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\title{Autonomous Underwater Vehicle Navigation}
\author{John J. Leonard, Christopher Smith, Jacob Feder\\ 
Dept.\ of Ocean Engineering \\
Massachusetts Institute of Technology\\
Cambridge, MA 02139-4307\\
\and
Andrew A. Bennett\\Walt Disney Imagineering\\
P.O. Box 1403\\
Cambridge, MA 02142-0010
} 
\date{}
\markright{\fbox{DRAFT: \today}}

\begin{document}
\maketitle
\pagestyle{myheadings}
\thispagestyle{myheadings}

\begin{abstract}
This paper surveys the problem of navigation for autonomous underwater
vehicles (AUVs).  Marine robotics technology has undergone a phase of
dramatic increase in capability in recent years.  Navigation is one of
the key challenges that limits our capability to use AUVs to address
problems of critical importance to society.  Good navigation
information is essential for safe operation and recovery of an AUV.
For the data gathered by an AUV to be of value, the location from
which the data has been acquired must be accurately known.  The three
primary methods for navigation of AUVs are (1) dead-reckoning and
inertial navigation systems, (2) acoustic navigation, and (3)
geophysical navigation techniques.  The current state-of-the-art in
each of these areas is summarized, and topics for future research are
suggested.
\end{abstract}

\section{Introduction}

Autonomous underwater vehicles (AUVs) have the potential to
revolutionize our access to the oceans to address critical problems
facing the marine community such as underwater search and mapping,
climate change assessment, marine habitat monitoring, and shallow
water mine countermeasures.  Navigation is one of the primary
challenges in AUV research today.  The goal of this paper is to survey
previous work in AUV navigation and to make suggestions for future
research in this area.

Navigation is an important requirement for any type of mobile robot,
but this is especially true for autonomous underwater vehicles.  Good
navigation information is essential for safe operation and recovery of
an AUV.  For the data gathered by an AUV to be of value, the location
from which the data has been acquired must be accurately known.  Some
of the important concerns for AUV navigation, such as the effects of
acoustic propagation~\cite{jensen94}, are unique to the ocean
environment.  Other aspects of the problem, such as managing
uncertainty, are generic to mobile robotics research.  New techniques
for AUV navigation have potential to be useful for mobile robots
operating in natural and dynamic environments on land and in space.

The structure of this paper is as follows.  Section~\ref{auv-sec}
summarizes the current state of AUV technology.  Section~\ref{dr-sec}
describes methods for AUV navigation based on the use of dead
reckoning, inertial navigation systems (INS), and doppler velocity
sonar (DVS) systems.  Section~\ref{acoustic-sec} describes methods for
positioning based on the use of acoustics beacons, such as the use of
a Long baseline (LBL) array.  New methods that integrate navigation
with acoustic tomography and communications are described.
Section~\ref{geo-sec} describes methods
for geophysical navigation, in which the goal is to use sensor
measurements of geophysical parameters or environmental features to
estimate the position of the robot.  This section also discusses the
problem of concurrent mapping and localization (CML), in which the
goal is for the robot to build a map of an unknown environment while
simultaneously using that map to navigate.
Finally, Section~\ref{fr-sec} summarizes the paper and makes
suggestions for future research.

\section{Autonomous Underwater Vehicles}\label{auv-sec}

The capabilities of marine robot systems have improved dramatically in
recent years.  Many autonomous underwater vehicle (AUV) systems have
moved from the prototype stage to become important field assets for
difficult scientific, commercial, and military missions.  The research
community has expended considerable effort in defining the most
appropriate applications for the introduction of AUV
technology~\cite{bellingham92b}.  To make sense economically, an AUV
must provide a cost-effective alternative to other available
technologies, such as manned submersibles~\cite{kaharl90}, remotely
operated vehicles (ROVs)~\cite{ballard98}, and towed instruments
sleds.  The benefits offered by autonomous data gathering have to be
weighed against the difficulties faced by AUVs in power, sensing,
information processing, navigation, and control.  Untethered
operations impose a severe restriction on power consumption and
present challenging problems in intelligent control.  Acoustic modem
technology can enable remote control of AUVs, but communications
bandwidth and reliability are restricted by challenging acoustic
propagation conditions~\cite{catipovic90}.

Under-ice and covert surveillance missions have provided the
motivation for the development of large, long-endurance AUV systems.
Examples include the Theseus AUV, developed by International Submarine
Engineering~\cite{butler95}, the DARPA UUVs, developed by Draper
Laboratories~\cite{pappas91,paglia96}, and the LDUUV and 21UUV
developed by the Naval Undersea Warfare Center in Newport, Rhode
Island~\cite{levine95}.  These vehicles possess high performance
navigation sensors and high capacity battery systems, and are desiged
to operate for long duration missions at high speeds.  For example,
the Theseus vehicle has performed an autonomous under-ice run of more
than 300 kilometers~\cite{butler95}.

AUVs designed for scientific applications tend to be much smaller and
cheaper than vehicles designed for surveillance applications. Examples
include the Autonomous Benthic Explorer (ABE)~\cite{singh95} and
Remus~\cite{vonalt94} vehicles developed at Woods Hole Oceanographic
Institution, the Odyssey II vehicles developed at MIT Sea
Grant~\cite{bellingham94}, the Ocean Explorer vehicles developed at
Florida Atlantic University~\cite{sam_smith95}, and the MARIUS AUV
being developed by a team of European partners~\cite{egeskov94}.  High
performance INS systems typically cannot be integrated into small AUVs
because of size, cost, and power restrictions.  Hence, these vehicles
typically rely on acoustic navigation systems and/or GPS navigation
resets for shallow water operations~\cite{an96}

Autonomous oceanographic sampling networks (AOSN) represent a new
ocean sampling concept that promises to increase the deployment
possibilities for AUVs~\cite{curtin93}.  The idea behind AOSN is to
deploy multiple AUVs with communications and power-recharging moorings
in a remote location to enable long-term, large-scale oceanic data
gathering.  The motivation for this type of system comes from the
difficulty that oceanographers face in obtaining enough data to
understand ocean processes and to develop predictive ocean models.
The technology to realize these capabilities is currently in
development.  Components of the AOSN have been tested recently in the
Haro Strait Experiment~\cite{schmidt96}, which studied tidal front
mixing, and the Labrador Sea Experiment~\cite{visbeck98}, which
measured oceanic deep convection.

\section{Dead Reckoning and Inertial navigation systems}\label{dr-sec}

The most obvious and longest established navigation technique is to
integrate the vehicle velocity in time to obtain new position
estimates~\cite{dutton85}.  Measurement of the velocity components of
the vehicle is usually accomplished with a compass and a water speed
sensor.  The principal problem is that the presence of an ocean
current will add a velocity component to the vehicle which is not
detected by the speed sensor.  In the vicinity of the shore, ocean
currents can exceed 2 knots.  Consequently, dead reckoning for
power-limited AUVs, operating at small speeds (3-6 knots), involving
water-relative speed measurements can generate extremely inaccurate
position estimates.

In inertial navigation, the accelerations of the vehicle are
integrated twice in time to derive the updated
position~\cite{kuritsky90}.  Position drift rates for high quality
commercial grade INS units are on the order of several kilometers per
hour.  Initialization of the INS system can be difficult.  Cost and
power consumption have historically made INS systems unattractive for
small AUVs, however this may change as systems get smaller and cheaper
in the future.

For operations near the seabed, Doppler Velocity Sonar (DVS) sensors
can be used to measure vehicle's velocity relative to the ground.  The
integration of this information in the navigation Kalman filter can
result in greatly improved performance.  For example, the DARPA UUV
has achieved navigation performance of 0.01\% of distance traveled
using an integrated INS/DVS system~\cite{paglia96}.

The problem with exclusive reliance on dead reckoning or inertial
navigation is that position error increases without bound as the
distance traveled by the vehicle increases.  The rate of increase will
be a function of ocean currents, the vehicle speed, and the quality of
dead reckoning sensors.  Radio and satellite navigation systems can
provide an accurate position update provided the vehicle can travel at
or near the surface periodically for a position fix.  The maximum
vehicle travel time between surfacing for a position update will be
governed by dead reckoning/inertial navigation accuracy.  Poor quality
dead reckoning will dictate an unacceptably high frequency of
surfacing.  Also, vehicles operating close to the coast are in
appreciable danger of collision with surface vessels if they need to
frequently approach the surface for position fixes.  For deep water
applications, the time and energy needed by a small AUV for transiting
to the surface from near bottom are very unfavorable.  Finally,
surfacing is impossible in ice-covered oceans.

\section{Acoustic Navigation}\label{acoustic-sec}

Electromagnetic energy cannot propagate appreciable distances in the
ocean except at very low frequencies. Acoustic energy, however,
propagates well in the ocean, and hence acoustic transponders can be
used as ``beacons'' to guide the motion of an AUV without the need for
resurfacing. Two types of system have been primarily
employed~\cite{heckman73,hunt74,milne83}: long baseline (LBL) and
ultra-short baseline (USBL).  Both systems employ external transducers
or transducer arrays as aids to navigation.  In LBL navigation
systems, an array of transponders is deployed and surveyed into
position.  The vehicle sends out an acoustic signal which is then
returned by each beacon as it is received.  Position is determined by
measuring the travel time between the vehicle and each beacon,
measuring or assuming the local sound speed profile, and knowing the
geometry of the beacon array.  With this information the relative
distances between the vehicle and each array node can be calculated.
Thw two primary techniques are (1) to compute position fixes by
locating the intersection point of spheres of appropriate radii from
the beacons in the array, and (2) to integrate the raw TOF
measurements into an appropriate Kalman filter~\cite{vaganay96}.  In
more difficult acoustic environments such as in shallow water or in
the Arctic, it becomes difficult to distinguish between the direct
arrival and multipath interference, and rejection of outliers becomes
a key issue.  In a fix computation scheme, one can rule out spurious
fixes, whereas in a Kalman filter-based system, one can gate the raw
TOF values~\cite{vaganay96}.

A variant of this system is \emph{hyperbolic navigation}, in which the
vehicle does not actively ping but instead listens to an array of
beacons whose geometry is known~\cite{bellingham92a}.  Each beacon
pings in a specific sequence relative to the others at its specified
frequency.  By knowing which beacon pings when and the geometry of the
array, the vehicle can reconstruct where it must be in space in order
to hear the ping sequence as recorded.  This system has the advantage
of saving the vehicle the power expenditure of active pinging, and is
especially useful for multiple AUV operations.  With an active
(spherical) LBL system, multiple AUV operations require careful
sequencing of the pings between vehicles~\cite{atwood95}.

Most LBL systems work at a frequency of approximately 10 kHz and
provide position accuracy to within a few meters with a maximum range
on the order of a few kilometers.  Alternative systems operating at
300 KHz have been created that can provide positioning repeatability
down to 1 centimeter resolution in a triangular operating area that is
100 meters to a side~\cite{imetrix98}.

In USBL navigation, the vehicle has a two or three element receiver
array that enables it measure the angle as well as the range
to an acoustic beacon.  This system is a variant of a popular system
for tracking an underwater vehicle from a surface ship~\cite{ore98}.
By measuring the arrival time (phase) difference of a single sonar
ping between two or more hydrophones, the bearing from the vehicle to
the beacon can be determined.  If the beacon responds to vehicle
interrogation, then the time delay (and hence distance, as with an LBL
array) can be calculated.  Knowing distance and direction to the
beacon allows for local navigation~\cite{tracey92}.  Knowing the
latitude/longitude of the beacon allows for geodetic navigation.  This
type of system is especially effective for homing and docking
operations, which are important for Arctic~\cite{bellingham95a} and
autonomous ocean sampling network~\cite{singh96} deployments.

Errors in both LBL and USBL arrays come from many sources.  The key
sources of error can be broken down into two primary categories:
errors in the assumed array geometry and errors in the assumed sound
speed profile.  Positioning error comes from inadequately or
improperly surveying the relative and/or geodetic positions of the
array beacons.  In the event that only local navigation is desired,
then only relative beacon positions are relevant.  If the navigation
is to be geodetic-referenced, then the beacons must be located
globally as well.  Sophisticated software packages are available for
accomplishing this.  Self-calibrating beacons simplify the task by
reducing the surveying task to only one beacon with the others
determining their own positions relative to the first.  However, this
raises the possibility of relative position errors due to errors in
the assumed local sound speed.

A significant difficulty in acoustic navigation can be caused by an
error in the assumed sound speed profile.  An inaccurate sound speed
profile will appear as a distance bias in the calculations.
Reflection or multipath errors will result in incorrect time-of-flight
values and hence erroneous position fixes.  Typically, LBL works well
in a deep water and with array separations of a few kilometers.  Over
longer distances in shallower water, more complex propagation effects
come into play and increase the frequency of bad position fixes.  If
the topography is sufficiently severe, beacons may be occluded by
rocks or other seabed formations.  Even if the sound speed profile is
known at the start of an AUV mission, the acoustic propagation
environment can change during the mission.

To address this issue to provide navigation in complex and dynamic
acoustic environments, Deffenbaugh has developed a technique for very
long baseline navigation~\cite{deffenbaugh94,deffenbaugh96a}.  The
approach uses the extra information provided by the multipath arrivals
to invert for sound speed profile variations in space and time, and in
the process provide a more accurate position estimate.  This technique
was motivated by the particularly challenging conditions of the
Arctic, which is characterized by an upwardly refracting sound speed
profile~\cite{jensen94}.

Acoustic tomography refers to the goal of using travel time
information between one or more vehicles and vertical hydrophone
arrays to estimate the sound speed profile and other information at
various places in the intervening water column~\cite{munk95}.  These
techniques are being investigated from scales of a few
kilometers~\cite{schmidt96} to the global scale~\cite{wunsch96}.  To
perform moving source acoustic tomography with an AUV, one needs to
know the location of the vehicle to a high precision.  In addition,
one needs to be able to identify different the propagation paths of
the different arrivals received by each hydrophone~\cite{munk95}.
This same information (effectively, knowing the channel impulse
response of the environment) is vital for providing effective acoustic
communications~\cite{catipovic90}.   Hence, the problems of acoustic
tomography, communication, and navigation are closely intertwined.
The development of integrated methods for performing these tasks
concurrently in dynamic environments presents a challenging  and
exciting topic for future research. 

\section{Geophysical navigation}\label{geo-sec}

For some applications of AUVs, the use of acoustic beacons is
undesirable or impractical.  If an accurate \emph{a priori} map of the
environment is available, one approach to globally-referenced position
estimation is to use measurements of geophysical parameters, such as
bathymetry, magnetic field, or gravitational
anomaly~\cite{tuohy96,tyren82,may78,geyer87}.  These approaches are
based on matching sensor data with an \emph{a priori} environment map,
under the assumption that there is sufficient spatial variation in the
parameter(s) being measured to permit accurate localization.

All forms of map-based navigation are motivated by the desire to
operate at an arbitrary location without the additional expense or
problems associated with the installation of artificial beacons.  In
principle, the process appears straightforward: gather information
about the surrounding terrain and match that information to an
on-board map or database of terrain information.  When the vehicle has
a match to the database, then it knows its location on the map.  This
is analogous to the method which humans use to navigate; we find our
way to our destination by locating and identifying landmarks which are
familiar to us -- either from past experience or via a map which has
been constructed for our benefit.

In practice this form of navigation is not so simple.  The vehicle is
attempting to navigate by matching a set of sensed data with an
\emph{a priori} map or dataset of stored data.  Two key problems are
the cost and difficulty of generating the \emph{a priori} maps and the
computational complexity of searching for a peak in the
\emph{n}-dimensional correlation surface, where \emph{n} is the number
of dimensions in the map or sensor data set.  Typically, map making
expense is governed by both the type of data being collected and the
desired resolution of that data.  Determining the map resolution has a
direct effect on the size and level of detail of the search needed to
locate the vehicle in space.  Since the vehicle could be in any of a
large number of possible orientations relative to the original
dataset, the search must be performed over all possible locations and
orientations.  This is a potentially large search space, necessitating
some simplifications and/or simplifying assumptions in order to make
the search more tractable.  Typical simplifications are: restricting
the types of map data stored (what sensor values, how many different
sensors), lowering map resolution, ``patchy'' maps (maps of key areas
only), restricting vehicle orientations (to reduce the correlation
problem), and using inertial navigation or dead reckoning systems to
limit the valid search area.

%% \subsection{Geophysical navigation sensors}

Evidence exists that geomagnetic navigation is employed by birds,
fish, and other animals for migration and general
navigation~\cite{waterman89}.  The magnetic flux density of the earth
varies according to latitude, the presence of man-made and natural
anomalies, and even one's depth in the ocean, increasing from 6 to 30
nanoTeslas per 1 km of depth, depending on location~\cite{myers69}.
Additionally, there are small but predictable variations in the
earth's magnetic flux from day to night, and large arbitrary changes
during magnetic storms (which are approaching the height of their 11
year cycle at this time); magnetic maps can be rendered useless for
the duration of such storms.  Useful magnetic maps, generated by
satellites or surface ships, can be employed by underwater vehicles by
accounting for the daily field variations and by calculating the
effective magnetic field at depth using a Laplace field equation,
setting the boundary conditions at the ocean surface~\cite{tuohy93b}.

Research into the nature of the earth's gravitational field has
demonstrated that it is far from uniform and indeed possesses a varied
topography~\cite{kahn84,whitmarsh93}.  These variations are due to a
variety of factors, especially the effects of local
topography~\cite{forsberg87} and density
inhomogeneities~\cite{turcotte82}.  Variations in the earth's
gravitational field on the ocean's surface relative to a regular
ellipsoidal model have been measured to be on the order of 30-50
mgal~\cite{jircitano90}\footnote{$1 milligal = 1 mgal = 10^{-5}
m/sec^2$}.  Gravity maps were originally gathered on behalf of the US
Navy for the purposes of inertial navigation system
calibration~\cite{sandwell90}.  To an INS, the effects of a change in
the local gravitational field are indistinguishable from accelerations
of the vehicle itself.  Gerber~\cite{gerber78} proposed the use of a
gravity gradiometer as an aid to inertial navigation systems.
Jircitano \emph{et al.} extended this idea to the AUV community,
performing navigation simulations using a model of the Bell Aerospace
Textron Gravity Gradiometer System (GGS)~\cite{jircitano90} with good
preliminary results.  The drawbacks to such a system are the size,
expense, and complexity of a gradiometer (see Geyer~\cite{geyer87}).
In addition, the gradiometer must be mounted on an inertially
stabilized and vibrationally isolated platform, making its use
difficult on small, low-cost scientific AUVs.


Geophysical navigation algorithms have origins in techniques of
navigating at sea using depth soundings that have been in use for
centuries~\cite{dutton85}.  Kamgar-Parsi has developed techniques for
performing geophysical navigation that are based on fitting contour
lines to sensor data and matching these curves to an {\em a priori}
map using matching techniques from computer
vision~\cite{kamgar-parsi89,kamgar-parsi97}.  Lucido {\em et al.} have
also investigated the segmentation and registration of of bathymetric
profiles.  Tuohy has investigated geophysical navigation using maps of
multiple geophysical parameters based on contour intersection
methods~\cite{tuohy96}.  The reliability of any of these approaches
will depend on the accuracy of the {\em a priori} map.

In practice, an up-to-date, high-quality
map may be unavailable in the operating area of interest.  This
motivates research into the problem of concurrent mapping and
localization.  The goal of concurrent mapping and localization is for
the AUV to build a map of its environment and to use that map to
navigate in real time.  A seminal technique for concurrent mapping and
localization, called the stochastic map, was published by Smith, Self,
and Cheeseman~\cite{smith87}.  The stochastic map consists of a single
state vector that represents the estimates of the vehicle and feature
locations and an associated covariance matrix.  As the vehicle moves
around its environment, taking measurements of environmental features,
the stochastic map is updated using an extended Kalman filter.
Moutarlier and Chatila~\cite{moutarlier89a}, Rencken~\cite{rencken93},
and Chong and Kleeman~\cite{chong97} have implemented variations of
the stochastic map using land robots.  To our knowledge, CML has not
been implemented with an underwater vehicle.

The major problems encountered by the stochastic map are the failure
of the extended Kalman filter to properly track the highly nonlinear
transformations involved in geometric estimation and the fact that the
technique scales (at best) quadratically with the number of features
present.  Also, Smith, Self, and Cheeseman ignored errors which may
arise from ambiguity in the source of sensor data.  Some of these
drawbacks have recently been considered by Uhlmann~\cite{uhlmann95} in
a theoretical investigation of concurrent mapping and localization.
However, there are many important issues to address in future research
to realize this capability on-board an AUV~\cite{smith97c}.


\section{Conclusion}\label{fr-sec}

This paper has reviewed the literature relating to the problem of
autonomous underwater vehicle navigation.  Current practice in AUV
navigation is limited primarily to dead-reckoning, INS, and acoustic
systems.  High performance, tactical-sized AUVs have demonstrated
positioning accurate to 0.01\% of distance traveled using a coupled
INS and DVS system.  Smaller, low-cost vehicles generally rely on
compass and speed sensors for dead-reckoning, with correspondingly
poorer performance. However, this performance can be expected to
improve as commercial, off-the shelf sensors become smaller and more
affordable.  Long baseline navigation is the key technique for
scientific AUV missions, and ultra-short baseline homing systems will
take on new importance as autonomous ocean sampling network systems
continue to be developed.  Geophysical navigation techniques continue
to be an interesting topic for research.  These techniques have not
yet been employed in the field, in large part due to the requirement
that accurate {\em a priori} maps be available.  Techniques by which
the AUV can build a map of an unknown environment and use that map to
navigate promise to extend the range of applications for geophysical
navigation techniques.


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