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### Ionospheric Parameter Estimation Using GPS

Attila Komjathy, Lawrence Sparks and Anthony J. Mannucci

Jet Propulsion Laboratory

California Institute of Technology

M/S 238-600

4800 Oak Grove Drive

Pasadena CA 91109

Email: [email protected]

This lecture

covers:

Why?

Topics

IONOSPHERE ESTIMATION USING GPSUsing GPS signals to measure the ionosphere

Understand purpose and operation of reference stations

Understand how ionospheric corrections are formed

Forming ionospheric measurements from GPS observables

Data quality and editing

Calibration of GPS data

Introduction

- Currently the largest error sources in GPS positioning is that of ionospheric refraction causing signal propagation delays L

What can be done?

- If we have a dual-frequency GPS receiver, then the ionospheric effect can be almost totally accounted for J
- What if we have a single-frequency receiver?
- We can ignore the effect and live with the consequences M
- We can minimize it using various processing techniques J
- We can model it using empirical ionospheric models such as the GPS single-frequency Broadcast model, IRI2000 model, PIM, etc. J
- We can measure it using nearby dual-frequency receiver observations (pseudorange only, carrier-phase only, pseudorange/carrier-phase combined) and apply it as a correction to the single-frequency observations. J
- What is the error in positioning accuracy caused by the ionosphere and how can we reduce it?

GPS Observation Equations

GPS pseudorange observation equation:

GPS carrier phase observation equation:

Range, clock, ambiguity, ionosphere, troposphere, satellite bias, receiver bias, multipath, noise

Generating GPS Ionospheric Observables

phase-leveled ionospheric observable

precise but ambiguous

less precise but unambiguous

Leveling the Phase Using Code Measurements

The level is computed by averaging PI-LI using an elevation-dependent weighting.

Higher elevation data is weighted more heavily.

(The weighting is based on historical Turborogue PI-LI noise/ multipath data giving a historical PI-LI scatter of th(E) where E is elevation.)

The level is computed as:

where E is the elevation angle. The uncertainty on the level

is computed in a rather rough way using a combination of

th(E) and observed pseudorange scatter:

The TEC sigma in the JPL Processed Data files are the level uncertainty.

Global Ionospheric Mapping: GIM

For three shells, our model is

For single shell, our model is

where

is the slant TEC;

is the thin shell mapping function for shell 1, etc;

is the horizontal basis function (C2, TRIN, etc);

are the basis function coefficients solved for in the filter,

indexed by horizontal (i) and vertical (1,2,3 for three shells) indices;

are the satellite and receiver instrumental biases.

WAAS Ionospheric Models

WAASplanar fit ionospheric model is

Pseudo-IGP approach:

IPP treated as if it were

collocated with IGP

where

are the planar fit parameters,

are the distances from the IGP to

the IPP in the eastern and northern directions, respectively.

WAAS-type quadratic fit ionospheric model is

are the additional planar fit parameters

describing quadratic and cross terms.

All-Site GPS Data Processing Algorithm

Bias Fixing Algorithm using all available GPS stations worldwide:

GIM TEC prediction

Biased TEC

observation

GIM satellite

bias estimate

is the biased phase-levelled ionospheric observable

is the thin shell mapping function for shell 1, etc;

is the horizontal basis function (C2, TRIN, etc);

are the basis function coefficients solved for in the filter,

indexed by horizontal (i) and vertical (1,2,3 for three shells) indices;

are the satellite and receiver instrumental biases.

Single Vs. Three-Shell Model Limitations

The concept of multi-shell GIM:

Single-shell 2-D maps

Does not capture small-scale variations in the ionosphere

Multi-shell is more realistic and accurate than the single-shell approximation

Slant TEC Bias-Fixing Method

Estimated bias time series:

errors caused by GIM, multipath,

noise, sub-daily bias drift

Bias-removed slant TEC

Location of station

Coverage of Daily IGS Network and Regional Networks

(10 degree elevation mask; 450 km shell height)

Example for Single Shell Model Results

An Example of the Diurnal Variation of TEC for a Geomagnetically Quiet Day

Components in TECU, TECU/hour, TECU/km

November 20, 2003 Storm

Details are difficult

to interpret

5-day average of quiet

ionosphere removed:

structures are easier to

detect

Quiet ionosphere

following the storm

An Example for Repeatibility of Estimated Satellite Biases: Multi-Shell versus Single-Shell

- Multi-shell significantly improves repeatibility in daily bias estimates
- We compare bias averages over 7–10 days
- Scatter (std. dev.) over a week improved by factor of 2 to 4
- Satellite biases
- 7-day scatter improved from 2–6 cm to 8–24 mm
- This may indicate reduction of systematic errors in bias estimation

6 cm

0 cm

An Example for Repeatibility in Estimated Receiver Biases:Multi-Shell versus Single-Shell

0.6 m

- Receiver biases
- 7-day scatter improved from 8–64 cm to 0.5–19 cm
- Larger scatter due to stations in low latitude sector
- Systematic error?
- Examine long time-series of biases
- Look for shifts in ionospheric delay level for all biases simultaneously

0 m

Comparison of Single and Multi-Shell Results for ENG1

Postfit

Residuals

ENG1 = English Turn, LA

Improvement at low elevation angles

Prediction Residuals

Comparison of Single and Multi-Shell Results for MBWW

Postfit

Residuals

Improvement at low elevation angles

MBWW = Medicine Bow, WY

Prediction Residuals

Low-Earth Orbiter

GPS

COSMICIonospheric Weather Constellation

Electron

Density

Profile

COSMIC coverage: 2500 profiles/day

Six-satellite COSMIC constellation

Launched April 14, 2006

State and

covariance

Analysis

State and

covariance

Forecast

Adjustment

Of Parameters

Kalman Filter

4DVAR

Global Assimilative Ionospheric Model

Data Assimilation Process

Driving

Forces

Physics

Model

Mapping State

To Measurements

Innovation Vector

- Kalman Filter
- Recursive Filtering
- Covariance estimation and state correction

Optimal interpolation

Band-Limited Kalman filter

- 4-Dimensional Variational Approach
- Minimization of cost function by estimating driving parameters
- Non-linear least-square minimization
- Adjoint method to efficiently compute the gradient of cost function
- Parameterization of model “drivers”

Input Data Types

- Ground GPS Data (Absolute TEC)
- >200 5-min. to Hourly Global GPS Ground Stations
- Assimilate >300,000 TEC points per day (@ 5 min rate) per day
- Space GPS Data (Absolute or Relative TEC)
- CHAMP (@ 440 km)
- SAC-C (@ 700 km)
- IOX (@ 800 km)
- GRACE (@ 350 km)
- Topex/Poseidon (@1330 km) (Upward looking only)
- Jason 1 (@1330 km) (Upward looking only)
- C/NOFS & COSMIC constellation
- UV airglow data (135.6 nm radiance)
- LORAAS on ARGOS, GUVI on TIMED
- SSUSI/SSULI on DMSP
- TIP on COSMIC
- Other Data Types
- TEC from TOPEX/JASON Altimeters
- Ionosonde bottomside profiles
- DMSP in situ
- CHAMP in situ
- GRACE cross-links

Kalman Assimilation Runs for June 26, 2006

- Three runs:
- GAIM Climate (no data)
- Ground GPS TEC (200 sites)
- Ground + COSMIC links (upward & occultation)
- Resolution: 2.5 deg. Lat. 10 deg. Lon. 40 km Alt.
- No. of grid cells: 100,000
- Sparse Kalman filter:
- Update & propagate covariance
- Truncate off-diagonal covariance that is beyond physical correlation lengths

GAIM Driven By Ground GPS Onlyversus JASON VTEC

June – Nov. 2004: 137 days

COSMIC Demo 2007

Global ground network data: 5-minute and 1-hour latency

COSMIC data: 120+ minutes latency

GAIM

3-D global electron density grids

15-minute cadence

Start of orbit

End of orbit;

data downloaded

Limb TEC available

Data received at CDAAC

Profiles (Abel) available

CDAAC: COSMIC Data Analysis and Archiving Center at UCAR

What You Have Learned

Ionosphere is the largest error source in GPS positioning

Empirical models can be used to mitigate effects

Dual-frequency GPS data can be used to solve for the ionospheric effect

Error sources affecting GPS-based ionospheric estimation: arc length,leveling, biases, multipath, noise, etc.

Global Ionospheric Mapping techniques: single vs multi-shell approaches: ionospheric delay and biases estimation

Validation of maps, point plots, movies, etc.

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