# Do we need scan-matching in radar odometry?

Vladimír Kubelka, Emil Fritz and Martin Magnusson This work was supported by
Sweden’s Innovation Agency under grant number 2021-04714 (Radarize). The
authors would also like to express their gratitude to Annika Nilsson for her
part in the implementation and experimental evaluation of this work.Vladimír
Kubelka<EMAIL_ADDRESS>and Martin Magnusson
<EMAIL_ADDRESS>are with the MRO lab of the AASS research centre at
Örebro University, Sweden. Emil Fritz is with Örebro University, Sweden.

###### Abstract

There is a current increase in the development of “4D” Doppler-capable radar
and lidar range sensors that produce 3D point clouds where all points also
have information about the radial velocity relative to the sensor. 4D radars
in particular are interesting for object perception and navigation in low-
visibility conditions (dust, smoke) where lidars and cameras typically fail.
With the advent of high-resolution Doppler-capable radars comes the
possibility of estimating odometry from single point clouds, foregoing the
need for scan registration which is error-prone in feature-sparse field
environments. We compare several odometry estimation methods, from direct
integration of Doppler/IMU data and Kalman filter sensor fusion to 3D scan-to-
scan and scan-to-map registration, on three datasets with data from two recent
4D radars and two IMUs. Surprisingly, our results show that the odometry from
Doppler and IMU data alone give similar or better results than 3D point cloud
registration. In our experiments, the average position error can be as low as
0.3% over 1.8 and 4.5 km trajectories. That allows accurate estimation of 6DOF
ego-motion over long distances also in feature-sparse mine environments. These
results are useful not least for applications of navigation with resource-
constrained robot platforms in feature-sparse and low-visibility conditions
such as mining, construction, and search & rescue operations.

###### Index Terms:

4D Radar, Radar Odometry, Mobile robot, Localization

##  I Introduction

Rapid development in millimeter wave imaging radars, driven by the automotive
industry, has enabled localization and mapping in environments where we expect
deteriorated visibility conditions and dirt deposition on the sensors.
Deploying autonomous vehicles in the mining industry, construction or search &
rescue are example applications that demand such capability. Modern imaging
radars, similarly to 3D lidars, provide 3D scans of the surroundings. They are
additionally able to estimate the radial velocity of each sensed 3D point by
leveraging precise phase measurements of the returning signal. This Doppler
velocity, as we further denote it, has proven to be advantageous for odometry
methods, aiding in the segmentation of dynamic and static objects [1], as well
as introducing more constraints to the ego-motion estimation [2, 3]. Moreover,
the velocity measurement comes without the need to perform data association,
which can be challenging in feature-sparse environments, such as underground
mines.

In recent years, several approaches to radar odometry and simultaneous
localization and mapping (SLAM) have emerged. Motivated by the problem of
developing a SLAM system for an underground mining environment, we compare
several representative radar odometry estimation methods. To that end, we
deploy them on three datasets that include two distinct modern imaging radars.
Two datasets have been recorded with our mobile sensor rig: in an underground
mine (Fig. 1) and in an outdoor testing site for large wheel loaders (Figs. 3
and 4). The third dataset has been published by Zhang et al. [4] and
represents a structured urban environment. Surprisingly, using the simplest
method of directly fusing the Doppler-based radar ego-velocity with the
orientation provided by an inertial measurement unit (IMU), we are able to
achieve localization drift as low as 0.3% over $4.5\text{\,}\mathrm{km}$ and
$1.8\text{\,}\mathrm{km}$ trajectories from the mine and the outdoor testing
site. We find this experimental result useful for designing localization and
mapping systems for the mentioned applications and worth spreading in the
robotics community for further investigation. Moreover, we make our dataset
publicly available at https://github.com/kubelvla/mine-and-forest-radar-
dataset as the high-grade radars are still difficult to obtain.

Figure 1:  Detail from the Kvarntorp mine environment captured by two sensor
modalities, lidar and radar. The radar modality suffers from limited FOV,
lower resolution and fewer returns. It is however more suitable for low-
visibility conditions expected in mining.

##  II RELATED WORK

In this section, we briefly review radar odometry algorithms based on 2D
scanning radars. Then, more closely relevant to this article, we focus on the
state of the art in modern 4D radar odometry.

Classical 2D scanning radars usually provide the scans in the form of
_spectral images_ , which encode signal intensity in the radial direction for
every azimuth they measure during a single radar scan. Cen et al. [5, 6]
proposed methods to extract radar key points from such spectral images and
showed how their approach improves the scan matching. Later works such as
Barnes et al. [7] include machine-learning techniques to improve the key point
detection. Burnett at al. [8] shows the importance of addressing motion
distortion and Doppler shift in the radar data. Contrary to searching for key
points, Adolfsson et al. [9] approach the problem from the point cloud
perspective, focusing on local geometry that could better constrain the
matching process. Park et al. [10] avoid point matching altogether by applying
Fourier-Mellin transform to find correlation between subsequent radar scans.

The rapid development of 4D Doppler-capable imaging radars opens new
possibilities in object detection, motion estimation and localization. The
surveys by Venon et al. [11] and Zhou et al. [12] provide comprehensive
overview of the state of the art in this research direction. The mmWave
sensors by Texas Instruments have gained a lot of attention, as they are
lightweight and still provide tens of 3D points with Doppler velocity. Doer
and Trommer [2] propose a loosely-coupled extended Kalman filter (EKF)
filtering method, which fuses radar ego-velocity, inertial and barometric
measurements to track the pose of UAV unmanned aerial vehicle (UAV). They
develop a RANSAC-based least squares optimization algorithm to extract the
radar ego-velocity from the radar data. In their later work [13], they
incorporate global navigation satellite system (GNSS) measurements as well. In
our work, we adopt their open-source implementation to perform experiments
with our sensor suite. Contrary to a filtering approach, Kramer et al. [14]
propose a sliding window optimization algorithm that fuses Doppler and
inertial measurements to track a pose of a mobile sensor rig. They verify
their results in underground and outdoor environments. Focusing on the UAV
application, Michalczyk et al. [3, 15] propose a tightly-coupled, EKF-based
radar odometry. Their approach includes point matching, where the perceieved
distance between the matched points, together with the Doppler velocity,
serves as the residual vector for the EKF. Lu et al. [16] takes a different
direction, both radar measurements and inertial measurement are processed by a
deep neural network (DNN) to estimate pose of a mobile agent. They use a
convolutional neural network (CNN) to extract features from the radar data and
a recurrent network to analyze the inertial data. The features are fused in
following DNN stages to produce pose estimates.

As the 4D imaging radars evolve and their resolution increases, classical 3D
scan-matching methods have become feasible. Zhuang et al. [17] fuse inertial
data, Doppler-based ego-motion estimates and scan-to-submap constraints by an
iterative EKF to obtain radar odometry. In a separate module, they complete
the system into a full SLAM solution by performing a generalized ICP
(GICP)-based loop closure and global map optimization. They use a Continental
ARS548 radar with $300\text{\,}\mathrm{m}$ range and $0.3\text{\,}\mathrm{m}$
resolution that produces approximately 400 points per scan. Zhang et al. [4]
choose a classical SLAM approach with their Oculii Eagle radar sensor
(approximately 5000 points per scan in their public dataset). They modify the
SLAM network from Koide et al. [18] by adding a modified GICP matching
algorithm that takes into account the specific spatial uncertainties in radar
point clouds. Since their work and dataset are open-source, we include them in
our experimental evaluation.

Figure 2:  The pick-up truck driving through the Mine with the multi-sensor
rig attached to the roof (top). The sensor rig detail (bottom).

##  III Radar odometry variants

Figure 3:  Aerial view of the Forest environment (left, source: Google Maps©)
and the Volvo CE wheel loader equipped with the sensor rig (right).

From the variety of radar odometry methods, we choose a representative set
which is available open-source, applicable to our sensors and spans from
simple sensor fusion to advanced scan-matching.

###  III-A Doppler velocity and IMU

The simplest approach to pose estimation tested in this work exploits the
orientation provided by an IMU and ego-velocity as measured by a Doppler-
capable radar sensor. The ego-velocity is first transformed from the
coordinate frame of the moving platform to the world coordinate frame based on
the IMU attitude. It is then numerically integrated assuming constant velocity
between consecutive radar scans. This way, a trajectory expressed in the world
coordinate frame is generated. Further in the text, we refer to this approach
as to _IMU+Doppler_.

Since the radar does not directly provide the ego-velocity measurement but
rather radial components of its detected target velocities, it is necessary to
robustly process this information to estimate the ego-velocity of the radar.
For this purpose, we deploy the approach and
implementation111https://github.com/christopherdoer/reve by Doer and Trommer
[2]. Their _3-Point RANSAC-LSQ_ ego-motion estimation method applies RANSAC to
the underlying least squares optimization problem (eq. 27–32 in [2]). This
algorithm is highly efficient. The average processing time for one radar scan
is $10\text{\,}\mathrm{ms}$ in our dataset.

Figure 4:  Top-view of a yellow wheel loader navigating a forest road. From
its suite of sensors, lidar, radar and front camera are shown. The dark black
points denote the active lidar scan, which is in contrast with the colored,
front-facing radar scan.  Figure 5:  Assembled radar map of the Car Park
environment (left) denoted by black points with a live radar scan (red
points). The sensor rig (bottom right) was manually pushed along the
trajectory. The data and figures adopted from [4].

###  III-B Extended Kalman Filter fusion

In contrast to direct Doppler+IMU fusion, employing the EKF allows more
principled handling of noise in the sensor measurements and provides pose
confidence estimates. We benefit from the
implementation222https://github.com/christopherdoer/rio by Doer and Trommer
[2] which combines their 3-Point RANSAC-LSQ ego-motion estimation with
inertial and barometric measurements. The sensor measurements are fused in a
loosely-coupled manner by an EKF. There are several extensions of the
algorithm available. We choose the original _ekf-rio_ version as it does not
require a precise radar trigger signal, which we unfortunately do not get from
our radar. The algorithm applies, in that case, the incoming ego-motion
measurements with a lag of approximately $100\text{\,}\mathrm{ms}$ which can
impede the state estimation quality, especially during highly dynamical
motion. Moreover, we omit the barometer measurements as our sensor rig lacks
this sensor. The results we obtain here therefore represent a lower bound on
the odometry quality achievable by the filtering methods. We refer to this
approach as to EKF in the following text.

It is noteworthy that the works of Michalczyk et al. [3, 15] report
improvements upon [2] by employing a tightly-coupled EKF filtering for radar-
inertial odometry. They are able to achieve localization drift below 1%. It
remains an interesting question how the tightly-coupled algorithm handles the
high-grade radar scans of thousands of targets.

###  III-C Point-to-plane Iterative Closest Point with local map

The high resolution of the tested radars allow us to test methods originally
developed for registration of lidar point clouds. For testing the scan-to-
submap matching variant, we use the _norlab-icp-mapper_
333https://github.com/norlab-ulaval/norlab_icp_mapper which is open-source and
highly configurable. It supports a range of iterative closest point (ICP)
variants, from which we choose the _point-to-plane_ variant as it generally
performs well in structured and semi-structured environments. This mapper does
not support map optimization by loop closure identification, it rather builds
a monolithic map and thus behaves as a lidar odometry method. The mapper is
set to add new points into the map up to a maximum density defined by the
minimum distance between points, which is $0.1\text{\,}\mathrm{m}$ in our
experiments. Point-to-plane ICP also requires estimation of normal vectors
based on local geometry around each point in the map. In our experiments, we
use 15 nearest points for that. Also, preliminary tests have shown that this
mapper requires a prior motion estimate when deployed on the radar data. We
thus provide the Doppler+IMU pose as the prior in all experiments.

The ICP algorithm in the mapper offers full 6- degrees of freedom (DOF) pose
estimation, or a constrained 4-DOF pose estimation. In the 4-DOF variant, only
position and heading are optimized in the point cloud registration, the other
two DOF are directly adopted by the mapper from the IMU-provided orientation.
In this work, we test both variants, and refer to them as to _ICP_ and _ICP
4DOF_.

###  III-D Scan-to-scan matching variants

The final group of radar odometry variants tested in this work employs the
scan-to-scan matching, which is often used in front-end modules of larger SLAM
frameworks. Zhang et al. [4] successfully applies this approach in a SLAM
framework with a modern imaging radar (Oculii Eagle). Since their
implementation of the SLAM framework is open-
source444https://github.com/zhuge2333/4DRadarSLAM, we include it here for
testing their radar odometry with our radar dataset. Moreover, they provide
one session from their dataset which in turn allows us to test all the other
approaches with the Oculii Eagle radar. Their radar odometry front-end is
highly configurable, allowing users to choose from several other scan-matching
algorithms. We choose to test their adaptive probability distribution-GICP
(APDGICP) variant of GICP. Their scan-matching method can function without a
prior motion estimate, yet we modify the code to include the option to use the
Doppler+IMU odometry prior. This makes the comparison with the scan-to-submap-
matching variants fair. When providing the prior, we refer to the method as to
_APDGICP IMU Prior_ , _APDGICP_ otherwise.

We also choose to test their implementation normal distributions transform
(NDT) scan-matching algorithm as it is often used in lidar odometry solutions.
For NDT, we always use the Doppler+IMU prior and refer to it as to _NDT_ in
the evaluation.

##  IV Experiments and Analysis

Figure 6: The Mine environment recorded with the Sensrad Hugin radar. The 4DOF
ICP is omitted from this plot for clarity, its vertical drift would be limited
compared to the standard ICP shown in red. Similarly, the scan-to-scan
matching odometries are not shown for their fast divergence. Figure 7: The
translation component of APE in the Mine for all discussed odometry variants.
Figure 8: The translation component of APE in the Forest for all discussed
odometry variants. Figure 9: The Car Park experiment from [4] recorded with
the Oculii Eagle radar. Only selected odometry variants shown for better
clarity. Figure 10: The APE values for the Car Park environment for all
discussed odometry variants.

This section first introduces the two environments used for recording the
experimental trajectories and then one experiment adopted from the dataset
published by Zhang [4]. The details about the sensor suites used to record the
experiments are provided as well. Subsequently, the performance of the
discussed radar odometry approaches is studied by the means of the absolute
pose error (APE) and relative pose error (RPE) metrics which are widely used
for this purpose.

###  IV-A Environment and sensor setup

Motivated by research towards SLAM in harsh environmental conditions, two
field datasets were recorded: one in the Kvarntorp research mine outside of
Örebro, Sweden, and one at an outdoor testing site for Volvo Construction
Equipment wheel loaders and dumpers in Eskilstuna, Sweden.

The Kvarntorp test mine provides a model environment for underground mining
industry applications. A $4500\text{\,}\mathrm{m}$-long run was recorded with
a sensor rig attached to the roof of a pick-up truck as shown in Fig. 2. The
average speed was $21\text{\,}\mathrm{km}\text{\,}{\mathrm{h}}^{-1}$ which is
close to the max safely drivable speed in the mine. Fig. 1 gives a general
impression of the underground tunnels. At some locations, the tunnels are
straight with no side-tunnels and these sections are generally the most
demanding for any kind of SLAM, regardless the modality. On the other hand,
locations with side-tunnels provide a large number of geometrical constraints
a SLAM algorithm can benefit from. Fig. 1 shows such an area, with two
modalities presented, lidar in greyscale points and radar in colored points.
For reference, the view from an RGB camera is also provided. Further in the
text, we will refer to this experiment as _Mine_.

The Eskilstuna outdoor testing site is used by Volvo CE for development and
testing of their products, including the large wheel loaders as shown in Fig.
3. For our experiments, the sensor rig used in Mine was moved from the pickup
truck to the Volvo wheel loader. A $1800\text{\,}\mathrm{m}$-long trajectory
was recorded which took the wheel loader through open space and on a forest
road (see Fig. 4). The trajectory was a loop, repeated twice, with the average
speed of $13.6\text{\,}\mathrm{km}\text{\,}{\mathrm{h}}^{-1}$. Precise RTK-GPS
reference was recorded but for the purposes of this study, we base our metrics
on a lidar-SLAM-based reference, which provides the full 6-DOF pose. We only
confirm here that the positioning from the RTK-GPS agrees with our reference
SLAM results. Further on in the text, we will refer to this testing site as to
_Forest_.

The sensor suite used in the experiments is detailed in Fig. 2. The sensors
are attached to a metal rig and connected to an Intel NUC computer that runs
Ubuntu with ROS installed. Raw data are saved to ROS bag files for later
processing. The suite consists of three radars, one lidar, three cameras and
an IMU. The radar used in Mine and Forest is the Sensrad Hugin A3 radar, with
horizontal and vertical FOV $80\text{\,}\mathrm{\SIUnitSymbolDegree}$ and
$30\text{\,}\mathrm{\SIUnitSymbolDegree}$ respectively. Thanks to its
configuration of 48 $\times$ 48 transmitting and receiving antennas, the
horizontal and vertical resolution is
$1.25\text{\,}\mathrm{\SIUnitSymbolDegree}$ and
$1.7\text{\,}\mathrm{\SIUnitSymbolDegree}$. The radar is operated in _short
range_ settings, which implies maximum range $42\text{\,}\mathrm{m}$, but
grants the highest range resolution of $0.1\text{\,}\mathrm{m}$. The frame
rate is $16\text{\,}\mathrm{Hz}$ and the scans contain approximately 10000
points in our environments. For reference localization, an Ouster OS1-32 lidar
is used. The lidar frame rate is $10\text{\,}\mathrm{Hz}$ and the all point
are time-stamped under PTP synchronization with the master computer. Finally,
inertial data are recorded by an Xsens MTi-30 IMU at $400\text{\,}\mathrm{Hz}$
rate. The IMU is running its own attitude estimation using the _VRU General_
profile, which does not use magnetometer data to absolutely reference the
heading angle. Yet, the magnetometer measurements are still used to estimate
gyro biases and thus limit the heading drift down to
$3\text{\,}\mathrm{\SIUnitSymbolDegree}\text{\,}{\mathrm{h}}^{-1}$ in ideal
conditions.

The Car Park trajectory is a part of the dataset recorded by Zhang et al. [4].
In their setup, they used the Oculii Eagle radar that provides FOV of
$120\text{\,}\mathrm{\SIUnitSymbolDegree}$$\times$$30\text{\,}\mathrm{\SIUnitSymbolDegree}$
(horizontal, vertical) and resolution of
$0.5\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$1\text{\,}\mathrm{\SIUnitSymbolDegree}$ and $0.16\text{\,}\mathrm{m}$
(horizontal, vertical, range). In the Car Park experiment, the radar scans
contain approximately 5000 points. The range of the sensor is over
$350\text{\,}\mathrm{m}$ and the manufacturer indicates that adaptive
modulation is used to boost resolution while maintaining long range. From the
point clouds provided in the dataset, it is apparent that some enhancement is
applied by the sensor software. Zhang’s sensor rig, shown in Fig. 5, also
includes a lidar, barometer, camera and two IMUs, a standalone Vectornav IMU
and an internal IMU of the lidar sensor. For testing the odometry variants
that require inertial data, we use the Vectornav IMU measurements. The
trajectory of the Car Park experiment is a rectangle recorded by a hand-pushed
trolley with the sensor rig attached to it. The environment is a parking lot
between buildings at a university campus. The pre-computed ground-truth
localization based on a lidar SLAM solution is available in the dataset and
used by us.

Figure 11: RPE values for the two distinct sensor setups. Each pair of the
violin plots represents the step sizes for evaluating RPE, $1$m and $10$m
respectively. The median RPE value is shown directly in each plot.

###  IV-B Odometry performance evaluation

To compare the performance of the radar odometry variants presented in Section
III, we use the widely adopted APE and RPE metrics, in the _Evo_ library
implementation [19]. APE together with trajectory plots provides the initial,
general idea about the odometry variant behavior for the given sensory and
environmental combinations, but is susceptible to the multiplicative,
nonlinear effect of the accumulated attitude error. RPE complements this
metric, with the indication of the rate of error accumulation. For APE, we
provide its translation component, as the rotation error is apparent in the
accompanying trajectory plots. For RPE, we provide an overall statistic for
both the translation and rotation component. The ground truth for evaluating
the odometry error comes from lidar-based SLAM. The lidar map and subsequently
the reference localization was created by the open-source _HDL Graph Slam_
[18] implementation.

Fig. 6 and Fig. 7 demonstrate the perfomance of the discussed radar odometries
in the Mine experiment. The scan-to-scan matching APDGICP variants (with and
without our prior provided) together with NDT are not suitable for the type of
output the Hugin radar provides. We omit them from the Fig. 6 plot since they
randomly diverge, as can be seen in the APE plot. We attribute this to the low
density and high variance in subsequent radar scans, which causes the scan-to-
scan matching approach to quickly diverge. This behavior is similar also in
the case when we provide the more accurate IMU+Doppler prior estimate. The
main source of error, as we later show in RPE, is the strong drift in
attitude.

The scan-to-submap matching represented by the ICP variants (4DOF and 6DOF)
performs better in the Mine experiment, although the drift is much stronger
compared to what would be expected with lidar odometry in similar environments
(e.g., refer to the SLAM results of the Subterranean DARPA robotic challenge
[20]). Constraining the ICP to 4DOF reduces the vertical drift and results in
overall lower APE.

Comparable results are obtained from the EKF approach, which is free from the
scan-matching problems, but suffers from abrupt changes in the measured
Doppler velocity. As long as the ground is smooth, the localization drift is
comparable to lidar odometry drift rates, i.e. below 1%. Once the truck hits a
bump, the EKF reacts by inappropriate corrections, which can be observed at
180 and 250 seconds in the Mine experiment. As the Hugin radar does not
provide a measurement trigger signal, we assume that the measurement lag
causes mismatch with the inertial measurements. The radar scans are time-
stamped, however the available EKF implementation does not recompute the past
states, it rather counts on timely trigger signals and the _state cloning_
technique. This problem can be partially alleviated by increasing the
measurement uncertainty in the Doppler velocity, which makes the estimated
trajectory smoother, but also reduces the EKF capacity to quickly estimate
sensor biases and to sense minor motions. We denote this altered variant as
_Doppler dampened_ in the plots.

Surprisingly, the simplest IMU+Doppler approach shows the best results. The
drift is minimal, comparable to the best state-of-the-art lidar odometry
techniques. We attribute this to the high accuracy of the Hugin radar in the
Doppler velocity values, and to the capability of the particular IMU unit to
suppress the heading drift by benefiting from the magnetometer measurements.
The downside is that it does not, contrary to the other techniques, provide
any confidence estimate.

The results from the Forest experiment follow the trend of the Mine
experiment. Fig. 8 shows that the scan-to-scan techniques diverge immediately
and the scan-to-submap ICP drifts with similar rate compared to the Mine
experiment. The main difference is in the behavior of the Doppler dampened
EKF. Thanks to the slower pace and the overall stability of the large and
heavy wheel loader, it does not suffer from the abrupt Doppler velocity jolts
and closely follows the simple IMU+Doppler odometry.

In the Car Park experiment from the dataset based on the Oculii Eagle radar,
we see a different trend. Fig. 9 shows that the simpler methods, i.e.
IMU+Doppler and EKF, suffer from vertical and heading drift. We assume that
this is mainly due to the type of IMU used by [4] when recording the dataset.
The Doppler dampened EKF is omitted from the trajectory plot because it
immediately diverges due to accelerometer bias, which takes a minute to
estimate (see Fig. 10). Moreover, the Doppler velocity estimation is less
accurate in this dataset, which affects the smoothness of the trajectory. We
assume that the scan enhancement process inside the sensor may affect the
quality of the Doppler velocity values. On the other hand, all the scan-
matching techniques perform well. The longer range and the adaptive modulation
in the Eagle radar make the the task of scan matching more reliable. In fact,
all variants of ICP, APDGICP and NDT perform similarly and stay within
$10\text{\,}\mathrm{m}$ in APE as shown in Fig. 10.

We summarize the performance of the odometry methods with the two distinct
radars in Fig. 11 using the RPE metric. For clarity, we omit the sub-variants
in this plot as their RPE does not differ substantially. The trajectories are
divided into $1\text{\,}\mathrm{m}$ and $10\text{\,}\mathrm{m}$ steps for the
RPE evaluation. The plot shows the distribution of the translation and
rotation errors with the median value directly in the plot. The translation
error is expressed as percentage of the step, the rotation error is left in
the absolute value, therefore the longer steps yield larger rotational error.
Also note that in translation, we observe higher relative errors in the
$1\text{\,}\mathrm{m}$ steps. Given the already high accuracy of all the
methods, we are approaching the noise in the ground-truth localization based
on the lidar SLAM. This is also why we do not consider single-frame-sized
steps, for which more accurate reference would be necessary.

The Mine and Forest experiments with the Hugin radar are mainly affected by
the noise in the estimated attitude, as the translation error differences
between the methods are not as profound as the resulting APE. The rotation
part of the RPE metric confirms the trend seen in APE. The raw orientation
provided by the Xsens IMU supports the highly accurate Doppler velocity and
leads to the highly accurate results.

The Car Park experiment reveals that the translation is worse for the methods
depending on the Doppler velocity (IMU+Doppler, EKF). In the rotation errors,
we see the limiting effect of the scan matching, which prevents larger errors
to accumulate, contrary to IMU+Doppler and EKF.

##  V CONCLUSIONS

In this work, we have compared several radar odometry estimation methods on
three datasets recorded in underground and outdoor environments with two
distinct modern imaging radars. With the Oculii Eagle radar, the scan-matching
methods achieved higher accuracy than the filtering methods. On the other
hand, thanks to the highly accurate Doppler velocity measurement in the
Sensrad Hugin radar, the simplest sensor fusion method IMU+Doppler achieves
only 0.3% position drift in the Mine and Forest experiments. This makes the
method suitable for resource-constrained machines operating in harsh
environments, such as heavy machinery in the mining industry.

In future work, we will investigate the source of the inaccuracy of the
Doppler velocity in the Eagle radar and extend the radar odometry into a full
SLAM solution.

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  *[SLAM]: simultaneous localization and mapping
  *[IMU]: inertial measurement unit
  *[FOV]: field of view
  *[EKF]: extended Kalman filter
  *[UAV]: unmanned aerial vehicle
  *[GNSS]: global navigation satellite system
  *[DNN]: deep neural network
  *[CNN]: convolutional neural network
  *[GICP]: generalized ICP
  *[ICP]: iterative closest point
  *[DOF]: degrees of freedom
  *[APDGICP]: adaptive probability distribution-GICP
  *[NDT]: normal distributions transform
  *[APE]: absolute pose error
  *[RPE]: relative pose error
  *[IMUs]: inertial measurement unit