Toward Underwater Acoustic-based SimultaneousLocalization and Mapping.

Experimental results with the Typhoon AUV atCommsNet13 Sea Trial

F. Di Corato, D. Fenucci,A. Caiti

ISME - Interuniv. Res. Ctr.Integrated Sys. Marine Env. and

Centro Piaggio, University of PisaLargo Lazzarino 1

Pisa, ItalyEmail: andrea.caiti@ing.unipi.it

R. Costanzi, N. Monni, L. Pugi,A. Ridolfi, B. Allotta

ISME - Interuniv. Res. Ctr.Integrated Sys. Marine Env. and

MDM Lab, Dept. Industrial Eng., University of Florencevia di Santa Marta 3

Florence, ItalyEmail: benedetto.allotta@unifi.it

Abstract—An algorithmic framework and experimental re-sults on acoustic self-localization and mapping for an AUVequipped with an USBL modem are reported. The methodologyproposed is quite general and applicable to a wide range ofAUV and of navigation needs; however, the results presentedrefer to the Typhoon AUV and to the experimental configurationas available in the CommsNet13 cruise, led by the NATO S&TCtr. for Maritime Research and Experimentation. The obtainedresults show that, even with a low cost, inertial motion units, andin presence of hostile acoustic channel conditions, the approachis able to keep the navigation error bounded and within 3 - 4times GPS accuracy.

I. INTRODUCTION

In this paper we report some results obtained in our on-going efforts in the development of acoustically-based map-ping and navigation procedures for autonomous underwatervehicles (AUVs). In particular, in the recent past we have beenemploying the self-developed AUV Typhoon, a 300 m depthrated low-cost AUV with acoustic communication capabilities[1], shown in Figure 1, as experimental platform. There area wealth of different approaches to AUV mapping and nav-igation (see [2]–[6] and references therein); our investigationconcentrates on the use of acoustic modems with range andUltra Short Base Line (USBL) capabilities. In particular, theAUV navigates with an on-board USBL modem within a fieldof acoustic beacons in initially unknown positions. Acousticfixes are integrated in the vehicle inertial navigation system,and the navigation corrected accordingly. In this paper, wereport experimental results obtained through this approach,and we give an account of its mathematical formulation.The data were collected during the CommsNet13 experiment,which took place in September 2013 in the La Spezia Gulf,North Tyrrhenian Sea. The experiment was organized andscientifically coordinated by the NATO S&T Org. Ctr. forMaritime Research and Experimentation (CMRE, formerlyNURC). In the experiment, the Typhoon vehicle was equippedwith the USBL modem, a GPS antenna and a low-cost, low-

Fig. 1. Typhoon AUV during CommsNet13 experiment

accuracy Inertial Measurement Unit (IMU). The USBL modemcould communicate with an ad-hoc installation of fixed sensorsconsisting of some battery-operated acoustic modems.

In [7] we addressed the problem of fixed-nodes local-ization within an underwater acoustic network, presenting amethodology to map the acoustic nodes of an underwaternetwork using GPS and USBL measurements. While navi-gating on surface within the network, the vehicle started toperiodically interrogate each node of the network using theUSBL modem, which provides the relative position of theagent with respect to the interrogated modem. The USBLmeasurements was thus combined with the GPS position ofthe vehicle to compute the absolute position of the acousticsource. This procedure was then iterated until a set of roughestimates for each node is obtained. Finally, the positionsof the nodes could be evaluated by meaning each set ofabsolute positions. This methodology provides a sufficientlyprecise estimate of the fixed-nodes position, but it requiresthe continuous availability of the GPS measurements, whichis instead not ensured during an underwater operation.

Once the position of the fixed nodes of a network isknown, the USBL measurements can be exploited in datafusion procedures to improve self-localization accuracy and

navigation capabilities for a marine vehicle. In [8] we re-ported a preliminary analysis of some raw navigation data,highlighting the potential of using the USBL measurements toestimate the vehicle position. Successively, in [9] we presenteda navigation algorithm based on the fusion of the acoustic andthe inertial measurements through a classical Extended KalmanFilter (EKF). The algorithm was tested on the same navigationdata, showing that the USBL corrections, even if coming atrandom distributed intervals of time, was effectively able toreduce the drift induced by the inertial measurements in theposition estimate.

In this work we present a procedure to simultaneouslyperform autonomous underwater navigation and estimate thetopology of the acoustic network, i.e. the map, supposedunknown. The algorithm is formally casted into an optimalstochastic filtering problem, which aims at estimating theinertial navigation (namely position, velocity and accelerom-eter biases) of the vehicle and the position of the modemswith respect to a fixed navigation frame (NED). The roughestimations of the vehicle position and velocity and of themap are refined by using the relative measurements availableon the acoustic channel and the longitudinal propeller thrust.The estimation algorithm relies on a classical EKF structurewith a dynamic database of the discovered modems, initiallyempty.

The paper is organized as follows: in Section II the problemof the estimation of both the vehicle navigation and thetopology of an acoustic network is introduced, supposing theknowledge of the dimension of the network. Then, Section IIIdescribes in detail the proposed algorithm, showing somepreliminary result. In Section IV the previous algorithm isextended to the case in which no information is given about thenetwork, showing the corresponding results. Finally, Section Vreports the conclusion.

II. PROBLEM FORMULATION

The Simultanous Localization and Mapping (SLAM) tec-nique provides a way in which an agent (or a team of agents)can build up a map within an unknown enviroment, i.e. themapping, while at the same time keeping track of its ownposition, i.e. the localization. In this particular application,the agent is represented by an underwater vehicle, which issupposed to navigate whitin a network of r fixed acousticsensors mi, which represents the map. The vehicle is supposedto be equipped with some navigation sensors, namely a GPS,an IMU, a depth sensor and an USBL, which is used tocommunicate with the nodes of the network. The goal ofthe presented algorithm is to employ the measurements ofthe navigation sensors in order to simultaneously estimate thetopology of the network, supposed unknown, and the naviga-tion of the vehicle. For the purposes of this work, we assumethat the local navigation frame (NED) can be considered notto change its orientation with respect to the global (ECEF)frame, during the whole navigation task. This means that theEarth is approximated as a flat surface in the neighborhoodof the starting point. By putting the NED reference frameon the Earth surface at the location corresponding to thestarting point, all the inertial quantities can be consideredin local coordinates. This is a realistic assumption in theframework of the proposed work, since the motion of thevehicle was assumed to be enclosed inside a small enough

area. Moreover, the attitude of the vehicle was assumed known.More specifically, the attitude θ was pseudo-measured bythe inertial unit on-board the vehicle, via integration of thegyroscopes measurements together with the sensed gravity andthe Earth magnetic field measurements in an Attitude-HeadingReference System (AHRS) fashion [10], [11].

In the classical SLAM implementations, the map can beconstructed dinamically without any a priori knowledge ofthe environment or it can be updated starting from a map ofa known environment. In order to verify the feasibility of theproposed strategy, some preliminary elaborations based on apriori information were performed. In particular, we supposeto know the number of the nodes constituting the network. Tothis aim, we consider the model of the navigation equationspresented in [9] and we extend it by adding other states, firstof all the positions of the r modem resolved in the localnavigation frame, namely pmi,n. Since we assume that thenodes of the network are fixed, their dynamics can be modeledby the following equations:

pmi,n = νmi i = 1, . . . , r (1)

where νmi ∼ N (0,Qmi) is a zero-mean white noise with

constant variance Qmi. Moreover, we approximate the relation

between the desired thrust and the velocity along the surgeaxis with the linear function τsurge = Kthrvsurge, in which thegain Kthr is supposed to be constant and initially unknown.To estimate the value of this gain, we introduce in the systemmodel the following additional equation:

Kthr = νK (2)

where the white noise νK ∼ N (0, Qk) takes into account themodeling uncertainty. Upon the above hypothesis, the localcontinuous-time navigation and mapping equations in the NEDframe can be written by simply adding the equations (1) and(2) to those of the model in [9]:

pn = vnvn = nRb(θ) (ab − εb + νa) + gnεb = νε (3)

Kthr = νKpmi,n = νmi i = 1, . . . , r

where pn and vn are respectively the position and velocityof the system, both expressed in the NED frame, whereas εbdenotes the the accelerometers bias term. Since we assumenot to have a prior information regarding the nature of biastime evolution, their dynamics were modeled as random walks,where νε ∼ N (0,Qε) is a zero-mean white noise withconstant variance. Note that the velocity dynamics employ thebody accelerations measured by the accelerometers depuratedby the bias term and then converted in the local navigationframe through the transformation matrix nRb(θ). Finally, thevehicle acceleration is obtained by compensating for the grav-ity term g. The body-to-navigation matrix nRb is evaluatedbased on the vehicle attitude θ, expressed in Euler angles,computed by the inertial sensors suite. The random variableνa ∼ N (0,Qa) accounts for the noise that intrinsically affectsthe inertial sensor. This latter noise term was supposed whiteas well.

In this work it is assumed that the navigation systemrelies on the measurements from the USBL, depth sensor and

Table I. STATISTICS OF THE PRELIMINARY ELABORATIONS

Initial modemserror (m)

USBL& GPS

Vehicle positionmean error (m)

Modems final error (m)1 3 7 8 10 11

0 Yes 8.07 0 0 0 0 0 0No 8.05 0 0 0 0 0 0

14.142 Yes 10.98 1.25 9.51 3.31 4.27 10.00 3.42No 13.53 14.16 16.19 11.85 15.88 18.00 15.26

70.711 Yes 10.98 1.25 9.51 3.31 4.27 10.00 3.42No 13.53 14.16 16.17 11.85 15.89 18.02 15.25

141.421 Yes 10.98 1.25 9.51 3.31 4.27 10.00 3.42No 13.53 14.16 16.15 11.86 15.90 18.04 15.24

surge propellers thrust. The further measurement from the GPSdevice was used as a navigation aid in the first time instantsonly, to initialize the navigation algorithm, i.e. to make theaccelerometers bias and the velocity gain converge. Then, theselatter measurements were used as ground truth only, meaningthat the navigation system did not take advantage of the globallocalization system during the normal operation phase. Themeasurement equations can be thus written as:

ygps = pgps,n + ηgps (4a)yusbli = pu-mi,u + ηusbl (4b)ydepth = pdepth,n + ηdepth (4c)

ysurge =nRb(θ)

([τsurge,b 0 0]

T+ ηsurge

)(4d)

where pgps,n contains the North-East coordinates of the vehicleposition in the local navigation frame, pu-mi,u is the relativeposition of the i-th acoustic source with respect to the vehicleexpressed in the coordinate frame of the device, pdepth,n is thedepth of the vehicle in the NED coordinates and τsurge,b is thedesired thrust along the surge axis of the vehicle, which istransformed through the matrix nRb(θ) in the desired thrustresolved in the local navigation frame. Each measurement isaffected by a measurement noise, denoted with the η symbol,that we assume white, with zero mean and constant covariancematrix Rgps, Rusbl, Rdepth and Rsurge respectively.

In order to fuse such measurements with the inertial naviga-tion system, it is convenient to make explicit the dependence ofthe above measurements with the inertial mechanization states.For this reason, we can write:

ygps = [I2 02×N−2]x+ ηgps (5a)

yusbli =[−uRb

bRn(θ) 03×7+3(i−1)

uRbbRn(θ) 03×3(r−i)

]x+ ηusbl

(5b)

ydepth = [0 0 1 01×N−3]x+ ηdepth (5c)ysurge = Kthrvn + nRb(θ)ηsurge (5d)

where N denotes the dimension of the state vector x. In (5b)the position of both the vehicle and the ii-th node positions arefirst transformed in the body-fixed frame through the matrixbRn(θ) = nRb(θ)

T and thus in the USBL frame throughthe transformation matrix uRb. Finally, the relative position ofthe acoustic modem with respect to the vehicle is obtained bysubtracting the resulting measures. The equation (5d) simplyexpress the linear approximation of the surge thrust to obtainthe surge velocity and it is nonlinear with respect to the stateof the model.

III. FILTERING MOTION AND MAP: THE ACOUSTIC-BASEDSLAM ALGORITHM

According to the motion and sensitivity parameters dynam-ics in Equation (3), given the defined measurements model (4),an Extended Kalman Filter [12] was designed and tested. Thefiltering process is composed by two steps: in the predictionstep, a rough estimation of the state is obtained by evolvingthe dynamical model (3) of the system, by using the measuredinertial measurements. The second step is the correction step,which is executed when a new measurement is available fromone or more of the auxiliary sensors, in order to reduce theerror of the predicted state estimate. As soon as a new acousticmeasurement is made available, the filtering algorithm checksif the source is already present in the database; in this caseit uses the observation as a fix to refine the predicted state.Otherwise, the source corresponding to this measurement isadded to the database, the filter state is augmented with theposition of the new detected modem and the current vehiclenavigation is used together with the USBL measurement toinitialize the new states. Should this modem be visible againin the future, its measurements are used as a fix to the filter.

For the purpose of numerical implementation, the motionand measurements model equations were time-discretized us-ing the Euler integration method. The model of the system canbe thus rewritten in the following compact form:

xk+1 = f (xk,uk) + g (xk,uk)νk (6)yk = h (xk) + J (θk)ηk (7)

Here, the subscript k indicates that the quantity is referredto the k-th time instant. The prediction step is executed ateach time instant k > 0 when a new inertial measurement ismade available, by calculating the predicted state x−

k+1 andthe predicted covariance matrix of the estimation error P−

k+1,starting from the initial conditions x0, P0:

x−k+1 = f

(x+k ,uk

)P−k+1 = FkP

+k F

Tk +GkQGT

k

(8)

The variables with the ’+’ superscript in the prediction equa-tion are the refined estimations of the state and of the covari-ance matrix at the previous time step, obtained by runninga Kalman update step with the past measurements from theavailable auxiliary sensors. In (8), the matrices Fk and Gk

are obtained from (6) as follows:

Fk =∂f (x,u)

∂x

∣∣∣∣x+

k ,uk

, Gk = g(x+k ,uk

)and Q = diag (Qa,Qε) is the noise covariance matrix.

When a new measurement from the auxiliary sensors is

−500 −400 −300 −200 −100 0 100 200 300 400

−300

−200

−100

0

100

200

300

Estimated path

East direction [m]

Nort

h d

irection [

m]

WP1

WP2

WP3

GPS OFF

Typhoon programmed route

GPS

EKF (GPS on)

EKF (GPS off)

(a)

0 500 1000 1500−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

Vehicle velocity

Time [s]

Ve

locity [

m/s

]

v

n

ve

(b)

0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

Time [s]

Err

or

[m]

Error between GPS and EKF

Error

USBL fixes

(c)

0 200 400 600 800 1000 1200 14000

50

100

150

Time [s]

Err

or

[m]

Modems errors

M2

M1

F1

F2

ALLIANCE

USBL

(d)

Fig. 2. Results of the worst case elaboration. In Fig. 2(a) are illustrated the estimations of the fixed-nodes positions and of the North-East path followed by thevehicle. In the first part (solid green line), the GPS was used to feed absolute position correction to the estimation filter. During the remaining part (solid blueline), the GPS signal loss is simulated and the forward speed and the USBL measurements only were used as position correction feeds to the estimation filter.The black circle on the map indicates the point where the GPS signal loss begins; starting from here, GPS was used as ground truth only. The coloured circlesrepresent the estimation of the map: the heavy circles indicates the considered initial position for each node, while the crosses represent the actual position ofthe respective modem. Fig. 2(b) shows the North and East components of the estimated velocity of the vehicle. In Fig. 2(c) is illustrated the norm of the errorbetween the GPS measurement and the estimated vehicle position; the green diamonds indicate the time instant of the USBL fixes availability. Finally, Fig. 2(d)shows the norm of the error between the estimated and the known positions of the modems.

available, the Kalman update step is executed, in order tocorrect the prediction obtained in the current step. It is worthto mention that each measurement has its own notification rate,thus it usually happens that at a given time step, not all themeasurements can be available. Under these assumptions, thecorrection step is made by employing the available measure-ments at the current time, namely yk, and by selecting theentries in the matrices of the output model which correspondwith the currently available maesurements. The correction stepis then executed by calculating the state estimate x+

k+1 and the

covariance matrix of the estimate error P+k+1 as:

x+k+1 = x−

k+1 +Kk

(yk − h

(x−k+1

))P+k+1 = (I−KkHk)P

−k+1

(9)

where Hk is obtained from (7) as follows:

Hk =∂h (x)

∂x

∣∣∣∣x−

k+1

andKk = P+

k+1HTk

(HkP

+k+1H

Tk + JkRJTk

)−1

Table II. NUMBER OF USBL MEASUREMENTS PER NODE

Name Node ID # of fix

M2 1 3M1 3 1F1 7 4F2 8 6

ALLIANCE 10 1USBL 11 5

is the Kalman gain matrix, being Jk = J (θk) and R =diag (Rgps,Rusbl, Rdepth,Rsurge).

A. Results

The algorithm presented above was tested off-line on realexperimental data, collected during the sea-trial of Sept. 12,2013. In the following, we refer to the fixed-nodes constitutingthe network as M1, M2, F1, F2, USBL and ALLIANCE. In Ta-ble I we report some statistics of the preliminary elaborations,starting from different initial conditions in the fixed-nodespositions with respect to the true, known values. We refer to[9] for the implementation details. For the discussion here, itis sufficient to state that the Typhoon AUV was navigatingat the sea surface, i.e., with availability of the GPS signal,that can thus be used to initalize the filters, when needed,and as ground truth reference. Note however that, with theAUV at the sea surface, the USBL transponder is about 0.3 mbelow the seasurface, hence suffering from multi-path effectsto a much greater extent with respect to what expected inunderwater navigation. All the elaborations were performedusing in the initial part the GPS signal to initialize thealgorithm. The second column of the table indicates whetherthe USBL measurements were used during the initializationphase together with the GPS or not. Since the GPS givesabsolute, non divergent measurements, the position estimationof the nodes observed through the USBL measurements duringthe initialization was more accurate in the former case, as weexpected. However, we note that even in the latter case, thefinal error in the map is enough to obtain a good navigationestimate, as can be seen from the third column. In Table II arereported the number of USBL measurements received fromeach node. As can be seen from a comparison with Table I,the final error in the position estimation of the nodes withonly one correction, i.e. nodes 3 and 10, is bigger than theothers. Finally, Fig. 2 shows the results of the elaboration inthe worst case, i.e. initial error in the map of 100 m on both thetrue North and the East coordinates, GPS and USBL mutuallyexclusive. We can see that even in this case the results on boththe network topology estimation and the vehicle navigation aresatisfactory for our purposes.

IV. EXTENDING THE ACOUSTIC-BASED SLAM: NO APRIORI KNOWLEDGE

Starting from the previous considerations, we approachedthe problem supposing to have no a priori information regard-ing the network topology. Since in this case the dimensionof the network is unknown, it is not possible to define a statewith a prefixed dimension. To deal with this aspect, the part ofthe state relative to the map can be constructed dinamically,augmenting the state vector by 3 more components (i.e. theposition in the local reference frame) every time an acoustic

measurement from a still unknown node is received. To thisaim, we relied on a dynamic database of the detected modems,initially empty. The system model (3) was thus modified bychanging the last equation with the following one:

pmi,n = νmi i ∈ V (t) ⊆ {1, . . . , r} (10)

where V (t) denotes the set of the visible node at the timeinstant t. It explicitly depends on time because each nodebecomes visible only after the first reception of a measurement.Initially, V (t) is empty and its dimension increases with thereception of new acoustic observations, reaching eventually themaximum value, i.e. the dimension of the network, when eachnode has provided at least one measurement.

In the correction step of the filtering algorithm, an eventualacoustic measurement is used only if the source is alreadypresent in the set V (k), otherwise it will be temporarily savedand used to extend the filter state after the correction. At thatpoint, the algorithm checks whether any acoustic measurementfrom an unobserved node was previously saved; in this case,the state of the filter is augmented with the position of thenode (and the set V (k) increases contextually) and initializedwith the value:

p+k+1 +nRb(θ)

bRuyusbl,k

where p+k+1 is the estimation of the vehicle position. Moreover,the covariance matrix Pk+1 is also extended as follows:

Pk+1 = diag (Pk+1,Pp,k+1 +Rusbl)

where Pp,k+1 is the submatrix P corresponding to the esti-mation of the vehicle position.

A. Results

The modified algorithm was tested on the same data usedin the elaborations of Section II. In Fig. 3 are shown the resultsof the run; we considered the case in which the GPS and theUSBL are mutually exclusive, i.e. the USBL is disabled in theinitialization phase. In particular, we can see in Fig. 3(d) thatthe estimation of the fixed-nodes position begins only after thefirst measurement reception. In Table III are summarized thenorms of the estimation errors: as can be noted, the resultsare comparable to the worst case elaboration presented inSection II.

V. CONCLUSION

Experimental results on acoustic self-localization and map-ping for an AUV equipped with an USBL modem have beenreported. While these results have to be intended as prelimi-nary, and certainly influenced by the specific configuration ofthe acoustic transponders and by the available instrumentationon board the Typhoon AUV, the methodology proposed isquite general and applicable to a wide range of AUV and ofnavigation needs. The obtained results show that, even witha low cost, inertial motion units, and in presence of hostileacoustic channel conditions, the approach is able to keep thenavigation error bounded and within 3 - 4 times GPS accuracy.

Table III. STATISTICS OF THE PRELIMINARY ELABORATIONS

Vehicle positionmean error (m)

Modems final error (m)1 3 7 8 10 11

12.89 5.02 11.97 9.77 8.51 16.31 14.32

−500 −400 −300 −200 −100 0 100 200 300

−300

−200

−100

0

100

200

Estimated path

East direction [m]

Nort

h d

irection [m

]

WP1

WP2

WP3

GPS OFF

Typhoon programmed route

GPS

EKF (GPS on)

EKF (GPS off)

(a)

0 500 1000 1500−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

Vehicle velocity

Time [s]

Ve

locity [

m/s

]

v

n

ve

(b)

0 200 400 600 800 1000 1200 14000

5

10

15

20

25

30

Time [s]

Err

or

[m]

Error between GPS and EKF

Error

USBL fixes

(c)

0 200 400 600 800 1000 1200 14000

5

10

15

20

25

Time [s]

Err

or

[m]

Modems errors

M2

M1

F1

F2

ALLIANCE

USBL

(d)

Fig. 3. Results of the elaboration for the modified SLAM algorithm. We refer to Fig. 2 for the legend.

ACKNOWLEDGMENT

This work has been partially supported by THESAURUSproject, funded by PAR FAS REGIONE TOSCANA (http://thesaurus.isti.cnr.it) and by MARIS project, funded by MIUR.

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