investigations about the vrs methodology for network-rtk within a local area presented by:ben chan...

Investigations about the VRS Methodology for Network-RTK within

a Local Area

Presented by: Ben Chan Siu-bun, LS/G(HK&Is)

Acknowledgements

Abstracts

Contents(Network-RTK)

• Carrier Phase Measurement and RTK Operation• What is Network-RTK?• How it works? What’s the theory and algorithm

of Network-RTK? How does it improve the accuracy of position fixing?

• What are the core issues of VRS-RTK?• Some common approaches – NetAdjust, FKP, VR

Contents(The Project Investigation)

• Is VRS accurate? reliable? and robust?• What constitutes a sound or weak VRS?• Does VRS improve Static GPS? In terms of

accuracy and reliability.• Does VRS improve RTK? In terms of

accuracy, reliability and robustness.• What are the crucial factors affecting the

accuracy and performance of VRS? Could the problem be resolved?

• Practical Issues for Implementation.

Carrier Phase Measurements.

Count the carrier cycle & rec

ord the ɸ0 + ϕ0

100 + ɸ1

200 + ϕ2

300 + ɸ3

ρ range between satellite & receive

rρ (s0 , r )ρ (s1 , r)ρ (s2 , r )ρ (s3 , r)

Approx r from pseudoran

ge, DGPSor others

Ambiguity

Carrier Phase Measurement Errors

• satellite and receiver clock offsets

• satellite orbit error

• Multipath (station-dependent)

• antenna phase centre variation (station-dependent)

• ionospheric effect

• tropospheric effect

Use predicted ephemeris of IGS,

may be significant even for short baselines, antenna-dependent

the most important distance-dependent factors that affect the accuracy of baselines over long distances.

insignificant after double differencing

Double Differenced Carrier Phase Meas.

• If the baseline length is short, say up to a few km, errors in the satellite coordinates and biases due to atmosphere can be assumed the same; and the equation becomes

eoab dtrop

eoabba

oeeoabba

eoab NTTTT

f ),,,(),(

eoabba

oeeoabba

eoab NTTTT

f ),,,(),(

Double Differenced Carrier Phase Meas.

• The above equation is effective for short baselines since the effect of ionosphere, troposphere, satellite orbit may in general be neglected.

• Any significant errors from these neglected terms will spill over into the unknown parameters, namely station coordinates and ambiguities; and degrade the positional accuracy as well as the integer nature of the ambiguity (Hofmann-Wellenhof, 2001: p.213).

eoabba

oeeoabba

eoab NTTTT

f ),,,(),(

Static GPS using Carrier Phase

• Use precise orbit IONEX files downloaded from the International GPS Service (IGS)

• Use model or Ionospheric-free frequency to account for the dispersive effect of the ionosphere (coed delay/ phase advance)

• Use a model e.g. Hopfield or Saastamoinen, to account for the majority of the zenith hydrostatic delay

• Solve for the troposheric delay bias (zenith tropospheric scale factor = actual delay – modelled delay) as an additional unknown parameter in least squares

General RTK operation• Transfer GPS signals of the Reference

Station (RS) to the rover• Extrapolate the RS data to the same epochs

in which the corresponding rover measurements have been generated (software dependent)

• solve the carrier phase ambiguity in a short time – with the help of either float ambiguity or DGPS solution

• Compute the baseline (vector between RS and rover)

Accuracy Performance ofRTK positioning

• Depends on the ability of the algorithms to resolve the integer ambiguities and

to model the differential errors that occur between the RS and the rover.

• To solve the ambiguity, many conditions must exist, including a relatively short distance between RS and rover.

Constraints of Single-base RTK

• Single Reference Station:- No independent check

• The station-dependent errors (multipath, APC variation) of the RS would affect the RTK accuracy

• Ionospheric, tropospheric and orbit errors at RS and rover de-correlate as their inter-distance increases induce errors to integer ambiguity & coordinates

Constraints of Single-base RTK

• What’s the effect? How serious? long Time to Fix Ambiguity (1 minutes? 1 hour?) unable to solve ambiguity incorrect ambiguity fix limited distance for RTK operation ( 10 km? 5 km ? Or less?)

What is Network-RTK?

• The technique generally refers to those investigations made on the optimal means of processing data from Multiple Reference Stations, and the Provision of ‘Correction' information to users in Real-time (Rizos, et al, 2002).

Basic Concepts of Network-RTK (1)

• Reference:- Rizos et al (2002), Lachapelle et al (2000a) and Vollath et al (2002).

• Use a network of GPS reference stations spreading over a wide geographic area to reduce the distance-dependent errors in RTK positioning.

• With different approaches of error modelling, GPS observations at each single or pair of reference stations are compared to the known coordinates of the stations.

• Provision of a set of correction parameters at the locations of the corresponding reference stations over the area covered by the station network.

Figure 1: Network Sketch

Figure 2: Rover transmits NMEA message for VRS position to the network server

Basic Concepts of Network-RTK (2)

• Such parameters are used to interpolate the corrections to be made at any position of a rover.

• The interpolated correction could be applied either direct in the RTK measurements or through the generation of a virtual reference station (VRS). implies single or bi-directional

• The correction parameter (FKP) or VRS would be broadcasted to the users through telecommunication link. The use of either method depends on the communication infrastructure between the rovers and the GPS reference network service provider. (Wübbena, et al. , 2001b)

Figure 3: Network server transmits RTCM correction stream for VRS position

Benefits of Network-RTK (1)• The accuracy performance of RTK positioning dep

ends on the ability of the algorithms and software to resolve the integer ambiguities and to model the differential errors that occur between the reference station(s) and the remote. The use of a network of reference stations is effective in enhancing the solution to both problems (Lachapell et al, 2000b).

• help solve the integer ambiguities shorter search time ( initialization time ) more reliable (independent check from RSs)

Benefits of Network-RTK (2)• better model the differential errors between RS

and rover changes the error characteristics

The behavior of correlated errors (orbital and atmospheric) can be modelled throughout the region covered by the network (parameterization techniques), while the uncorrelated errors (multipath and noise) can be averaged out through filtering

improve the performance of RTK positioning• multiple RS more availability of the service• able to use RTK for long range positioning

Benefits of Network-RTK (3)

• Able to use spare network (less Reference Stations) to achieve the same performance

• Wübbena et al (1996) showed that the post-processing simulation of a reference station network could reduce the effects to generally less than 1 cm without any distance dependencies.

Core Issues of Network-RTK

• Modelling of Errors

• Network Ambiguity Fixing

• Error Interpolation

• Broadcasting the correction parameters

(1) Modelling of Errors

Modelling of Errors (1)

• satellite orbit error

• Multipath (station-dependent)

• antenna phase centre variation (station-dependent)

• satellite and receiver clock offsets

• ionospheric effect

• tropospheric effect

Use predicted ephemeris of IGS,

may be significant even for short baselines, antenna-dependent

the most important distance-dependent factors that affect the accuracy of baselines over long distances.

insignificant after double ifferencing

Modelling of Errors (2)• GNSMART -- model all individual errors in the

State Space approach• Trimble VRS -- models the ionospheric delays

by a simple 2-dimensional polynomials over geomagnetic latitude and hour angle of the sun; and handles the tropospheric errors with a scaling technique based on the geometry of receivers and satellites.

• Combinations of signal frequencies (e.g. Ionospheric-free frequency) are commonly used for the analysis of errors in GPS measurements eliminates the first order effect of the ionosphere on the measurements.

(2) Network Ambiguity Fixing

Network Ambiguity Fixing (1)• After modelling of errors at each or pair of the

reference stations• Solve the ambiguities of the 3 ‘baselines’ that

form the sides of a triangle of reference station network by double differencing.

• Ambiguity resolution 'engine' (Network Ambiguity Fixing)– handle double-differenced data from stations– operate in real-time– for each satellite– for every epoch– resolved with a fixed or float solution (software

dependent)

Network Ambiguity Fixing (2)

Prior to generation of the VRS data file

• The integer ambiguity for each of the 3 baselines fixed (for each epoch, each satellite)

• check on the triangle loop closure, say 20 mm (software dependent)

(3) Interpolation and Extrapolation

Interpolation and Extrapolation

• Calculate the remaining errors per station or per ‘baseline’ of the triangle as compared to the known coordinates of the 3 reference stations.

• Interpolate/ Extrapolate the errors at the approximate position of the rover.

• Generate the correction parameters for Network-RTK or VRS.

Figure 4: Linear Interpolation Error

Figure 5: Interpolation and Extrapolation

User 2 (extrapol.)

User 1 (interpol.)

User 2 (extrapol.)

User 1 (interpol.)

Error Interpolation (1)

• Usually the interpolation algorithms are separately applied to the dispersive (ionospheric) and to the non-dispersive (geometric, i.e. tropospheric and orbit) biases.

• The correction model parameters are known as area correction parameters (in German Flächenkorrekturparameter, abbreviated FKP).

Error Interpolation (2)The common approaches of error interpolation

include• Linear Interpolation (Linear Combination Mod

el, Distance-based linear Interpolation Method, Linear Interpolation Method)

• Low-order Surface Model; and• Least-Squares Collocation.(Dai, et al 2001).

– all the above methods significantly reduce the distance-dependent biases in the carrier phase and pseudo-range measurements at the GPS user station;

– Similar performance of all the above methods

(4) Broadcast the Correction Parameters

Broadcasting the correction parameters (1)

Two steps:-

• Prepare the correction parameters or establishing a virtual reference stations with corrected observations (rover position requirement: method dependent)

• Broadcast the correction data or parameters to uses for RTK processing.

(Wanninger, 2002)Network observations on common ambiguity level:

• Broadcast of the observations of a master reference station and observation differences between pairs of reference station, all being on the same ambiguity level

• With the network corrections and information on their qualities, user performs the interpolation step on his own

Area Correction Parameter

• (Flächenkorrekturparameter, FKP): Broadcast of the observations of a master RS and FKP (Wübbena et al. 2000)

• The user applies the FKP to the reference station observation data set according to his position and thus obtains VRS-observations

Gridded corrections

• Broadcast of the observations of a master reference station and gridded corrections of the distance-dependent biases

• The user interpolates individual corrections within the grid and applies them to the observation data set in order to obtain VRS-observations

Virtual Reference Station

• The user sends his approximate position to a central computing facility

• by return receives VRS-observations to be used for baseline positioning

Some Common Approaches

• NetAdjust Multi-Reference Station Approach

• State Space Approach with FKP

• VRS Approach

NetAdjust Multi-Ref Station Approach (1)

• A condition adjustment method developed by the University of Calgary (Raquet, 1998).

• Principle of the methodUse least squares to estimate the code and carrier phase observable errors improve the integer ambiguity resolution over longer distances (Lachapelle, et al. 2000b).

• The least squares condition is that all of the double differences of the adjusted measurements minus the calculated ranges is zero (which would be true if there were no errors).

• The calculated ranges ρ are the distances between the known receiver positions and the position of the satellites as calculated from the ephemeris data (Raquet, 1997).

Observation Equation

))((ˆ NBBBCBCl Tl

Tllr r

))((ˆ NBBBCBCl Tl

correction vector to carrier-phase observables collected

at the user receiver, in metres,

covariance matrix of the carrier-phase observables

collected at the reference stations

correction vector to carrier-phase observables collected at the reference stations,

in metres,

Cross-covariance matrix between the

carrier-phase observables collected at the user receiver and at the reference

stations

double difference integer ambiguity vector between the reference stations

(assumed to be known), in cycles

double difference matrix (made up of the values +1, -

1 & 0)

measurement-minus-range

carrier-phase observable

Representation of Error Modelling

• The covariance matrices and represent the behavior of the correlated errors (ionospheric, tropospheric, and satellite position errors) over the region covered by the network and their dependency on the satellite elevation. In addition, it is necessary to know the variance of the uncorrelated errors (multipath effects and receiver noise) for each station in the network ( Fortes, 2002).

lC llrC

Representation of Error Modelling

• The NetAdjust method models the correlated errors and uncorrelated errors of the reference and rover stations through the covariance matrix of the carrier-phase observables collected at the reference stations, and the cross-covariance matrix between the carrier-phase observables collected at the user receiver and at the reference stations.

Covariance matrix for modelling the spatial correlation/ decorrelation

• Each of the correlated errors that affect GPS positioning may not have the same behaviour of spatial decorrelation across the region covered by the reference network.

• The covariance matrix could cater for different values in different regions and different time of survey.

• Separate models for different kinds of correlated errors among the multiple reference stations, such as changing values of ionospheric at different local time, geographic location, season and solar cycle (Fortes, 2002).

Figure: The NetAdjust Method

• The NetAdjust method corrects the reference receiver measurements, as opposed to providing differential range corrections to be applied to the mobile receiver’s measurements.

• Standard differential positioning or ambiguity resolution is then performed between a mobile receiver and one of the adjusted reference receivers.

Accuracy of the Method

• The accuracy of the method depends on

accurate information about the position of the reference stations (!!)

correct modelling of errors over the region through the covariance matrix being tuned by observations taken at the reference stations at different location, different time, different season and solar cycle.

Pre-assessment of the Performance

• The covariance function used by the NetAdjust method can also be used to determine the covariance matrix of the corrected measurements.

• It provides a means to predict the performance of the NetAdjust corrections, without having the measurements available (Raquet, 1998).

State Space Approach

State Space Approach• Developed by Geo++® GmbH • State Monitoring And Representation Technique

(SMART) to analyze the data from a reference station network to estimate and represent the state of individual components of the GPS error budget in real-time.

• Instead of generating just one lumped parameters, the state of each error component is determined from observations of a network of reference stations. (Wübbena, et al. , 2001b)

GMSMART- Error Modelling• Individual modelling of orbit, ionosphere, and tr

oposphere.• Multipath effects – determined in the simultane

ous adjustment and complete modeling of multi-station observations.

• Antenna phase center variations (APCV) – corrected by using calibrated antennas. This enables the use of different antenna types within a network.

• Complete model for satellite receiver clocks.• Aims to completely model the absolute stat

e of the system with carrier phase accuracy (GNSS State Monitoring and Representation Technique).

Modelling Undifferenced Data

• Undifferenced observation data is used in modelling of errors.

• It was considered that the differencing process eliminates not only the clock error and time delays of the hardware, but also operates on all other error sources. The consequence is that all absolute error effects are eliminated and only their differences remain in the system. However, the modelling of such differences becomes markedly harder than the modelling of undifferenced effects.

Parameters of GNSMART

• The determination of system state information in a GNSS SMART system need not take place in one continuous stream

• parameters of global character, e.g. satellite orbits and clocks drawn from global networks

• regional parameters e.g. wide-area ionospheric delay effects, local ionospheric disturbances and tropospheric effects drawn from regional and local networks respectively.

Figure: Linear FKP planes for four reference stations

(source: Wübbena, 2001a)

Trimble’s Virtual Reference Station Method

VRS – General

• Developed by Trimble Terrasat• 4 steps in the generation of VRS

Error modelling

Network Ambiguity Fixing

Reference Data Dispplacement

Error (Correction) Interpolation

Trimble’s VRS Approach (1)

• Data from the reference station network is transferred to a computing center

• The network data is used to compute models of ionospheric, tropospheric and orbit errors

• The carrier phase ambiguities are fixed for the network baselines

• The actual errors on the baselines are derived in cm accuracy using the fixed carrier phase observations

Trimble’s VRS Approach (2)

• Linear or more sophisticated error models are used to predict the errors at the user location

• A Virtual Reference Station (VRS) is created at the user location

• The VRS data is transmitted to the user in standard formats (RTCM).

(Vollath , et al, 2000,2002a)

VRS - Error modellingError modelling at 3 different levels• Removal of coarse code outliers, coarse

carrier phase fluctuations and cycle slips by comparing the pseudorange and carrier phase measurements

• Use single difference of baseline observations between two stations to remove the common satellite clock error

• Use single layer ionospheric model and tropospheric scaling technique to model the atmospheric errors on undifferenced data each station.

VRS - Network Ambiguity Fixing

• The ambiguity estimates NI from ionosphere model and NC from troposphere model could be mapped back into the original N1/N2 domain of the integer ambiguities of the basic carrier phase observables on L1 and L2 with the following equation:-

where and are the integer ambiguity and wavelength of the L1 and L2 carrier phase measurements respectively

21, NN 21 ,

VRS - Reference Data Displacement• To make the transmitted data look like it came fr

om a different position, it has to be displaced geometrically.

• The pseudorange between the satellite and the virtual reference station can be approximated by

the appprox.pseudorange between satellite and the virtual reference station

the pseudorange between satellite and the original

reference station

the appprox. geometric range between satellite and the virtu

al reference station

the exact geometric range between satellite and the original reference station

VRS - Error Interpolation

• The differential errors between the 3 stations of the triangle selected are used to set up a linear model.

• One station of a triangle is selected as pivotal station, with coordinates.

• The double differences between the stations can be interpolated with the formula:

rrECrNCc PP cos)()(),( ,,

Lat./ Long Interpolation parameter

Figure 4: Linear Interpolation Error

VRS - Error Interpolation• The differential errors between the 3 stations

of the triangle selected are used to set up a linear model.

• Carrier phase measurements on ionosphere on the ionospheric-free combination are handled separately. One station of a triangle is selected as pivotal station, with coordinates . The double differences between the station can be interpolated with the formula:

),( rr

rrECrNCC PP cos),( ,,

VRS – Error Interpolation• Given the double differences to the other two

triangle stations and , the interpolation parameters for the north direction and for east are defined by the equation:

• To interpolate or extrapolate, the formula above is applied to the Virtual Reference Station coordinates .

rrECrNCC

cos),(

2,2,12

1,1,11

),( 11 ),( 22

NCP , rECP ,

B R E A K

The Project

Contents(The Project Investigation)

• Is VRS accurate? reliable? and robust?• What constitutes a sound or weak VRS?• Does VRS improve Static GPS? In terms of

accuracy and reliability.• Does VRS improve RTK? In terms of

accuracy, reliability, robustness and speed.• What are the crucial factors affecting the

accuracy and performance of VRS? Could the problem be resolved?

• Practical Issues for Implementation.

The Objectives

• Does VRS improve the performance of GPS?

- in both Static GPS and RTK

• Does VRS provide a better solution than Single Reference Station under all circumstances?

What to investigate ?– Compare the Performance• What are the performances of the

single reference station, multiple reference stations and VRS for relative positioning, in terms of accuracy, reliability, robustness and speed? Does VRS provide a solution better than the other two methods?

What to investigate ?– Temporal Changes

• Any temporal change to performance of the single reference station, multiple reference stations and VRS methods, in terms of accuracy, reliability, robustness and speed?

What to investigate ?– Factors affecting Performance

• What constitute a sound or weak VRS? What are the crucial factors affecting the VRS performance?

Design of the tests• Positional accuracy

achieved by the VRS achieved by single/ multiple reference station methods

• Change of Positional Accuracy single reference station, multiple reference stations and VRS at different time of observations

Figure: The Test Site

Fanling

Shatin

Kam Tin

Lam Tei

Siu Lang Shui

Stonecutter0 5 10 km

Software

• Trimble Total Control - release 2.7.3 with the modules of Network Adjustment and Post-processing VRS

• The software could simulate real-time and post-processing operations with functions that control the use of observation data by different time and processing mode settings.

The Test Control

The control• 5 stations including Fanling, Kam Tin, Lam Tei

and Siu Lang Shui were surveyed on 8-15 Oct 2000. The other station at Stonecutter was surveyed on 10-18 Oct 2002.

• The coordinates were determined by using observations from two stations, Fanling and Kau Yi Chau with respect to 6 IGS stations, including Cocos Islands (Indian Ocean), Guam (Pacific Ocean), Lhasa (Western China), Shanghai (Eastern China), Tsukuba (Japan) and Yarragadee (Australia).

• 2 months of data, ITRF 96, GAMIT software processing. The repeatability of the solution (global accuracy) is 2-3cm.

Purposes of Re-computation of Control Pt Coordinates

• To know if the published values are suitable to be adopted as control in the test.

• To know the difference of the results of static long observation (14 days) as compared to the published values.

• So as to know if the difference between test results (Static GPS and RTK) and the published values are significant.

Station Name

Recomputed Coordinates(weighted mean of resultsfrom 14-day observations)

Different from Published

Values (mm)Sigma (mm)

Latitude Longitude Height (m) Lat Long Ht Lat Long Ht

Fanling N 22° 29' 40.87008''

E 114° 08' 17.40609''

41.2100 0 0 0 - - -

Kam Tin N 22° 26' 41.66172''

E 114° 03' 59.63442''

34.5731 -6.0 4.5 9.1 0.7 0.3 2.0

Lam Tei N 22° 25' 05.28288''

E 113° 59' 47.84457''

125.9356 4.8 7.5 0.6 1.3 1.6 3.2

Stonecutter

N 22° 19' 19.81947''

E 114° 08' 28.27638''

20.2388 -0.9 -2.7 11.8 1.3 1.0 1.9

Siu Lang Shui

N 22° 22' 19.21710''

E 113° 55' 40.73309''

95.2910 5.7 9.3 -12.0 1.5 0.6 3.1

Shatin N 22° 23' 42.97460''

E 114° 11' 03.27037''

258.7420 6.6 4.5 26.0 1.1 0.4 2.9

Table: Comparison between the Published and Re-computed Coordinates

Static GPS Positional Accuracy

by differentref. station approaches

Does VRS improve Static GPS?

• Compare positional accuracy by

single RS (Fanling 9.2 km)

multiple RS (Fanling, Shatin, Lam Tei)

• Use 1 hour data (static GPS)

• 24 sets of results (any temporal change)

Table: Results of Static GPS1 hour observation data (1)

Local TimeSingle RS Multi RS VRS

Lat Long Ht Lat Long Ht Lat Long Ht

08:00 – 09:00 -14 -10 3 -4 -8 7 -4 -3 2309:00 – 10:00 -14 -9 1 -7 -9 6 -9 -4 1910:00 – 11:00 -23 -10 3 -12 -6 5 -9 -4 1411:00 – 12:00 -18 -13 4 -11 -6 11 -10 -5 2212:00 – 13:00 -103 11 -39 -8 5 -27 -14 -6 1113:00 – 14:00 -12 -3 9 -5 9 14 -10 0 27

14:00 – 15:00 -95 65 -129 17 -19 13 -1 -8 5

15:00 – 16:00 -99 -35 -39 -7 5 -20 -9 -48 65

16:00 – 17:00 -5 -8 3 2 0 19 - - -17:00 – 18:00 -4 -9 -6 17 -17 31 -2 -10 10

18:00 – 19:00 -9 -9 -1 12 -11 0 -10 -4 20

19:00 – 20:00 -11 -13 122 -13 -1 84 -8 -1 9

Table: Results of Static GPS 1 hour observation data (2)

Local TimeSingle RS Multi RS VRS

Lat Long Ht Lat Long Ht Lat Long Ht

20:00 – 21:00 83 216 -62 22 12 36 - - -

21:00 – 22:00 -8 -2 -1 -4 -9 10 -3 -1 222:00 – 23:00 -13 -7 1 -5 -7 -2 -13 -4 22

23:00 – 24:00 71 66 117 -6 -9 -3 -8 -7 900:00 - 01:00 -8 0 -2 12 2 -8 -2 -5 9

01:00 - 02:00 -5 -14 -4 9 -2 10 -7 -6 18

02:00 - 03:00 -31 -1 -11 -3 -4 4 -6 -4 2103:00 - 04:00 -17 -6 -20 -1 -5 17 -3 0 3404:00 – 05:00 -9 -7 8 -1 -3 13 -4 -1 2005:00 – 06:00 -9 -5 18 -2 -5 13 0 2 14

06:00 – 07:00 -10 -11 30 -2 -11 20 -7 -3 24

07:00 – 07:59 -17 -10 22 -5 -8 11 -8 -4 20

Static GPS – Performance and Quality of Single

Reference Station Method

• Single Reference Station

– Max. deviations 10 cm in latitude22 cm in longitude13 cm in height.

– 75% of the results deviate from the truth by < 3 cm in horizontal,<3 cm in height.

Static GPS – Performance and Quality of Multiple

• Multiple Reference Station

– 100% of the lat/long results deviate from the truth by < 2.5 cm

– 96% of the height displacements from the truth by < 3.5 cm

Static GPS – Performance and Quality of Multiple

• Virtual Reference Station

- Max. deviation from truth by< 1.5 cm in lat./long< 3.5 cm in height

- Positional accuracies < 2 cm (1σ) in lat/ long< 2.5 cm (1σ) in height.

Static GPS — Performance and Quality of the VRS Method (1)

• For static GPS using one-hour dual frequency data, VRS could only be generated at certain time (midnight and morning sessions) of a day with the use of all satellite signals;

• The failure of VRS generation was due to the problem of network ambiguity fixing. Disabling of 1 or more satellite signals would help fixing the network ambiguity and improve the generation of VRS;

• With the suppression of selective satellite signals, 21 out of 24 hourly sessions could generate ‘an effective VRS’ that contains 5 or more satellite data

• With ‘an effective VRS’Max. deviation from truth< 1.5 cm in lat./long ;< 3.5 cm in heightPositional accuracies < 2 cm (1σ) in lat/ long ; < 2.5 cm (1σ) in height.

• A systematic bias : a few cm was found. All results deviate from the truth in the same southerly (lower latitude), westerly (lower value in East longitude) and upper (higher elevation) directions of the truth. This might be due to the known coordinates of the reference stations or other reasons. A good control of this bias is necessary to ensure the quality of the VRS solution.

Static GPS – Performance and Quality of the VRS Method (2)

Note this

magnitude

A Sound VRS for Static GPS

• With signals of at least 5 satellites generated.

• With sufficient VRS data (continuous)

• Positional accuracy of 2 cm (1σ) in lat/ long can be achieved in static GPS (1 hour observation)

What constitutes a Weak VRS or even

Failure in VRS Generation ?

Investigate the Causes of Failure in VRS generation

• Two tests were conducted on using data of carefully planned time differences.

• Period of GPS satellites :11 hours and 58 minutes. Two series of tests were carried out using data of 15 days (1 hour shift) and 157 days (10 hours 30 minutes shift) later respectively.

• The results of static GPS using hourly data with the method of VRS on 20 April 2003 and 9 September 2003.

Table: VRS Investigation Results (1)

VRS2,16Y13:32 – 14:32VRSN/A23:00 – 24:00VRSN/A00:00 - 01:00

VRSN/A12:32 – 13:32VRSN/A22:00 – 23:00VRS25Y23:00 – 24:00

VRSN/A11:32 – 12:32VRS-N/A21:00 – 22:00VRS25Y22:00 – 23:00

VRSN/A10:32 – 11:32VRS-N/A20:00 – 21:00VRS5Y21:00 – 22:00

VRSN/A09:32 – 10:32VRS-N/A19:00 – 20:00--Y20:00 – 21:00

VRSN/A08:32 – 09:32VRS10,14,23Y18:00 – 19:00VRS17Y19:00 – 20:00

-Y17:00 – 18:00VRS9Y18:00 – 19:00

VRS9,10,21Y16:00 – 17:00VRS-N/A17:00 – 18:00

Y15:00 – 16:00VRS26Y16:00 – 17:00

Y14:00 – 15:00VRS4,10Y15:00 – 16:00

VRS-N/A13:00 – 14:00VRS10Y14:00 – 15:00

VRS-N/A12:00 – 13:00VRS7Y13:00 – 14:00

VRS-N/A11:00 – 12:00VRSN/A12:00 – 13:00

VRS-N/A10:00 – 11:00VRSN/A11:00 – 12:00

-N/A09:00 – 10:00VRSN/A10:00 – 11:00

-N/A08:00 – 09:00VRSN/A09:00 – 10:00

VRSN/A08:00 – 09:00

SV #Y/NSV #Y/NSV #Y/NSol’n

Need todisable SV?9 SeptSol’n

Need todisable SV?20 AprilSol’n

Need to disable SV?5 April

Remarks:- Periods of no VRS or VRS with less than 5 satellites are highlighted

Table: VRS Investigation Results (2)

VRSN/A06:28 – 07:28VRS9,10,21Y16:00 – 17:00VRS17:00 – 18:00

VRSN/A05:28 – 06:28

VRSN/A04:28 – 05:28

--Y15:00 – 16:00VRS26Y16:00 – 17:00

VRS26Y14:00 – 15:00VRS4,10Y15:00 – 16:00

VRSN/A03:28 – 04:28VRS-N/A13:00 – 14:00VRS14:00 – 15:00

VRSN/A02:28 – 03:28VRS-N/A12:00 – 13:00VRS13:00 – 14:00

VRSN/A01:28 – 02:28VRS-N/A11:00 – 12:00VRS12:00 – 13:00

VRSN/A00:28 – 01:28VRS-N/A10:00 – 11:00VRS11:00 – 12:00

VRSN/A23:28 – 00:28VRS-N/A09:00 – 10:00VRS10:00 – 11:00

VRSN/A22:28 – 23:28VRS-N/A08:00 – 09:00VRS09:00 – 10:00

VRSN/A21:28 – 22:28VRSN/A06:56 – 07:56VRS08:00 – 09:00

VRSN/A20:32 – 21:32VRSN/A06:00 – 07:00VRSN/A07:00 – 07:59

31,VRS13,15,20,25Y19:32 – 20:32VRSN/A05:00 – 06:00VRSN/A06:00 – 07:00

VRS11,15,27Y18:32 – 19:32VRSN/A04:00 – 05:00VRSN/A05:00 – 06:00

VRSN/A03:00 - 04:00VRSN/A04:00 – 05:00

VRS13,14,31Y16:32 – 17:32VRSN/A02:00 - 03:00VRSN/A03:00 - 04:00

VRS1,3,6,14Y15:32 – 16:32VRSN/A01:00 - 02:00VRSN/A02:00 - 03:00

--Y17:32 – 18:32

--Y14:32 – 15:32VRSN/A00:00 - 01:00VRSN/A01:00 - 02:00

VRS2,16Y13:32 – 14:32VRSN/A23:00 – 24:00VRSN/A00:00 - 01:00

SV #Y/NSV #Y/NSV #Y/NSol’n

Need todisable SV?9 SeptSol’n

Need todisable SV?20 AprilSol’n

Need to disable SV?5 April

Remarks:- Periods of no VRS or VRS with less than 5 satellites are highlighted

The Causes of Failure in VRS generation

• The weak VRS solution (not being able to generate VRS with 5 satellite signals) not due to the satellite configuration.

• Weak VRS all happened in the afternoon and/or early evening.

• Inspect the VRS observation data file

No. of satellite plots of the VRS file

Satellite elevation plot of the VRS file

The Causes of Failure in VRS generation

• The weak VRS solution (not being able to generate VRS with 5 satellite signals) not due to the satellite configuration.

• Weak VRS all happened in the afternoon and/or early evening.

• Inspect the VRS observation data file

• Inspect the Network Ambiguity Fixing

What constitutes a Sound VRS?

• The stringent requirements of network ambiguity fixing provide an effective means for the quality control of the satellite signals to be used for the generation of VRS make the VRS solution more reliable.

• Satellite signals that could not resolve the baseline ambiguity might to certain extent be contaminated by multipath effects, atmospheric disturbances or other effects. Such satellite signals, failed in network ambiguity fixing, would not be used in the generation of the VRS.

Baseline Ambiguity Resolution(with all satellite signals)

Sessions of observa

tion(local time)

Ambiguity Resolution ofDifferent Baselines

VRS generated after selective disabling

Shatin/Lam Tei

Fanling/ Lam Tei

Fanling/ Shati

Yes/No

SV disabled

13:00 – 14:00

Float LIF Fixed LIF Fixed LIF Y 7

14:00 – 15:00

Fixed LIF Float LIF Float LIF Y 10

15:00 – 16:00

Float LIF Float LIF Float LIF Y* 4,10

16:00 – 17:00

Fixed LIF Fixed LIF Float LIF Y* 26

18:00 – 19:00

Fixed LIF Fixed LIF Float LIF Y 9

19:00 – 20:00

Float LIF Fixed LIF Float LIF Y 17

20:00 – 21:00

Fixed LIF Float LIF Float LIF N -

21:00 – 22:00

Float LIF Fixed LIF Fixed LIF Y 5

22:00 – 23:00

Fixed LIF Fixed LIF Float LIF Y 25

23:00 – 24:00

Fixed LIF Float LIF Fixed LIF Y 25

Critical examination of the observation data for the

cause of failure in Network Ambiguity Fixing

• As the Fanling/Shatin baseline has the most serious problem in ambiguity fixing, the corresponding 7 sessions of observations with unfixed ambiguity were selected for examination and analysis of the causes of failure in ambiguity fixing.

Critical examination of the observation data

• Double difference L1 carrier phase residual detects cycle slips, noise remaining after double difference L2 is often with more noise than L1.

• Double difference range residual cycle slips, multipath, ionospheric effect and other measurement noises that have different amount of influence on code and carrier phase measurements.

• Double difference ionospheric residualshow the magnitude of ionospheric residuals of a baseline observation not being cancelled out double difference.

Critical examination of the observation data

Double Difference Phase Residuals –On 5 April 2003At local time 19:00 – 20:00(Ref: SV09) Double Difference Range Residuals –On 5 April 2003At local time 19:00 – 20:00(Ref: SV09) Double Difference Ionospheric Residuals On 5 April 2003At local time 19:00 – 20:00(Ref: SV09)

Analysis by Stacking Results on Consecutive Days of Observations

• The stacking results of static positioning at consecutive days of observations would show the same pattern if multipath exists under certain satellite-receiver geometry and the signals pass through the same atmospheric conditions.

Stacking Results on Consecutive Days of Observations

Factors affecting the VRS Performance (1)

• The network ambiguity fixing is found to be the first and most stringent requirement to meet in generating the VRS.

• Fixing the network ambiguity is a real challenge even for short base of 10 km in the Hong Kong environment.

• Elevation angles of satellite signals, multipath effects, decorrelated ionospheric effects and decorrelated tropospheric delay bias at the reference stations are found to be the most important factors.

Factors affecting the VRS Performance (2)

• In general, signals at low elevations up to 25o would be more seriously affected by tropospheric, ionospheric and multipath effects.

• The ionospheric effects on satellite signals were not prominent after double differencing (in this test project). Most of the double difference ionospheric residuals are less than 0.5 cycle.

• Ionosphere scintillation effects in the near-equatorial regions are at approximately 1 hour after local sunset to local midnight might account for the problems of network ambiguity fixing in the evening sessions until midnight.

Findings - for generating an effective VRS

• network ambiguity fixing is an important process in the generation of VRS

• the VRS observation data file must be with sufficient data sufficient number of satellites at the same epoch. 4 satellites are required for static GPS whilst 5 satellites are needed in RTK processing continuity of data for a certain period of time. (Observation data in a VRS file discontinuous with gaps not being able to serve as a functional VRS for static or kinematic GPS surveys.)

Factors affecting the Network Ambiguity Fixing

• Satellite geometry• Elevation angles of satellite signals• Multipath effects• Cycle slips and other signal noises• Decorrelated ionospheric effects at the reference

stations• Decorrelated tropospheric delay bias at the reference

stations• Decorrelated effects of the orbit errors at the

reference stations• Antenna phase centre variation is not included for the

same type of choke ring antenna was used in all reference stations of this project.

Factors affecting the VRS performance

• Network ambiguity fixing• Accurate known coordinates of the reference stations• Station-dependent errors such as multipath (if not rejected

in network ambiguity resolution and the VRS generation process) would be absorbed in the interpolation errors and become errors on the correction parameters.

• Meteorological information at the unknown station would significantly affect the resulting coordinates of the unknown station in the VRS methods with the use of tropospheric model.

Effect of Meteo Data

Deviated from Published Values (mm)

Lat Long Ht

-9 -4 14

Temperature Change Humidity Change

+2.5 °C -16 -2 -37 +5% -7 -5 39

+5 °C 4 -5 118 +10% -2 -4 57

+10 °C 9 14 251 +20% 4 -5 98

-2.5 °C -1 -5 64 -5% -12 -3 -11

-5 °C -19 19 -96 -10% -16 -2 -36

-10 °C -25 41 -181 -20% -19 20 -101

Temperature and Humidity Change

+5 °C +5% 13 6 150+5 °C +20

%11 10 226

+5 °C +10% 5 1 166

Same Temperature & humidity

Effect of temperature and humidity change (at the unknown station) on the positional accuracy

Effect of Inaccurate Meteo Data

• Inaccurate meteorological information

be absorbed in the error modelling at the reference stations and affect the resulting coordinates of the unknown station through the process of error interpolation

lead to failure in network ambiguity fixing and problem in the generation of VRS under the Trimble’s algorithm

Does VRS improve RTK ?

• Compare RTK positional accuracy by single RS (Fanling 9.2 km) VRS

• Compare TTFA single RS (Fanling 9.2 km) VRS

• Assess the time required for VRS generation for RTK (with 5-minute backward data)

Two series of testsSingle-base RTK• at every 5 minutes, local time 8:00 - 10:00

(continuous performance)• at every 30 minutes for the whole day

(change of accuracy at different time and conditions of a day)

VRS-RTK• at every 5 minutes, local time 08:00 - 14:00

(continuous performance and the behaviour of VRS generation)

• at every 30 minutes for the remaining hours of the day

Single-base RTK Positioning (2 hrs)Latitude Shift - Single-base RTK

(favourable atmospheric conditions)

-100-80-60-40-20

020406080

Local Time 5 April 2003 (2 hrs)

+ Sigma

Latitude

- Sigma

Longitude Shift - Single-base RTK(favourable atmospheric conditions)

-30-25-20-15-10-505

101520

+ Sigma

Longitude

- Sigma

Height Displacements - Single-base RTK(favourable atmospheric conditions)

-150-130-110-90-70-50-30-101030507090

110130150

+ Sigma

Height

- Sigma

VRS-RTK Positioning (4.5 hrs)Latitude Shift - VRS-RTK

(favourable atmospheric conditions)

-40-35-30-25-20-15-10-505

101520

Local Time 5 April 2003 (4.5 hrs)

+ Sigma

Latitude

- Sigma

Longitude Shift - VRS-RTK(favourable atmospheric conditions)

-20-15-10-505

101520

+ Sigma

Longitude

- Sigma

Height Displacements - VRS-RTK(favourable atmospheric conditions)

-40-30-20-10

010203040506070

+ Sigma

Height

- Sigma

Findings: single-base RTK vs VRS-RTK under favourable atmospheric conditions

• Single-base-RTK< 7cm Lat , 2 cm Long< 10 cm in height

• VRS-RTK: < 2 cm Lat & Long.< 4 cm height from the truth.

• The VRS-RTK is more reliable and consistent in achieving high positional accuracy under the favourable atmospheric conditions, even during the periods with time slots of PDOP=8 (due to correction already built in the VRS)

• a systematic shift was found in the test results of the VRS-RTK method. This bias must be controlled to ensure high accuracy results.

Local Time

NoofSV

TTFA (s) Local Time

NoofSV

TTFA (s)Single- base RTK

VRS-RTK Single- base RTK

VRS-RTK

08:05 6.3 5 8 7 09:05 2.1 7 4 4

08:10 7.6 5 11 5 09:10 2.1 7 4 4

08:15 8.6 5 8 9 09:15 2.7 6 4 4

08:20 8.4 5 8 10 09:20 2.9 6 4 5

08:25 2 6 6 14 09:25 3.2 6 4 4

08:30 2.1 6 7 4 09:30 3.4 6 4 4

08:35 2.1 6 4 4 09:35 2.7 7 4 4

08:40 1.8 7 6 4 09:40 2.9 7 5 5

08:45 1.8 7 4 4 09:45 3.1 7 4 4

08:50 1.9 7 4 4 09:50 3.2 7 4 4

08:55 1.9 7 4 4 09:55 3.2 7 4 4

09:00 2 7 4 4 10:00 3.2 7 4 4

Results of TTFA single-base RTK and VRS-RTK

Findings: TTFA by using single-base RTK and VRS-RTK• The time to fix ambiguity (TTFA) in both

single-base-RTK and VRS-RTK methods under favourable atmospheric conditions are more or less the same.

• TTFA within 4 seconds in either method.• Both methods indicate that a longer TTFA

would be required as PDOP > 4 or number of satellites < 6. However, this relationship does not hold under the unfavourable atmospheric conditions of observations in the afternoon and evening.

Single-base RTK Positioning (24 hrs)Latitude Shift - Single-base-RTK

Local Time 5 - 6 April 2003 (24 hrs)

+ Sigma

Latitude

- Sigma

Longitude Shift - Single-base-RTK

-250-200-150-100-50

100150200

+ Sigma

Longitude

- Sigma

Height Displacements - Single-base-RTK

-450-400-350-300-250-200-150-100-50

100150200250300350400

+ Sigma

Height

- Sigma

VRS-RTK Positioning (24 hrs)Latitude Shift - VRS-RTK

-50-45-40-35-30-25-20-15-10-505

101520

+ Sigma

Latitude

- Sigma

Longitude Shift - VRS-RTK

-30-25-20-15-10-505

101520

+ Sigma

Longitude

- Sigma

Height Displacements - VRS-RTK

-50-40-30-20-10

01020304050607080

+ Sigma

Height

- Sigma

Table: Compare the Overall Performance of Single-base RTK & VRS-RTK

Latitude/ longitude shift(shift +/-2 sigma)

No. of cases (tests)Single-

base RTKVRS-RTK

0 – 30 mm 6 5

31 – 60 mm 19 12

61 – 100 mm 6 6

101 – 200 mm 4 0

200 – 500 mm 5 0

> 500 mm 5 0

No RTK solutions 3 25

Findings: Overall Performances of Single-base RTK & VRS-RTK

• Both methods have 5 to 6 results (1.2%) that can achieve a high accuracy of less than 3 cm deviation from the truth at 95% level of confidence (2 sigma).

• All VRS-RTK solutions < 10 cm (2 sigma) shift from the truth.

• 55% (25/45) of the single-base-RTK solutions shift from the truth < 10 cm (2 sigma).

• Single-base-RTK continues to provide solutions under unfavourable conditions (need 1-2 minutes in ambiguity fixing)

• VRS-RTK stopped to provide the low accuracy solution in unfavourable conditions.

Table: Successful VRS generation using hourly data of all satellite data

Local Time(Hourly

sessions)

Any VRS (with 5 or more satellites) be generated

by using all satellite data?

08:00 – 13:00 Yes

13:00 – 17:00 No

17:00 – 18:00 Yes

18:00 – 00:00 No

00:00 - 08:00 Yes

Table: Time required for VRS generation using raw data

Local Time

Time for VRS

generation

Any VRS file with 5 or more satellites

generated? (Yes/ No)

08:00- 12:10 5 s Yes

12:15 – 12:30 5 - 18 sYes

12:35 – 00:00> 5 s

(up to > 1 hr)

00:30 – 07:30 5 s Yes

Table: Start an End Time of VRS generation under adverse conditions

No213:5012:436713:50

No313:4512:436213:45

No313:4012:435713:40

No313:3512:435213:35

No313:3012:434713:30

No313:2512:434213:25

No413:2012:443613:20

No413:1512:443113:15

No413:1012:442613:10

No313:0012:293113:00

No312:5512:292612:55

No312:5012:292112:50

No312:4512:291612:45

Yes512:2512:071812:25

Yes512:2012:071312:20

Yes512:1512:07812:15

End TimeStart Time

Able to provide

RTK solution?

No. of satellites in the VRS

VRS GenerationTime to generate

VRS (mins)

Local Time

Table: Time to Generate VRS-RTK

259823-5-9553.11 second12:00

21110-4-10753.01 second11:00

185511-4-9473.21 second10:00

83432-5-3472.01 second09:00

3051731-331355.21 second08:01

HtLongLatHtLongLat

Sigma (mm)Diff from Published

Values (mm)

TTFA (s)

No Of SV

Time to

GenerateVRS

(mins)

LocalTime

Time required for VRS generation

• The test results show that the increase of the observation time does not help improve the VRS generation.

• The successful generation of VRS depends on the network ambiguity fixing that can only be possible with satellite signals not adversely affected by multipath, atmospheric bias and other noises remained after double differencing.

• Even 1 second of data could generate a correct VRS under favourable atmospheric conditions.

Practical Issues for Implementation

of Network-RTK

Practical Issues for Implementation

• RTCM format for data transmission• Choice of Ephemeris data• Effect of Meteorological Data • Understand different effects on GPS

measurements• :• :

GPS Data Transmission

• RTCM (Radio Technical Commission for Maritime) Services Special Committee 104 v 2.2

• Initially format for DGPS messages (v 2.1)• DGPS corrections include:- ephemeris errors,

SV clock prediction errors, ionospheric biases, tropospheric biases, differential tropospheric delay errors

Fixed RTCM Messages (1 … 12)

1 Differential GPS corrections

2 Delta Diff GPS Corrections

3 GPS reference station parameters

5 GPS constellation health

6 GPS null frame

7 DGPS beacon almanac

9 GPS partial correction set

10 P-code differential corrections

11 C/A code Ld Delta corrections

12 Pseudolite station parameter

Fixed RTCM Messages (15 … 59)

15 (T) Ionospheric Delay Message

16 GPS Special Message

17(T) GPS Ephemerides

18 RTK uncorrelated carrier phases

19 RTK uncorrelated pseudoranges

31-37 GLONASS Diff Message

59 Propriety Message

Choice of Ephemeris data

Broadcast 2.6 m

Predicted Ultra-Rapid (12 hrs ahead) 0.25 m

The importance of Meteo Information at RS and Rover

• Different meteorological information would lead to different amount of corrections made by the tropospheric model to the GPS measurements.

• As advised in (Hugentobler, et al., 2001: p. 195), the surface meteorological information and tropospheric parameters are important except for those areas with network < 10km diameter and height differences <100 metres.

Scintillation effects• Klobuchar (1996) – “the time of strong

scintillation effects in the near-equatorial regions are at approximately 1 hour after local sunset to local midnight.” Hong Kong is inside the near-equatorial region of maximum scintillation.

• “Precise GPS measurements should be avoided during the approximate local time 19:00- 24:00 (in the near-equatorial region) during the year of high solar activity, and during the months of normally high scintillation activity (April to August for Hong Kong) to reduce the chance of encountering scintillation effects.

The Atmosphere (1)20,200 km

350 km

120 km

GPS Satellites

IONOSPHERE

Thermosphere

Mesosphere

Stratosphere

TROPOSPHERE (water vapour & gas)

The Atmosphere (2)

20,200 km GPS Satellites

IONOSPHERE

Thermosphere

Mesosphere

Stratosphere

TROPOSPHERE (water vapour & gas)

350 km

Quoted Examples on Network-RTK

Current GNSMART NetworksProduction:• Dubai – 5 stations• WALCORS, Belgium – 23 stations• COSMOS, Russia – 7+19 stations• OSI, Ireland – 16 stations• LGTB, Switzerland – 6 stations

Evaluation:• Ordnance Survey GB – 23 stations• Italy - Milan; Turin• Hong Kong

Our Challenges

Key Skills ( extracted from GNSS Applications & Market, IESSG lecture notes)

• Knowledge of GPS and Galileo• Knowledge of Regional and Local Augmentation

System• Awareness of other ‘position’ sensors, e.g. INS• Ability to integrate Satellite Navigation with other s

ensors• Awareness of communication options thru’ terrestri

al, satellite, local and global aspects• Ability to develop Combined positioning/communic

ation systems• Knowledge of Key Markets and Applications

Open Discussions

investigations about the vrs methodology for network-rtk within a local area presented by:ben chan...

carrier phase ambiguity

carrier phase measurements

reference station rs

performance of vrs

accuracy of baselines

terms of accuracy

rtk operationwhat

vrs methodology

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