Global High Accuracy Navigation

Transcription

1 Global High Accuracy Navigation gage/upc, Barcelona, Spain

2 Outline 1. Introduction 2. Differential Positioning 2.1 Real-Time-Kinematic (RTK) 2.2 Network-RTK 3. Precise Point Positioning (PPP) 3.1 PPP with Ambiguity Fixing: PPP-AR 3.2 PPP using RTK networks: Faster Convergence 3.3 Fast-PPP at a Global Scale 4. Conclusions 2 2

3 1.- Introduction Global navigation Satellite System (GNSS) provides different kinds of applications and accuracies, having an increasing demand for precise navigation and positioning. Examples of applications requiring high accuracy are: civil engineering, mapping and surveying, agricultural uses, mining, marine navigation Precise GNSS positioning/navigation techniques: Differential GNSS positioning (e.g. RTK, Network-RTK) At least two operating receivers are needed. It makes use of the spatial correlation of the errors between stations to remove/mitigate their effects in differential mode, improving accuracy. Precise absolute (point) positioning (e.g. PPP, PPP-AR, Fast-PPP) It uses observation data of a single receiver and additionally state information on individual GNSS errors (orbits, clocks ) derived from a GNSS network. 3

4 2.1- Differential positioning: Real-Time-Kinematic Centimetre level accuracy positioning in real-time based on GPS (or GNSS) was developed in mid 1990s and nowadays is referred as RTK. The main drawback of the single base RTK is that the maximum distance between rover and reference stations cannot exceed 10 to 20 km in order to be able to rapidly and reliably resolve the carrier ambiguities. Many reference stations are needed to provide service to a larger region or a whole country: e.g. about 30 stations to cover km 2. Note: Corsica island km 2 - or Cyprus islands km 2 - (Picture from usgs.gov/os w/gps/index. html ) 4

5 2.2- Differential positioning: Network-RTK Network RTK includes a Master station and several reference stations: The master station collects measurements from the reference stations and process this data to generate the differential corrections, which are broadcast to the users. Three main steps: 1. Ambiguity fixing is performed in the reference stations network Image courtesy of Trimble Dual frequency carrier measurements with ambiguities fixed are used for precise modelling of distance-dependent biases (site coordinates are known, helping the network ambiguity fixing). 2.- Correction model coefficients are estimated Several techniques are developed to model or interpolate the distancedependent biases between reference stations and user receivers. It is advantageous to separate different error components: dispersive (ionosphere), geometric (orbits ), as they have different spatial and temporal correlations. 3.- Broadcasting of optimal reference data. Different approaches: Broadcast observations virtually shifted to rover location, based on correction model (Virtual Reference Station: It requires two way communication link). Broadcast observations of closest station + correction model coefficients. 5

6 Limitations of Network-RTK include: Limitation in the distance between reference stations (over km), which depends on the geographic location of the network and the level of ionospheric activity. There is a high cost of setting up and maintaining the RTN: Note: With typical baselines between reference stations are km, about 5 to 10 reference stations are still needed per km 2 (e.g. Corsica km 2 - or Cyprus islands km 2 -). Use of the RTN can be limited by data link coverage and system latencies or down times. Availability is dependent on network extent and accuracy can be affected by the network density. In the case of VRS, it requires a two way communication link. Then, the number of potential VRS users is limited. 6

7 3.- Precise (Absolute) Point Positioning: PPP Zumberge et al. (1997), proposed the Precise Point Positioning (PPP) method for absolute positioning of a single receiver. Using precise orbits and clocks (post-processed or Real-time, e.g. from IGS) and with an accurate measurements modelling, provides centimetre (static) or decimetre (kinematic) level of accuracy for any worldwide user with a dual-frequency receiver (iono-free combination). Static: Centimetre level accuracy over 24h data The main disadvantage of PPP is that the solutions take longer to converge than the RTK or NRTK differential solutions. Kinematic: Decimetre level accuracy or better after several tens of minutes 7

8 Precise orbits and clocks can be derived from corrections to Broadcast Ephemeris. RTCM's 'State Space Representation' (SSR) Working Group has developed appropriate v3 messages to disseminate such Corrections in real-time. 8

9 Pros PPP provides absolute worldwide positioning for a single receiver, from a reduced reference stations network (some tens for the whole planet). The state-space modelling used in PPP, where the different error components (orbits, clocks ) are treated separately, is more close to the physical error sources. It also allows to reduce the message bandwidth for transmission. Different time update rates can be used for different state parameters. Cons: The main disadvantage of PPP is the large converge time. Decimetre level navigation can require from tens of minutes to more than one hour, depending on the satellite geometry. Also it is limited in accuracy, because in the conventional PPP, carrier ambiguities are estimated as real numbers (floated), i.e. cannot be fixed as integer values as in RTK. Note: The ionosphere-free ambiguity parameter estimated in the conventional PPP is a combination of integer ambig. and the satellite and receiver carrier hardware biases. Then the integer property is lost Note: these biases are canceled in RTK when forming Double-Differences of measurements between pairs of satellites and receivers. 9

10 3.1- PPP with ambiguity fixing: PPP-AR Nevertheless, these carrier hardware biases (or fractional part of carrier ambiguities) can be estimated together with the orbits, clocks, ionosphere and DCBs from measurements of a worldwide reference stations network. The fractional part of carrier ambiguities are slow varying parameters that can be broadcast to the user, together with the other differential corrections. Then, the user can remove them and estimate the remaining ambiguities as integer numbers. This can allow world-wide PPP users to perform ambiguity fixing, without baseline length limitation, improving accuracy and reducing convergence time. 10

11 3.1- PPP with ambiguity fixing: PPP-AR Several PPP integer ambiguity fixing techniques have been developed. Examples of such techniques are: Single-difference between satellites (Ge et al., 2008), (Mervart et al., 2008), (Juan et al, 2012) Decoupled clock (Collins, 2008). Integer phase-clock (Laurichesse et al., 2008). There are some practical differences among these three methods, however they provide equivalent results once the ambiguities are fixed to their integer values (a detailed comparison is given in J. Shi and Y. Gao, 2014). Single-difference between satellites (SD) provides two fractionalambiguity corrections to recover the integrity property in SD. Decoupled clock and Integer phase-clock uses two different clocks terms for code and carrier. 11

12 June 2013 The main weakness of PPP is the large convergence time, which depend on satellites geometry, quality of data (code noise, cycle-slips ). There is a sudden improvement when fixing carrier ambiguities, but also several tens of minutes are needed to achieve centimeter level of accuracy. This picture is from (Mervart et al., 2013) 12

13 PPP monitoring Real-time positioning errors (sliding window over one day) using the complete set of corrections provided by CNES. 13

14 3.2- PPP using RTK networks: Faster Convergence It is a combination of the original PPP concept and differential positioning techniques. PPP corrections of satellite orbits and clocks are independent of user location and can be applied worldwide. The atmospheric corrections (ionosphere, troposphere) computed from a regional network are broadcast to users to accelerate the filter convergence, over a local area. These position dependent atmospheric effects can be described by satellite dependent or gridded parameters. The ionospheric corrections are used to accelerate the filter convergence and fix the ambiguity quickly. (the troposphere also helps, but is of less importance) 14

15 Regional Iono. Corrections helping fast ambiguity fixing Hokkaido island (Japan) The satellite dependent STECs from the nearest 3 surrounding reference stations are linearly interpolated to the user location. This iono. correction is used to accelerate the filter convergence These pictures are from (Mervart et al., 2013) June 2013 Zoom of top Figure 5 minutes of data followed by 5 minutes of gap 15

16 Regional Ionosphere interpolation: baseline effect Using all reference stations: June 2013 Hokkaido island (Japan) Using only the reference stations indicated by blue stars 16

17 3.2- PPP using RTK networks: Faster Convergence Pros Provides absolute worldwide positioning for a single receiver, with faster convergence over a Regional Network. The convergence time is reduced thanks to the Regional Network corrections (ionosphere and troposphere). Cons: The main disadvantage is that a dense regional network is needed to compute the ionospheric corrections, a they are computed by interpolating the STECs form reference stations to the user location. A Wide-Area coverage for faster convergence would require a large number of reference stations (like with Network-RTK). The use of a Global Ionospheric Grid Model instead of interpolating the Network-RTK STECs has been explored as a solution to reduce the number of reference stations needed. 17

18 Convergence using a Global Ionospheric Grid (from IGS GIM) This figure is from (Banville et al., 2014) 2 March 2008 Canada: (low solar activity) PPP PPP+AR [PPP]+GIM [PPP+AR]+GIM 68 th percentile 95 th percentile Time to 10cm 68 th 95 th PPP 30 min 60 min [PPP]+GIM 30 min 60 min PPP+AR 8.5 min 27 min [PPP+AR]+GIM 4.5 min 24 min The IGS Global Ionospheric Maps (GIMs) are assessed in (Banville et al., 2014) to accelerate the PPP convergence. IONEX: 2.5º x 5º x 2 hours Plots show the 68 th and 95 th percentile of Horizontal error for 24 stations processed in 24 independent intervals of 1h. Benefits of applying external ionospheric corrections are expected, provided its quality is superior to that of code noise. The IGS-GIM helps to improve the accuracy, mainly at the beginning of the session (under favorable iono. conditions). 18

19 These figures are from (Juan et al, 2012) 3.3- Fast-PPP and 2-Layers Iono. Grid Model The single layer IGS-GIM model is not accurate enough to significantly accelerate the convergence of PPP solution. During the early 2000s gage/upc developed a two layers grid model, and afterwards assessed its suitability to help the PPP convergence Fast-PPP based on an accurate iono. model With iono 24 November 2009 (low solar activity) Horizontal No iono Vertical 24h of data: The full user state has been reset every two hours to better characterize the convergence process. 10 cm PCT/EP2011/ MLVL (252km), EUSK (170km) and EIJS (95km) (km from the nearest reference receiver) This last study was done in the context of ESA project Fast-PPP and the technique is protected by an ESA patent since (PCT/EP2011/001512) More recently, the accurate ionospheric model has been extended to worldwide (Rovira, et al 2014) 19

20 Actual GNSS Data: Year 2014 (close to Solar Maximum) gage iono. Model: (Rovira et al., 2014) Iono model covers the range -130º < λ < 130º -90º < ɸ < 90º Rovers are located at distances are orders of magnitude greater than RTK baselines Close to maximum Solar Cycle conditions Moderate Geomagnetic Dst Values 20

21 Assessment of Ionospheric Models for GNSS 1.- [Two-layers] Fast-PPP STECs estimates in real time (close to reference stations) in real-time: tenths of TECUs: Ambiguity Fixing Strategy Dual-layer 2.- [Two-layers] Fast-PPP ionospheric model is smoothed (interpolated) to account for the interpolation error at the user location. Degradation of the well-sounded Ionospheric Grid Points (IGPs). Fast-PPP GIM accurate at ~1 TECU level. 3.- [One Layer] IGS-GIM: several TECUs GIMs error: Local Time periodicity Equator no suited singlelayer See details on this assessment in (Juan et al., 2014) 21

22 FPPP 2F Convergence: DoYs of Positioning modes per rover, resets every 2h: a) Reference Iono-Free sol IONEX 2F PPP 2F b) Iono Sol: IONEX (IGS-GIM): c) Iono Sol. Fast-PPP IONO: Rover EIJS (5ºE, 50ºN): Mid Latitude, 76 km FPPP 1F IONEX 1F GRAPHIC 1F Rover LKHU (95ºW, 29ºS): Low latitude, 455 km Results from (Rovira et al., 2014) (Close to Solar Maximum) GRAPHIC 1F PPP 2F IONEX 1F PPP+IONEX 2F Fast-PPP 1F Fast-PPP 2F EIJS Benefits of applying external ionospheric corrections are expected, provided its quality is superior to that of code noise. LKHU 22

23 Dual-Frequency (GPS L1 GPS L2) Once converged, same accuracy than PPP: no missmodelling in iono corr. Single Frequency (GPS L1) Iono model is the main limiting factor in accuracy of SPP (massmarket). Self-consistence of sigmas vs accuracy Not only the accuracies of the corrections are relevant, but also their confidence bounds (sigmas). Stanford plots are used to assess how the confidence bounds of the corrections are transfer to the user solution. Results show the consistency of parameterization and hypothesis done. (1 month worldwide network results) Pictures from (Rovira et al., 2014) 23

24 4.- Conclusions Two different categories of precise positioning have been presented: Differential positioning (RTK or Network-RTK). Precise (Absolute) Point Positioning (PPP, PPP-AR, PPP-NRTK, Fast-PPP). RTK and Network-RTK, are based on integer ambiguity fixing and provides high accuracy quickly, but are limited by baseline, requiring a large number of stations to cover a continent. PPP provides worldwide positioning, overcoming the baseline limitation, but requires large convergence time. PPP-AR (with ambiguity fixing) improves PPP accuracy and reduces converg. time, but several tens of minutes are still needed to start the ambiguity fixing PPP using RTK networks provides worldwide positioning, with faster convergence over a regional network (used to compute/interpolate STEC corrections), but as in Network-RTK, a dense network is needed. Fast-PPP: A two layers grid model has been developed, able to help improve the PPP convergence at a global scale. 24

25 Bibliography 1. Juan, JM., M. Hernández-Pajares, J. Sanz, P. Ramos-Bosch, A. Aragón-Àngel, R. Orús, W. Ochieng, S. Feng, M. Jofre, P. Coutinho, J. Samson, and M. Tossaint (2012). Enhanced Precise Point Positioning for GNSS Users, IEEE transactions on geoscience and remote sensing, April 2012, Issue: A. Rovira, JM Juan, J. Sanz (2014). A Real-time World-wide Ionospheric Model for Single and Multi-frequency Precise Navigation. Proceedings of the 27th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa, Florida, September 8-12, J.M. Juan, J. Sanz, G. González-Casado, A. Rovira-García, D. Ibáñez, R. Orús, Prieto-Cerdeira and S. Schlüter (2014). Accurate reference ionospheric model for testing GNSS ionospheric correction in EGNOS and Galileo. Proceedings of NAVITEC 2014: ESA Workshop on Satellite Navigation Technologies and GNSS Signals and Signal Processing. Nordwijk (The Netherlands), December 3-5, L. Mervart, C. Rocken, T. Iwabuchi, Z. Lukes and M. Kanzaki (2013). Precise Point Positioning with Fast Ambiguity Resolution Prerequisites, Algorithms and Performance. Proceedings of the 27th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2013), Nashville, Tennessee, September 16-20, J. Shi, Y. Gao (2014). A comparison of three PPP integer ambiguity resolution methods. GPS Solutions, 18, S. Banville, P. Collins, W. Zhang and R. Langley (2014). Global and Regional Ionospheric Corrections for faster PPP Convergence. Navigation. Journal of the Institute of Navigation, USA, Vol 61. No 2, Summer

26 7. Ge M, Gendt G, Rothacher M, Shi C, Liu J (2008). Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. J Geod 82(7): Collins P (2008). Isolating and estimating undifferenced GPS integer ambiguities. Proceedings of ION NTM-2008, Institute of Navigation, San Diego, California, Jan, pp Laurichesse D, Mercier F, Berthias J, Bijac J (2008). Real time zerodifference ambiguities blocking and absolute RTK. Proceedings of the ION NTM-2008, Institute of Navigation, San Diego, California, Jan, pp J. Sanz Subirana, JM. Juan Zornoza, M. Hernández-Pajares, GNSS Data processing. Volume 1: Fundamentals and Algorithms. ESA TM - 23/1. ESA Communications, May JPL/NASA. The Global Differential GPS GNSS Data Center (GDC), Real-time Precise Point Positioning Monitor, CNES, The PPP-WIZARD project Precise Point Positioning With Integer and Zerodifference Ambiguity Resolution Demonstrator, Fast-PPP: International Patent Application PCT/EP2011/ International patent: G01S19/44 (ESA ref.: ESA/PAT/566). 26

27 Back Up Slides 27

28 Multi-constellation and Multi-frequency GPS: IONO + FIX GPS+GAL: IONO + NO FIX GPS+GAL: IONO + FIX GPS: NO IONO + NO FIX GPS: NO IONO + FIX GPS: IONO + NO FIX This figure is from (Juan et al, 2012) GPS+GAL: NO IONO +NO FIX Simulated data with low code noise and multipath. Only relative performan ces can be assessed. 28

29 3.3- Iono. Model for Fast-PPP at a Global Scale 1.- Derived from the geometry-free combination of code and carrier-phases: PI=P2-P1 and LLLL = LLL LLL 2.- Ambiguities are fixed (thanks to the CPF accurate geodetic modelling): Unambiguous Carrier-phase noise (mm) LLLL ii jj BBBB ii jj = SSSSSSSS ii jj + DDDDDD ii DDDDDD jj 3.- The Slant Total Electron Content (STEC) is estimated with Vertical STEC VVVVVVVV kk (VTEC) on each k Ionospheric Grid Point (IGP) at the two-layers: IIIIII kk satellite j lon (LT) IIIIII kk SSSSSSSS ii jj = Σ αα kk VVVVVVVV kk Δlon = 500 km jj SSSSSSSS ii lon (LT) SSSSSSSS ii jj receiver i IIIIII kk Δlon = 250 km IIIIII kk VVVVVVVV kk Orbit errors (4cm) + sat Clocks (6cm) 29 Iono Accuracy <= 1 TECU (16 cm in L1)

30 Assessment of Ionospheric Models for GNSS 1.- [Two-layers] Fast-PPP STECs estimates in real time (close to reference stations) in real-time: tenths of TECUs: Ambiguity Fixing Strategy Dual-layer 2.- [Two-layers] Fast-PPP ionospheric model is smoothed (interpolated) to account for the interpolation error at the user location. Degradation of the well-sounded Ionospheric Grid Points (IGPs). Fast-PPP GIM accurate at ~1 TECU level. 3.- [One Layer] IGS-GIM: several TECUs GIMs error: Local Time periodicity GIMs error: proportional Equator to no Solar suited Flux singlelayer See details on this assessment in (Juan et al., 2014) 30

31 A new metric to assess Iono Models for GNSS 1.- Reference data based on precise iono determinations of the CPF: SSSSSSSS tttttttt = LLLL II DDCCBB rrrrrr DDDDDD ssssss BB II ffffff Carrier-phase meas. LI=L1-L2 Unbiased 2.-The difference between the prediction of any ionospheric model and the reference should be separated as DCBs: SSSSSSSS mmmmmmmmmm SSSSSSSS tttttttt = KK rrrrrr + KK ssssss Unambiguous (fixed) Any bias is absorbed in the DCBs 3. - The KK rec and KK sat on the right hand of the previous equation are estimated by a Least Minimum Squares (LMS) process. 4.- Metric: the post-fit residuals of the K s fit is computed for all reference stations used by the ionospheric filter. 31

32 A new metric to assess Iono Models for GNSS Outcomes based on test results: 1.- IGS GIMs are more precise than NeQuick or Klobuchar Models (as expected). 2.- IGS GIMs (post-processed with 15 days of latency) are not suitable to be used as a reference to assess EGNOS iono (which is real-time), since their error contribution is at the level of the model under testing. DoY 300 Year 2013 (first day of valid NeQuick broadcast coefficients) Similar Nequick and Klobuchar performance. Each point is 24h of postfit RMS of a given station 32

33 Fast-PPP User equations Meas. Eqs Corr. Eqs dp dl - Capabilities: a) Multi-constellation ( 2 common Frequencies ) b) Multi-frequency ( All frequencies available per constellation) - Additional terms DCB s linked to the PC satellite clock determination. ˆ [ Tuser + TGNSS T ] + M t ΔTropuser + α~ 1 (M i TEC + DCB21 + DCB )+εp j [ Tuser + TGNSS T ] + M t ΔTropuser α~ 1 (M i TEC + DCB21 + DCB21 )+εl B [ Tuser + TGNSS T ] + M t ΔTropuser + α~ 2 (M i TEC + DCB21 + DCB )+εp j [ T + T T ] + M ΔTrop α~ (M TEC + DCB + DCB )+ε B dp1 = ρ ΔR+c 21 1 = ρ ΔR+c dl ˆ = ρˆ ΔR+c dl2 = ρˆ ΔR+c user GNSS t user 2 i L + 2 dp 21 j 3 j 3 j = ρˆ ΔR+c j = ρˆ ΔR+c [ Tuser + TGNSS T ] + M t ΔTropuser [ Tuser + TGNSS T ] + M t ΔTropuser j T corr = T + εcorr j j DCB21, corr = DCB21 + ε j DCB DCB31 + TEC = TEC + ε j 31, corr International = Technical Symposium on Navigation and Timing, j corr j + α ~ 3 (M i TEC + DCB31 + DCB31 ) + α~ 1 (DCB21 + DCB21 )+ εp j ~ (M TEC + DCB + DCB ) α~ (DCB + DCB )+ε + B j α3 i L 3 ion j dcb j εdcb 33

34 3.3- Fast-PPP at a Global Scale Station network GNSS Measurements (multi-frequency Slow Filter [5 min] B c, B I Troposphere Orbits Station clocks Satellite clocks Preprocessing Satellites under eclipse Cycle-slip detector Outlier detector Modelling Satellite orbits (Broadcast, predicted IGS-IGU, rapid IGS-IGR) multi-constellation) Fractional part of Ambiguities [5min] Iono Filter [5min] Ionospheric Model Differential Code Biases (DCBs) Fast Filter [30 sec] Station clocks Satellite clocks Orbit Predictor (for the next day) FPPP-CPF at a glance[*] User Corrections Satellite orbit and clocks Fractional part of ambiguities, DCBs Ionospheric corrections Message Generator [*] Juan J., M. Hernández-Pajares, J. Sanz, P. Ramos-Bosch, A. Aragón-Àngel, R. Orús, W. Ochieng, S. Feng, M. Jofre, P. Coutinho, J. Samson, M. Tossaint, Enhanced Precise Point Positioning for GNSS Users, IEEE Transactions in Geosciences and Remote Sensing, DOI /TGRS ,

35 Geodesy computations at the Fast-PPP CPF 1.- Satellite orbit and clocks accuracies are comparable to other Analysis Centres for real-time determinations: IGS Real Time Pilot Project (RTPP): RMS ~ 4cm 2.- Accuracy of ionospheric model must be at 1 TECU is (16 cm in L1) to keep the satellite and orbit accuracies. RMS ~ 0.2ns ~ 6cm 35

36 Fractional Part of Ambiguities Satellite determination δδbb jj : L1 band (B1) & Wide-Lane combination: BW = ff 1BB 1 ff 2 BB 2 ff 1 ff 2 Assessment: 1. Slow-varying parameters broadcast with a low rate (5 mins). 2. Discontinuities on a day-to-day basis (independent 24h batches) I. B1 ambiguity: typically smaller than a 0.1 cycle (2 cm) B1 Wide-Lane BB ii jj = λλnn ii jj + δδbb ii + δδbb jj II. BW ambiguity: negligible (no geometry, no ionosphere) 36

37 Fractional Part of Ambiguities Satellite determination of: - L1 band (B1) - Wide-Lane combination (BW) Assessment: 1. Similar results using both orbit sources: IGS rapid (IGR) and predicted IGS ultra-rapid (IGU). 2. Slow-varying parameters broadcast with a low rate (5 mins) 3. Discontinuities of the fractional B1 ambiguity on a day-to-day basis: i. typically smaller than a 0.1 cycle (2 cm) when IGU orbits are corrected. ii. slightly degraded when no orbit correction (IGR), indicating that some residual orbit error is transferred. 4. Repeatability of the BW fractional ambiguity does not depend on the orbit source. Wide- Lane BB ii jj = λλnn ii jj + δδbb ii + δδbb jj B1 37

38 Satellite Differential Code Biases (DCBs) 1.- Key for users applying ionospheric corrections: If not applied, biases worse the positioning accuracy (especially the single-frequency). 2.- Accurately estimated from pseudorange measurements: Codes are x100 noiser than Carrier-phase measurements Rays from several different Local Times are mixed in the iono model. High redundancy: observations from the same sat (or rec) have the same DCB. high consistency on a day to day basis: one month (days of 2014) 38

39 CPF Corrections Correction Coverage Time Update Content Fast Global ~5s Satellite Clocks Slow Global 300s Orbit Corrections Satellite DCBs Fractional part of ambiguities (B1, BW) Ionospheric Continental 300s Iono. corrections Integrity Global/ Continental ~5/300s Confidence bounds Service + Added capability Classic PPP + Ambiguity Fixing + Fast PPP + Single Frequency + Integrity The additional required bandwidth of F-PPP is about 10% of the classical PPP bandwidth 39

40 Thank you!! gage/ UPC Research group of Astronomy & Geomatics Technical University of Catalonia, Spain Contact: Campus Nord UPC Jordi Girona 31, Barcelona (Spain). T: