (${n}_{G}=2$) (column (

**c**)), compared with the reference (GNSS-based) solution (column (

**a**)). Solid black lines connecting vehicles are shown when the corresponding UWB V2V range measurements are available. Figure 25 confirms the positioning performance improvement that is typically obtained when ${n}_{G}\ge 2$.

#### 6.4. Discussion

- First, the results reported in Table 7 show that the use of UWB V2V measurements allowed to assess car relative distances with an uncertainty approximately at meter level. Instead, the car relative distance assessment reached an uncertainty at decimeter level when ranges from at least other two cars are available on all the vehicles (${n}_{c}\ge 2$). Hence, in such working conditions, the relative distance between cars can be quite effectively assessed.
- The first goal of Table 8 is that of evaluating the collaborative positioning performance of the V2I + V2V approach: the obtained 2D positioning error is at meter level (median = 2.4 m, MAD = 3.2 m), with a quite clear improvement when working in good V2V measurement conditions, i.e., median error = 2.0 m, MAD = 2.0 m when ${n}_{c}=3$. The positioning error increases with the outage time (see Figure 20a), as expected. The median error is lower than 2 m for approximately 8 s of outage. It is worth noting that V2I ranges were available only for the GPSVan; hence, V2I enables computing the absolute positioning of the GPSVan, whereas the positions of the other cars can be assessed only through the V2V measurements.
- Then, Table 8 and Figure 20b show that the introduction of vision in the positioning algorithm can reduce the error (median = 2.3 m, MAD = 2.0 m) and its increase with the outage time (the median error is lower than 2 m for approximately 12 s of outage). Similarly to the V2I + V2V case, the positioning error is reduced when working in good V2V measurement conditions: median error = 1.5 m, MAD = 1.6 m, when ${n}_{c}=3$. Since video frames have currently been extracted from the video (and processed) at 10 Hz, processing them at the original video frame rate is expected to improve the overall positioning results.
- Figure 22 shows an example of the (
**b**) V2I + V2V and (**c**) V2I + V2V + vision performance on a portion of the car tracks, to be compared with (**a**) the reference one. By comparing the car positions in (**b**) with those in (**a**), it is quite apparent that the relative distances between cars are quite consistent with the correct ones when the corresponding range measurements are available, as expected. However, since only the GPSVan absolute position can be assessed (from the V2I ranges), the absolute positioning problem for the other cars is ill posed. Let us consider the static positioning problem on a certain time instant: any rotation, pivoting on the GPSVan, of the real car configuration is equally acceptable. Instead, since the vision-aided solution includes also some (indirect) information on the car configuration orientation (i.e., the angle $\alpha $ in Figure 7), such solution is less prone to the above mentioned ill-posedness. - The above considerations suggest that, in order to avoid ill-posed solutions in the UWB-based cooperative positioning, either some information shall be provided by external sensors (e.g., vision), or more than one vehicle shall be provided with measurements to enable absolute positioning, e.g., V2I measurements.
- The results reported in Table 9 aim at investigating the absolute positioning performance that can be achieved when GNSS is partially available in the main road area. In particular, the performance is evaluated varying the percentage of available GNSS measurements. Comparing the results of Table 9 with those of Table 10, it is quite apparent the importance of the availability of a sufficient number of successful V2V range measurements in order to effectively propagate to the other vehicles the information provided by the few available GNSS positions. In particular, the results obtained when ${n}_{c}=3$ (Table 10) with a certain amount of GNSS measurements are similar to those obtained in Table 9, doubling the percentage of GNSS measurements. Overall, the obtained positioning error is at meter level, reaching sub-meter level in good working conditions for the V2V communications and with 4% of the GNSS measurements (last column in Table 10). The median error is usually lower than 2 m for more than 20 outage seconds when at least 2% of the GNSS measurements are available, as shown in Figure 23. These results confirm that the use of a cooperative approach and an effective V2V ranging system can reduce the need for GNSS measurements when aiming at meter/sub-meter positioning of groups of vehicles.
- Finally, the last three columns of Table 11 and Table 12 aim at evaluating the performance of the cooperative positioning (evaluated on the same car, e.g., Toyota) when varying the number of vehicles ${n}_{G}$ provided with GNSS measurements in the main road area. The obtained results show a significant improvement when increasing ${n}_{G}$ from 1 to 2, whereas the difference between ${n}_{G}=2$ and 3 is quite modest. Similarly to the previously considered cases, Table 12 confirms that good V2V ranging is very important for the efficiency of the cooperative approach, as expected. Furthermore, Figure 25 shows that, despite the fact that ${n}_{G}=2$ is not sufficient for theoretically ensuring to avoid ill-posedness of the positioning solution, it is enough to avoid it in the considered example and in most real-world scenarios as well.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**A group of four vehicles equipped with GPS/GNSS, UWB, IMU and camera sensors. Red lines show 3 out of the 6 inter-vehicle ranges (V2V), blue lines show 4 ranges from 2 infrastructure points to 3 vehicles (V2I), and dashed lines show GPS/GNSS signals; note that not all signal receptions are shown.

**Figure 2.**Four vehicles, bicycle and pedestrian platforms used in the experiments with the network of infrastructure nodes.

**Figure 4.**Typical drive pattern of vehicles (blue track) and TimeDomain UWB anchors (circular red marks).

**Figure 8.**TimeDomain UWB static network: Comparing UWB ranging with distance computed using GPSVan reference trajectory for two different anchors, namely UWB204 (

**a**) and UWB102 (

**b**).

**Figure 9.**Influence of distance on the UWB measurement success rate. UWB networks: (

**a**) TimeDomain V2I static network, (

**b**) TimeDomain V2V network, (

**c**) Pozyx V2V right network, (

**d**) Pozyx V2V left network.

**Figure 10.**Influence of distance on the UWB error. UWB networks: (

**a**) TimeDomain V2I static network, (

**b**) TimeDomain V2V network, (

**c**) Pozyx V2V right network, (

**d**) Pozyx V2V left network.

**Figure 11.**TimeDomain UWB static network: (

**a**) number of simultaneously available range measurements, (

**b**) ranging error distribution.

**Figure 12.**TimeDomain UWB V2V network: ranging error distribution of the TimeDomain rover mounted on the GPSVan with those on the other three vehicles.

**Figure 13.**Pozyx UWB V2V ranging. (

**a**) Comparing UWB ranging with distance computed using GNSS trajectories for GPSVan−Toyota, (

**b**) ranging error distribution: left (violet) and right (yellow) net.

**Figure 14.**Examples of car detection in the GoPro video: (

**a**) Acura SUV and (

**b**) Toyota Corolla detected in two different frames.

**Figure 18.**(

**a**) 2D positioning error obtained combining vision with UWB and decomposition of such error along the GPSVan heading direction and its orthogonal one. (

**b**) Relation between the 2D positioning error and the vision−based angle measurement error.

**Figure 19.**(

**a**) Distribution ofthe vision−based angular measurement error [deg]. (

**b**) Example of vehicle with associated detection box larger than expected.

**Figure 20.**(

**a**) 2D positioning error as a function of the outage time. Comparison between: (

**a**) UWB V2I + V2V and (

**b**) UWB V2I + V2V + vision approaches.

**Figure 21.**Example: four vehicles divided in two groups moving in the main road area in opposite directions.

**Figure 22.**Positioning results in four successive time instants (${t}_{1},\cdots ,{t}_{4}$) during the example of Figure 21: ith row of the figure corresponds to time instant ${t}_{i}$. Comparison of different approaches: (

**a**) GNSS (reference), (

**b**) UWB V2I + V2V, (

**c**) UWB V2I + V2V + vision.

**Figure 23.**2D positioning error as a function of the outage time. Comparison between the performance obtained in 100 Monte Carlo simulations varying, from 0.5% to 4%, the percentage of available GNSS measurements in the main road area.

**Figure 24.**Example: four vehicles moving in the main road area in the same direction on two different lanes.

**Figure 25.**Positioning results in three successive time instants (${t}_{1},\cdots ,{t}_{3}$) during the example of Figure 24: ith row of the figure corresponds to time instant ${t}_{i}$. Comparison of different approaches: (

**a**) GNSS (reference), (

**b**) UWB V2I + V2V, (

**c**) UWB V2I + V2V + (${n}_{G}=2$).

Platforms | GPS | TD V2I | TD V2V | Pozyx-L | Pozyx-R | IMU | Camera |
---|---|---|---|---|---|---|---|

GPSVan, reference vehicle | X | X | X | X | X | X | X |

Honda Accord | X | X | X | X | |||

Acura SUV | X | X | X | X | |||

Toyota Corolla | X | X | X | X | |||

Bicycle | X | X | |||||

Pedestrian | X | X | X | X |

V2I TD | V2V TD | V2V Pozyx R | V2V Pozyx L | |
---|---|---|---|---|

Avg. measurement sample period [s] | 0.032 | 0.031 | 0.018 | 0.018 |

Avg. ranging loop period [s] | 0.32 | 0.24 | 0.16 | 0.15 |

Avg. success rate [%] | 13.4 | 34.9 | 39.0 | 31.3 |

Max. range [m] | 96 | 168 | 139 | 73 |

V2I TD | V2V TD | V2V Pozyx R | V2V Pozyx L | |
---|---|---|---|---|

Average [cm] | 6 | 1 | 27 | 15 |

Median [cm] | −1 | −1 | 20 | 11 |

Stand. dev. [cm] | 74 | 108 | 70 | 69 |

MAD [cm] | 18 | 45 | 37 | 29 |

Mean. Abs. err. [cm] | 17 | 41 | 41 | 30 |

RMS [cm] | 74 | 109 | 75 | 71 |

Max [m] | 13 | 21 | 39 | 46 |

$\%\left|\mathrm{err}.\right|\ge 1$ m | 1.8 | 6.4 | 9.6 | 4.3 |

% unreliable ranges (QR) | 3.1 | 6.0 | – | – |

V2I TD | V2V TD | V2V Pozyx R | V2V Pozyx L | |
---|---|---|---|---|

Data examined by RF (%) | 60.8 | 44.7 | 89.6 | 88.3 |

RF accuracy (%) | 99.6 | 97.6 | 94.1 | 96.7 |

Median [cm] | 0 | 0 | 2 | 2 |

MAD [cm] | 13 | 36 | 33 | 27 |

Mean. Abs. err. [cm] | 12 | 34 | 32 | 27 |

RMS [cm] | 61 | 88 | 67 | 68 |

$\%\left|\mathrm{err}.\right|\ge 1$ m | 1.4 | 5.2 | 5.8 | 3.4 |

All Area | Main Road | Main Road Along Track | Main Road Across-Track | |
---|---|---|---|---|

Median [cm] | 16 | 12 | 2 | −3 |

MAD [cm] | 268 | 31 | 15 | 21 |

Mean. Abs. err. [cm] | 182 | 30 | 15 | 21 |

RMS [cm] | 764 | 73 | 36 | 63 |

$\%\left|\mathrm{err}.\right|\ge 2$ m | 13.3 | 3.1 | 2.7 | 4.6 |

2D Error | Heading | Transverse | |
---|---|---|---|

Median [cm] | 24 | 12 | −11 |

MAD [cm] | 50 | 26 | 37 |

Mean. Abs. err. [cm] | 53 | 31 | 39 |

RMS [cm] | 91 | 58 | 70 |

$\%\left|\mathrm{err}.\right|\ge 1$ m | 16.7 | 8.9 | 11.0 |

V2I | V2I + V2V | V2I + V2V (${\mathbf{n}}_{\mathbf{c}}\ge \mathbf{2}$) | V2I + V2V (${\mathbf{n}}_{\mathbf{c}}=\mathbf{3}$) | |
---|---|---|---|---|

Median [m] | 0.0 | 0.00 | 0.00 | 0.00 |

MAD [m] | 16.0 | 0.80 | 0.30 | 0.24 |

Mean. Abs. err. [m] | 11.5 | 0.79 | 0.30 | 0.24 |

RMS [m] | 34.2 | 2.36 | 0.52 | 0.41 |

V2I | V2I + V2V | V2I + V2V (${\mathbf{n}}_{\mathbf{c}}=\mathbf{3}$) | V2I + V2V + Vision | V2I + V2V + Vision (${\mathbf{n}}_{\mathbf{c}}=\mathbf{3}$) | |
---|---|---|---|---|---|

Median [m] | 13.4 | 2.4 | 2.0 | 2.3 | 1.5 |

MAD [m] | 33.6 | 3.2 | 2.0 | 2.0 | 1.6 |

Mean. Abs. err. [m] | 31.2 | 4.2 | 3.0 | 3.1 | 2.4 |

RMS [m] | 61.7 | 5.9 | 4.0 | 4.2 | 3.3 |

**Table 9.**Cooperative positioning: 2D positioning error, excluding GPSVan, varying the percentage of GNSS measurements available in the main road area.

0.5% | 1% | 2% | 4% | |
---|---|---|---|---|

Median [m] | 2.1 | 1.4 | 0.9 | 0.6 |

MAD [m] | 4.1 | 2.8 | 1.7 | 0.9 |

Mean. Abs. err. [m] | 4.5 | 3.1 | 1.9 | 1.1 |

RMS [m] | 8.1 | 5.9 | 3.7 | 1.9 |

**Table 10.**Cooperative positioning: 2D positioning error, excluding GPSVan, varying the percentage of GNSS measurements available in the main road area, restricted only to time instants when cars received V2V measurements from all vehicles (${n}_{c}=3$).

0.5% | 1% | 2% | 4% | |
---|---|---|---|---|

Median [m] | 1.5 | 1.0 | 0.7 | 0.5 |

MAD [m] | 2.4 | 1.5 | 0.8 | 0.5 |

Mean. Abs. err. [m] | 2.8 | 1.8 | 1.1 | 0.7 |

RMS [m] | 4.6 | 3.0 | 1.7 | 1.0 |

**Table 11.**Cooperative positioning: Toyota 2D positioning error varying the number of cars ${n}_{G}$ provided with GNSS measurements in the main road area.

V2I + V2V | V2V + $({\mathit{n}}_{\mathit{G}}=1)$ | V2V + $({\mathit{n}}_{\mathit{G}}=2)$ | V2V + $({\mathit{n}}_{\mathit{G}}=3)$ | |
---|---|---|---|---|

Median [m] | 4.0 | 3.7 | 1.2 | 1.2 |

MAD [m] | 6.6 | 5.5 | 3.6 | 2.9 |

Mean. Abs. err. [m] | 7.7 | 6.6 | 3.5 | 3.0 |

RMS [m] | 12.8 | 11.5 | 8.5 | 5.9 |

**Table 12.**Cooperative positioning: Toyota 2D positioning error varying the number of cars ${n}_{G}$ provided with GNSS measurements in the main road area, restricted only to time instants when Toyota received V2V measurements from all cars.

V2I + V2V | V2V + (${\mathit{n}}_{\mathit{G}}=1$) | V2V + (${\mathit{n}}_{\mathit{G}}=2$) | V2V + (${\mathit{n}}_{\mathit{G}}=3$) | |
---|---|---|---|---|

(${\mathbf{n}}_{\mathbf{c}}=\mathbf{3}$) | (${\mathbf{n}}_{\mathbf{c}}=\mathbf{3}$) | (${\mathbf{n}}_{\mathbf{c}}=\mathbf{3}$) | (${\mathbf{n}}_{\mathbf{c}}=\mathbf{3}$) | |

Median [m] | 4.0 | 3.7 | 0.8 | 0.8 |

MAD [m] | 4.4 | 4.3 | 1.2 | 0.9 |

Mean. Abs. err. [m] | 6.0 | 5.5 | 1.5 | 1.2 |

RMS [m] | 8.3 | 7.6 | 2.7 | 2.2 |

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## Share and Cite

**MDPI and ACS Style**

Masiero, A.; Toth, C.; Gabela, J.; Retscher, G.; Kealy, A.; Perakis, H.; Gikas, V.; Grejner-Brzezinska, D.
Experimental Assessment of UWB and Vision-Based Car Cooperative Positioning System. *Remote Sens.* **2021**, *13*, 4858.
https://doi.org/10.3390/rs13234858

**AMA Style**

Masiero A, Toth C, Gabela J, Retscher G, Kealy A, Perakis H, Gikas V, Grejner-Brzezinska D.
Experimental Assessment of UWB and Vision-Based Car Cooperative Positioning System. *Remote Sensing*. 2021; 13(23):4858.
https://doi.org/10.3390/rs13234858

**Chicago/Turabian Style**

Masiero, Andrea, Charles Toth, Jelena Gabela, Guenther Retscher, Allison Kealy, Harris Perakis, Vassilis Gikas, and Dorota Grejner-Brzezinska.
2021. "Experimental Assessment of UWB and Vision-Based Car Cooperative Positioning System" *Remote Sensing* 13, no. 23: 4858.
https://doi.org/10.3390/rs13234858