Ionosphere Scintillation-Induced

Phase Transitions (Cycle Slips)

in Triple-Frequency GPS Measurements

Brian Breitsch, Jade Morton, Dongyang Xu

24 January 2020

ION ITM/PTTI 2020

are ionosphere-induced phase transitions?

What

Why

How

Outline

are they so difficult to deal with?

can we mitigate their impact?

are ionosphere-induced phase transitions?

What

Why

How

Outline

are they so difficult to deal with?

can we mitigate their impact?

Ascension Island - 2013-10-05 - G24

(typically equatorial) ionosphere plasma bubbles / structures

signal diffraction

Ionosphere Scintillation

[Xu et al 2017]

Signal Model

IONOSPHERE EFFECTS

BIASES

NONDISPERSIVE EFFECTS

\frac{\lambda_k}{2\pi} \phi_k = G + I_k + B_k

I =I_\text{refr} + I_\text{diffr}

phase model

ionosphere effect

REFRACTIVE

DIFFRACTIVE

WARNING: \(I_\text{diffr}\) may contain phase transitions...

...but why?

Ionosphere Diffraction Simulations

instantiate realistic phase screen structure \(\bar{\phi}\) from stochastic model

\bar{\phi}

\tilde{\phi}

propagate using parabolic wave equation methods

generate complex field \(\Psi(t)\) at the receiving antenna

Simulated Phase Transitions

Most of common variation in \(\phi_k(t)\) is due to ionosphere refraction, which is approximately captured by the model phase screens \(\bar{\phi}(t)\).

[Rino et al 2017]

Origin of Phase Transitions

Assume the phase screen structure approximates refractive phase, i.e. \(I_\text{refr} \propto \bar{\phi}\).

Then \(\tilde{\phi}(t) = \text{unwrap}\left(\angle \tilde{\Psi}(t) \right)\) is the diffractive phase and \(I_\text{diffr} \propto \tilde{\phi}\)

histograms of \(\tilde{\Psi}\)

We can decompose \(\Psi(t)\) as \(\Psi(t) = \tilde{\Psi}(t) \exp(i\bar{\phi}(t))\).

Phase Transitions

not instantaneous!

phase rate-of-change as cycle slip indicator would produce many false positives!

singularity at origin causes phase bifurcation

Phase Transitions as Cycle Slips

[phase transitions] occur gradually over many samples...[they are] distinct from cycle slips, which are abrupt phase changes of a cycle (or more)

- Carrano et al 2013

Phase transitions and cycle slips due to other factors are often indistinguishable

- Me (Brian) 2020

"[The] increased measurement noise associated with an active ionosphere makes correcting cycle slips an ongoing challenge which requires further investigation."

- Banville 2010

"...precise navigation is possible under strong scintillation conditions as long as the problem with the cycle slips could be properly addressed."

- Juan et al 2018

are ionosphere-induced phase transitions?

What

Why

How

Outline

are they so difficult to deal with?

can we mitigate their impact?

Cycle Slip Detection

Things that make cycle slip detection hard

Effects of ionosphere diffraction

large phase noise

unknown trends / dynamics

frequent / consecutive slips

Geometry-Free Cycle Slip Detection

Geometry-Free combination not viable during diffraction

are ionosphere-induced phase transitions?

What

Why

How

Outline

are they so difficult to deal with?

can we mitigate their impact?

Mitigation Strategies

multi-frequency observations
- triple-frequency [de Lacy 2012, etc.]
- quadruple-frequency [Juan et al 2019]
geodetic detrending [Juan et al 2017]
cascaded detection [Qile Zhao 2014]
- first remove easy-to-detect slips
- allows detection of weaker signatures
expanding window of observations [Tao Li 2018]

What remains is to carfully apply these techniques to the diffraction-induced cycle slip problem.

Linear Combinations of Phase

\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}

Ionosphere-Free

Geometry-Free

\text{GIF} = 0.14 \cdot \Phi_\text{L1} - 0.77 \cdot \Phi_\text{L2} + 0.63 \cdot \Phi_\text{L5}

Geometry-Ionosphere-Free

\Phi_k = G + I_k + B_k

not so useful during diffraction

need to know your clocks!

need triple-frequency

Linear Combinations of Phase

Septentrio PolaRxS - Hong Kong - 2013-10-05 - G24

Slip Detectability

(1, 1, 1)

(0, 1, 1)

(1, 0, 0)

(1, 1, -)

(1, -, 1)

cycle-slip combinations

Geometry-Ionosphere-Free Combination

Key Points

GNSS phase measurements are plagued by diffraction-induced cycle slips (and phase transitions) during strong ionosphere scintillation

Diffraction-induced cycle slip detection is challenging

methods that only use GF combination are not viable
many consecutive slips with large noise residuals

A combination of strategies will be necessary to detect cycle slips during diffraction

triple-frequency offers unique advantages
cycle slip combinations (1, 1, 1), (0, 1, 1), and (1, 0, 0) are especially challenging

References

Xu, Dongyang, and Yu Morton. "A semi-open loop GNSS carrier tracking algorithm for monitoring strong equatorial scintillation." IEEE Transactions on Aerospace and Electronic Systems 54.2 (2017): 722-738.

Rino, Charles, et al. "A New GNSS Scintillation Model." Proc. ION GNSS. 2017.

de Lacy, Maria Clara, Mirko Reguzzoni, and Fernando Sansò. "Real-time cycle slip detection in triple-frequency GNSS." GPS solutions 16.3 (2012): 353-362.

Wang, Yaoding, et al. "Real-Time Quadruple-Frequency Cycle Slip Detection and Repair Algorithm Based on the Four Chosen Linear Combinations." IEEE Access 7 (2019): 154697-154710.

Juan, José Miguel, et al. "Feasibility of precise navigation in high and low latitude regions under scintillation conditions." Journal of Space Weather and Space Climate 8 (2018): A05.

Zhao, Qile, et al. "Real-time detection and repair of cycle slips in triple-frequency GNSS measurements." GPS Solutions 19.3 (2015): 381-391.

Li, Tao, and Stavros Melachroinos. "An enhanced cycle slip repair algorithm for real-time multi-GNSS, multi-frequency data processing." GPS Solutions 23.1 (2019): 1.