Analysis of Real and Simulated Carrier Phase Residuals

Brian Breitsch\(^1\)

Jade Morton\(^1\)

Charles Rino \(^2\)

In the Geometry-Ionosphere-Free Combination

URSI NRSM 2018

1. University of Colorado Boulder

2. Boston College

Background and Motivation

Geometry-Ionosphere-Free Combination

Derivation and Examples

Analysis and Comparison

Description of IPE Method

Comparison of Real and Simulated GIFC

GNSS Carrier Phase

Scintillation

Dual vs Triple-Frequency GPS

Phase Simulation During Scintillation

SI, S4, detrended phases and phase combinations

Qualitative look at triple-frequency scint. examples

Carrier Phase Measurement

\Phi_i = r + c\Delta t + T + I_i + \lambda_i N_i + H_i + S_i + \epsilon_i
Φi=r+cΔt+T+Ii+λiNi+Hi+Si+ϵi \Phi_i = r + c\Delta t + T + I_i + \lambda_i N_i + H_i + S_i + \epsilon_i

 BIASES

IONOSPHERE RANGE ERROR

CARRIER AMBIGUITY

SYSTEMATIC ERRORS / MULTIPATH

FREQUENCY INDEPENDENT EFFECTS

STOCHASTIC ERRORS

I_i \approx -\frac{\kappa}{f_i^2} \text{TEC}
Ii≈−κfi2TECI_i \approx -\frac{\kappa}{f_i^2} \text{TEC}

scintillation

Scintillation Effect

fairly weak

S_4 < 0.5
S4<0.5S_4 < 0.5

6th-order Butterworth Highpass with 0.1 Hz cutoff

Estimation Using Dual-Frequency GNSS

\text{TEC} = \displaystyle -\frac{\Phi_1 - \Phi_2}{\kappa \left(\frac{1}{f_1^2} - \frac{1}{f_2^2}\right)}
TEC=−Φ1−Φ2κ(1f12−1f22)\text{TEC} = \displaystyle -\frac{\Phi_1 - \Phi_2}{\kappa \left(\frac{1}{f_1^2} - \frac{1}{f_2^2}\right)}
G = \displaystyle \frac{f_1^2 \Phi_1 - f_2^2 \Phi_2}{f_1^2 - f_2^2}
G=f12Φ1−f22Φ2f12−f22G = \displaystyle \frac{f_1^2 \Phi_1 - f_2^2 \Phi_2}{f_1^2 - f_2^2}

ionosphere-free combination

geometry-free combination

\Phi_i = G + I_i + S_i + \epsilon_i
Φi=G+Ii+Si+ϵi\Phi_i = G + I_i + S_i + \epsilon_i

"geometry" term

\Phi_i = r + c\Delta t + T + I_i + \lambda_i N_i + H_i + S_i + \epsilon_i
Φi=r+cΔt+T+Ii+λiNi+Hi+Si+ϵi \Phi_i = r + c\Delta t + T + I_i + \lambda_i N_i + H_i + S_i + \epsilon_i

we can solve bias terms

scintillation will impact residuals of range and TEC estimates

Multi-Frequency GNSS

  • GPS Block IIF / Block III
  • Galileo (E1, E5a/b)
  • GLONASS-K2
Signal Frequency (GHz)
L1CA 1.57542
L2C 1.2276
L5 1.17645

triple-frequency GPS

12 satellites since 2016

(higher-quality signal)

Estimation Using Triple-Frequency GNSS

ionosphere-free combination

geometry-free combination

\Phi_i = G + I_i + S_i + \epsilon_i
Φi=G+Ii+Si+ϵi\Phi_i = G + I_i + S_i + \epsilon_i
\sum_i c_i = 0
∑ici=0\sum_i c_i = 0
\sum_i \frac{c_i}{f_i^2} = 0
∑icifi2=0\sum_i \frac{c_i}{f_i^2} = 0
\begin{matrix} \text{Estimate} & c_1 & c_2 & c_3 & \text{noise amp.} \\[.5em] & & & & \\ & & & & \\ G_\text{L1,L2,L5} & 2.3 & -0.4 & -1.0 & 2.5 \\ & & & & \\ & & & & \\ & & & & \\ \text{TEC}_\text{L1,L2,L5} & 8.3 & -2.9 & -5.4 & 10.3 & \\ \end{matrix}
Estimatec1c2c3noise amp.GL1,L2,L52.3−0.4−1.02.5TECL1,L2,L58.3−2.9−5.410.3\begin{matrix} \text{Estimate} & c_1 & c_2 & c_3 & \text{noise amp.} \\[.5em] & & & & \\ & & & & \\ G_\text{L1,L2,L5} & 2.3 & -0.4 & -1.0 & 2.5 \\ & & & & \\ & & & & \\ & & & & \\ \text{TEC}_\text{L1,L2,L5} & 8.3 & -2.9 & -5.4 & 10.3 & \\ \end{matrix}
c_1 \Phi_1 + c_2 \Phi_2 + c_3 \Phi_3
c1Φ1+c2Φ2+c3Φ3c_1 \Phi_1 + c_2 \Phi_2 + c_3 \Phi_3

Triple-Frequency GPS Coefficients

Background and Motivation

Geometry-Ionosphere-Free Combination

Derivation and Examples

Analysis and Comparison

Description of IPE Method

Comparison of Real and Simulated GIFC

GNSS Carrier Phase

Scintillation

Dual vs Triple-Frequency GPS

Phase Simulation During Scintillation

SI, S4, detrended phases and phase combinations

Qualitative look at triple-frequency scint. examples

Geometry-Ionosphere-Free Combination

ionosphere-free combination

geometry-free combination

\sum_i c_i = 0
∑ici=0\sum_i c_i = 0
\sum_i \frac{c_i}{f_i^2} = 0
∑icifi2=0\sum_i \frac{c_i}{f_i^2} = 0
c_1 = \alpha \left( \frac{1}{f_3^2} - \frac{1}{f_2^2} \right)
c1=α(1f32−1f22)c_1 = \alpha \left( \frac{1}{f_3^2} - \frac{1}{f_2^2} \right)
c_1 \Phi_1 + c_2 \Phi_2 + c_3 \Phi_3
c1Φ1+c2Φ2+c3Φ3c_1 \Phi_1 + c_2 \Phi_2 + c_3 \Phi_3
c_3 = \alpha \left( \frac{1}{f_2^2} - \frac{1}{f_1^2} \right)
c3=α(1f22−1f12)c_3 = \alpha \left( \frac{1}{f_2^2} - \frac{1}{f_1^2} \right)
c_2 = \alpha \left( \frac{1}{f_1^2} - \frac{1}{f_3^2} \right)
c2=α(1f12−1f32)c_2 = \alpha \left( \frac{1}{f_1^2} - \frac{1}{f_3^2} \right)

Triple-Frequency GIFC Coefficients

\alpha =
α=\alpha =

arbitrary scaling factor

IFC

GFC

GIFC

~TEC

GIFC Examples

PRN 24, Peru

PRN 24, Hong Kong

PRN 25, Peru

PRN 01, Alaska

2013-01-01

2014-05-15

2013-01-01

2014-06-29

GIFC

Sat. Elevation

Coeff. normalized to IFC norm

Background and Motivation

Geometry-Ionosphere-Free Combination

Derivation and Examples

Analysis and Comparison

Description of IPE Method

Comparison of Real and Simulated GIFC

GNSS Carrier Phase

Scintillation

Dual vs Triple-Frequency GPS

Phase Simulation During Scintillation

SI, S4, detrended phases and phase combinations

Qualitative look at triple-frequency scint. examples

Scintillation Simulator

SI Power Spectral Density

from real data

Use Iterative Parameter Estimation (IPE) to resolve structure model params.

Use structure model parameters to derive PSD of complex field at receiver / generate random realization

Background and Motivation

Geometry-Ionosphere-Free Combination

Derivation and Examples

Analysis and Comparison

Description of IPE Method

Comparison of Real and Simulated GIFC

GNSS Carrier Phase

Scintillation

Dual vs Triple-Frequency GPS

Phase Simulation During Scintillation

SI, S4, detrended phases and phase combinations

Qualitative look at triple-frequency scint. examples

Peru G25 2013-10-30 Example

moderately weak

S_4 < 0.5
S4<0.5S_4 < 0.5

10 minute zoom on real GIFC

10 minute GIFC simulation

model appears to slightly under-represent noise present in real-data GIFC

Hong Kong G24 2013-09-24 Example

moderately strong

S_4 > 0.8
S4>0.8S_4 > 0.8

10 minute zoom on real GIFC

10 minute GIFC simulation

more jumps in model realization than actual 10-min data segment

Hong Kong G24 2013-10-05 Example

moderately strong

S_4 > 0.8
S4>0.8S_4 > 0.8

10 minute zoom on real GIFC

10 minute GIFC simulation

again -- more jumps in model realization than real data

Peru G25

Hong Kong G24

Hong Kong G24

10-06

GFC, IFC, GIFC Spectra

Difficulties With IPE and Weak Scintillation

Bad fit?

Bizarre spectrum

Conclusions

  • GIFC is an indicator of the presence diffraction effects on GNSS signals
  • weak scintillation will not have large effect on GIFC
    • although model appears to under-represent small noise increase during weak scintillation
  • scintillation model shows many more "jumps" than real data
  • need to classify scintillation events
  • we can look at more data and start making statistical comparisons
  • IPE fitting for scintillation model is still finicky
    • need to explore robustness of current IPE method

Next Steps

Acknowledgements

This research was supported by the Air Force Research Laboratory.

Studying Carrier Phase Residuals Using Triple-Frequency Observations

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