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Advances in Space Research 59 (2017) 2750–2763

Variometric approach for real-time GNSS navigation:First demonstration of Kin-VADASE capabilities

Mara Branzanti a,⇑, Gabriele Colosimo b, Augusto Mazzoni a

aGeodesy and Geomatics Division, Dept. of Civil, Building and Environmental Engineering, University of Rome ‘‘La Sapienza”, Rome, ItalybLeica Geosystems AG, Heerbrugg, Switzerland

Received 29 October 2015; received in revised form 7 September 2016; accepted 23 September 2016Available online 3 October 2016

Abstract

The use of Global Navigation Satellite Systems (GNSS) kinematic positioning for navigational applications dramatically increasedover the last decade. Real-time high performance navigation (positioning accuracy from one to few centimeters) can be achieved withestablished techniques such as Real Time Kinematic (RTK), and Precise Point Positioning (PPP). Despite their potential, the applicationof these techniques is limited mainly by their high cost. This work proposes the Kinematic implementation of the Variometric Approachfor Displacement Analysis Standalone Engine (Kin-VADASE) and gives a demonstration of its performances in the field of GNSS nav-igation. VADASE is a methodology for the real-time detection of a standalone GNSS receiver displacements. It was originally designedfor seismology and monitoring applications, where the receiver is supposed to move for few minutes, in the range of few meters, around apredefined position. Kin-VADASE overcomes the aforementioned limitations and aims to be a complete methodology with fully kine-matic capabilities. Here, for the first time, we present its application to two test cases in order to estimate high rate (i.e., 10 Hz) kinematicparameters of moving vehicles. In this demonstration, data are collected and processed in the office, but the same results can be obtainedin real-time through the implementation of Kin-VADASE in the firmware of a GNSS receiver. All the Kin-VADASE processing werecarried out using double and single frequency observations in order to investigate the potentialities of the software with geodetic classand low-cost single frequency receivers. Root Mean Square Errors in 3D with respect to differential positioning are at the level of 50 cmfor dual frequency and better than 1 meter for single frequency data. This reveals how Kin-VADASE features the main advantage of thestandalone approach and the single frequency capability and, although with slightly lower accuracy with respect to the established tech-niques, can be a valid alternative to estimate kinematic parameters of vehicle in motions.� 2016 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: GNSS; Real-time navigation; High rate; Variometic approach; Kin-VADASE

1. Introduction

The use of Global Navigation Satellite Systems (GNSS)in kinematic positioning dramatically increased over thelast decade for many navigational applications. Therequired accuracy depends on the specific application and

http://dx.doi.org/10.1016/j.asr.2016.09.026

0273-1177/� 2016 COSPAR. Published by Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: mara.branzanti@uniroma1.it (M. Branzanti),

gabriele.colosimo@leica-geosystems.com (G. Colosimo), augusto.mazzoni@uniroma1.it (A. Mazzoni).

ranges from few meters to few centimeters. Lower accuracycan be easily achieved with mass market receivers (e.g., bymeans of single point positioning with code observations),whereas better results can be achieved only through phaseobservations.

The most widely used technique in kinematic applica-tions is the RTK (Real Time Kinematic) positioning, basedon double frequency phase observations differentialapproach (double differences) between rover and referencereceiver(s) (Kaplan and Hegarty, 2006). On one hand RTKis a high-performance technique (positioning accuracy at

M. Branzanti et al. / Advances in Space Research 59 (2017) 2750–2763 2751

few centimeters level); on the other hand it requires thesupport of a GNSS Network infrastructure (Kim et al.,2013) and a continuous data link between the rover andthe network caster.

Precise Point Positioning (PPP) utilizes the double fre-quency phase observations of a single GNSS receiver andthe precise satellite products (mainly clocks and orbits).In order to operate in real-time, a data link betweenthe rover and the precise product provider is needed(IGS real time Service, 2015; Ge et al., 2012; Genget al., 2010).

Over the last years the use of GNSS-PPP has been con-tinuously growing. Experiments demonstrated an accuracyat the level of millimeters to detect seismic motion (Xuet al., 2013); other studies (Jiang et al., 2014; Wang,2013; Kuo et al., 2012) discuss accuracy values rangingfrom few mm to the meter depending on the specific appli-cations and used orbits and clocks (final, rapid, ultra-rapidobserved, ultra-rapid predicted). Altough PPP has beenwidely applied to many disciplines of research, it stilldoesn’t get as much attention and coverage as RTK forcommercial and real-time purposes.

The availability of these techniques paved the way forthe use of GNSS kinematic positioning in many applica-tions such as vehicle precise navigation, land and marinegeophysical surveying, airborne mapping, forestry and nat-ural resources surveying, precision farming, open-pit min-ing and others (El-Rabbany, 2006; Dabove and Manzino,2014). Despite its potential the GNSS system is not wide-spread, mainly due to the high cost of state-of-the-art tech-nology associated with it (geodetic class receivers,infrastructures, communications, etc.).

Here we presents a new methodology in GNSS kine-matic positioning which we will refer to as Kin-VADASE(i.e., Kinematic VADASE). This approach derives fromthe original VADASE algorithm (Colosimo, 2013) toaddress positioning and navigation of kinematic objects.The main advantage of the approach with respect to theother techniques is the total autonomy of the GNSS recei-ver (Stand-Alone mode, no need for other data sources).This work is therefore motivated by two main goals: (i)to validate the model implemented in the Kin-VADASEextension of the variometric approach; (ii) to assess itsachievable accuracy with single and double frequencyobservations.

An overview of the variometric approach is given in Sec-tion 2. The functional model is first described and then themain applications and limits of the native VADASE areintroduced. Section 3 introduces Kin-VADASE, the Kine-matic implementation of the variometric approach. Herethe main differences in the implementation of the twoalgorithms are presented. Section 4 is devoted to verifyKin-VADASE model and implementation using simulateddata. Then, in Section 5, real data are considered to addressthe achievable accuracy and the high rate capability.Finally, in Section 6 some conclusions and perspectivesare given.

2. The variometric approach

2.1. Functional model

The variometeric approach is based on time single differ-ences of carrier phase observations (Hofmann-Wellenhofet al., 2008) continuously collected using a standaloneGPS receiver on standard GPS broadcast products (orbitsand clocks) available in real-time.

Here we recall the functional model of the least squareestimation of the variometric approach in order to betterassess the developments discussed in the next subsections.For a complete description of the VADASE estimationmodel, please refer to the previous published papers(Colosimo et al., 2011; Colosimo, 2013).

We assume that subscript r refers to a particular receiverand superscript s refers to a satellite; Us

r is the carrier phaseobservation of the receiver with respect to the satellite; k isthe carrier phase wavelength; qs

r is the geometric range (i.e.,the distance between the satellite and the receiver); c is thespeed of light; dtr and dts are the receiver and the satelliteclock errors, respectively; T s

r is the tropospheric delay alongthe path from the satellite to the receiver; psr is the sum ofthe other effects (relativistic effects, phase center variations,and phase windup); and ms

r and �sr represent the multipathand the noise, respectively. Eq. (1) is the difference in timeðDÞ between two consecutive epochs (t and t + 1) of carrierphase observations in the ionospheric-free combination (aand b are the standard coefficients of L3 combinationreferred to the two phases L1 and L2)

a½kDUsr�L1 þ b½kDUs

r�L2 ¼ ðesr � Dnr þ cDdtrÞ þ ð½Dqsr�OR

� cDdts þ DT sr þ ½Dqs

r�EtOlþ DpsrÞ þ Dms

r þ D�sr ð1Þ

where esr is the unit vector from the satellite to the receiver,Dnr is the (mean) velocity of the receiver in the interval tand t + 1, ½Dqs

r�OR is the change of the geometric rangedue to the satellite’s orbital motion and the Earth’s rota-tion, ½Dqs

r�EtOl is the change of the geometric range due tothe variation of the solid Earth tide and ocean loading.The term ðesr � Dnr þ cDdtrÞ contains the four unknownparameters (the 3-D velocity Dnr and the receiver clockerror variation DdtrÞ and ð½Dqs

r�OR � cDdts þ DT srþ

½Dqsr�EtOl þ DpsrÞ is the known term that can be computed

on the basis of known orbits and clocks and of properwell-known models (for a complete orbits, clocks andatmosphere error analysis, please refer to Colosimo(2013)). To account for higher disturbances on signalsreceived by low elevations satellites, the observations areweighted by the squared cosine of the satellite zenith angle(Zs

r) (Dach et al., 2007, p. 144), as follows

w ¼ cos2ðZsrÞ ð2Þ

Moreover, the different observations are treated asuncorrelated in the estimation process. The least squares

Fig. 1. Main processing blocks of the VADASE implementation. Theinitial receiver position P0 is retrieved from the RINEX header. Then, forall epochs, P0 is used to compute the terms of variometric Eq. (1) and toestimate the receiver epoch-by-epoch displacement (i.e., velocity).

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estimation of the 3-D velocities is based upon the entire setof variometric Eq. (1), which can be written for two genericconsecutive epochs (t and t + 1). The number of variomet-ric equations depends on the number of satellites commonto the two epochs. At least four satellites are necessary inorder to estimate the four unknown parameters for eachconsecutive epoch couple. Differently from other data pro-cessing schemes (i.e. differential positioning (DP) and PPP),the variometric approach does not require phase ambiguityresolution (Teunissen and Keusberg, 1996) and it is alsoable to work with single-frequency data only.

Overall, one receiver works in standalone mode and theepoch-by-epoch displacements (which are equivalent tovelocities) are estimated. Then, velocities are integrated(and derivative calculated) over the time interval of interestto retrieve the comprehensive receiver displacements (andaccelerations). The integration process is affected by esti-mation biases due to possible mismodeling in Eq. (1) thataccumulate over time and display their signature as a trendin the displacements (Colosimo et al., 2011). In static sce-narios, the trend in the integrated velocities (i.e., displace-ments) is significant with respect to the displacementsabsence; on the other hand, when the receiver undergoesmovements, the biases are concealed in the displacements,which are accurately and effectively retrieved by the vario-metric approach.

2.2. The native VADASE: major applications and limits

The first implementation of the variometic approachwas proposed in 2011 (Colosimo et al., 2011) in theVADASE software, as an innovative solution to estimatein real-time rapid movements of GPS receivers in a globalreference frame (Crespi et al., 2015). To prove the effective-ness of the approach, the algorithm was implemented in adesktop application capable to process standard ReceiverIndependent EXchange format (RINEX) files containingobservations and ephemeris acquired by a GNSS receiver.Its validity was proved in the GPS seismology field throughthe application to the catastrophic Tohoku-Oki earthquake(Branzanti et al., 2013; Colosimo et al., 2011) (Mw 9.0,March 11, 2011), when VADASE was the first approachcapable of computing accurate displacements caused on 2International GNSS Service (IGS) Japanese stations (i.e.,MIZU and USUD), immediately after the availability ofdata (Group on Earth Observations (GEO), 2011).VADASE was also applied to the Emilia earthquake(Benedetti et al., 2014) (Mw ¼ 6:1, May 20, 2012) in caseof small displacements. A comparison between VADASEsolutions and credited software (GAMIT kinematic GPSprocessing module (TRACK, Herring et al., 2010), Auto-matic Precise Positioning Service (NASA Jet PropulsionLaboratory Automatic Precise Positioning Service, 2015))was performed both using dual and single frequency obser-vations. The agreement among the software resulted at thelevel of 1.1 cm and 1.5 cm for the horizontal and verticalcomponents, respectively, for the dual frequency solutions

and of 1.7 cm and 1.8 cm, for the horizontal and verticalcomponents, respectively, for the single frequency solu-tions. Moreover VADASE results and velocity and acceler-ation solutions retrieved from accelerometers co-locatedwith the GNSS receiver, were compared.

The variometric algorithm was conceived to detect, inreal-time, fast and short duration displacements occurringto a single GNSS receiver. However, the original imple-mentation in the VADASE software focused on seismologyand monitoring applications, where the initial coordinatesare known with high accuracy (i.e., better than 0.5 m,which is normally the case for reference stations receiversor monitoring markers) and the receiver is expected toundergo limited movements (up to few meters) around itsstarting position. Such choice reflected in the implementa-tion of the software, as it is described in Fig. 1.

The initial receiver position P0 was simply retrieved fromthe RINEX header and used to compute, for all available Nepochs, the known terms of the variometric Eq. (1) in orderto derive the displacements between epoch t and t þ 1. Fol-lowing the described processing design it appears evidenthow the performances of VADASE were significantlydecreasing in kinematic applications, where the errors inthe functional model (Eq. (1) computed using initial receiverposition P0) grew proportionally to the receiver movements.A more detailed analysis of the relation among accuracyerror and receiver position is given in Colosimo (2013).

Fig. 2. Main processing blocks of the Kin-VADASE implementation. Theprincipal differences with respect to Fig. 1 are highlighted in blue. Thereceiver position Pi used to compute Eq. (1) at epoch i is updated on thebasis of the estimated velocity. (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of thisarticle.)

M. Branzanti et al. / Advances in Space Research 59 (2017) 2750–2763 2753

3. Kin-VADASE: the kinematic implementation of the

variometric approach

The goal of Kin-VADASE is to retrieve accurate kine-matic parameters of moving receivers so that the variomet-ric algorithm can be exploited also in GNSS navigationapplications. In this section, the main differences betweenthe original VADASE and the proposed Kin-VADASEare presented with specific focus on the implementationchanges required.

3.1. Software architecture

The original implementation of the variometricapproach for GNSS seismology and monitoring purposeswas meant to detect velocities and displacements ofpermanent stations, which were modeled as receivers inpseudo-static conditions. As such, the initial coordinateswere supposed to be known with high accuracy and theywere constantly used in the variometric Eq. (1), as shownin Fig. 1 and explained in Section 2.2.

In Kin-VADASE initial coordinates, are continuouslyupdated by the epoch-by-epoch variometric solutions,accounting for the estimated displacement with respect tothe previous position. If the initial coordinates (i.e., startingposition of the moving vehicle) are not known, they areestimated on the basis of code observations. Because ofthe nature of our approach (use of phase observationsaimed to estimate velocities and not absolute position ofthe receiver), in this case the entire track of the movingvehicle will be biased by the starting point positioning error(e.g. few meters), but velocities and displacements will beretrieved with high accuracy.

In order to satisfy the kinematic requirements, the initialscheme used for implementing VADASE software wasrevised and updated as it is shown in Fig. 2. Initial coordi-nates P0 are taken from the RINEX observation fileheader, or, if not available, are estimated for the first epochon the basis of code observations. Then, at each epoch i anew receiver position Pi, derived on the basis of theprevious position and of the estimated velocity, is used tocompute the variometric Eq. (1). Eq. (3) shows how thereceiver position Piþ1 is updated based on the position Pi

and the computed velocity Viþ1 (expressed in terms ofdisplacement):

P iþ1 ¼ P i þ V i;iþ1 ð3ÞAdditionally, in order to satisfy requirements related to

navigation, Kin-VADASE allows direct visualization ofthe receiver’s trajectory on Google Earth platform by pro-viding a suited Keyhole Markup Language (KML) outputfile.

4. Application to simulated data and model assessment

In order to validate the Kin-VADASE implementation,at first, several tests were performed on simulated data. A

Spirent GNSS signal simulator (Spirent et al., 2007), ableto reproduce in laboratory the framework of a navigationreceiver installed on a dynamic platform, was used underdifferent configurations. Radio Frequency (RF) signalswere simulated as similar as possible to real conditions:the effects of high-dynamic host vehicle motion was exhib-ited, satellite motion was considered, ionospheric and tro-pospheric effects were reproduced through suitablemodels in order to consider the impact of the atmospherein the signal propagation from the satellite to the receiver.A Septentrio PolarRx3eG dual frequency geodetic receiverwas used to record and acquire the simulated data. Atmo-spheric delays were simulated considering Klobuchar andSaastamoinen models for ionosphere and troposphere,respectively. In addition to the signals, Spirent simulatorprovides trajectory reference coordinates for each epoch,which were used to assess Kin-VADASE accuracy. In thisrespect, the starting coordinates, needed only for the firstepoch of Kin-VADASE processing, were supplied accord-ing to Spirent motion initial position. Here, two simula-tions are reported with the receiver placed on board landand aerial vehicle. In both experiments data were collectedat 1 Hz sampling rate. In data processing, Saastamoinenmodel was used to take account of the tropospheric delay.

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For each scenario, at first ionospheric free (L3) combina-tion solutions were computed. Then, a second processingwas carried out using only L1 observations and Klobucharmodel (Klobuchar, 1987), in order to investigate Kin-VADASE capabilities for single frequency receivers.

4.1. Land vehicle

A receiver is simulated on board of a land vehicle movingon a horizontal rectangular trajectory of 2 � 1 km for sev-eral laps. Velocity is variable between 10 and 30 km/h (themotion could be compared with the one of an agriculturalvehicle), decelerations and accelerations are performed20 mbefore and after every 10 m radius curve (all the param-eters can be set through the Spirent software interface). Thetotal traveled distance was 21899.27 m over an interval of2720 s. Statistics over the epoch-by-epoch differencesbetween Kin-VADASE and Spirent reference coordinatesare shown in Table 1. Both L1 and L3 solutions present anaccuracy of few centimeters in terms of RMSE of positionsdifference (0.035 m, 0.012 m and 0.019 m for East, Northand Up components, respectively, in L1 and 0.028 m,0.012 m and 0.028 m for East, North and Up components,respectively, in L3).With respect to the reference total trajec-tory length (longer than 20 km), Kin-VADASE trajectorylength relative error (computed as the absolute value of thedifference between the length of the Kin-VADASE esti-mated trajectory and the reference one, divided by the refer-ence one itself) is at the level of fewmm/km (0.001 m/km and0.002 m/km for L1 and L3, respectively). The comparisonbetween Kin-VADASE and Spirent was also performed interms of velocity (native output of Kin-VADASE) andacceleration (derived from velocities). The agreement is atthe level of fewmm/s andmm/s2. Since Kin-VADASE coor-dinates are obtained by an integration process errors canincrease over time. To evaluate the impact of this error,the 3D RMSE over time was computed and interpolatedwith a linear regression. It was found that 3D RMSE overtime is 0.050 m/h for L1 and 0.043 m/h for L3 processing.

4.2. Aerial vehicle

The receiver is simulated to be on board of an air vehicleexecuting a full flight (take-off, cruise and landing). The

Table 1Land vehicle moving on a horizontal rectangular trajectory of 2� 1 km: com

Land vehTraj. length = 21899.27 m

L1

Position [m] E NSt. dev. 0.019 0.007Average �0.030 0.010RMSE 0.035 0.012

Rel. error in Traj. [m/km] 0.0013D RMSE [m] 0.0423D RMSE over time [m/h] 0.050

aim of this experiment is to test Kin-VADASE potentiali-ties when processing data acquired by a vehicle movingat high speed and subjected to a significant altitude varia-tion. A maximum velocity of 460 km/h is reached in theflight phase, the total traveled distance is 68115.85 m overan interval of 733 s. Even if the characteristics of this sim-ulation are completely different from the ones investigatedin Section 4.1, Kin-VADASE confirmed its effectiveness.Statistics are reported in Table 2. Both L1 and L3 solutionspresent an accuracy at the decimeter level (0.071 m,0.177 m and 0.181 m for East, North and Up components,respectively, in L1 and 0.051 m, 0.090 m and 0.116 m forEast, North and Up components, respectively, in L3). Withrespect to the reference total trajectory length, Kin-VADASE trajectory length relative error is 0.002 m/kmand 0.001 m/km for L1 and L3 respectively. 3D RMSEover time is 1.354 m/h for L1 and 0.752 m/h for L3. Veloc-ity and acceleration differences are at the level of few mm/sand mm/s2 for the horizontal components and at the levelof one cm/s and cm/s2 for the vertical component.

5. Application to real data

Here we present the first application of Kin-VADASEto real kinematic data with the twofold aim of: (i) assesthe accuracy of the new kinematic implementation and,(ii) clearly show the limitations of the original VADASEapproach. Moreover, the results presented in this sectionprove how Kin-VADASE does not significantly suffer theimpact of the bias in the velocities estimation over kine-matic data spanning a long period of time (e.g., severalhours). In fact, as discussed in Section 2.1, when the recei-ver is moving, the displacements are dominant with respectto the bias. The same considerations do not hold for staticcases: if several hours of static data are processed with thevariometric approach, the drift over time is stronglyimpacting the final solution, which completely looses itsreliability. For this reason the analysis of long period staticdata was not considered useful for the sake of the presentwork. Two test cases were studied using data collectedfrom a dual frequency Leica Geosystems geodetic receiver.In the first test, presented in details in Section 5.1, observa-tions at 2 Hz sampling rate were collected on board of asail boat; in the second test, discussed in Section 5.2,

parison of Kin-VADASE with Spirent.

icle, duration = 2720 s

L3

U E N U0.016 0.015 0.004 0.013�0.010 �0.023 0.012 �0.0240.019 0.028 0.012 0.028

0.0020.0410.043

Table 2Aerial vehicle take-off, cruise and landing: comparison of Kin-VADASE with Spirent.

Aerial vehicleTraj. length = 68115.856 m, duration = 733 s

L1 L3

Position [m] E N U E N USt. dev. 0.037 0.121 0.170 0.024 0.057 0.115Average 0.060 �0.129 0.063 0.045 �0.070 �0.015RMSE 0.071 0.177 0.181 0.051 0.090 0.116

Rel. error in Traj. [m/km] 0.002 0.0013D RMSE [m] 0.262 0.1553D RMSE over time [m/h] 1.354 0.752

M. Branzanti et al. / Advances in Space Research 59 (2017) 2750–2763 2755

10 Hz observations were acquired from a receiver on boardof a car. For the sake of the comparison, data were pro-cessed using both VADASE and Kin-VADASE. A refer-ence solution was obtained by the post-processing relativepositioning (Kaplan and Hegarty, 2006) algorithm imple-mented in the LGO (Leica Geosystems Office) software.

5.1. Navigation off-shore

Observations at 2 Hz sampling rate were collected froma receiver installed on board of a sail boat, during a navi-gation off-shore the Riva di Traiano (Civitavecchia, CVTV,Central Italy) Harbor. The total traveled distance was38006.69 meters over a time interval of 14399 s. The boatwas moving with an average speed of 15 km/h with a max-imum distance from the coast of about 18 km. Fig. 3,shows the boat trajectory in East-North obtained withVADASE (in green) and Kin-VADASE (in Blue). Bothsolutions start from Riva di Traiano Harbor, which is rep-resented as a red square in the Figure; however, only Kin-VADASE solution ends again in the harbor, heading backfairly accurately nearby the starting point. Instead, whendata are processed with the original implementation ofthe variometric approach, errors due to inappropriatemodel cumulate over time causing a wrong final positionof the boat (green square in the plot), far from the Harborabout 2 km in the West component and 4 km South.

A deeper analysis was performed comparing VADASEand Kin-VADASE solutions with the one coming fromLGO (Leica Geosystem Office) software. CVTV station(1 Hz acquisition rate), located in Civitavecchia (Rome),less than 10 km away from the harbor, and belonging toRegione Lazio GNSS Network, was used as reference sta-tion. This favorable configuration ensures a maximumbaseline length for the relative positioning processing ofroughly 25 km. As stated before, the on board receiverwas set at 2 Hz sampling rate. The variometric approachhas no limitation regarding the sampling rate and high rate(>1 Hz) observations can be completely exploited to esti-mate high rate kinematic parameters. Differently, referencestation data used for LGO solutions were available at 1 Hzsampling rate (this is the standard acquisition rate ofGNSS permanent stations devoted to positioning services,

like RTK), so it was possible to obtain a reference solutionfor the comparison at 1 Hz only. Thus the statistics overthe comparisons LGO/VADASE and LGO/Kin-VADASE were computed exclusively over commonepochs.

Figs. 4 and 5 show residuals of VADASE and Kin-VADASE, in the three components East, North and Up,respectively, in terms of final position displacements, withrespect to LGO solution. Residuals are plotted in functionof time (on X axis) and distance from the starting point ofthe navigation (colored bar). The plots can be interpretedas follows: the gradient of the curves represents the errorin the epoch by epoch variometric solution (velocity),whereas the curve itself represents the error in the trajec-tory estimation. VADASE velocity error (Fig. 4) increaseswith the distance from the origin and reaches the maximumvalue (gradient of the residual over time) when the distancefrom the origin is maximum (i.e., red part of the plot). As amatter of fact, when the distance from the origin increases,using the initial position to compute the variometric solu-tions (as designed in the static implementation of the vari-ometric approach) is proved to be not a validapproximation. After the first half of the plot, the distancefrom the origin decreases (the boat is returning to the har-bor), causing also the velocity error in the VADASE solu-tion to shrink. Nonetheless, the total cumulated errorcontinuously increases over time for all the components(Fig. 4)). Kin-VADASE residual with respect to LGO arein Fig. 5. In these solutions residuals seem to be completelyindependent to the distance from the initial position. Suchstatement is confirmed by Figs. 6 and 7 that show,VADASE and Kin-VADASE, respectively, 3D velocitesresiduals as function of the distance from the origin. In caseof VADASE, the correlation coefficient between the resid-uals and the distance reaches 0.98, whereas the Kin-VADASE residuals correlate with the distance only witha coefficient of 0.22.

To assess the accuracy of Kin-VADASE, statistics overthe residual with respect to LGO were computed. Resultsare reported in Table 3 for Kin-VADASE L3 and L1 pro-cessing. When both frequency are used to process data, anoverall horizontal accuracy of few decimeters was achieved(RMSE value is 0.43 m and 0.32 m in East and North

Fig. 3. Comparison between VADASE and Kin-VADASE results (in a 2D view), when processing 2 Hz observations collected during a navigation off-shore the Riva di Traiano Harbor (red square). (For interpretation of the references to colour in this figure legend, the reader is referred to the web versionof this article.)

Fig. 4. VADASE position residuals with respect to LGO in function of time and distance from the origin (test 1: navigation off-shore, receiver installed onboard of a sail boat).

2756 M. Branzanti et al. / Advances in Space Research 59 (2017) 2750–2763

respectively), while the RMSE value increases up to 0.60 min 3D.

As expected, since the real ionospheric delay is only par-tially removed by the Klobuchar model broadcastedparameters, the accuracy decreases (RMSE is 0.89 m and1.17 m in East and North, 1.74 m in 3D) when solutionsare obtained with L1 only. The achievable accuracy in tra-jectory length estimations is 0.050 m/km for L3 processingand 0.075 m/km in single frequency processing. Velocityand acceleration differences are at the level of few mm/s

and few mm/s2 for the horizontal and vertical components.RMSE variation over time is shown in Fig. 8 for single anddouble frequency processing. With a linear regression (dis-played as dashed line in the figure), we found an accuracyof 1 dm/h and 4 dm/h for L3 and L1 processing.

The above considerations and statistics refer to the Kin-VADASE solution retrieved using accurate starting posi-tion of the receiver: at the first epoch, Kin-VADASE andLGO coordinates are the same. Some further tests wereperformed to evaluate how errors on initial position could

Fig. 5. Kin-VADASE position residuals with respect to LGO in function of time and distance from the origin (test 1: navigation off-shore, receiverinstalled on board of a sail boat).

Fig. 6. VADASE 3D velocities residuals with respect to LGO in function of distance from the origin (test 1: navigation off-shore, receiver installed onboard of a sail boat).

M. Branzanti et al. / Advances in Space Research 59 (2017) 2750–2763 2757

propagate into the variometric solution (i.e., velocities anddisplacements of the receiver). To this aim, an error overeach component of the starting position of 0.3 m, 1 m,2 m, 5 m (that is an initial 3D error of 0.52 m, 1.73 m,3.46 m and 8.66 m respectively) was imposed and therelated Kin-VADASE solution (in L3 configuration) wereestimated. Fig. 9 shows that each solution suffers, asexpected, an initial bias and that the impact over the epochby epoch velocities estimation increases after roughly 2 h ofprocessing. The 3D RMSE was 1.08 m, 2.72 m, 5.20 m,12.66 m respectively.

5.2. High rate capability

The experiment was performed in a small airport nearArezzo (Tuscany, Italy). With the aim of testing high ratecapabilities of Kin-VADASE, 10 Hz observations were col-lected for a short interval (about 7 min) with a LeicaGeosystems double frequency geodetic class receiver,installed on board of a car. In this experiment a 10 Hz ref-erence solution could not be computed with the standarddifferential approach, due to the fact that 10 Hz observa-tions from a permanent station were not available.

Fig. 7. Kin-VADASE 3D velocities residuals with respect to LGO in function of distance from the origin (test 1: navigation off-shore, receiver installed onboard of a sail boat).

Table 3Sail boat: comparison of Kin-VADASE solutions (L3 and L1) with LGO L3 solutions.

Navigation off-shoreTraj. length = 38006.69 m, duration = 14399 s

L1 L3

Position [m] E N U E N USt. dev. 0.469 0.615 0.554 0.367 0.294 0.176Average �0.757 1.000 �0.747 �0.219 0.125 �0.197RMSE 0.891 1.174 0.930 0.427 0.320 0.595

Rel. error in Traj. [m/km] 0.075 0.0503D RMSE [m] 1.742 0.5953D RMSE over time [m/h] 0.408 0.122

0

0.5

1

1.5

2

0 2000 4000 6000 8000 10000 12000 14000 16000

3D R

MS

E [m

]

Epoch [sec]

Kin-VADASE 3D RMSE over time3D RMSE, L33D RMSE, L1

Fig. 8. Kin-VADASE 3D RMSE over time. The dashed line represents a simple linear regression model over the curves (test 1: navigation off-shore,receiver installed on board of a sail boat).

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Fig. 9. 3D difference between LGO and Kin-VADASE solution computed when each component of the starting position is affected by an error of 0.3 m,1 m, 2 m, 5 m (test 1: navigation off-shore, receiver installed on board of a sail boat).

Fig. 10. 10 Hz car trajectory estimated with Kin-VADASE on GoogleEarth platform.

M. Branzanti et al. / Advances in Space Research 59 (2017) 2750–2763 2759

Therefore, the original observations were decimated to1 Hz sampling rate and a standard L3 differential solution(using the LGO software) was obtained using as referenceCAMU permanent station, placed in Cortona (about20 km far from the test area) and belonging to ItalPosGNSS network. The comparison among 10 Hz Kin-VADASE solution and 1 Hz LGO solution was performedwith respect to pairs of corresponding epochs. Fig. 10shows the 10 Hz car trajectory estimated with Kin-VADASE on Google Earth platform.

Figs. 11 and 12 show position residuals of VADASEand Kin-VADASE with respect to LGO in function of timeand distance from the origin; Figs. 13 and 14 show 3Dvelocities residuals in function of distance from the origin.As it was already described for the test in Section 5.1, theincrease of the residuals suffered by VADASE grows pro-portionally to the distance from the origin (correlationcoefficient is 0.92, Fig. 13). On the contrary, the residualsof Kin-VADASE do not correlate with the distance (corre-lation coefficient is 0.03, Fig. 14) and seem to follow a nondeterministic pattern (Fig. 12).

Statistic over the 1 Hz epoch-by-epoch comparison arereported in Table 4. An accuracy of few centimeters inplanimetry and one decimeter in the Up component wasachieved with L3 solution; L1 solution accuracy is at thedecimeter level in planimetry and slightly better than onemeter (0.93 m) in the Up component.

Velocity and acceleration differences with respect to thereference trajectory are at the level of few mm/s and fewmm/s2 for the horizontal and vertical components. Withrespect to the reference total trajectory length, Kin-VADASE trajectory error is 0.241 m/km and 0.157 m/kmfor L1 and L3 respectively. 3D RMSE over time is8.892 m/h for L1 and 0.702 m/h for L3, while the total3D RMSE is 0.932 m and 0.123 m for L1 and L3

respectively. The lower global accuracy obtained for L1solutions is mainly due to a major bias and dispersion inthe Up component (average and standard deviation values

Fig. 11. VADASE position residuals with respect to LGO in function of time and distance from the origin (test 2: high rate capability, receiver installed onboard of a car).

Fig. 12. Kin-VADASE position residuals with respect to LGO in function of time and distance from the origin (test 2: high rate capability, receiverinstalled on board of a car).

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of L1 Up position are �0.823 m and 0.426 m as reported inTable 4). Actually, if only the horizontal components areconsidered, the 2D RMSE over time improves up to1.105 m/h and the total 2D RMSE is 0.106 m (values notreported in Table 4). The root cause of the notable differ-ence in the L1 and L3 solutions’ accuracy, which is dram-matically lower with respect to the previous experiment, isbeing currently investigated in more details.

Finally, Kin-VADASE solution when each componentof the starting position was affected by an error of 0.3 m,1 m, 2 m, 5 m was computed. Epoch by epoch velocitiesand the trajectory of the vehicle is still retrieved with highaccuracy and the solution is mainly affected by the initial

bias. The global 3D RMSE of the epoch by epoch differ-ence with LGO is 0.55 m, 1.72 m, 3.42 m, 8.46 m whenthe initial 3D error is respectively 0.52 m, 1.73 m, 3.46 m,8.66 m (3D difference over time are represented in Fig. 15).

This experiment showed that the variometric approachhigh rate capability is an added value with respect to stan-dard real-time positioning approaches, since it allows toovercome the problem of the availability of high rate obser-vations from permanent stations. From an applicationpoint of view, it could be realized an integration betweenstandard RTK positioning and Kin-VADASE: RTK couldprovide 1 Hz positioning and VADASE could increase theposition density at a higher desired rate (at present,

Fig. 13. VADASE 3D velocities residuals with respect to LGO in function of distance from the origin (test 2: high rate capability, receiver installed onboard of a car).

Fig. 14. Kin-VADASE 3D velocities residuals with respect to LGO in function of distance from the origin (test 2: high rate capability, receiver installed onboard of a car).

Table 4Application to high rate real data. Comparison between Kin-VADASE 10 Hz solutions and 1 Hz differential approach solutions (comparison performedwith respect to pairs of corresponding epochs). Statistics over East, North, Up and 3D differences of L3 and L1 solutions.

High rate solutionsTraj. length = 1653 m, Duration = 389 s

L1 L3

Position [m] E N U E N USt. dev. 0.023 0.059 0.426 0.032 0.033 0.086Average 0.031 0.080 �0.823 0.075 0.003 0.003RMSE 0.039 0.099 0.926 0.082 0.034 0.086

Rel. error in Traj. [m/km] 0.241 0.1573D RMSE [m] 0.932 0.1233D RMSE over time [m/h] 8.892 0.702

M. Branzanti et al. / Advances in Space Research 59 (2017) 2750–2763 2761

Fig. 15. 3D difference betwenn LGO and Kin-VADASE solution computed when each component of the starting position is affected by an error of 0.3 m,1 m, 2 m, 5 m (test 2: high rate capability, receiver installed on board of a car).

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receivers able to acquire at 100 Hz are commercially avail-able). Moreover, Kin-VADASE could supply a bridgingsolution in case of failure of RTK positioning.

6. Conclusion and perspectives

This work shows the results of the Kinematic implemen-tation (Kin) of the Variometric Approach for Displace-ment Analysis Standalone Engine (VADASE) tosimulated and real data. Kin-VADASE builds onVADASE, already implemented within seismological andmonitoring applications, to fully extend its use in the nav-igation field. This new methodology allows real-time esti-mation of kinematic parameters from a single receiverplaced on a moving vehicle using single (or double) fre-quency observations. After describing the Kin-VADASEalgorithm, this work validates its theoretical model per-forming preliminary tests based on synthetic data. Thepaper also shows how Kin-VADASE overcomes the limita-tion of the original implementation of the variometricapproach (static VADASE).

A thorough analysis on Kin-VADASE results was per-formed over data acquired under two completely differentconditions. In the first test, 2 Hz data were acquired witha double frequency geodetic class receiver, installed onboard of a sail boat, during a long (about 4 h) navigationoff-shore. In the second experiment, 10 Hz observationswere collected for a short interval (about 10 min) from ageodetic class receiver, installed on the roof of a car. Datawere processed both with VADASE and Kin-VADASE.The final accuracy of Kin-VADASE was assessed compar-ing its solution with the one obtained by a standard post-processing relative positioning (LGO, Leica GeosystemsOffice software).

In both experiments Kin-VADASE outperformed itspredecessor. VADASE error in velocities estimation ishighly correlated with the epoch-wise distance of the recei-ver from the starting point of the movement: the correla-tion coefficient between VADASE residuals (with respectto LGO) and distance from the origin is higher than 0.9in both experiments. Consequently, the final trajectoryobtained through velocities integration might not be accu-rate. Differently, Kin-VADASE results were independentfrom the distance from the origin, allowing a reliablereconstruction of the entire motion. In the first experimentan overall 3D RMSE of 0.6 m for L3 and 1.74 m for L1was achieved with respect to LGO solutions. In the secondexperiment the total 3D RMSE is 0.123 m and 0.932 m forL3 and L1 respectively. The lower global accuracyobtained for L1 solutions is mainly due to a major biasand dispersion in the Up component. In fact, if only thehorizontal components are considered, 2D RMSEimproves up to 0.106 m.

Moreover, both experiments showed that the accuracyof retrieved velocities and displacements is dependent onthe quality of the initial receiver position. In moredetails, when applied to long period navigation (morethan 1 h data), Kin-VADASE has a lower accuracy withrespect to the one of the established techniques. Despitethis, it presents significant and very promising advan-tages, i.e. the use of a unique GNSS receiver and thepossibility to exploit high rate (>1 Hz) observations toretrieve high rate kinematic parameters. Also, sinceKin-VADASE algorithm requires only broadcast prod-ucts and needs no ambiguity resolution, it can, in princi-ple, run in real-time directly on board the GNSSreceiver, as it was already shown for the originalVADASE (Tawk et al., 2016).

M. Branzanti et al. / Advances in Space Research 59 (2017) 2750–2763 2763

In order to figure out the best applications suiting Kin-VADASE, further experiments should be performed underdifferent acquisition condition, such as obstructed environ-ment, or with real data collected by aerial vehicles. Further,in order to confirm its single frequency capabilities, futureexperiments are planned using observations collected bylow-cost single frequency receivers.

The efficiency of the proposed technology, in terms ofcosts and computational complexity, pushes towards theuse of the variometric approach not only for scientific pur-poses, but also for industrial aims to reach many activitiesof our everyday life.

Acknowledgements

The authors are indebted with the Centro Avanzado deTecnologas Aeroespaciales (CATEC) research center inSevilla, for the great opportunity to collect synthetic datausing Spirent GNSS signal simulator, for the precious sci-entific support in simulating GNSS data, and for the warmhospitality during the research period spent in the center.Also, the authors would like to thank the Regione LazioGNSS Service for providing observations collected atCVTV (Civitavecchia) permanent station and ItalPos forthe observations collected at CAMU (Cortona) permanentstation. Variometric approach, implemented in theVADASE software in its ‘‘static” version, is subject of aninternational pending patent, generously supported bythe University of Rome ‘‘La Sapienza”. VADASE wasawarded the German Aerospace Agency (DLR) SpecialTopic Prize and the Audience Award at the EuropeanSatellite Navigation Competition 2010 and was partiallydeveloped thanks to one-year cooperation with DLR Insti-tute for Communications and Navigation at Oberpfaffen-hofen (Germany).

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