Keywords

1 Introduction

Autonomous vehicles (AVs) can not only free people from driving but are also expected to solve various social problems. One key technical factor for autonomous vehicles on the road is vehicle localization. It is important because the autonomous system will maneuver the vehicle based on this understanding. It requires high accuracy, precision (the modest error accepted for a typical 2 m wide vehicle running in a 3 m wide lane is 50 cm), and robustness towards various road conditions. Conventional localization methods use GNSS (global navigation satellite system) or visual sensors such as cameras and LiDARs (light detection and ranging) [3]. However, these methods have conditions where their localization accuracy can degrade. Therefore, in practice, multiple methods complement each other to increase robustness.

Fig. 1.
figure 1

Image of vehicle localization by EMF. The geomagnetic field is altered by artificial objects such as manholes and other ferromagnetic objects.

Full size image

This work proposes to use the environmental magnetic field (EMF) for AV localization to complement the conventional methods. Here, EMF refers to the combination of the Earth’s geomagnetic field and magnetic field induced by man-made objects. EMF has two features that are useful for localization: it has local fluctuations that can be paired with coordinate positions and is time-invariant within a practical time scale [9]. Figure 1 shows the concept image of the proposed AV localization method using EMF. Various ferromagnetic objects can be found in road environments, such as manholes, railroad tracks, and underground structures. Fluctuations of the magnetic field caused by these objects are used for localization.

EMF localization has recently been studied for relatively small indoor mobile robots such as in [1, 5, 7]. However, there are a few examples of EMF localization for road vehicles and problems when applying the works for AV localization. One of them is that their localization accuracy is unacceptable, possibly because there are less useful magnetic field features in outdoor environments. [6] proposed a method using only the magnetometer data, but the localization accuracy was poor, with several hundred meters of error in worst cases. Another problem is that previous works have only made a topological map of the measured magnetic field along the vehicle trajectory. However, this is insufficient for AV localization since the vehicle needs information about the position along the path and within the road or lane width.

2 Proposed Localization Method

This work proposes to overcome the problems of the current EMF localization for road vehicles by the following methods: First, a two-dimensional magnetic field map is created using Gaussian process (GP) regression. Second, magnetic markers can be embedded on roads in places with few magnetic features to enhance such features. Finally, the Monte Carlo method is utilized for the localization algorithm.

GP regression is a non-parametric and Bayesian approach to regression that can model non-linear function relations [4]. Therefore, it is suitable for modeling EMF with limited observation points, and previous works aimed at an indoor environment produced a 2D EMF map from limited observations [1, 7].

In areas where EMF fluctuations are expected to be scarce, magnetic markers are added to enhance the fluctuations of EMF. Unlike the conventional methods such as the magnetic positioning system [2], where the markers’ coordinate information is measured and stored in a database for localization, the proposed method does not require such coordinate information. This is because the fluctuations of EMF caused by magnetic markers are modeled into the EMF map with other EMF fluctuations caused by various other reasons.

The Monte Carlo localization (MCL) algorithm utilizes the particle filter algorithm, expressing the vehicle states, such as its coordinate position and heading, as multiple “particles.” Unlike other localization methods, such as Kalman filtering, MCL can approximate any distribution without an explicit landmark [8].

Fig. 2.
figure 2

Image of experimental vehicle running on the experimental field. Magnetic markers are embedded in the lane where the experiment vehicle is running.

Full size image

3 Experimental Condition

The proposed method was validated through data obtained from the experiment vehicle. Figure 2 shows the overview of the experimental setup. Data collection was conducted at the ITS R&R experimental field at the University of Tokyo. The experimental field has an actual scale model of a road environment. Some sections have magnetic markers embedded at the center of the lane at 2 m intervals, which can be used to generate the EMF fluctuations needed for the proposed method. EMF measurement was conducted at a 50 m straight section with magnetic markers embedded in the road.

Measurements were done by a sensor unit attached to an experiment vehicle provided by Aichi Steel Corporation. The sensor unit is attached to the vehicle’s rear, as shown in Fig. 2. The sensor unit comprises 16 3-axis magnetometers installed in a straight line 50 mm apart. The vehicle also has a velocity sensor, inertial measurement unit (IMU), and GNSS antenna.

Conditions with and without other vehicles were conducted to assess the proposed method’s robustness towards other road members. An electric vehicle (Mitsubishi iMiev) was used for the other nearby vehicle, with 4 different situations considered: the vehicle being parked with its power off, the vehicle parked with power on, the vehicle running next to the experiment vehicle, and the vehicle running towards the vehicle in the adjacent lane.

4 EMF Map Generation and Discussion

Figure 3 shows the EMF map generated by the proposed method. It was generated within X = −2 m to + 2 m and Y = −1 m to + 53 m at the resolution of 1 cm. The figure is plotted with the original measurement data plotted in blue points. The X and Y axes show the coordinate positions, and the Z-axis with the color bar shows the magnetic field intensity in µT.

As seen in Fig. 3, the proposed method generated the EMF map that retained the magnetic field fluctuations of the original measurements. A distinctive spike shape can be seen around the locations of magnetic markers.

Fig. 3.
figure 3

The generated Z-axis EMF map.

Full size image

5 Localization Results and Discussion

The proposed localization method was applied to measurement data obtained from the experiment vehicle to validate the proposed method. Figure 4 shows the localization result of the condition without any other vehicles nearby. The X and Y axis show the coordinates, and the vehicle ran in the upward direction of the figure. The blue dots show the reference GNSS positions, the red line shows the estimated path of the proposed localization algorithm, and the yellow dots show the final state of the particles. It can be seen that the localization result follows the reference GNSS positions.

Fig. 4.
figure 4

The localization result of the condition without any other vehicles.

Full size image
Fig. 5.
figure 5

The localization error of different conditions.

Full size image

Figure 5 shows the localization error from the reference GNSS position of various conditions. The horizontal axis shows the GNSS position in the direction of the Y axis, and the vertical axis shows the localization error at each Y coordinate. The blue line shows the error of the condition with no other vehicle, as we saw in Fig. 4, the red line shows the error of the condition with an EV parked with its power off, the yellow line shows the error of the condition with an EV parked with its power on, and the purple line shows the error of the condition with an EV coming towards the experiment vehicle in the adjacent lane. The horizontal dashed line shows the 0.5 m error border, and the vertical line shows the Y coordinate position of the last marker observed within the experiment condition.

As seen in Fig. 5, the proposed method was able to localize the vehicle for most of the length of the experiment in the conditions listed in the legend. In the condition with an EV parked and oncoming, the vehicles passed by at around Y = 25 m, but very little effect on localization is seen. A relatively large localization error is seen for EV parked and EV oncoming conditions after the vehicle passes the last marker. This was mainly caused by a large measurement error by IMU when the vehicle stopped at the end of the measurement.

However, the localization of the condition with an EV running in parallel with the experimental vehicle was not successful, and it is not plotted in the figure. The localization failure may be due to the continuous offset from the original EMF in the measurement caused by the presence of a nearby vehicle. Our preliminary analysis in a simulated environment had a similar outcome when the measured EMF had some offset error from the original EMF.

6 Conclusion

This paper proposes a new vehicle localization method for AVs. The method uses EMF, which is a combined magnetic field of the Earth’s geomagnetic field and magnetic field induced by manmade objects. The proposed method generates a 2-D EMF map using GP regression, utilizes magnetic markers where EMF fluctuation is less present, and uses the MCL method to localize the vehicle using the generated EMF reference map.

The proposed method was validated by data obtained from an actual vehicle. It successfully localized the vehicle with high accuracy. The method also showed some robustness towards the existence of other vehicles, but it failed to localize in a condition where an EV was running parallel to the experiment vehicle. We will continue to refine the method to localize the vehicle even in the constant existence of a surrounding vehicle.