Eur. Transp. Res. Rev. (2017) 9: 1DOI 10.1007/s12544-016-0217-5

ORIGINAL PAPER

On fault detection and exclusion in snapshotand recursive positioning algorithms for maritimeapplications

Ralf Ziebold1 ·Luis Lanca1 ·Michailas Romanovas1

Received: 4 November 2015 / Accepted: 28 November 2016 / Published online: 27 December 2016© The Author(s) 2016. This article is published with open access at Springerlink.com

AbstractIntroduction Resilient provision of Position, Navigation andTiming (PNT) data can be considered as a key element of thee-Navigation strategy developed by the International Mar-itime Organization (IMO). An indication of reliability hasbeen identified as a high level user need with respect toPNT data to be supplied by electronic navigation means.The paper concentrates on the Fault Detection and Exclu-sion (FDE) component of the Integrity Monitoring (IM) fornavigation systems based both on pure GNSS (Global Navi-gation Satellite Systems) as well as on hybrid GNSS/inertialmeasurements. Here a PNT-data processing Unit will beresponsible for both the integration of data provided by allavailable on-board sensors as well as for the IM function-ality. The IM mechanism can be seen as an instantaneousdecision criterion for using or not using the system and,therefore, constitutes a key component within a process ofprovision of reliable navigational data in future navigationsystems.Methods The performance of the FDE functionality isdemonstrated for a pure GNSS-based snapshot weightediterative least-square (WLS) solution, a GNSS-based

This article is part of Topical collection on Young ResearchersSeminar ECTRI-FERSI-FEHRL 2015

� Ralf ZieboldRalf.Ziebold@dlr.de

1 German Aerospace Centre (DLR), Institute of Communicationsand Navigation, Kalkhorstweg 53, 17235, Neustrelitz,Germany

Extended Kalman Filter (EKF) as well as for a clas-sical error-state tightly-coupled EKF for the hybridGNSS/inertial system. Pure GNSS approaches are evaluatedby combining true measurement data collected in port oper-ation scenario with artificially induced measurement faults,while for the hybrid navigation system the measurementdata in an open sea scenario with native GNSSmeasurementfaults have been employed.Results First, the performance of the proposed FDE schemesin terms of the horizontal error is evaluated for bothweighted and unweighted approaches in GNSS-based snap-shot and KF-based schemes. Here, mainly due to availabilityof the process model, the KF approaches have demon-strated smaller sensitivity to the injected GNSS faults, whilethe methods with CNo weighting schemes have resultedin reduced spread of the obtained position solutions. Thestatistical evaluation of the proposed FDE schemes havebeen performed for pure GNSS schemes by consideringthe fault detection rate as a function of the amplitudefor the randomly injected GNSS faults. Although the KF-based approaches have clearly outperformed the memory-less schemes, lower detection rates for weighted schemescould be clearly seen due to inability of the FDE to detectfaults of fixed amplitude for satellites with lower CNo

values. Moreover, the evaluation of the FDE schemes interms of maximum horizontal position error have indicatedbounded response of the FDE schemes when compared tothat of non-FDE methods. Finally, the superiority of theFDE-enabled tightly-coupled GNSS/inertial EKF over thenon-FDE solution have been demonstrated using a scenariowith native GNSS faults.Conclusions The work had successfully demonstrated anapplicability of the developed FDE schemes in snapshotand RBE-based algorithms for maritime applications using

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both non-inertial GNSS-based positioning and a hybridIMU/GNSS EKF-based approach. The proposed methodsform a solid foundation for construction of a more reli-able and robust PNT-Unit, where state-of-the-art hybridnavigation algorithms are augmented with integrity mon-itoring functionality to ensure the system performance inthe presence of GNSS faults. The FDE mechanism providesconsistent improvements in terms of the horizontal accuracyboth in LS and KF-based methods. Although only port oper-ation case and one example of a true GNSS fault in opensea was considered, the presented results are believed to begeneral enough and the scheme could be adopted for otherapplications in future.

Keywords Integrated navigation system · Kalmanfiltering · GNSS · Inertial sensors · Integrity monitoring

1 Introduction

The last decades had witnessed a rapid development of newtechnologies for nautical applications both in order to sup-port the constantly increasing marine traffic and the require-ments to improve the safety of navigation. Here the processof vessel navigation is supported by a variety of independentsources of navigational information (sensors or sensor sys-tems), where GNSS (Global Navigation Satellite Systems),in particular the Global Positioning System (GPS) is oftenadopted as main source for provision of absolute Position,Velocity and precise Time information (PVT). Nevertheless,GNSS sensors are often not integrated with other on-boardsensors and sensor systems such as speed log, gyro com-pass, RADAR, etc., and, therefore, are mostly used as stan-dalone sensors. However, with numerous independent anddecoupled sources of navigational information available(e.g. non-hybrid systems, where the information from dif-ferent sensors is not fused), the process of navigation can beformulated as a real-time decision making process that re-quires an extreme focus and constant attention from the nav-igator. In spite of all the efforts to improve the quality andreliability of different sensors, 43 % of the total number ofaccidents in the Baltic Sea during 2012 were actually causedby human factors such as mistakes in the planning processor skill-based errors, such as slip and lapse [9].

In order to improve the overall safety and efficiencyof berth-to-berth navigation, the International MaritimeOrganization (IMO) has started the so-called e-Navigationinitiative. Here resilient on-board provision of Position,Navigation, and Timing (PNT) data is recognized as acore functionality to improve the reliability, resilience andintegrity of the navigation information provided by thebridge equipment [1]. Based on the concept of MaritimePNT System, the PNT data processing Unit will use all

available on-board sensors and employ methods of sensorfusion in order to provide both the PNT data and the associa-ted integrity information to the user. In a modular approachof a future Integrated Navigation System (INS) this PNT-Unit will serve as a module responsible for the on-boardPNT data provision.

Moreover, it is rather well-known that an integration ofmultiple complementary positioning sensors could highlyimprove the overall system resilience against Radio Fre-quency (RF) channel contamination and is crucial in achie-ving a reliable provision of PNT data even for challengingscenarios with severe RF signal multipath and Non-Line-Of-Sight (NLOS) effects (especially important for inlandwaterways or port operations), jamming or effects caused byionosphere weather conditions. Therefore, it is consideredto be advantageous to augment the GNSS system with yetanother sensor or sensor system with different error and/orfailure patterns such as inertial sensors or Doppler VelocityLog (DVL). These sensors are able to provide a positionwith slowly degrading level of accuracy for a specifiedperiod of time while the GNSS information is either notavailable or is considered to be unreliable. The inertial navi-gation systems are able to overcome the GNSS vulnerabilitydue to their inherent independence from the surroundingsand, therefore, are often integrated with GNSS informationso that the short term performance of the Inertial Mea-surement Unit (IMU) and long term stability of GNSS areincorporated optimally within the final hybrid navigationsystem.

Although the integrity algorithms are rather well-knownin aviation applications, few works have reported on applyingthese or similar techniques to other scenarios such as terres-trial or nautical navigation under real operational conditions.The presented work tries to close this gap by introducing thediscussion on performance of Fault Detection and Exclu-sion (FDE) methods for both snapshot and Recursive Baye-sian Estimation (RBE) positioning algorithms in maritimeapplications and concentrates on the performance analysisof both the least-squares residuals (LSR) and Kalman FilterInnovation (KFI)-based FDE algorithms.

The presented work starts with the discussion on integrityalgorithms for pure GNSS (GPS) systems. As the GNSSoutput in the form of position and velocity solutions isoften employed by hybrid navigation systems in loosely-coupled configurations, it becomes crucial to understandthe performance of FDE mechanisms when GNSS data areused in snapshot techniques. The discussed FDE approachis compared against the corresponding FDE extension fora RBE scheme. The obtained results confirm that even fora pure GNSS-based system the RBE methods with FDEfunctionality clearly outperform the non-RBE methods dueto presence of an additional source of information in theform of the assumed process model. The performance of the

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developed techniques is assessed in terms of horizontal posi-tioning accuracy using real data with artificially introducedfaults and the results are evaluated for weighted and non-weighted GNSS measurement noise models. For this pur-pose a GNSS fault simulator based on Monte Carlo methodswas developed, which is capable adding in a controlled man-ner faults to raw measurements recorded previously duringtypical maritime operational scenarios (e.g. port operationor coastal approach).

Within the second part of the work the FDE scheme isevaluated within a real hybrid navigation solution usingboth GNSS and inertial sensor data. As the hybrid navi-gation solutions are becoming more and more popular fornon-aviation applications, mainly due to appearance of rel-atively cheap inertial sensors of tactical grade, odometeror Doppler velocity measurements, more advanced tech-niques for Integrity Monitoring (IM) in RBE methods arebecoming necessary. In order to assess the performance ofthe proposed techniques for hybrid navigation, we employa classical hybrid inertial/GNSS system. This allows theresults to be easily extrapolated to other applications suchas automotive and outdoor robotics scenarios. Furthermore,the obtained results are based on real operational condi-tions including the unmodelled GNSS effects and errorsin inertial sensors such as misalignment. The performanceof the hybrid navigation system with FDE functionality iscompared to that of non-FDE loosely-coupled EKF usingreal measurement data collected during a coastal approachoperation with native GNSS faults.

The rest of the paper is organized as follows. In Section 2a brief discussion is provided on state-of-the-art FDE meth-ods in IM both for snapshot and RBE positioning algo-rithms. The details on relevant mathematical methods aregiven in Section 3 with the description of the system setuppresented in Section 4. The experimental results are shownin Section 5 with the summary and the outlook for futureresearch provided in Section 6.

2 Current research status

The Snapshot LSR Receiver Autonomous Integrity Moni-toring (RAIM) algorithms developed by the civil aviationcommunity [16] or the statistical reliability testing adop-ted by the geodetic community [19] are the classic refer-ences for non-augmented (i.e. autonomous and completelyself-contained) GPS-based LSR algorithms. All these app-roaches make use of the redundancy within the availablemeasurements to check, on a measurement-by-measurementbasis, the relative consistency among estimated residuals,and, correspondingly, to detect the most likely measurementfault. Most of the known approaches are based on the com-parison between a test statistic depending on the estimated

least-squares (LS) residuals and a given threshold underGaussian noise assumption. The decision threshold is setconsidering a priori knowledge of the statistical distribu-tion of the test residuals in the fault-free case and a givenfalse detection rate. Although the classical methods mainlyuse snapshot techniques, some works have been reported onintroducing the FDE algorithms for RBE techniques [17].These techniques are usually formulated in a well-knownform of a Kalman filter (KF), where it has been proven thatthe KF innovations follow a similar statistical distribution tothat of the LS residuals under equal noise assumptions [23].

The trivial assumption that all GNSS code measure-ments are contaminated with noise of constant and knownvariance is often violated in real scenarios and severalapproaches have been reported on increasing the robustnessof integrated solutions by using more advanced GNSS noisemodels, where the measurement covariance is not fixed andconstant in time, but instead depends on the measurementsignal quality, elevation angle, etc. [6, 7, 22]. Although ithas been widely agreed that the number and the impactof possible error sources is strongly related with the satel-lite elevation, the elevation angle itself is not necessarilythe best indicator of the actual signal quality [7] and CNo

(received carrier (i.e. the signal) power (watts) divided bythe measurement noise power density) is often consideredas a fairly good alternative. Hence the measurements withhigher CNo values are good indicators of less noisy rangemeasurements and, therefore, should be weighted more toprovide an improved precision of the positioning solution[6, 7, 24].

The augmentation of GNSS systems with inertial sensorsin order to mitigate intentional or unintentional RF sig-nal interference has a fairly long history. The work of [12]addressed both the issues of IM in a tightly-coupled (TC)IMU/GNSS system and the availability of hybrid navigationsolutions. The latter one is defined as the ability of the sys-tem to coast upon the loss of all GNSS signals while stillmaintaining a certain accuracy. The authors in [12] used aGNSS ramp error model (GNSS pseudorange error, whichconstantly grows at a particular rate starting from zero error)and evaluated two IM strategies: solution separation methodand extrapolation method. Within the first approach the teststatistic is the horizontal separation between the full-set andsubset solutions where the failure is claimed if the test statis-tic exceeds the associated decision threshold. The secondapproach detects the slowly growing (ramp) errors by con-sidering the GPSmeasurements over a relatively long period(up to 30 minutes) and using KF innovations averaged over2.5, 10 and 30 minutes. Nevertheless, both methods maynot detect measurement failures during periods of low (lessthan four) satellite visibility. Note that GNSS ramp errorsare often considered to be far more challenging comparedto step errors as the latter generate instantaneous jumps in

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the measurement biases and can be relatively easy detectedboth via consistency check or by comparison to the actualoutput of inertial integration. The authors conclude thatinnovations can be only used to detect the failures causedby relatively fast growing errors, while the statistic for theextrapolation method, which averages the innovation vec-tor elements over time, can be used to detect slower errorramps.

Although the Microelectromechanical Systems (MEMS)sensors have attracted an increasing attention for the pedes-trian localization [4], robotics, automotive applications orlow-cost Unmanned Aerial Vehicle (UAV) design, theirapplicability to Safety Critical Applications (SCA) such asmaritime navigation has been until recently limited by theirrelatively high noise and bias instability, causing a rapiddrift of the standalone inertial solution when reference posi-tioning information is not available. Some recent works [14]have also assessed the possibility of replacing Fiber OpticGyroscopes (FOG) with higher performance MEMS IMUsand have confirmed that a combined IMU/GNSS systemis able to deliver position and velocity information at highupdate rate while preserving a low noise content due tosmoothing performance of the inertial integration. Still, theperformance of the hybrid system was not assessed underthe presence of measurement faults and no IM algorithmswere evaluated in that study.

3 Mathematical development

Obviously, the algorithms employed in maritime SCA mustmeet stringent reliability requirements. Here, for simplic-ity, we adopt an integrity concept from the aviation sector,where one of these reliability requirements is the so-calledintegrity risk. The integrity risk is the likelihood of an unde-tected navigation state error, that results in HazardouslyMisleading Information (HMI). In practice, it is defined asa confidence bound for the navigation system state, whichconfines all state output errors with a confidence equal orhigher than 1-α, where α is the integrity risk (in general, thevalue has to be adjusted according to the requirements of thetarget application). There is a case of loss of integrity whenthe navigation system state error exceeds the confidencebound without warning the system user. The probability ofloss of integrity is also called probability of HMI. This prob-ability can be mapped onto the state space and, in the caseof KF-based navigation systems, it can be interpreted as theprotection level (in physical units) of the state uncertainty(covariance) ellipsoid. SCA IM algorithms must providefunctionality for real-time detection of navigation systemstate integrity loss and optionally, fault identification andexclusion mechanisms (so-called FDE) in order to guaranteeservice continuity.

The algorithms for positioning and hybrid navigation areusually formulated as state estimation problems using acombination of measurements from multiple sensors withcomplementary noise properties. A desired set of the param-eters to be estimated from noisy measurements usuallyincludes the object’s position, velocity and attitude as wellas some of the sensor errors. Here one can utilize a well-established estimation strategy based on the RBE frame-work [5, 20], while a classical LS solution can be consideredas a non-recursive memory-less (snapshot) approach. Theclassical RBE cycle is performed in two steps:

Prediction The a priori probability is calculated from thelast a posteriori probability using a probabilistic process(state transition) model f (·).

Correction The a posteriori probability is calculated fromthe a priori probability using a probabilistic measurementmodel h (·) and the current measurement zk .

In practice, however, the theoretical methods formulatedwith probability densities do not scale up very well and canquickly become intractable even for estimation problemsof reasonable dimensionality. Various implementations ofRBE algorithms differ in the way the probabilities are rep-resented and transformed in the process and measurementmodels [5, 20]. If the models are linear and the probabili-ties are Gaussian, the linear KF is an efficient and optimalsolution of the estimation problem. Unfortunately, most ofthe useful real-world navigation systems are nonlinear andmodifications to the linear KF have been developed to dealwith nonlinear models. The Extended Kalman Filter (EKF)is one of the most popular nonlinear estimators and is histor-ically considered as a standard tool within the engineeringcommunity. In the EKF the nonlinear models are linearizedabout the current estimate using Taylor series expansion,where model f and observation model h are replaced bythe corresponding Jacobians. The system at every time tk isrepresented by the state xk and an associated covariance Pk

with the rest of the filtering scheme being essentially iden-tical to that of the classical linear KF. Although the EKFinherits many advantages of the KF such as limited compu-tational costs and a clear filtering structure, it still suffersfrom two main problems. Firstly, the performance of theestimator strongly depends on the validity of the linearizedmodel assumption and can become inaccurate and lead tofilter instabilities if these assumptions are violated. Sec-ondly, the required Jacobians can be potentially difficult oreven impossible to derive if the dynamical models involvecomplex approximation coefficients and/or discontinuities,or generative sensor models are used (e.g. 2D planar laser).

We start the discussion on the mathematical back-ground by considering the non-recursive FDE method,where the corresponding FDE RBE scheme can be seen

Eur. Transp. Res. Rev. (2017) 9: 1 Page 5 of 15 1

as an extension of this well-known strategy. The usualsnapshot GNSS-based position determination involves fourunknowns: receiver coordinates (X, Y,Z) and the GNSSreceiver clock offset δt with the number of unknowns n = 4.For the memoryless LS estimation we follow a classicalapproach based on the linearization of the measurementfunction at each epoch tk around a point x0 and finding thecorrection factor δx using [2]:

δx =(HT R−1H

)−1HT R−1δz, (1)

and the iterative update of the initial estimates xi = xi−1+δxi ,where δz is the misclosure vector and R is the measure-ment noise covariance. In the expression above the matrixH is the corresponding Jacobian of the measurement model,which, in this case, corresponds to the linearized GNSSpseudorange measurement model. If there are five or moreobservations z available (i.e. m > n), the redundant mea-surements could be used to check the consistency among thefull set of measurements. This forms a fundamental prin-ciple for the fault detection using the LS method, wherethe measurement space with dimensionality m is separatedinto two subspaces: the state space and the parity spacewith the dimensionality n and m − n respectively [10]. TheLSR methods are based on a detection test derived from themeasurement residual norm

∥∥e∥∥:

e = z − Hx = (I − H(HT R−1H)−1HT R−1)z. (2)

The test statistic is based on the estimated residual vectore normalized by the standard deviation of the measurementerrors

∥∥e∥∥2 = eT R−1e. The probability density function of

the normalized LS estimation residuals is shown in Fig. 1 for

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Least−squares estimation residuals, e [m]

N(e

)

e − LS

e − WLS

Theoretical(μ=1,σ2=1)

Fig. 1 Least-squares estimation residuals probability density func-tion: normalized residuals of non-weighted GNSS snapshot solution(e-LS), normalized residuals of CNo weighted snapshot solution(e-WLS) and the theoretical model

a fault-free scenario (real measurements passing global con-sistency check with conservative confidence level). The plotcompares the theoretical distribution (assumed to be Gaus-sian with zero mean and unit standard deviation) and theexperimental results for both classical equally weighted LSsnapshot GNSS solution (e-LS) and a GNSS solution withCNo weighted measurement model (e-WLS, see below).One clearly sees that in both cases the residuals e approx-imately follow the assumed Gaussian distribution as thetheory predicts.

Here one should notice that the test statistic is observablewhile the positioning error of the LS solution is not. In thefault-free case (the individual residuals follow N (0, 1), seeFig. 1), the test statistics value follows a central Chi-Squaredistribution withm−n degrees of freedom (see Fig. 2). Herethe classical LS detection method is based on the hypothesistesting where the test statistic with the given threshold iscompared to the LSR statistic defined as [21]:

ts =√∥∥e

∥∥2. (3)

For the fault-free case the test threshold Th for a givenprobability of false alarm (Pf a) and redundancy (or equiva-lently, degrees of freedom) is found by inverting the incom-plete gamma function [21]. A common procedure consistsof fixing Pf a according to the application requirements andletting the threshold vary with the availability of the mea-surements. A typical value for Pf a in maritime applicationsis 0.1 % [18]. The hypothesis test is given by the followingcondition:

Global-Test ={

H0 if ts ≤ Th,

H1 if ts > Th.(4)

0 1 2 3 4 5 60

0.05

0.1

0.15

0.2

0.25

0.3

Normalized global test statistics, ts [m]

χ2 DoF

=5(ts)

ts − LS

ts − WLS

Theoretical

Fig. 2 Least-squares estimation residuals normalized global teststatistic probability density function: test statistic of non-weightedGNSS snapshot solution (ts-LS), test statistic of CNo weighted snap-shot solution (ts-WLS) and the corresponding theoretical centralChi-Square distribution

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This test can be seen as a global one as it checks the consis-tency of a full measurement set. The threshold determineswhether the null-hypothesis H0 of the global test shouldbe accepted or rejected (H1). If it is rejected, an inconsis-tency in the tested measurements is assumed and the faultsource should be identified and further excluded using, e.g,the local tests [11, 17]. These tests assess the standardizedresiduals defined as follows:

ri =∣∣∣∣∣

ei√Ui,i

∣∣∣∣∣ , i = [1, . . . , m], (5)

where U is the covariance matrix for the residualsU = R − H(HT R−1H)−1HT .

In order to detect a fault, each standardized residual riis tested using the quantile of a normal distribution corre-sponding to the Pf a . In the local test, the residual under testis excluded if the respective standardized residual exceedsthe test threshold. Similarly to the global test, the localtest assumes the residuals to follow N (0, 1). The localhypothesis test is given by the following condition:

Local-Test ={

H0,i if ri ≤ a(1−Pf a/2),

H1,i if ri > a(1−Pf a/2),(6)

where ap is the quantile of the probability p of the standardnormal distribution. Each measurement ri is tested againsttheH0,i , as the measurement fault affects multiple standard-ized residuals. The measurement i is selected as a candidateto be excluded if and only if both of the following conditionsare fulfilled:{

ri ≥ rk, ∀k,

ri > a(1−Pf a/2).(7)

The method as described above is based on an exten-sion of the standard FDE methodology as suggested in[11], where some minor modifications are introduced interms of forward-backward propagation in the process ofmeasurement subset selection. Although further modifica-tions of this standard scheme are still possible, we do notbelieve that significant improvement can be achieved fornon-augmented GNSS snapshot positioning and assume thisbasic implementation to be sufficient for the purpose ofthe presented comparative study. Moreover, more advancedschemes, which could mitigate the problem of the algorithmto converge to a local minimum could require correspondingmodification of the RBE-based techniques for the fairnessof the comparison and, therefore, are beyond the scope ofthe presented work.

The corresponding RBE FDE algorithms are imple-mented either in the form of non-inertial position/velocity(constant velocity - CV model) filter (Scenario 1: non-inertial applications) or IMU/GNSS EKF-based fusion filter(Scenario 2: inertial filter). In the former case, the estimatedstate consists of 3D position and 3D velocity as well as the

GNSS receiver clock offset and clock offset rate. The lat-ter filter is far more advanced, where the estimated stateincludes the 3D attitude, 3D position and 3D velocity as wellas the accelerometer and gyroscope offsets for each sensoraxis. For the TC EKF architectures one also includes thereceiver clock offset and offset rate to the filter state to beestimated. As the measurements we employ C/A L1 codeand Doppler shift, where for loosely-coupled approaches,the solutions from external to KF snapshot solvers (posi-tion or velocity) are used as a direct observation of the state.The presented IMU/GNSS filter is a classical implementa-tion of IMU/GNSS fusion mechanism with direct strapdowninertial mechanization model and the relevant mathematicaldetails can be found elsewhere (e.g. see [8]).

The FDE approach for RBE algorithm (in our caserepresented by EKF, although the strategy can be easilyextended for other filters such as Unscented KF [20]) can bederived from the one used in snapshot GNSS positioning asdescribed above. The predicted residual vector (often calledinnovation vector) is given as follows:

dk = zk − h(x−k ), (8)

where h(xk) is a non-linear function relating the estimatedstate to the observations. The innovation vector can beconsidered as an indicator of the amount of informationintroduced in the system by the actual measurements andthe respective normalized norm can be used again as themeasurement quality indicator. For a fault-free situation,this norm follows a central Chi-Squared distribution but inthis case not with m − n, but with m degrees of freedom

and the global test statistic given as tsKF =√

dTk S−1

k dk .Here Sk is the innovation vector covariance matrix definedas Sk = HkP

−k HT

k + Rk , where P −k is the predicted error

covariance of the state estimate. The global test and thelocal tests are performed following essentially the same pro-cedure as for the LS methods described before. Again, itis assumed that under fault-free conditions the innovationshave to follow a zero mean Gaussian distribution.

The RBE-based FDE scheme implemented in this workalso consists of a two-step procedure as shown in Fig. 3.Firstly, the global test, as described before, checks the con-sistency among the full set of measurements. If an inconsis-tency is detected, the scheme performs a local test. The localtest is recursively applied whenever a fault is detected untilno more faults are found [11]. According to [3], the inno-vation property of the KF makes it also possible to detecteven very slowly changing errors (e.g. drift) by estimatingthe mean of the residuals over a longer time interval, wherein order to avoid contamination of the KF estimated state,the measurements and residuals are stored in buffers forperiods up to 30 minutes. However, the performance of themethods under slowly changing errors is beyond the scope

Eur. Transp. Res. Rev. (2017) 9: 1 Page 7 of 15 1

Fig. 3 Two-step FDE test procedure scheme: LS residuals (left) and KF innovations (right)

of the presented work. Note that both described procedures(snapshot RAIM-like and KF-based) are only some of thepossible approaches and more advanced schemes can beimplemented. Still, these algorithms are simple enough and,therefore, provide a fair ground for the method comparison.

Many practical applications address the problem of vary-ing GNSS link quality by assuming non-constant measure-ment noise variance as a function of the elevation angle ormeasured signal quality indicators like, for instance, CNo.In order to evaluate the impact of similar methods on theFDE functionality, a realistic GPS L1 pseudorange noisemodel was extracted (further referred as weighted scheme),where the pseudorange measurement covariance depends onthe actual measurement of CNo reported by the receiver. Asthe basis for the adaptive pseudorange measurement noisecovariance model σ 2 we have adopted the following generalexpression [11]:

σ 2 = a + b · 10− CNo−c10 , (9)

with three model parameters a, b and c, where the parame-ter a can be roughly mapped to the receiver correlator noisebaseline. In the expression above the CNo is the measuredcarrier to noise density ratio for a particular pseudorangeobservation. The experimental data for model extractionhave been obtained from a reference receiver of known posi-tion (previously surveyed) over 24 hours using broadcastionospheric and tropospheric corrections (the same correc-tions were adopted in the presented filters) with the errorstatistic computed by analyzing the differences between theexpected and the observed ranges. The obtained data havebeen binned according to the associated CNo values andfor each bin a variance was estimated. Note that in thissimplified approach only variance was modeled as a func-tion of the signal quality and the non-zero mean offset wasignored. Figure 4 shows the experimental results and the

extracted model using a nonlinear least squares fit. Thepoints with lowerCNo values have been manually excludedas having insufficient statistic and fit was found only tothe CNo values larger than 40 dBHz, where the valuesbetween 45-55 dBHz are considered typical for the GPS L1C/A signal. Moreover, the performance of the Delay LockedLoop (DLL) correlator in the GNSS receiver to track thesatellite pseudoranges is often poor for low CNo valuesand the obtained values are simply not representative andshould not be used for a model fit. The extracted model wasused in weighted methods for both adaptive snapshot andRBE-based schemes within the first evaluation scenario.

Of course, one has to ensure that the Gaussian noiseassumption is still valid as the performance of both LS andKF methods can be compromised or become far from opti-mal for other noise models. To verify the assumption from[11] that for the given CNo value the satellite noise can bewell approximated by zero-mean Gaussian and covariancefrom Eq. 9, we have explicitly checked the Gaussianity ofthe residual distributions. For CNo > 40 dB-Hz the dis-tributions were passing classical Gaussianity test, while forsmaller CNo values heavier tails in distributions have beenobserved and some of the tests failed.

Note that the experimental data show also a small noiseforCNo larger than 55 dBHz. The observed values are closeor even smaller than the correlator base noise level and areprobably caused by the insufficient sample size for higherCNo values. Still this effect has been effectively elimi-nated from the fit model as the parameter a is almost 60cm2, which is close to the rough theoretical calculations forthe associated hardware. This also allows us to not excludethese points manually as both LS and KF algorithms haveshown relatively low sensitivity to small variations in vari-ance models. As the equivalent constant noise model, theadditive zero-mean Gaussian noise with σ = 2.3 meters

1 Page 8 of 15 Eur. Transp. Res. Rev. (2017) 9: 1

Fig. 4 Experimental data forpseudorange error model andthe model fit results usingidentical static receiver. Onlyvalid data points were employedfor the noise model extraction

was considered. This value was obtained from the same24 hours data set by taking the mean of all residuals irre-spectively whether CNo values were large or not. Althoughthis value can be considered as over-pessimistic for mod-ern higher performance GNSS receivers, we believe that itis representative if one addressed challenging GNSS sce-narios with significant NLOS, multipath etc. For simplicitywe have not employed an adaptive noise model for Dopplershift measurements and used instead a constant noise modelconsisting of equivalent 5 cm/s range rate where applicable.

4 System setup

With the purpose to overcome the previously identifiedissues and to commit with the IMO recommendations forfuture developments, we have developed a PNT-Unit con-cept and an operational prototype in order to confirm thethe performance under real operational conditions. Herethe core goals are the provision of redundancy by supportof all on-board PNT relevant sensor data including Differ-ential GNSS (DGNSS) and future backup systems (e.g.,eLoran, R-Mode), the design and implementation of parallel

processing chains (single-sensor and multi-sensor architec-tures) for robust PNT data provision and the developmentof the IM algorithms in order to evaluate the events or con-ditions that have the potential to cause or contribute to HMIand could, therefore, compromise safety.

The experimental sensor setup for the PNT-Unit develop-ment is shown in Fig. 5. For the first scenario (pure GNSS-based positioning) the original sensor measurements wererecorded using the multipurpose research and diving vesselBaltic Diver II (length 29 m, beam 6.7 m, draught 2.8 m,GT 146 t) as a base platform. The vessel was equipped withthree dual frequency GNSS antennas and receivers (JavadDelta), tactical grade FOG (type IMAR FCAI) and MEMSIMUs, gyrocompass, DVL and echo sounder (see Fig. 6).The IALA (International Association of Marine Aids toNavigation and Lighthouse Authorities) beacon antenna andreceiver were employed for the reception of DGNSS code-based corrections. The VHF modem was configured for thereception of RTK (Real-Time Kinematics) phase correctiondata from the Maritime Ground Based Augmentation Sys-tem (MGBAS) station located in the port of Rostock [13,15]. All relevant sensor measurements are provided eitherdirectly via Ethernet or via serial to Ethernet adapter to a

Fig. 5 The PNT-Unit prototypein laboratory conditions

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Fig. 6 Baltic Taucher II test vessel. Yellow circle represents the IMUplacement and red circles stand for GNSS antenna positions

Box PC, where the measurements are processed in real-timeand stored in a SQlite3 database along with the correspond-ing time stamps. The described setup enables record andreplay functionality for further processing of the originalsensor data. The system consists of a highly modular hard-ware platform and a Real-Time software Framework (RTF)implemented in ANSI-C++.

For the first scenario (GNSS-based positioning only) thedata have been recorded on the 1st. of September 2014 ina quasi-static scenario, where the vessel was moored at itshome port “Alter Fischereihafen” on the river Warnow closeto the Rostock port. At this time there was only a weak windand little waves, so that only minor vessel motion could beobserved. The evaluation is based on data (GPS L1 pseudo-range and Doppler shift measurements) from the mid shipantenna, which is located besides the main mast of the shipand, therefore, some shadowing effects due to mast can beexpected. The chosen environment represents a typical mar-itime port application. The recorded measurement data forthe first scenario constitute the input data for the corre-sponding Monte Carlo GNSS fault simulator (or, in otherwords, the software based fault emulator). The general con-figuration of the simulator allows the user to select eitherstatic or dynamic fault profiles including both step-wise(instantaneous) and ramp errors. Step-wise faults simulatemeasurement additive faults (e.g. signal multipath) whilethe ramp faults correspond to slowly-varying cumulativeerrors (e.g. satellite clock drift), although the ramp errors arenot addressed within the present work due to requirementof equivalent modifications of RBE-based FDE approaches.The simulated fault profile consisting of amplitude rangeand fault duration time is configurable for single satellitesseparately. As the fault impact on the estimated state isstrongly influenced by the satellite constellation geometry,the fault onset time is randomly selected within the periodthe satellite is visible.

The simulation approach consists of adding a step of re-quired amplitude to a particular pseudorange measurementa pre-defined number of times. For each amplitude simu-lation run the respective pseudorange satellite ID and faultstart time are selected randomly while the respective faultduration is kept constant. Once the fault start/end point andsatellite ID are defined, the fault of a given amplitude isinjected. A particular constraint was imposed in the caseof RBE algorithms to ensure that the fault was injectedafter the filter had converged. The simulated amplitude stepranged between negative and positive values in order toensure a fair comparison for both snapshot and RBE algo-rithms. During the Scenario 1 the number of LOS satellitesis always higher than seven and the satellite constellationgeometry is assumed to be approximately constant duringthe simulation time with Dilution of Precision (DOP) lowerthan 3. Although the evaluation time for Scenario 1 can beconsidered relatively short, it was required to avoid possiblevariations in DOP. As the recorded GNSS data have beenproved (both manually and with corresponding global tests)to be free of significant native GNSS faults, we were ableto add in a controlled manner faults to raw code measure-ments and to count exactly the number of detected errors.The duration of the Scenario 1 with injected GNSS faultsis 10 minutes with an output GNSS data rate of 1 Hz. Thesimulator was configured for 10 simulations per amplitudestep of 1 meter with amplitude ranging from -30 to +30meters.

The sensor data for the Scenario 2 (dynamic sce-nario used to test the IMU/GNSS integrated system) wererecorded using the ferry vessel Mecklenburg-Vorpommernfrom Stena Lines, which is plying continuously between theports of Rostock and Trelleborg. The vessel was equippedwith essentially the same setup as the one described abovewith the GNSS antennas placed on the compass deck. Dueto the computational complexity of the EKF filter no MonteCarlo simulation has been implemented for the hybrid sce-nario and the performance of the filters with and withoutFDE functionality is demonstrated using a single set of data.The advantage of the approach is that the presented datacontain true significant GNSS faults and the performance ofthe EKF with FDE functionality is demonstrated using real(non-simulated) data recorded in open sea with the GNSSfaults probably caused by multipath or similar effects.

5 Results

5.1 Scenario 1

Let us start the discussion on FDE performance by consid-ering the accuracy of the implemented techniques for thecase of single simulated GNSS faults in a pure GNSS-based

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approach. The provided figures are generated by convert-ing the solver solution (X, Y,Z) coordinates from ECEF(Earth-Centered-Earth-Fixed) frame to ENU (East-North-Up) coordinate frame and centering them with respect tothe RTK estimated mean position, which corresponds tothe coordinates (0,0,0). In all non-weighted approaches themeasurement noise standard deviation σ = 2 meters wasused, which is reasonably close to the average GPS L1 noisevalue of 2.3 meters extracted from reference data employedfor adaptive model calculation as described previously inSection 3. The corresponding weighted schemes use theCNo weighting model as described in Section 3, wherethe noise assumed for each GPS L1 pseudorange is calcu-lated with respect to the CNo value obtained for that rangefrom the receiver. The same holds for RBE-based methodsin Scenario 1 and Scenario 2, where the measurement noisecovariance matrix R of the EKF is either populated withconstant values (i.e. corresponding to σ = 2 meters) oris also calculated dynamically depending on reported CNo

using Eq. 9.The top-left plot in Fig. 7 demonstrates the perfor-

mance of the snapshot LS (non-RBE) algorithm with themeasurement noise model assuming fixed measurement

noise covariance for all available range measurements (non-weighted scheme). The main position cloud correspondsto the non-contaminated GNSS solutions, while a smallercloud corresponds to the contaminated solutions, where thepseudorange measurement of one of the available satel-lites was combined with a step fault of 15 meters (usually,between 7 and 9 satellites are available for the presentedscenarios). One can clearly see that the suggested LS FDEmechanism is able to completely eliminate the GNSS faultas the LS algorithm with the FDE functionality never resultsin the position within the second cloud and, furthermore, thesolution spread is slightly improved as some faulty solutionsclose to the lower-right boundary of the main cloud are alsoeliminated. The performance of the corresponding LS solu-tion for the case of weighted GNSS measurement model isshown in the top-right plot in Fig. 7. Similarly as in the caseof the unweighted approach one can clearly see two distinctclouds of position solutions, where the smaller one corre-sponds to the time instances, when the satellite fault of 15meters was added. First of all, one clearly sees the benefit ofthe adaptive noise model itself as it significantly reduces thespread of the position solutions by downweighting the satel-lites with low values of CNo (often corresponding to the

Fig. 7 Precision of theapproaches with and withoutFDE scheme for non-inertial(pure GNSS) positioning staticScenario 1: LS with constantnoise model (top-left), LS withweighted noise model(top-right), EKF with constantnoise model (bottom-left) andEKF with weighted noise model(bottom-right)

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satellites with lower elevation). Moreover, the FDE mech-anism for the weighted approach works fine as well bycompletely eliminating the second cloud. In this case it isimportant to remember that due to adaptive noise model thetest statistic is, in general, different for non-weighted andweighted LS methods as we will see later.

The results of the corresponding pure GNSS-based EKFare shown in the bottom-left and bottom-right plots in Fig. 7.Both plots demonstrate the impact of the process model asthe position solution is far less random compared to thememory-less LS solution. Obviously, when the GNSS faultis applied, it takes a while for the position error to developtowards the offset position due to inertia imposed by theprocess model. Similarly, as in the case of LS methods,the spread of the position solutions is improved in weightedEKF (WEKF) when compared to non-weighted (EKF)approach, although a slight shift in the mean position solutionseems to be preserved. The latter effect can be explainedby a slight mismatch of the constant and adaptive noisemodels in terms of an overall impact with respect to theassumed noise dynamics as well as to the particular satel-lite geometry. Here again, the proposed FDE mechanism isable to detect and eliminate the corresponding measurementfaults. In all cases the adaptive noise approach seems to sig-nificantly improve the spread of the solutions around themean (although the effect of a slight shift of the mean posi-tion needs some further investigations) and the proposedFDE schemes were able to eliminate the imposed GNSSfault of 15 meters both in RBE and non-RBE approachessupported with constant and adaptive noise models.

Note that in all cases the solution clouds are not cen-tered around the origin. Here one should recall that thetest data have been obtained using both broadcast tropo-sphere and ionosphere models and only code data have beenused within the LS solver. Obviously, the real range errorsare not Gaussian and non-random errors can be introducedto some of the links depending on the satellite elevation,actual ionosphere state, etc. All these effects can result insignificant position offset with respect to the reference posi-tion. Obviously, an improved barycentric mean could beexpected for solutions supported with ground augmentationservices.

Although the performance as shown in Fig. 7 confirmssimilar functionality of all the approaches, the imposedGNSS fault can be considered relatively large. Although theRBE approaches seem to be far more conservative in takinginto account the applied GNSS faults, the general behaviorof the approaches can be hardly deduced from a single case.In order to address this issue the FDE exclusion rate statis-tic (number of detected GNSS faults relative to the totalnumber of injected GNSS faults for a given fault ampli-tude) is shown in Fig. 8 both for weighted and non-weighted

LS and KF methods using the Monte Carlo simulation withinduced GNSS faults as discussed before. Although for rea-sonably large fault amplitudes all the methods converge toa detection rate of 100 %, the performance for moderatefault amplitudes is different. The KF-based FDE schemesare superior to the equivalent snapshot LS methods due totheir inherent reliance on the available process model. Still,the provided results represent an averaged behavior of themethods and the impact of each satellite is not clearly visi-ble as the performance statistic could be different from theshown averaged behavior depending on the actual geometryand associated CNo values. Due to the short duration of thetest scenario we were not able to sample different satellitegeometries and the impact of the geometry is left for futureinvestigation.

The results confirm that FDE KF-based techniques cons-tantly outperform the snapshot techniques when an equiva-lent measurement noise model is used. This, however, shouldcome at no surprise as the KF has an explicit dynamicsmodel (e.g. static position model for non-inertial approach)which fits nicely to the scenario and the results could beworse when the KF process model does not match thetrue object dynamics. This is, fortunately, not a problemfor the second system (see Scenario 2 below) where theinertial sensors are employed within the prediction stepusing the methods of strapdown inertial mechanization. Inthis case the process dynamics is based not on the assump-tions on expected motion models (as in Scenario 1), but ona true dynamics provided by a direct integration using theinertial sensors and, therefore, is able to capture all thedetails of the corresponding motion. The inertial unit pro-vides a true short-term stable dynamics and the FDE mech-anism benefits from this information as we can see at theend of this section.

Note that Fig. 8 shows the fault exclusion rate to becomerather noisy for both the LS and EKF using the weightedobservation model as the rates converge to 100 % onlyfor the fault amplitudes close to 30 meters, whereas themethods using non-adaptive models demonstrate 100 %already at the fault amplitudes of 10 meters. We believethat this is a direct result of the nature of the adaptivenoise model which assigns increased measurement noisevariance for satellite signals with low CNo values andcould lead to situations where even the faults of significantamplitudes can be still considered ’within’ the measure-ment statistic and, therefore not excluded from the finalsolution. Note that this does not imply that the positionsolution is unacceptable as the selected satellite is stronglydown-weighted within this solution due to its low CNo

value, but the performance figures in terms of the detectionrates become significantly lower when compared to non-weighted schemes. Here comes an important conclusionthat a direct adoption of the weighted measurement model,

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although resulting in precision improvement, could alsolead to the failure of the FDE (although, probably, not fail-ure in IM itself) or similar mechanisms even for relativelylarge GNSS faults. Thus, both adaptive noise model andFDE scheme seem to be mutually exclusive strategies: whilethe FDE scheme tries to check the measurement consistencyusing a given measurement statistic and eliminates the mea-surements which violate correct measurement assumption,the weighted approach tries to adjust the statistic to fit themeasurements and simply down-weights the measurementsof possibly poor quality. Still, this complementary behaviorof the two strategies (higher detection rate of non-weightedmethod and lower spread of weighted solution) could forma basis for a hybrid positioning system, where the FDEmechanism on a non-weighted method is used to detectthe GNSS faults, and the weighted measurements of theremaining satellites are used to calculate the solution. Al-though such algorithm configuration could potentially com-bine the benefits of both schemes, further research is neces-sary, especially, with respect to the lower availability of thecorresponding position solution.

Obviously, a constant amplitude step can hardly be con-sidered as the most representative sensor failure approach.For example, the performance of the KF-based techniquescan become much worse for the ramp-like scenarios, wheresmall amplitude and prolonged duration offsets in one ofthe measurements, when initially undetected, could forcethe filter to drift significantly from the true estimate. Onthe other hand, the step-like faults form a fairly represen-tative error model when one considers multipath effects inmaritime environments [18].

In Fig. 9 (left) we can see the average impact of theamplitudes of injected faults (artificial faults introduced inMonte Carlo GNSS fault simulator to the random satellite)on the estimated state (horizontal position) in both LS solverand non-inertial EKF for Scenario 1. For comparison, the im-pact on the system augmented with FDE functionalityis also shown for both strategies. As expected, the RBEmethods achieve an improved error performance comparedto memory-less LS approaches due to the availability ofexplicit dynamic models. Consistently, the performance ofthe KF with FDE is also better than the performance of thesnapshot algorithms with FDE as the KF approach results inalmost two times smaller maximum position error (note thatthe exact gain is a trade-off of both process and measure-ment noises and, therefore, could be different for alternativefilter configurations). Moreover, the fault amplitudes whichcorresponds to the inflection point is also smaller for the KFmethod compared to the LS techniques and this is consistentwith the earlier rise of the exclusion rate curve as shown inFig. 8 (left). Those values can be also interpreted as HMI forthe system user as they represent the maximum impact in theestimated position caused by the undetected measurementsfaults.

5.2 Scenario 2

All results above have been demonstrated for pure GNSS-based approaches for a static scenario, where the FDEfunctionality has been embedded into either the snapshot LSor the corresponding EKF with explicit assumptions regard-ing the process dynamics (e.g. constant velocity model).

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Although the obtained results demonstrated a consistent per-formance improvement of FDE schemes over the methodswithout FDE functionality, the question remains on howthe FDE methods would perform in more advanced hybrid(sensor fusion) solutions (Scenario 2) and dynamic scenar-ios (the vessel is moving). In order to address this problemwe evaluate the FDE performance of the TC IMU/GNSSarchitecture (see [8] for mathematical details) and assess,how the presence of relatively high performance IMUaffects the final accuracy of the integrated navigation solu-tion during the coastal operation of the vessel Mecklenburg-Vorpommern. Note that the availability of the FOG IMUchanges only the process model of the corresponding EKFas well as the numerical values of the association estima-tion uncertainty (covariance), while the measurement modelfor the tightly-coupled architecture remains identical to thatof non-inertial EKF and all the discussion on FDE func-tionality from Section 3 is also valid for the presentedalgorithm.

Figure 9 (right) shows the horizontal position error (HPE)in the case of a real (non-simulated) fault in measure-ment data during a coastal approach. In order to distinguishbetween the effect of inertial smoothing and FDE, addition-ally the HPE of a loosely-coupled (LC) EKF (EKF fed withthe position solution from LS solver without FDE mech-anism) and a LS solution without FDE (referred as SPPin Fig. 9 (right)) are shown. Within the loosely-coupledarchitecture the SPP position and velocity solutions serveas direct observations instead of using separate measure-ment fusion as in the TC architecture, and, therefore, aFDE scheme based on single satellite signals is not appli-cable. One sees that the smoothing behavior of both TCand LC EKF is comparable, but during the measurementfault, the LC solution starts to slowly follow the wrong

position observation from the non-FDE SPP, whereas theFDE in the TC EKF ensures that the faulty measurementsare removed from the estimated navigation solution. A man-ual inspection of the faults during that 24h time span (notshown) leads to the conclusion, that all significant faultymeasurements are detected and removed by the TC EKFaugmented with the FOG IMU. One also expects the qual-ity of the inertial sensors not to play a significant rolefor the FDE algorithm performance, at least for the stepGNSS errors, although the performance could be differentfor the cases of ramp errors. We believe that the inertialsensor quality (in terms of additive noise and bias stability)is only important for bridging GNSS outages (standalonestrapdown inertial mechanization) - i.e. for contingencyfunctionality and reasonable FDE performance for stepGNSS faults can be essentially achieved even with mod-ern MEMS sensors of consumer grade, establishing thepath for the FDE methods to be adopted even in lower-costapplications. Clearly, an in-depth statistical analysis is stillnecessary in order to confirm that also smaller GNSS faultamplitudes can be also detected using, for example, lowercost MEMS IMUs.

6 Summary and outlook

Within this preliminary work we have successfully demon-strated an application of the proposed FDE mechanisms insnapshot and RBE-based positioning algorithms for mar-itime applications using both non-inertial GNSS-based posi-tioning (Scenario 1) and hybrid inertial/GNSS EKF-basedapproach (Scenario 2). The proposed methods form a solidfoundation for the construction of a more reliable androbust PNT-Unit, where state-of-the-art hybrid navigation

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algorithms are augmented with integrity monitoring func-tionality to ensure the system performance in the presenceof GNSS faults. The presented work is implemented withinthe framework of an integrated PNT-Unit with an additionalintegrity monitoring functionality, where the FDE mech-anism provides consistent improvements in terms of thehorizontal accuracy both in LS and RBE methods. An inter-esting behavior of the proposed FDE mechanism has beennoticed for the methods with CNo-dependent measurementnoise models as the fault detection rate had shown worseperformance compared to that of the non-adaptive meth-ods. The proposed methods were evaluated using either realmeasurements combined with Monte-Carlo simulation ofGNSS faults (Scenario 1) or employing true GNSS fault inhybrid approach (Scenario 2). Although only a port opera-tion scenario and one example of a true GNSS fault in opensea was considered, we believe the presented results to begeneral enough and the scheme could be adopted for otherapplications.

Further work is planned in extending the presented con-cepts for the GNSS Doppler shift measurements both insnapshot and RBE algorithms and more detailed analy-sis is required to assess the fault impact not only onthe position, but also on velocity and the attitude (inIMU/GNSS integrated approaches) solutions. Correspond-ingly, the proposed techniques have to be systematicallyverified for hybrid inertial and GNSS navigation systemsusing presented Monte Carlo or similar approaches includ-ing DVL sensors. Moreover, while implementing the pro-posed schemes, special attention has to be paid to thechallenging problem of the memory effects in RBE schemesas the typical KF-based implementations are, in principle,infinite memory filters. Clearly, the associated upper errorbounds in estimated position, velocity and attitude haveto be taken into account for the analysis to be consideredas complete. Finally, robust schemes should be developed,in order to enable the system real-time channel selectionfunctionality, where the PNT-Unit would switch betweendifferent channels (algorithms with different sensor com-binations or sensor/filter configurations) according to theavailable FDE results and corresponding channel integrityinformation.

Acknowledgments The authors would like to thank Baltic TaucherGmbH and Stena Lines and especially the crews of the vesselsBALTIC DIVER II and MECKLENBURG VORPOMMERN for theirsupport during the measurement activities. The authors are also grate-ful for the assistance of their colleagues Stefan Gewies, CarstenBecker, Anja Hesselbarth and Uwe Netzband. The authors would liketo thank the reviewers for their valuable comments and suggestions.

Open Access This article is distributed under the terms of theCreative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricteduse, distribution, and reproduction in any medium, provided you give

appropriate credit to the original author(s) and the source, provide alink to the Creative Commons license, and indicate if changes weremade.

References

1. (2014) Development of an e-navigation strategy implementationplan

2. Borre K, Strang G (2010) Algorithms for global positioningWellesley-Cambridge press

3. Diesel J, Luu S (1995) GPS/IRS AIME: Calculation of thresholdsand protection radius using chi-square methods. In: Proceedingsof the 8th international technical meeting of the satellite divisionof the institute of navigation (ION GPS 1995). CA, Palm Springs,pp 1959–1964

4. Foxlin E (2005) Pedestrian tracking with shoe-mountedinertial sensors. IEEE Comput. Graph. Appl. 25(6):38–46

5. Grewal MS, Andrews AP (2001) Kalman Filtering. Theory andPractice using MATLAB, 2nd edition. John Wiley & Sons, NewYork

6. Groves P, Jiang Z (2013) Height aiding, C/N0 weighting and con-sistency checking for GNSS NLOS and multipath mitigation inurban areas. J Navig 66(5):653–669

7. Groves P, Jiang Z, Rudi M, Strode P (2013) A portfolio approachto NLOS and multipath mitigation in dense urban areas. In:Proceedings of the 26th international technical meeting of thesatellite division of the institute of navigation (ION GNSS+ 2013).Nashville Convention Center, Nashville, Tennessee, pp 3231–3247

8. Groves PD (2007) Principles of GNSS, Inertial and MultisensorIIntegrated Navigation Systems (GNSS Technology and Applica-tions) Artech House Publishers

9. HELCOM (2014) Annual report on shipping accidents in thebaltic sea area during 2012

10. Joerger M, Pervan B (2010) Sequential residual-based RAIM. In:Proceedings of the 23rd international technical meeting of thesatellite division of the institute of navigation (ION GNSS 2010),pp. 3167–3180. OR

11. Kuusniemi H (2005) User-level reliability and quality monitor-ing in satellite-based personal navigation. Ph.D. thesis, TampereUniversity of Technology, Tampere

12. Lee YC, O’Laughlin DG (2000) A performance analysis of atightly coupled GPS/inertial system for two integrity monitoringmethod. Navig 47(3):175–189

13. Minkwitz D, Schluter S., Beckheinrich J (2010) Integrity assess-ment of a maritime carrier phase based GNSS augmentationsystem. In: ION GNSS. Institute of Navigation, Portland, USA,p 2010

14. Moore T, Hill C, Norris A, Hide C, Park D, Ward N (2008) Thepotential impact of GNSS/INS integration on maritime navigation.J Navig 61:221–237

15. Noack T, Engler E, Klisch A, Minkwitz D (2009) Integrity con-cepts for future maritime ground based augmentation systems.In: Proceedings of the 2nd GNSS vulnerabilities and solutionsconference. baska, Croatia

16. Parkinson BW, Axelrad P (1988) Autonomous GPS integrity mon-itoring using the pseudorange residual. Navigation: J Inst Navig35(2):255–274

17. Petovello MG (2002) Real-time integration of a tactical-grade imu and gps for high-accuracy positioning andnavigation. Ph.D. thesis, University of Calgary, Calgary,Alberta

Eur. Transp. Res. Rev. (2017) 9: 1 Page 15 of 15 1

18. Ryan SJ (2002) Augmentation of DGPS for marine navigation.Ph.D. thesis, Department of Geomatics Engineering, University ofCalgary, Calgary, Alberta, Canada

19. Teunissen P (1998) GPS for Geodesy, chap. Quality control andGPS Springer

20. Thrun S, Burgard W, Fox D (2005) Probabilistic robotics(intelligent robotics and autonomous agents) the MITpress

21. Walter T, Walter T, Enge P (1995) Weighted RAIM for precisionapproach

22. Wang J, Stewart M, Tsakiri M (1998) Stochastic modeling forstatic GPS baseline data processing. J Surv Eng 124(4):171–181

23. Wang JG (2008) Test statistics in Kalman filtering. J of GlobalPositioning Syst 7(1):81–90

24. Wieser A, Brunner F (2000) An extended weight model for GPSphase observations. Earth Planet Space 52:777–782