This document evaluates the performance of dead reckoning techniques for underwater navigation. It benchmarks 15 dead reckoning algorithms using an IMU and compares their accuracy on land versus underwater. The results show that displacement and attitude estimation errors are generally lower underwater compared to similar trajectories on land. Warp estimations like spirals and squares also have lower errors when performed underwater rather than on the ground. The document concludes that dead reckoning can be used underwater with around 5% error for displacement and turning, and its performance depends on the motion pattern and algorithm used.

1. Lost in the Deep? Performance
Evaluation of Dead Reckoning
Techniques in Underwater
Environments
Marko Radeta, Claudio Rodrigues, Francisco Silva, Pedro Abreu, João
Pestana, Ngoc Thi Nguyen, Agustin Zuniga, Huber Flores, Petteri Nurmi
1
October 10, 2023, Cancun, Mexico

2. Importance
• Widely adopted in several navigation applications
2
Source: https://www.freepik.com/premium-vector/footprint-trail-human-
walking-route-footsteps-track-vector_17570436.htm
Source: https://www.freepik.com/free-vector/road-tire-tracks-white-
background_1107072.htm#query=tire%20tread&position=23&from_view
=search&track=ais
Cars
Source: https://www.vecteezy.com/png/27388481-speed-boat-
travel-floating-water-transport-route-path-way-in-ocean-blue-sea
Important characteristics include affordable, lightweight, and
energy-efficient
Surface vessels
Smartphones

3. Dead reckoning
• Simply explained
3
Modelling through distance and angle estimates
Start

4. Dead reckoning
• Extraction of parameters
4
Modelling through distance and angle estimates
Start

5. Dead reckoning “underwater”
• Is the dead reckoning performance good underwater?
5
Underwater positioning (scuba, ROVs, AUVs)

6. Contributions
• Systematic evaluation: We benchmark
different (15) dead reckoning algorithms and
analyze their performance underwater
• Land vs underwater testbed: We design a
robust testbed that compares both conditions
• New insights: We present quantifiable
results about using dead reckoning
underwater
6
We can use it with 5% error for displacement and turn respectively –
some motion patterns underwater require specific algorithms
Source: DF Malan -
https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#/
media/File:Euler_AxisAngle.png

7. AEOLUS position estimation pipeline
7
Step 1:
IMU
calibration
Step 2:
Orientation
estimation
Step 3:
Linear
acceleration
Step 4:
Sampling
rate
selection
Step 5:
Displacement
estimation
Step 6:
Position
estimation
LoPy4
microcontroller
IMU (MPU-9250)

8. AEOLUS position estimation pipeline
8
Step 1:
IMU
calibration
Step 2:
Orientation
estimation
Step 3:
Linear
acceleration
Step 4:
Sampling
rate
selection
Step 5:
Displacement
estimation
Step 6:
Position
estimation

9. AEOLUS position estimation pipeline
9
Step 1:
IMU
calibration
Step 2:
Orientation
estimation
Step 3:
Linear
acceleration
Step 4:
Sampling
rate
selection
Step 5:
Displacement
estimation
Step 6:
Position
estimation
Attitude estimation
(Pitch, Roll and yaw)
Liner acceleration
Quaternions

10. AEOLUS position estimation pipeline
10
Step 1:
IMU
calibration
Step 2:
Orientation
estimation
Step 3:
Linear
acceleration
Step 4:
Sampling
rate
selection
Step 5:
Displacement
estimation
Step 6:
Position
estimation
Algorithms: AngularRate, AQUA,
Complementary, DavenPort, EKD, FAMC,
FLAE, Fourati, Madgwick, Mahony, OLEQ,
QUEST, ROLEQ, SAAM, Tilt

11. AEOLUS position estimation pipeline
11
Step 1:
IMU
calibration
Step 2:
Orientation
estimation
Step 3:
Linear
acceleration
Step 4:
Sampling
rate
selection
Step 5:
Displacement
estimation
Step 6:
Position
estimation

12. AEOLUS position estimation pipeline
12
Step 1:
IMU
calibration
Step 2:
Orientation
estimation
Step 3:
Linear
acceleration
Step 4:
Sampling
rate
selection
Step 5:
Displacement
estimation
Step 6:
Position
estimation

13. The experiments
Land
13
Drawn on the ground
We investigate the effects of distance on position
estimation at different distance magnitudes
Pre-defined geometrical shapes

14. The experiments
Underwater
14
Structure on the surface

15. The experiments
Underwater
15
Structure on the surface

16. Evaluation
Result: Average errors of displacement underwater lower are much
lower compared to the similar trajectory on the ground (warp).
16

17. Evaluation
Result: Attitude estimation (Pitch, Roll and yaw) computed using
some algorithms (e.g., FAMC, Fourati) result in high errors on the
ground but lower errors when the experiments were performed in
the underwater environment.
17

18. Evaluation
Result: Algorithm dependent performance for shape estimation
18
(a) 4 m (b) 16m (c) 28 m – Lower displacement errors
(d) 4 m (e) 16 m (f) 28 m – Lower turn errors

19. Evaluation
Result: Warp estimation is difficult on the ground
19
(a) (b) – Lower displacement and turn errors for spirals
(c) (d) – Lower displacement and turn errors for squares

20. Evaluation
Result: Warp estimations are easily captured underwater
20
(a) (b) – Lower displacement and turn errors
Thin rectangle indicates the base wooden surface structure

21. Summary and conclusions
• Systematic evaluation: We benchmark different (15) dead
reckoning algorithms and analyze their performance underwater
• Land vs underwater testbed: We design a robust testbed that
compares both conditions
• New insights:
• We can use it with 5% error for displacement and turn respectively
• Warp estimations are better captured underwater rather than on the
ground
• Performance of dead reckoning algorithm is quite volatile on the
ground
21

22. Questions?
Thank you! (Do not hesitate to reach us via e-mail)
Marko Radeta (marko.radeta@wave-labs.org)
Claudio Rodrigues (claudio.rodrigues@wave-labs.org)
Francisco Silva (francisco.silva@wave-labs.org)
Pedro Abreu (pedro.abreu@wave-labs.org)
João Pestana (joao.pestana@wave-labs.org)
Ngoc Thi Nguyen (ngoc.nguyen@helsinki.fi)
Agustin Zuniga (agustin.zuniga@helsinki.fi)
Huber Flores (huber.flores@ut.ee)
Petteri Nurmi (petteri.nurmi@helsinki.fi)
22