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 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: 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 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

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 - 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 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 109km 124km 108km KNTN

Experiments DD ionospheric residuals with respect to the reference “truth” 24 h, KNTN-DEFI (~100 km) 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-NR IGS GIM ICON MAGIC 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 windows KNTN-DEFI (~100 km) 04:00–06:00 UTC (“worst”)18:00–20:00 UTC (“best”) mean [m] PRNs MPGPS NR IGS GIM ICONMAGIC MPGPS NR IGS GIM ICONMAGICPRNs std [m]

Instantaneous RTK positioning analysis KNTN-SIDN ~60 km 0 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 KNTN-SIDN ~60 km 5 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 KNTN-DEFI ~100 km 1 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 known reference 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] 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) Modified MAGIC solution ~100 km baseline Modified MAGIC solution ~60 km baseline m m

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 data ICON FIT - No KNTN data MAGIC FIT - No KNTN data MAGIC FIT - KNTN data included* * in post-processing

Reference network and test baseline: October 29, 2003 – severe ionospheric storm Baseline map Network 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, %7.0%0.0% October 29, %23.6%5.8%3.2% “True” DD ionospheric delays (absolute values) within selected ranges, 24 h COLB-LEBA (121 km) 10 cm5 cm October 11, %71.4% October 29, %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 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