Robust Surface Vessel NavigationUsing Terrain Navigation

Ove Kent Hagen, Kjetil Bergh Anonsen and Atle SkaugenNorwegian Defence Research Establishment (FFI)

P O Box 25, NO-2027 Kjeller, NorwayEmail: ove-kent.hagen@ffi.no

Abstract—Terrain navigation has been used extensively byunderwater vehicles the last decade. By comparing bathymetricmeasurements with a digital terrain model, it estimates a globalposition of the vehicle underwater, where Global PositioningSystem (GPS) signals are unavailable. With the increasingthreat of GPS signal jammers and spoofers to marine vessels,GPS independent techniques are becoming more interesting forsurface vessels as well. This paper explores the idea of usingterrain navigation to detect GPS spoofing, and as a substituteposition source during GPS jamming. The results from anexperiment simulating GPS jamming of a surface vessel indicatethe feasibility of such a system.

I. INTRODUCTION

Marine vessels are today more and more reliant on the posi-tion accuracy and integrity offered by the Global PositioningSystem (GPS). The GPS signals at the sea surface are veryweak, and are therefore susceptible to GPS signal jammersand spoofers. The jammers deny GPS service in their coveragearea. They are cheap, easily deployable, and have been shownto be a serious threat to systems that depend solely on GPS.Spoofing a GPS receiver is more complicated, but the threatfrom several methods of attacks on civilian receivers has beenassessed in [1]. Sophisticated attacks require the spoofer toinitially know the position of the target, but will then resultin the receiver computing the desired position of the spooferinstead of that of the receiver. If the spoofing is not detected,it presents a grave danger to the safety of marine vessels.Military marine vessels can be equipped with military GPSreceivers that provide protection against some of the spoofingattacks, but they are still equally susceptible to jammers. Manysystems on board these vessels rely on position accuracy andintegrity for intended usage. A GPS jamming experiment bythe Green Lighthouse Authorities in 2008 [2] showed thatmany modern on board systems fail when not receiving theaccurate position offered by GPS. The mariners must in thissituation fall back to the older alternative methods of safenavigation, using radar and visual observations, lowering theposition accuracy. In [2] it was shown that eLORAN radionavigation provided an accurate position also during the GPSjamming period. The eLORAN receiver was initially aidedby GPS, making it possible to correct for biases in the rangeestimates to the LORAN stations. The accuracy of these biasestimates during GPS jamming is however reduced with timeas the propagation conditions for the radio signals change.

Here we explore another method using terrain navigation

GPS

Terr Nav

Integrity INS

Fig. 1. Block diagram of a robust surface vessel navigation system combiningGPS and terrain navigation with an INS. The research vessel H.U. Sverdrupis shown in the narrow straits of Trollfjorden (Photo: FFI).

combined with an inertial navigation system (INS). Terrainnavigation has in recent years been established as a solution forreal-time subsurface position updates of the inertial navigationsystems on board Autonomous Underwater Vehicles (AUVs)[3], [4], [5], [6]. A major advantage is that terrain navigationprovides global position estimates, where the accuracy isindependent on the duration of the GPS jamming period.The major drawback is that it only works in regions wherethe terrain is suitable and digital terrain models (DTMs) areavailable. In Section I we propose a more robust navigationsystem for surface vessels. A Bayesian approach to terrainnavigation is then reviewed in Section III, and the differenceand similarities of terrain navigation from surface vessels andunderwater vehicles are discussed. Section IV describes theresults of an experiment testing the feasibility of the systemby integrating the INS and terrain navigation systems of theHUGIN AUV with the research vessel H.U. Sverdrup II ofthe Norwegian Defence Research Establishment (FFI). Theconclusions and future work are presented in Section V.

978-1-4799-0002-2/13/$31.00 ©2013 IEEE

II. ROBUST SURFACE VESSEL NAVIGATION SYSTEM

One of the more advanced proposed techniques in [1] fordetecting some types of spoofing attacks is by integrating theGPS receiver with an INS. This will also enable the navigationsystem to endure GPS jamming attacks for shorter periods oftime, but an unaided INS will eventually drift off in position,at a rate of 1 nm/h if based on a navigation grade inertialmeasurement unit (IMU) [7].The system proposed herein is to complement the GPS/INSsystem with a terrain navigation system, see Fig. 1. Underregular circumstances the terrain navigation system will pro-vide a GPS independent global position measurement, and cantherefore be used both to improve the integrity of the surfacevessel navigation system, and to detect if GPS spoofing attacksoccur. If attacked by GPS spoofing or jamming, the terrainnavigation system can still provide a position update to theINS, thereby maintaining a bounded position error. Lastly,there is an aspect of inherent improved navigation safety asterrain navigation localizes the vessel relative to the DTM,assuming the DTM is of high quality.

III. TERRAIN NAVIGATION

Terrain navigation is a proven technology, used for decadesin many applications. By correlating terrain measurementsfrom a platform, with a digital terrain model (DTM), terrainnavigation estimates the position of the platform. It started outas a positioning system used in cruise missiles, and later inaircraft. Terrain navigation is still used as a backup positioningsystem to GPS in those applications, in the same way it isproposed here. The last decade has seen extensive use ofterrain navigation in underwater vehicles, since the GPS signalis unavailable underwater.Here we only consider a loosely coupled fusion of terrainnavigation with the INS. In the loosely coupled approach, thebathymetric measurements are processed in a parallel terrainnavigation filter until it converges or diverges, and in case ofconvergence, the position estimate from terrain navigation isfed back to the INS as a regular position measurement.Terrain navigation performance depends completely on thebathymetry, and our knowledge of the bathymetry through aDTM. The estimation problem is as nonlinear as the DTM is,making a characterization of the expected accuracy difficult.The main principle is that the accuracy of the final positionestimate depends on the terrain variability within the footprintof the bathymetric sensors. The variability however needs tobe on a scale that corresponds with the resolution of the DTM,i.e. the measured variability must also be present in the DTM.If this is the case, terrain navigation accuracy is usually withinthe resolution of the DTM.

A. Surface vessels versus underwater vehicles

Many challenges in terrain navigation are shared betweenthe case of a surface vessel and that of an underwater vehicle,the lack of globally available high accuracy DTMs being themost important one. The globally available electronic naviga-tional charts (ENCs) have too poor resolution for the most

demanding applications, but might still be used in scenarioswhere position accuracy is is of less importance. If the surfacevessel is to operate within a bounded area and is equipped withe.g. a multibeam echo sounder (MBE), a DTM can be createdon site. Should the vessel later come under a GPS jammingattack, it can still navigate robustly and accurately within theoperation area.Even if a DTM is available, there is the requirement of terrainsuitability for terrain navigation. The experience from theHUGIN terrain navigation system [8] is that with a wide swaththere is often some terrain variation found within a few pingsfrom high resolution systems. If that is not the case, increasingthe correlation period will often help on convergence. Fora surface vessel this is most favorable. Since it operateson the surface, the altitude above the sea floor is maximal,which increases the swath width of MBEs when compared tounderwater vehicles. In addition a surface vessel often travelsfaster than an underwater vehicle. Since the INS position driftswith time, the position error after a certain time without anyaiding of the INS, is equal for both the surface vessel andthe underwater vehicle. However, the surface vessel will havecovered more ground, and is therefore more likely to haveterrain variations in its MBE footprint than the underwatervehicle.Finally, the higher altitude of the surface vessel makes thebathymetric measurements less accurate due to errors in thesound speed used to convert travel time to footprint location.Since the sound speed profile usually changes most signifi-cantly in the upper layer of the ocean, the surface vessels aremore susceptible to sound speed error, than an underwatervehicle operating close to the sea floor, see Section III-D.The higher altitude is also a problem when using bathymetricsensors with large opening angles, such as single beam echosounders, a type of sensor found on most surface vessels. Ifthe echo sounder has a single beam with an opening angle of10◦, the footprint on the sea floor is about 87 meters wide at500 meters water depth, which means the single beam coversseveral grid cells of a high resolution DTM. If combined witha low resolution DTM, this should not pose a problem. Ifhowever, the echo sounder measures range based on the closestbottom echo, it will in general be a biased measurement, sincethis is not necessarily located in the center of the beam.

B. Mathematical model

To enable practical calculation for the nonlinear terrainnavigation problem, a simplified mathematical model for thedynamics of the surface vessel and the measurements of thebathymetric sensors is presented. Let xk = (xk, yk, zk) denotethe vessel’s position in a local north-east-down system at timet = tk. Consider the following dynamical model for theposition states of the vessel

xk+1 = xk + uk + vk, (1)

where uk is the integrated motion estimated by the INS in thetime interval tk to tk+1, and vk is a white stochastic processmodeling the error drift in the INS estimate.

Let (ξk,ηk, ζk) denote mk bathymetric depth measure-ments relative to the INS solution in a local level north alignedsystem, and let h(x, y) denote the global terrain function. Weconsider the following model for the measurements

ζk = hξk,ηk(xk) +wk. (2)

Here we have introduced the measurement vector functionhξk,ηk

(xk) = {hi}mki=1 with scalar components defined by

hi = h(xk + ξk,i, yk + ηk,i)− hk − zk + ζk, (3)

and wk is a stochastic process modeling the bathymetricmeasurement error. This particular form of the measurementfunction is called relative profile matching, where the averageof the measured profile ζk, and the corresponding averageDTM profile hk, have been subtracted to eliminate potentiallylarge unknown biases, e.g. due to tides. To simplify the model,the additional depth errors caused by errors in the footprint ofthe measurements, ξk and ηk, have been included in wk.

C. Point mass filter

The algorithm used in the HUGIN terrain navigation system[3] is based on the point mass filter (PMF). PMF is anonlinear Bayesian estimator that estimates the probabilitydensity function (PDF) of the state vector on a grid [9] [10].It was first used in aircraft terrain navigation [11], but haslater made its way into underwater terrain navigation. Beforeintroducing the actual PMF approximation, we consider theBayesian formulation of the estimation problem (1) and (2).

We define a 2D bounded domain Gk in the earth tangentplane, enclosing the current INS solution. Let δxk denote aposition vector in Gk (the error of the INS) with referenceto a north-aligned system with origin at the INS solution,and let Zk denote the set of all measurements between t1and tk. Our goal is to estimate the position error filter PDFp(δxk|Zk), conditioned on all the measurements so far in thecorrelation period [t0, tk]. From (1) we find that δxk is aMarkov process, and its PDF evolves in time according to theconvolution integral [12]

p(δxk+1|Zk) =

∫Gk

pvk(δxk+1 − δxk)p(δxk|Zk)dδxk, (4)

where pvk(·) = p(δxk+1|δxk) is the Markovian transitionkernel for the error drift.

The measurement update, following Bayes’ theorem, isgiven by

p(δxk|Zk) =pwk

(ζk − hξk,ηk(xk + δxk))p(δxk|Zk)

αk, (5)

where αk =∫Gkpwk

(ζk−hξk,ηk(xk+ δxk))p(δxk|Zk)dδxk

is a normalization constant, and pwk(·) denotes the PDF for

the sensor measurement error. Together the equations (4) and(5) form the recursive Bayesian estimator equations for terrainnavigation. The recursion is started by a known initial PDFp(δx0|Z0) = p0(δx0) at t0 that depends on the initial INS

0 50 100 150 200 250 300 350 400−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

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∆ c=−2.0

∆ c=−1.5

∆ c=−1.0

∆ c=−0.5

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∆ c=0.5

∆ c=1.0

∆ c=1.5

∆ c=2.0

Beam No

De

pth

err

or

[m]

Depth error from sound speed error

Fig. 3. Estimated depth error as function of sound speed error and beamnumber, for an EM710 multibeam echo sounder above a flat sea floor of 250m water depth.

accuracy, and the filter then runs recursively for each pinguntil a convergence or divergence criterion is met at tK . ThePMF approximation is found by representing the filter PDFin (4) and (5) by point masses on a regularly spaced gridrepresentation of Gk, and by calculating the integrals throughstraightforward quadrature. Once the PMF approximation ofthe PDF is found, estimates of the INS position error andthe accuracy of this estimate can be calculated directly fromthe approximated PDF [12]. Fig. 2 shows an example of theevolution of the PDF in the correlation period.

D. Measurement model

The model of the measurement noise in a calibrated system(2) can be modelled by the following sum of uncorrelatederrors [8]

wk = ws +wh +wz +wc, (6)

where ws denotes the sensor processing noise, wh is theDTM errors, wz is the residual error in transducer depth (thetidal error component is effectively removed by relative profilematching), and finally wc denotes the error due to error in thesound speed profile. The measurement noise is assumed to bewhite and Gaussian distributed, i.e.

pwk= N(0,Ck), Ck = E

[wkw

Tk

](7)

The model is discussed in detail in [8], but here we look closerat a simplification of the sound speed induced depth error. Letφi denote the beam angle from the vertical of beam i. If weassume the vessel has zero roll, the sound speed is a constantc in the water column, and the one-way travel time of theacoustic signal is given by τi, the beam depth is given by

ζi = cτi cos(φi). (8)

Derivation of (8) with respect to c gives

∂ζi∂c

= τi cos(φi)− cτi sin(φi)∂φi∂c

. (9)

(a) Position error PDF after 1 ping (b) Position error PDF after 10 pings

Fig. 2. Example of the position error PDF estimated by PMF after 1 (a) and 10 (b) pings, using only three beams from an EM710 multibeam echo sounderand 1 minute between each ping. True position is still recovered 100 m both south and west of the estimated position of the INS, which is always in thecenter of the 800 m x 800 m grid of the PMF.

By using (8), (9) can be rewritten as

∂ζi∂c

=ζic− ζi tan(φi)

∂φi∂c

. (10)

The beam angle dependency on c is ∂φi

∂c = tan(φi)c [8],

which gives the following first order relation between deptherror ∆ζi and the sound speed error ∆c:

∆ζi =(1− tan(φi)

2) ζic

∆c. (11)

The first part is the range error from sound speed error whenconverting acoustic signal travel time to range, and the secondpart is due to angular error arising from sound speed error nearthe sensor. Usually sound speed near the sensor is knownaccurately by direct measurements, while the sound speedprofile is less accurately known. Wrongful compensation ofray bending effects on the acoustic signal will result in bothrange and angular error, so even in this case the model (11)can serve as a crude first order approximation of an effectivesound speed error. See Fig. 3 for an example of this error asa function of beam angle and sound speed, for a case of aKongsberg Maritime EM710 and 250 meter water depth.

IV. EXPERIMENTAL RESULT

In February 2011 FFI conducted a feasibility experimentusing terrain navigation during a simulated GPS jammingscenario on board the research vessel H.U. Sverdrup II inthe middle of Vestfjorden in northern Norway. The vesselis equipped with an EM710 MBE that produces up to 400beams per ping (or up to 800 beams if counting its dual swathcapability.) The on board EM710 transmits acoustic signalswith an opening angle of 0.5 ◦ in the along track direction,and beamforms the reflected signal from the sea floor withina swath sector up to 140 ◦ in the across track direction. TheEM710 is integrated with Seapath 300 for position and motion

reference, which compensates the EM710 data for the vessel’sroll, pitch and heave motion. H.U. Sverdrup II is also equippedwith a Moving Vessel Profiler (MVP) that enables updates ofthe sound speed profile while in motion. The MVP was usedinfrequently during the day of the test, to simulate regularcasts to measure the sound speed profile, but it was not usedwhen the experiment took place.A DTM of 10 meters resolution was constructed based onearlier surveys with H.U. Sverdrup II. At that time, it wasequipped with an EM1002 MBE. The bathymetry in themiddle of Vestfjorden is rather flat on a large scale, but onfiner scale scouring from icebergs are very dominant featureson the sea floor, see Fig. 4. The experiment was carried outwhile H.U. Sverdrup II traveled northeast along a straight linefor 34 km at 13 knots into Vestfjorden, as shown in Fig. 4a.

A. System integration

A GPS/INS system capable of interfacing a terrain nav-igation system was installed on board, and integrated withon board systems in one day, without time for performingany calibration. A navigation grade IMU, Honeywell HG9900,was mounted to a table in the lab on board, its relativelocation was roughly estimated, and the heading alignmentwas compared to Seapath 300 for possible detection of anygross errors. A special version of the HUGIN aided INS [7],called FFINavP, has earlier been developed to support researchactivities at FFI that need real-time navigation. It was nowextended to interface the EM710 data available on the on boardnetwork. FFINavP interfaced HG9900 and a Trimble BD982GPS receiver via a data synchronization unit (DSU) developedat FFI.The DSU system is developed for time stamping data fromIMU, compass and GPS mainly for navigational purposes.It has 4 additional digital inputs which can be used to

(a) Trackline of H.U. Sverdrup II and Vestfjorden bathymetry (b) Details of Vestfjorden bathymetry

Fig. 4. The center of Vestfjorden is rather flat on a large scale (a). The depth along the 34 km long trackline varies only 20 m, but high resolution bathymetryreveals deep scouring from icebergs (b).

synchronize other units such as camera, sonar and radar. Anyunit sending out a 5V pulse can be time stamped using one ofthese four inputs. Time stamped data are in UTC time, as theDSU utilizes the PPS1 pulse and UTC time received from theGPS in order to synchronize the DSU internal timer giving atime resolution around 50µs. The DSU stream time stampeddata to the PC through a USB port. NavLog, a control andmeasurement program written in LabVIEW, is used to convertthe data to a format designed to work with NavLab [13] andFFINavP.Since the IMU data sent to FFINavP and the survey systemson board H.U. Sverdrup II were both synchronized with GPS,it enabled real-time synchronized usage of EM710 datagramsthat were made available on the on board network. FFINavPalso interfaced TerrP SA, a stand-alone version of HUGIN’sterrain navigation system [3]. The EM710 network datagramswere converted and sent to TerrP SA over its generic CORBAinterface for bathymetric sensors. TerrP SA then ran its pointmass filter until a convergence/divergence criterion was met.Before sending back the position solution to FFINavP, TerrPSA performs intrinsic integrity tests comparing measuredprofiles with DTM given the position solution. An extrinsicintegrity test on the position solution is also done by FFINavP,before actually using the position measurement in the Kalmanfilter inside the INS.

B. Integrity: map and measurement comparison

One of the possibilities of this system mentioned earlieris increased integrity of the navigation solution. When theGPS is not jammed, the terrain navigation system can beused to check the integrity of the GPS position by comparingmeasured profiles with the expected DTM profiles given theGPS position. Larger deviations may indicate that the GPSposition is spoofed or otherwise inaccurate. Fig. 5 gives an

example of how this can be visualized for a human operator.It shows a 3D model of about a 2.5 minutes set of themeasurements as a function of beam number and ping, sideby side with the corresponding values from the DTM. Thematch in position is easily verifiable by inspection, but aconstant level difference is notable. During test runs beforethe experiment we noticed a slowly varying level differenceof 2 - 3.5 meters magnitude. We did not compensate for tides,so some level difference was expected, but not that high. Itturned out that by a misunderstanding the source soundingsprovided for constructing the DTM was actually referencedto the Norwegian vertical datum SK0 (the lowest tide), whileTerrP SA requires DTMs referenced to mean sea level (MSL).The difference between the two datums in the experiment areais about 1.7 meters.In post processing we compensated for tides in the EM710data and the datum difference of the DTM. The time averageof the difference of the EM710 and the DTM in the same 2.5minutes as in Fig. 5, is shown in Fig. 6. The residual errornow resembles that of a typical sound speed error shown inFig. 3

C. Real-time result

Near the start of the line FFINavP was initialized byenabling aiding with GPS. Due to shadowing by the shipstructure the GPS signal was sometimes lost but adequatefor initialization. At the start of the line GPS jamming wassimulated by disabling GPS aiding in the FFINavP software.Instead terrain navigation aiding was enabled, and TerrP SAwas used as sole position measurement source for the 34 kmlong line in Vestfjorden.To reduce the measurement correlation caused by using asensor with much higher resolution than the DTM, TerrP SAwas configured to use a maximum of 50 of the 400 beams from

(a) EM1002 DTM (b) EM710 Measurements

Fig. 5. Details of the EM1002 DTM (a) at the footprint of the EM710, and the EM710 measurements (b).

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Beam No

Diffe

ren

ce

[m

]

Fig. 6. Mean difference (solid black) between EM710 and the EM1002 DTMof Vestfjorden, along with the standard deviation (broken blue).

EM710, and to only process every third second. Because ofthe large depth bias found between the EM710 data and theDTM, TerrP SA was configured to only use relative profilematching. The grid of the PMF was set to 800 m x 800 m at5 m resolution. This was the first time EM710 was integratedwith TerrP SA, so the integrity system was not specificallytuned towards this system. For two periods during this run,TerrP SA stopped providing position fixes. In the post analysiswe found that this was caused by an error in the generation ofDTM grids. TerrP stores overlapping subsections of the DTMin memory, but these were configured for a swath size typicalfor a MBE on the HUGIN AUV, rather than the EM710 on asurface ship. This caused two glitches in the DTM coverageprovided for the terrain navigation system.A reference solution was constructed by post-processing theIMU and GPS data logged by the DSU interface software withthe optimal smoother in NavLab [13]. This gave an adequate

TABLE ITERRP PERFORMANCE

Error North East

Mean -2.97 m -2.63 m

Std Dev 9.75 m 3.95 m

ground truth position reference (about 3 m 1σ) of H.U.Sverdrup II along the track line. Fig. 7 shows the performanceof TerrP SA and the integrated solution in FFINavP comparedto the NavLab solution. Except for a short period at the startof the line, and some occasional bad terrain navigation fixesthat passed the integrity system, the accuracy of TerrP SA waswithin expected performance. Table I summarizes the averageperformance. The error is very low in the eastern direction,well within the grid resolution. In the northern directionthe error is substantially larger with standard deviation atgrid resolution. Both directions do however have biased errorcomponents. Parts of this may be due to an inaccurate leverarm from the HG9900 unit to the position reference point usedby the EM710.The bad terrain navigation fixes did not pass the secondintegrity test in FFINavP, but in the short period at the startof the line, the INS is affected by a biased error in theTerrP SA position estimates. The large drift occurring attwo periods during the experiment are due to the glitchesin the map coverage provided to TerrP SA. During theseglitches FFINavP is in free-inertial mode, navigating with theIMU as the only input. This indicates what would happen ina GPS jamming scenario without terrain navigation aiding.When map coverage is back, the position error is immediatelyreduced both times.

V. CONCLUSION AND FUTURE WORK

A robust navigation system has been proprosed for surfacevessels in GPS jamming and spoofing scenarios. The naviga-

1000 2000 3000 4000 5000 6000−60

−40

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0

20

TerrP and FFINavP position vs post processed navigation

Time [s]

Nort

h d

iffe

rence [m

]

1000 2000 3000 4000 5000 6000

−20

−10

0

10

Time [s]

East diffe

rence [m

]

Fig. 7. The Error of FFINavP (solid black), and the error (blue dots) andestimated standard deviation (green solid) of TerrP SA during simulated GPSjamming. Notice the free-inertial drift when no measurements are received byFFINavP.

tion system fuses GPS and terrain navigation with an inertialnavigation system. The comparison of measured bathymetricprofiles with expected DTM profiles given the GPS positioncan be used by an integrity system to detect GPS spoofing. Ifthe GPS signals are jammed, terrain navigation can be usedto aid the inertial navigation system instead.With some modifications, HUGIN’s INS and terrain navigationsystems were successfully used to demonstrate robust andaccurate navigation during simulated GPS jamming of thesurface vessel H.U. Sverdrup II. We have also discussed thelimitations and challenges of terrain navigation, and comparedthem to the current usage with underwater vehicles.Some areas of future work have been identified, such asimproving the terrain navigation algorithm to better handlelarge depth errors due to a combination of tides and soundspeed errors. The usage of low resolution DTMs based onENCs should be explored, and methods for more accurateintegration of single beam echo sounders with large openingangles should be developed.

Another interesting point would be to integrate eLORANradio navigation with this system. Terrain navigation may helpthe bias estimation of the range estimates to the LORANstations during GPS jamming, and eLORAN may then provideaccurate position aiding while the vessel moves over flatterparts of the sea floor.

ACKNOWLEDGMENT

The authors thank the crew onboard H.U. Sverdrup II, andPetter Lagstad at FFI.

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