Part Va

Centimeter-Level Instantaneous Long-Range RTK:

Methodology, Algorithms and Application

GS894G

Presentation outline

Research Objectives

Methodology

Experiments and Test Results

Newest developments: algorithmic updates

Summary and Outlook

Research objectives

Performance analysis of ionosphere modeling techniques, derived from GPS permanent tracking network data

• Local

• Regional

• Global ionospheric models

Feasibility test for ambiguity resolution (AR) in long-range RTK applications

Instantaneous

OTF (on-the-fly)

Study the impact of the model’s accuracy on the positioning results

Study of the impact of the ionospheric conditions on the positioning results

Methodology

Compute the reference “truth” ionospheric corrections

Compute model-based corrections

Compare against the reference “truth”

Use model-based corrections to fix ambiguities

On-the-fly (OTF)

Instantaneously

Perform long-range kinematic positioning using model-based corrections interpolated to the user location

Compare AR success ratio

Compare positioning accuracy

Derive performance metrics for long-range RTK GPS

Quiet ionosphere

Active ionosphere

Methodology: the ionospheric models

MPGPS-NR — Network (NR) dual-frequency carrier phase-based model, decomposed from DD ionospheric delays

single layer

local – uses reference stations within 100-200 km from the rover

ICON — Absolute model based on undifferenced dual-frequency ambiguous carrier phase data

single layer

regional (~340 CORS stations)

MAGIC — Tomographic model using pseudorange-leveled L1-L2 phase data

3D

regional (~150 CORS and IGS stations)

IGS GIM — International GPS Service (IGS) global ionospheric map (GIM)

single layer

global (~200 stations)

Methodology:ICON and MAGIC models (NGS)

Derived for the continental United States

Provide the ionospheric information for all GPS satellites with a three-day delay

Both models are prototypes

Available to the general public at:

http://www.noaanews.noaa.gov/stories2004/s2333.htm

1. Smith, D.A. (2004), Computing unambiguous TEC and ionospheric delays using only carrier phase data from NOAA´s CORS network, Proceedings of IEEE PLANS 2004, April 26-29, Monterey, California, pp. 527-537.

2. Spencer, P.S.J., Robertson, D.S. and Mader, G.L. (2004), Ionospheric data assimilation methods for geodetic applications, Proceedings of IEEE PLANS 2004, Monterey, California, April 26-29, 2004, pp. 510-517.

Methodology: MPGPS™ - Multi Purpose GPS Processing software (OSU)

Modules

Long-range instantaneous and OTF RTK

Precise point positioning (PPP)

Multi-station DGPS

Local ionosphere modeling and mapping

Troposphere modeling

Operational modes: static, rapid-static, kinematic, instantaneous (single and multi-baseline)

The MPGPS™ software was used to derive the “true” DD ionospheric delays (MPGPS-L4) and the network RTK corrections (MPGPS-NR)

Mathematical model: network

1, 1 1,

2 22, 1 2 2 2,

1,

2,

( ) 0

( ) ( / ) 0

( ) 0

(

kl kl k l k l kl klij ij i i i i j j j j ij ij

kl kl k l k l kl klij ij i i i i j j j j ij ij

kl kl k l k l klij ij i i i i j j j j ij

kl kl k l kij ij i i i i j

T T T T I N

T T T T f f I N

P T T T T I

P T T

2 21 2) ( / ) 0l kl

j j j ijT T f f I

- receiver indexes - satellite indexes- DD phase observation on frequency n

(n=1,2)- DD code observation on frequency n- DD geometric distance - Total zenith delay (TZD)- troposphere mapping function- DD ionospheric delay- GPS frequencies on L1 and L2- GPS frequency wavelengths on L1 and L2- carrier phase ambiguities

,i j

,k l

,kln ij

,kln ijP

klij

,i jT

kiklijI

1 2,f f

1 2,

1, 2,,kl klij ijN N

• Sequential generalized least squares model

• DD ionosphere estimated from L4 combination every epoch after the ambiguities are fixed

• Decomposed to undifferenced iono

• TZD estimated every 2 hours per station

• Stochastic constraints on tropo and iono

• Reference coordinates fixed

• Integer ambiguity resolution

• LAMBDA method

• W-ratio to verify integer selection

Mathematical model: rover positioning

Mathematical model used for rover positioning is the same as for the network, but

• Ionosphere and troposphere are compensated from external models

Stochastic constraints are used on external corrections

LAMBDA AR method and W-ratio

Instantaneous (single-epoch) AR and rover positioning supported by external iono, or

Initial OTF AR using external ionosphere

• Processing continues in the instantaneous mode

Iono is predicted from the previous epoch

• May continue OTF for the entire rover positioning period

Rover positioning: single- or multi-baseline solution

Experiments - test data and model

Ohio CORS, August 31, 2003

24-h data set was processed in 12 sessions of 2-h

30-s sampling rate

different reference satellite for each session

varying ionospheric TEC levels

max Kp index = 2o

varying GPS constellation

KNTN CORS station was selected as rover

Known ITRF coordinates from a 24-hour BERNESE solution

October 29, 2003 – significant ionospheric storm

Experiments - test area maps

The network provides atmospheric

corrections to the rover (KNTN)

The rover station does not contribute to the estimation

of the atmospheric corrections

63km

98km

KNTN

LSBN

(rover)

Network map Baseline map

104km

109km124km

108km

KNTN

ExperimentsDD ionospheric residuals with respect to the reference

“truth”24 h, KNTN-DEFI (~100 km)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

MPGPS-P4

[m]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

MPGPS-NR

[m]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

IGS GIM

[m]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

ICON (NGS)

[m]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

MAGIC (NGS)

[m]

hours

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

MPGPS-L4 (Reference "truth")

[m]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

MPGPS-NR

[m]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

IGS GIM

[m]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

ICON (NGS)

[m]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

MAGIC (NGS)

[m]

hours

worst best

Residual statistics

Residuals in [%] below the cut-off 24 h

KNTN-SIDN (~60 km)KNTN-DEFI (~100 km)

±10 cm ±5 cm ±10 cm ±5 cm

MPGPS-NR99.394.299.394.2

IGS GIM94.971.481.754.3

ICON58.431.958.232.5

MAGIC98.083.390.167.1

Ionospheric delay residual statistics 5 and 10 cm cut-off limits for 24 h

Statistics-Mean and STD of DD iono residuals wrt the reference “truth”

2-h windowsKNTN-DEFI (~100 km)

04:00–06:00 UTC (“worst”)18:00–20:00 UTC (“best”)

mean [m]mean [m]

PRNsMPGPS

NRIGSGIM

ICONMAGICMPGPS

NRIGSGIM

ICONMAGICPRNs

28 - 40.00 0.00 0.030.01 0.01 0.08 0.06-0.0125 - 1

28 - 70.01 0.05 0.190.02 0.01-0.02-0.07 0.0225 - 2

28 - 80.01-0.01 0.010.07-0.01-0.02-0.12 0.0125 - 5

28 - 90.00 0.08 0.170.03 0.01-0.01-0.09-0.0125 - 6

28 - 110.00 0.13 0.070.06 0.01-0.04-0.03 0.0025 - 14

28 - 200.00 0.07-0.120.01 0.01-0.06-0.01-0.0025 - 16

28 - 240.01 0.05 0.100.02 0.01 0.04 0.04 0.0225 - 20

-0.00-0.13-0.08 0.0125 - 23

0.01-0.04-0.02 0.0425 - 30

std [m]std [m]

28 - 40.020.050.010.060.010.020.010.0325 - 1

28 - 70.060.070.030.070.020.040.010.0425 - 2

28 - 80.040.090.010.100.010.030.010.0325 - 5

28 - 90.030.050.020.050.020.030.020.0425 - 6

28 - 110.040.070.010.080.010.020.010.0225 - 14

28 - 200.040.080.030.060.010.040.010.0325 - 16

28 - 240.020.050.020.040.010.020.010.0325 - 20

28 - 40.020.050.010.060.020.040.030.0525 - 23

0.010.030.010.0425 - 30

0.010.020.010.0325 - 1

Instantaneous RTK positioning analysis

4 4.25 4.5 4.75 5 5.25 5.5 5.75 6

-0.2

-0.1

0

0.1

0.2

04:00 - 06:00 UTC

[m]

18 18.25 18.5 18.75 19 19.25 19.5 19.75 20

-0.2

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0

0.1

0.2

18:00 - 20:00 UTC

[m]

hours

neu

neu

KNTN-SIDN ~60 km0 cm constraint (1 sigma) for the ionospheric corrections

0 cm constraint“worst” iono

accuracy (MPGPS-NR)

0 cm constraint“best” iono accuracy

(MPGPS-NR)

Instantaneous RTK positioning analysis

4 4.25 4.5 4.75 5 5.25 5.5 5.75 6

-0.2

-0.1

0

0.1

0.2

04:00 - 06:00 UTC

[m]

18 18.25 18.5 18.75 19 19.25 19.5 19.75 20

-0.2

-0.1

0

0.1

0.2

18:00 - 20:00 UTC

[m]

hours

neu

neu

KNTN-SIDN ~60 km5 cm constraint (1 sigma) for the ionospheric corrections

5 cm constraint“worst” iono

accuracy (MPGPS-NR)

5 cm constraint“best” iono accuracy

(MPGPS-NR)

Instantaneous RTK positioning analysis

4 4.25 4.5 4.75 5 5.25 5.5 5.75 6

-0.2

-0.1

0

0.1

0.2

04:00 - 06:00 UTC

[m]

18 18.25 18.5 18.75 19 19.25 19.5 19.75 20

-0.2

-0.1

0

0.1

0.2

18:00-20:00 UT

[m]

hours

neu

neu

4 4.25 4.5 4.75 5 5.25 5.5 5.75 6

-0.2

-0.1

0

0.1

0.2

04:00 06:00 UT

[m]

18 18.25 18.5 18.75 19 19.25 19.5 19.75 20

-0.2

-0.1

0

0.1

0.2

18:00 - 20:00 UTC

[m]

hours

Instantaneous RTK positioning, 2h sessions, KNTN-SIDN (~60 km)

neu

neu

KNTN-DEFI ~100 km1 and 5 cm constraint for the ionospheric corrections

5 cm constraint“worst” iono

accuracy (MPGPS-NR)

1 cm constraint“best” iono accuracy

(MPGPS-NR)

OTF Ambiguity Resolution: number of epochs needed to resolve the integers: ~100 km baseline; the worst window

• * means that the correct ambiguity was found at the first epoch, however the method requires a minimum of three epochs to validate the choice

• Shown are different solutions with varying stochastic constraints applied to the externally provided ionosphere in the rover positioning solution

• Processing was restarted every 10 minutes, continued for 100 epochs

OTF Ambiguity Resolution: number of epochs needed to resolve the integers: ~100 km baseline; the best

window

• * means that the correct ambiguity was found at the first epoch, however the method requires a minimum of three epochs to validate the choice

• Shown are different solutions with varying stochastic constraints applied to the externally provided ionosphere in the rover positioning solution

• Processing was restarted every 10 minutes, continued for 100 epochs

OTF Ambiguity Resolution: summary

Different number of epochs needed to resolve the integers as a function of:

Ionospheric model type

Level of stochastic constraints applied to the external ionosphere

Ionospheric activity and baseline length (to some extent)

Level of local details recovered by the model

MPGPS-NR needs 7.4 (6.5)* epochs on average during the higher ionospheric variability and 3 (3) epochs during the period of lowest ionospheric variability, using 5 cm constraints on ionosphere; similarly for 1 cm constraint

MAGIC requires 12 (10) and 4 (3) epochs, respectively

ICON and GIM need more epochs

Stochastic constraints of 10 cm for MAGIC and GIM and 20 cm for ICON

8 (18) and 4 (3) for MAGIC

24 (68) and 22 (11) for ICON

15 (25) and 18 (22) for GIM

* The number in parenthesis correspond to the longer baseline

Position residuals with respect to the knownreference coordinates: summary statistics, MPGPS-NR

MPGPS-NR model

Algorithmic updates: ICON and MAGIC

ICON solution can be fitted to MAGIC solution to provide the best of both methods: correct biases from MAGIC and ionospheric details from ICON

MAGIC solution can use carrier phase fit after the biases have been fixed

L2-L1 data are fitted to the estimated MAGIC values, and the constant mean difference (bias) along the satellite arc is removed

Result: high accuracy ionospheric corrections matching the DD reference “truth” with 5-10 cm level of accuracy >90% of the time

Both models are, therefore, suitable for instantaneous and/or fast OTF AR

ICON and MAGIC: original vs. modified DD ionosphere [meters]

500 1000 1500 2000 2500

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-0.4

-0.3

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0

0.1

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500 1000 1500 2000 2500

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500 1000 1500 2000 2500

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0

0.1

0.2

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0.5

500 1000 1500 2000 2500

-0.5

-0.4

-0.3

-0.2

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0

0.1

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0.5

Original ICON solution: ~100 km baseline

Modified ICON solution: ~100 km baseline Modified MAGIC solution ~100 km baseline

Original MAGIC solution ~100 km baseline

Modified MAGIC solution: rover data (KNTN) fit included

(Applicable to high-accuracy analysis in post-processing)

500 1000 1500 2000 2500

-0.5

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0

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500 1000 1500 2000 2500

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Modified MAGIC solution ~100 km baseline

Modified MAGIC solution ~60 km baseline

mm

Modified ICON and MAGIC: summary statistics

Residuals in [%] below the cut-off 24-h

KNTN-SIDN (~60 km)KNTN-DEFI (~100 km)

10± cm ±5 cm ±10 cm ±5 cm

MPGPS-NR - No KNTN data99.394.299.394.2

ICON FIT - No KNTN data97.388.695.881.4

MAGIC FIT - No KNTN data97.687.497.185.2

MAGIC FIT - KNTN data included*100.0100.099.699.6

* in post-processing

Reference network and test baseline: October 29, 2003 – severe ionospheric storm

Baseline mapNetwork map

~200 km reference station separation

~120 km base-rover separation

Quality of ionospheric corrections during highly disturbed

ionospheric conditions (storm) :

baseline COLB-LEBA, 121 km

MPGPS-NR solution

October 29, 2003

Summary statistics: active vs. quiet ionosphere

Earlier findings show that 10-cm or better accuracy should assure instantaneous AR

COLB-LEBA (121 km)

0–20 cm20–50 cm50–100 cm>100 cm

October 11, 2003 93.0%7.0%0.0%0.0%

October 29, 200367.4%23.6%5.8%3.2%

“True” DD ionospheric delays (absolute values) within selected ranges, 24 h

COLB-LEBA (121 km)

10 cm5 cm

October 11, 2003 92.2%71.4%

October 29, 200374.4%52.5%

DD ionospheric delay residuals with respect to the reference “truth”within selected ranges, 24 h

Ambiguity resolution success ratio as a function of ionospheric activity: instantaneous solution

Success ratio is defined as the ratio of the number of correctly resolved epochs to the number of all processed epochs

1 .During the quiet day, the success ratio was over 94%2 .During the disturbed period, as expected, it dropped dramatically to 31%

OTF ambiguity resolution statistics: October 29, 2003

8 8.5 9 9.5 10

0

10

20

30

40

8 8.5 9 9.5 10

0

10

20

30

40

8 8.5 9 9.5 10

0

10

20

30

40

10 cm constra in t 20 cm constra in t 40 cm constra in t

Epo

chs

U T H our U T H our U T H our

Note: Quiet day data were processed with 10 cm stochastic constraints imposed

on the network-derived DD ionospheric corrections. All the ambiguities (in each of

the 24 shifted solutions) were solved using the required minimum of three epochs

Number of epochs required to fix the integers with different levels of constraints on external ionosphere

Summary and Outlook

Different ionospheric models were analyzed

• Varying TEC levels, benign and severe ionospheric conditions

• Varying GPS constellation

10 cm or better fit to the reference “truth” assures instantaneous AR and high-accuracy cm-level positioning

• Over 90% success ratio for benign ionosphere conditions

• 31% success ratio for severe storm

OTF AR time-to-fix vary with the model type, stochastic constraints and ionospheric activity

Stochastic constraints depend on the ionospheric activity level

• Needs significant relaxation under severe storms (from 5-10 to 40 cm)

MPGPS-NR, modified MAGIC and ICON – almost equivalent quality

MPGPS provides high accuracy kinematic positioning with all ionospheric models presented

Algorithmic modification towards real-time applications