
one or more sensors like cameras, lidars, radars, inertial
measurement units (IMUs) and the global positioning system
(GPS). Underwater robots face unique challenges when
it comes to localization. In real-world scenarios, sensors
like cameras and lidar are ineffective due to turbidity, and
signals from absolute positioning systems like GPS cannot
be received underwater. Most commercial AUVs rely on
sensors like Doppler velocity logs (DVLs), depth sensors
and IMUs for inertial navigation methods to help localize
themselves. Sonars and cameras can be used for aiding
inertial navigation by leveraging the geographical features of
the surrounding environment. As mentioned earlier, cameras
are effective only in clear water and sonars often make the
cost of underwater vehicles prohibitively expensive. Costs
and practicality aside, their weights and bulky form factors
limit them to be used only on larger robots. In this work, our
focus is on localization for small, low-cost and low-power,
untethered robots.
For localization of smaller and cheaper underwater robots,
such as bio-inspired robot fish, acoustic positioning methods
have more potential as a viable solution. The oldest and
most popular methods of acoustic positioning are long base-
line or short baseline (LBL/SBL) and ultra short baseline
(USBL) systems [8, 9]. These methods are two-way travel-
time (TWTT) methods, which means the beacons and the
AUVs need to be equipped with active acoustic systems to
communicate with one another. The use of atomic clocks
to synchronize both beacons and AUVs can allow for
localization using one-way travel-time (OWTT) methods.
Earlier approaches achieved range-only OWTT localization
and navigation by using filtering or fusion with other on-
board sensors [10, 11]. More recently, Rypkema et al. [12]
presented their novel method of one-way travel-time inverted
ultra-short baseline (OWTT-iUSBL), which allowed for real-
time on-board navigation using a single speaker and an
array of four passively listening hydrophones on the AUV.
Matched filtering and phased-array beamforming on the four
received signals from each hydrophone gives a range and
bearing estimate of the robot with respect to the speaker
position.
While the OWTT-iUSBL can perform effective local-
ization with a relatively cost effective setup compared to
commercial AUVs, the components used are still expensive
and too heavy to be used on much smaller bio-inspired
robots. Atomic clocks, which make OWTT methods possible,
are still expensive relative to other options. For a swarm of
robots, these costs can add up significantly. Accurate time-
of-arrival information is paramount for OWTT methods, and
cheaper embedded real time clocks (RTCs) are prone to
significant drift and lack the superior precision of atomic
clocks. Time-difference of arrival (TDOA) techniques, on the
other hand, allow us to avoid the need to know the exact time
a signal was sent. This is achieved by instead measuring the
differences between the arrival time of multiple signals which
were known to be transmitted simultaneously from different
beacons. This technique is commonly referred to as pseudo-
ranging, and is the foundation of GPS localization [13].
Fig. 2: System Overview: The transmitter module periodically plays a
sequence of identical chirps (black) followed by another, different, chirp
(blue) through a constellation of speakers. The receiver module uses the
information to estimate position as well as execute basic locomotion tasks.
In this paper we present a method for localization of a
small robotic fish that is based on acoustic pseudoranging.
This is accomplished using cheap, miniaturized, low power
sensors and computation. Referring to Fig. 2, pseudorange
localization and acoustic communication is performed on a
fish-inspired robot that swims in a water tank that is instru-
mented with acoustic speakers and receivers. The robotic fish
is embedded with a small and inexpensive micro-electro-
mechanical systems (MEMS) microphone that is used for
communication and localization through the estimation of
TDOA of signals sent simultaneously from the four speakers
in the water tank.
As an acoustically passive method on the receiver side,
pseudoranging allows for multiple agents to be localized
simultaneously without the need for individual signals spec-
ifying time of flight (TOF) information or cross commu-
nication between transmitter and receiver to achieve time
of arrival (TOA). Variations of acoustic pseudoranging have
been utilized for the localization of larger underwater vehi-
cles before. Jorgensen et al. [14] presented an observer to
estimate several parameters like position, velocity and IMU
biases. Leveraging pseudorange measurement differences
along with attitude and accelerometer gave better position
estimates. A long range underwater navigation algorithm
based on acoustic pseudoranging was tested in an area
spanning ~275,000km2by Mikhalevsky et al. [15] by using
GPS assisted beacons. Recent works by Berlinger et al. [16]
and Novak et al. [17] have also explored the localization of
a swarm of fish, both robotic and natural, through optical
and acoustic methods respectively. However both methods
perform localization from an external observer and not on-
board the agent, which makes acoustic pseudoranging more
suitable to use cases where geo-referenced data collection,
and on-board navigation are important.
II. SYSTEM ARCHITECTURE
This section will now describe the hardware and frame-
work for acoustic pseudoranging based localization and one-
way acoustic communication. A diagrammatic illustration is
shown in Fig. 2. There are a minimum of four speakers
connected to a single computer playing a sequence of chirps
followed by a single, different chirp, periodically. The re-
ceiver is time synchronized with the transmitter computer