gnss data processing investigations for characterizing … › position-location-and... ·...

ION GNSS+ 2014, Session C2, Tampa, FL, 8-12 September 2014 /12

GNSS Data Processing Investigations for

Characterizing Ionospheric Scintillation

M. Najmafshar, S. Skone and F. Ghafoori

Department of Geomatics Engineering, Schulich School of Engineering,

University of Calgary

BIOGRAPHY

Maryam Najmafshar is a PhD candidate in the PLAN

Group of the Department of Geomatics Engineering at the

University of Calgary. She received her BSc and MSc

degrees in electrical engineering from Amirkabir

University of Technology (AUT) and Iran University of

Science and Technology (IUST), respectively. Her

research interests include the fields of GNSS signal

processing.

Susan Skone, Ph.D., is an Associate Professor in

Geomatics Engineering and Associate Dean (Research),

Schulich School of Engineering, at the University of

Calgary. She has a background in space physics and

conducts research in ionospheric and tropospheric effects

on GPS. She has developed software for mitigation of

atmospheric effects and has conducted technical studies

for various agencies and industry.

Fatemeh Ghafoori is a post-doctoral fellow in Geomatics

Engineering, Schulich School of Engineering, at the

University of Calgary. Her research interests focus on

ionospheric scintillation effects on GNSS signals and

receivers.

ABSTRACT

Ionospheric scintillations are generally characterized via

scintillation indices, calculated from amplitude and phase

of the received GNSS signals. For many scintillation

monitoring and mitigation applications, it is important to

determine these indices accurately. Investigating

appropriate data algorithms (here, data detrending) in

deriving scintillation information for mitigation

applications is the focus of this paper.

Commonly, most GNSS receivers use a Butterworth filter

with a fixed cutoff frequency of 0.1 Hz to remove low

frequency trends from the data [Forte and Radicella

2002, Mushini, et al., 2012]. However, as shown in Forte

and Radicella, 2002, inherent characteristics of

ionospheric effects at different regions require different

detrending settings. In this study, four detrending methods

and effectiveness of each are examined using real data

sets from high latitude and equatorial regions. Based on

our results, it is observed that data detrending via wavelet-

based filter can result in cleaner (less noisier) signal. In

addition, correlation between computed amplitude and

phase scintillation indices improves when wavelet

filtering is used. Moreover, we present initial

considerations for scintillation monitoring and mitigation

via exploiting new GNSS signals to determine additional

information.

To examine real data, IF samples from scintillation events

are post-processed using the GSNRx™ software receiver,

developed by the Position, Location and Navigation

(PLAN) group at the University of Calgary. This software

receiver has the capability of processing GPS L1C/A and

L2C signals. Scintillation parameters are calculated using

the post-correlator in-phase (I) and quadra-phase (Q)

components and carrier phase measurements, all obtained

from the software receiver.

INTRODUCTION

Global Navigation Satellite System (GNSS) signals

encounter various error sources as they propagate from

satellite to earth. One of these error sources is ionospheric

disturbances, which can cause random and rapid

fluctuations in the amplitude and phase of the transmitted

signals. Deep amplitude fades and high dynamics of

phase changes, respectively referred to as amplitude and

phase scintillations, degrade the signal quality and can

cause challenges in acquisition and tracking capabilities

of GNSS receivers. Amplitude scintillation is

characterized by S4 (unit-less), which is defined as the

standard deviation of the received signal power

normalized by its mean value, and phase scintillation is

characterized using �� (in units of radians) which

represents the standard deviation of the detrended carrier

phase [Van Dierendonck et al., 1993].

While valuable information on ionospheric irregularities

and their properties can be obtained from continuously

monitoring the aforementioned indices, it is desirable to

mitigate the scintillation effects to increase range


estimation and positioning accuracy of the receiver. One

option is to weight the satellites’ measurements inversely

with the scintillation severity calculated along the signal

propagation path from the satellite to the receiver. In this

regard, as proposed by Aquino et al. [2007], the

scintillation indices can be translated into accurate

approximation of receiver tracking error and the estimated

error can be used as a weighting factor in positioning. The

effectiveness of this method in reducing positioning errors

is evaluated in Aquino et al. [2009] and Strangeways et

al. [2011].

The model for the L1 carrier phase lock loop (PLL),

proposed by Conker et al., [2003], accounts for the

effects of scintillation on the input phase, and computes

the tracking error variance at the output as

�� = �� + �� + �� (1)

where ��, �� and �� are the error variance

components relating to phase scintillation, thermal noise

(includes the effect of amplitude scintillation, S4) and

oscillator noise, respectively. Precise estimation of

scintillation parameters, therefore, is necessary to give an

accurate measure of scintillation severity for each

satellite.

In order to study scintillation, low frequency trends such

as satellite-receiver motion and other noise sources should

be removed from raw signal via detrending. In theory,

Fresnel frequency defines spectrum of scintillation

fluctuations versus non-scintillation and may be used as

the cutoff frequency of the detrending filters [Forte and

Radicella, 2002]. Most GPS receivers use Butterworth

filters with a constant cutoff frequency of 0.1 Hz. This

default frequency was originally designed for mid and

low latitude regions [Van Dierendonck et al., 1993];

however, for high latitude studies this is not a proper

choice. In high latitudes, the Fresnel frequency is pushed

to higher values and a low cutoff frequency (e.g. 0.1 Hz)

for filtering leads to overestimation of scintillation indices

[Forte and Radicella, 2002]. This effect has more impact

on phase scintillation compared to amplitude scintillation

index and may result in phase without amplitude

scintillation observations.

In this study, three different detrending methods are

introduced and compared to the standard fixed cutoff

Butterworth filtering:

a) Cascaded filters: when using Butterworth filters, to

overcome the problem of phase shift between filters

input and output, a number of lower order high-pass

Butterworth filters can be cascaded and employed

instead of one higher order filter.

b) Adaptive filters: to overcome the problem with a

fixed cutoff frequency, it can be selected adaptively

depending on the inherent characteristics of

scintillation data [Materrasi and Mitchell, 2007].

c) Wavelet: wavelet filtering is another method which

accounts for the non-stationary aspect of trans-

ionospheric signals and can effectively remove low

frequency trend and noise from raw data [Torrence

and Compo, 1998].

Both L1 and L2C signals are examined in evaluating the

abovementioned filtering methods to analyze the

characteristics of different GPS signals. In this work, we

also discuss additional scintillation information that can

be derived using new GNSS signals. It is known that

correlation between different GPS signals decreases as

they experience severe scintillation events. Therefore,

correlation coefficient between L1 and L2 signals can

potentially be exploited in a new indicator of scintillation

severity.

DATA SET AND ANALYSIS TOOLS

Real data from high latitude and equatorial regions are

used in this work.

High Latitude Data: The first high latitude data set is

collected on GPS L1 and L2C signals at Gakona, Alaska

on March 17, 2013 and contains 10 minutes of moderate

scintillation event starting at 21:30 Universal Time (UT).

These data were provided by Miami University (J.

Morton). PRN 25 dual frequency data is considered for

this work. The second high-latitude data set is collected

by Canadian High Arctic Ionospheric Network (CHAIN)

receivers at Sanikiluq, Nunavut and contains

approximately one hour of GPS L1 data (from 6:00 to

6:59 UT) during a moderate scintillation event.

Equatorial Data: This data set is collected as part of the

collaboration between Brazilian Institute of Geography

and Statistics (IBGE), the University of the State of Rio

de Janeiro (UERJ), Brazil, and the Position, Location and

Navigation (PLAN) group of the Department of

Geomatics Engineering, University of Calgary, Canada.

The data log system is located near the equatorial

anomaly, where strong ionospheric scintillations are

expected. Scintillation observations on modernized GPS

signal L2C are collected along with L1C/A signal using a

University of Calgary leap frog front-end. The data used

in this work were collected on October 24, 2012 from

20:00 to midnight local time corresponding to 23:00 (Oct.

24) to 03:00 (Oct. 25) UT. A 30-minute period from this

data set with severe scintillation effects on PRN 12 is

examined in this work.

The collected raw intermediate frequency (IF) samples

are post-processed using the GSNRx™ software receiver.

GSNRx™ is a C++ class-based GNSS receiver software

program capable of processing raw data samples from a

GNSS front-end [GSNRx™ User Manual, 2012]. The

software acquires and tracks incoming signals and

generates measurements for use in other data processing

software. Navigation solution capability is also included


in the software. Correlator outputs (1 KHz I and Q

samples) are used to calculate detrended signal intensity

(SI), which is then used to determine amplitude

scintillation index S4. Carrier phase observations are also

detrended to compute phase scintillation parameter ��,

following [Van Dierendonck et al., 1993].

�4 = ⟨��⟩ − ⟨��⟩�⟨��⟩� (2)

�� = �⟨��⟩ − ⟨�⟩� (3)

⟨. ⟩ in above denotes one minute average of data and � in

Eq (3) represents detrended phase of the signal.

Commonly, a 6-th order Butterworth filter is used to

detrend raw observations. This method as well as three

other detrending methods are described in some detail and

compared in the following sections.

POWER DISTRIBUTION OF SCINTILLATED

SIGNALS

The typical power distribution of a GPS signal varies

when the signal experiences moderate-to-strong

scintillation events compared to quiet propagation

scenarios. This can be seen in Figure 1(a) where power of

raw carrier phase signal for moderately scintillated

CHAIN data is plotted as a function of frequency and

time. In order to determine presence of high frequency

fluctuations related to phase scintillations, detrended

carrier phase of the same signal is plotted in Figure 1(b).

As observed in these two plots, higher power at higher

frequencies (red areas in the top panel) is consistent with

large fluctuations in the carrier phase (high phase

scintillation epochs). This power plot contains three

ranges of power distribution: (1) low-frequency band,

which is related to fluctuations due to satellite motion and

other slow variations, (2) mid-frequency band where

signatures of scintillation are observed, and (3) high-

frequency band associated with noise in the signal. An

effective detrending method should filter first and second

bands and retain the information of scintillations.

The major contribution of ionospheric scintillation

fluctuations spectra is at the Fresnel frequency �� [Rino,

1979]. This frequency is dependent on relative drift

between the ionosphere and GPS satellites (��), wavelength of the signal (�), and the vertical distance

between the irregularities and the receiver (�) and is

determined by [Forte and Radicella, 2002].

�� = ��√2�� (4)

Typically, the vertical distance of the ionosphere from

receiver is assumed to be 350 km, which makes the

denominator of Eq (4) equal to 360 m for GPS L1

frequency. �� does not have a constant value and it is

dependent on satellite velocity and ionospheric

irregularity drift which itself is temporally and spatially

variable.

Figure 1. (a) Time-frequency power distribution of carrier

phase for the CHAIN data set, and (b) detrended carrier

phase.

DETRENDING METHODS

The detrending methods investigated here are described

as follows.

1. Standard Butterworth

Since it is hard to calculate the values of �� for every

location and time, conventional receivers employ a fixed

approximation of cutoff/Fresnel frequency of 0.1 Hz. This

value was originally chosen for particular wideband

experiments [Fremouw et al., 1978]; however, in the case

of GPS scintillation investigation, the relative drift values

may vary - especially at high latitudes where this drift

value is even larger. The block diagram for Butterworth

filtering of raw signal intensity and carrier phase is shown

in Figure 2. A 6th

order Butterworth filter is used to filter

the data.

Time (min)

(a)

Fre

quency (

Hz)

0 10 20 30 40 500

5

10

15

20

25

-35

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Time (min)

(b)

Power of raw carrier phase data

De

tre

nd

ed

ca

rrie

r p

ha

se (

rad

)


2. Cascaded Butterworth

When using a high order filter, a phase shift is imposed

between the input and output of the filter. To overcome

this problem, Ghafoori et al. [2014] have shown that a

cascade of lower order filters can be employed instead of

one higher order filter. Therefore, in this work we have

cascaded six 1st order Butterworth high pass filters instead

of one 6th order high pass filter when detrending the

carrier phase. This implementation is conducted in the

orange box in Figure 2. Equivalent cut-off frequency of

cascaded filters is set to be 0.1 Hz consistent with the

conventional Butterworth method. It is shown in Ghafoori

et al. [2014] that the cutoff frequency of N cascade 1st-

order high-pass filter can be calculated from

f!"#$%%& = f!√2'/) − 1 (5)

For N=6 and f!"#$%%& = 0.1,�, cutoff frequency of each 1st

order high pass filter would be f! = 0.035 Hz.

3. Adaptive Butterworth

The choice of the detrending cutoff frequency is a

significant issue and, as mentioned before, is a function of

time variant factors such as satellite and irregularity

motion. One method of choosing f! is proposed in

Materrasi and Mitchell, [2007]; the cutoff frequency is

chosen such that small changes in frequency do not affect

the statistics of the detrended signal. Standard deviation

of the detrended time series is chosen to represent its

statistical properties; hence f! should be selected so that

dσ12#df ≈ 0 (6)

Conventional 6th

order Butterworth filters are used to

detrend amplitude and phase with varying cutoff

frequency. Derivation of the standard deviation of the

detrended signal intensity and carrier phase with respect

to frequency is plotted in Figure 3(a) and 3(b). CHAIN

high latitude data is used for this plot. It is observed that

for this particular dataset, 145671% of signal intensity merges

to zero very fast; however 145671% of phase approaches zero

values for frequencies larger than 0.1 Hz. This supports

Forte and Radicella, [2002] suggestion of using higher

cutoff frequency to detrend high latitude data.

Figure 3. Frequency derivation of the standard deviation of

(a) the detrended signal intensity, and (b) carrier phase for

the CHAIN data set.

4. Wavelet

Wavelet transform can be used to analyze time series that

contain non-stationary power at different frequencies,

such as scintillated signals. A brief description of wavelet

filtering implemented in this work is given as follows.

Wavelet Transform

A continuous wavelet 8,:(<) is defined with a mother

wavelet function 8=(<) as

8,:(<) = 8=((< − >)/?) (7)

For our wavelet analysis, we have used the Morlet mother

wavelet function, which is defined as

0 0.1 0.2 0.3 0.4 0.5 0.6-0.5

0

0.5

Frequency (Hz)

(a)

dσ

de

tre

nd

ed

po

we

r/d

f

0 0.1 0.2 0.3 0.4 0.5 0.6-0.5

0

0.5

Frequency (Hz)

(b)

dσ

de

tre

nd

ed

ph

as

e/d

f

1st

order

Butterworth LPF

6th

order

Butterworth HPF, @A

-

Raw phase observation

Detrended phase

6th

order BW

LPF, @A

Raw signal intensity observation

Detrended

SI

Norm

ali

ze

(a)

(b)

Figure 2. Block diagram of standard Butterworth

filtering for (a) signal amplitude, and (b) carrier phase

data.


8=(<) = BC=.�Dexp(HI=< − 0.5<�) (8)

where I= is the non-dimensional frequency (assumed to

be 6). Morlet wavelet is chosen here because of its small

time-bandwidth product that gives the best time and

frequency resolution [Torrence and Compo, 1998;

Materassi and Mitchell, 2007]. The continuous wavelet

transform of a discrete sequence JK at time ‘n’ and for a

given scale ‘s’ is defined as its convolution with a scaled

and translated version of 8=(<), as

L(M, ?) = N JKO8∗ Q(M& − M)R<? STC'KOU=

(9)

where (*) represents complex conjugate, R< is time step

of the time series and is equal to 0.02 sec for 50 Hz raw

data, and N is the length of the time series.

Scales are discretized as explained by above authors as

fractional powers of two:

?V = ?= × 2(VXY), Z = 0,1,2, … , \ (10)

\ = 2(R]C'^_`�(aR</?=)) (11)

where ?= = 2R< = 0.04 and R] = 0.125. Note that \

should be chosen large enough to account for low

frequencies (260 in this work) [Torrence and Comp,

1998].

Wavelet coefficients calculated in Eq. (9) can be used to

build wavelet statistical energy called scalogram given by

[Materassi and Mitchell, 2007].

b(M, ?) = |L(M, ?)|� (12)

Filtering raw signal by wavelet can be performed as

JK& = d R]. R<=.DeX . 8=(0)f N gh(L(M, ?i))(?i)=.D

ijiUik

(13)

where, JK& is the filtered signal, L(M, ?i) are wavelet

coefficients for a given scale ?i , and eX is the

reconstruction factor and its value is empirically derived

to be 0.776. The factor 8=(0) is equal to B=.�D [Torrence

and Compo, 1998]. In Eq. (13), H'and H� represent lower

and upper cutoff scales (or equally cutoff frequencies).

Mushini, et al., [2012] have obtained these values to be ?ik~0.09?hn ≡ 11,� and?ij~5?hn ≡ 0.2,�, after

observing 400 scalograms of scintillation events at high

latitudes. We use the same values in this work for high

latitude and ?ij~10?hn ≡ 0.1,� for equatorial datasets.

ANALYSIS AND RESULTS

In order to compare performance of different Butterworth

filtering methods as well as wavelet method, both high

latitude and equatorial raw intensity and phase data are

detrended and the results are presented here. Multi-

frequency (L1 and L2C signals) analysis is considered in

this work; therefore, for this section dual frequency

Alaska data is used. Figures 4 and 5 show high latitude

detrended raw data as well as derived scintillation indices

for L1 and L2C signals respectively. Cascaded

Butterworth method is implemented only for carrier phase

data. Figures 4(b) to 4(d) and 5(b) to 5(d) show that for

detrended signal intensity of this data set, adaptive

Butterworth method chooses same cutoff frequency as for

standard Butterworth (0.1 Hz) for both L1 and L2C

signals. Also it is observed that wavelet method provides

slightly less noisy results compared to the other methods.

In general, detrended L2C signal shows larger

fluctuations than L1 which is due to its lower

transmission power.

Figures 4(g) to 4(j) and 5(g) to 5(j) show detrended carrier

phase data using different methods respectively for L1

and L2C signals. Here, notably higher frequencies are

chosen by adaptive method compared to standard

Butterworth. Also, cutoff frequency is different for L1

and L2C signals and is slightly lower for L2C. This is in

agreement with Eq. (4) where Fresnel frequency is lower

for a signal with higher wavelength (L2C compared to

L1). Again, wavelet method reduces the fluctuations of

detrended signals.

Intensity and phase scintillation indices derived using

each of these methods are shown in Figures 4(e) and 4(k)

for L1, and in Figures 5(e) and 5(k) for L2C, respectively.

Consistent with the detrending results, scintillation

indices associated with the wavelet method are lower than

for other methods.

Same examination is performed for the equatorial region

data set which contains several minutes of a severe

scintillation event. Figures 6 and 7 show detrended

intensity and phase signals using the aforementioned

detrending methods as well as derived scintillation indices

for L1 and L2C signals, respectively. In this case, the

adaptive method chooses the same cutoff frequency as the

conventional Butterworth filters for detrending signal

intensity and different values for detrending carrier phase.

Similar to the high latitude analysis, wavelet filtering

results in a lower amplitude detrended signal and smaller

scintillation indices compared to results for Butterworth-

based methods. One issue with Butterworth filtering is

that it can result in very large S4 values. This happens

because low pass filtering of signal intensity can generate

very small values which can lead to very large detrended

signal intensities during normalizing process (vertical

lines in Figures 6(b), 6(c), 7(b) and 7(c)). These large

values of detrended signal intensity result in

unrealistically large S4 indices (e.g. Figures 6(e) and

7(e)). This does not occur when using wavelet method.


Figure 4. Alaska data: (a) L1 raw signal intensity; (b) standard Butterworth detrended signal intensity with @A = p. qrs; (c)

adaptive Butterworth detrended signal intensity, @A = p. qrs; (d) wavelet filtering detrended signal intensity; (e) derived S4 values;

(f) L1 raw carrier phase; (g) standard Butterworth detrended carrier phase with @A = p. qrs; (h) cascaded Butterworth detrended

carrier phase; (i) adaptive Butterworth detrended carrier phase, @A = p. qtrs; (j) wavelet filtering detrended carrier phase ; and

(k) derived uv values.

2 4 6 8 100

1

2

3x 10

12 Signal Intensity (SI)

(a)

Raw

SI

2 4 6 8 100

1

2

3

(b)

Detr

ended S

I

2 4 6 8 100

1

2

3

(c)

Detr

ended S

I

2 4 6 8 100

1

2

3

(d)

Detr

ended S

I

2 4 6 8 100

0.1

0.2

0.3

0.4

Time (min)(e)

S4

2 4 6 8 100

1

2x 10

5 Carrier Phase (CP)

(f)

Raw

CP

2 4 6 8 10

-0.2

0

0.2

(g)

Detr

ended

CP

(ra

d)

2 4 6 8 10

-0.2

0

0.2

(h)

Detr

ended

CP

(ra

d)

2 4 6 8 10

-0.2

0

0.2

(i)

Detr

ended

CP

(ra

d)

2 4 6 8 10

-0.2

0

0.2

(j)

Detr

ended

CP

(ra

d)

2 4 6 8 100

0.5

1

Time (min)(k)

σφ

Butterworth fc = 0.1

Butterworth fc adaptive

Wavelet

Cascade Butterworth


Figure 5. Alaska data: (a) L2C raw signal intensity; (b) standard Butterworth detrended signal intensity with @A = p. qrs; (c)


(f) L2C raw carrier phase; (g) standard Butterworth detrended carrier phase with @A = p. qrs; (h) cascaded Butterworth

detrended carrier phase; (i) adaptive Butterworth detrended carrier phase, @A = p. qqrs; (j) wavelet filtering detrended carrier

phase; (k) derived uv values.

2 4 6 8 100

1

2

3x 10

11 Signal Intensity (SI)

(a)

Raw

SI

2 4 6 8 100

1

2

3

(b)

Detr

ended S

I

2 4 6 8 100

1

2

3

(c)

Detr

ended S

I

2 4 6 8 100

1

2

3

(d)

Detr

ended S

I

2 4 6 8 100

1

2x 10

5 Carrier Phase (CP)

(f)

Raw

CP

2 4 6 8 10

-0.2

0

0.2

(g)

Detr

ended

CP

(ra

d)

2 4 6 8 10

-0.2

0

0.2

(h)

Detr

ended

CP

(ra

d)

2 4 6 8 10

-0.2

0

0.2

(i)

Detr

ended

CP

(ra

d)

2 4 6 8 10

-0.2

0

0.2

(j)

Detr

ended

CP

(ra

d)

2 4 6 8 100

0.5

1

Time (min)(k)

σφ



Wavelet

Cascade Butterworth

2 4 6 8 100

0.2

0.4

Time (min)(e)

S4


Figure 6. Equatorial data: (a) L1 raw signal intensity; (b) standard Butterworth detrended signal intensity with @A = p. qrs; (c)


(f) L1 raw carrier phase; (g) standard Butterworth detrended carrier phase with @A = p. qrs; (h) cascaded Butterworth detrended

carrier phase; (i) adaptive Butterworth detrended carrier phase, @A = p. qtrs; (j) wavelet filtering detrended carrier phase; and (k)

derived uv values.

5 10 15 20 25-5

0

5

10x 10

11

(a)

Signal Intensity (SI)

Raw

SI

5 10 15 20 25-5

0

5

10

(b)

Detr

ended S

I

5 10 15 20 25-5

0

5

10

(c)

Detr

ended S

I

5 10 15 20 25-5

0

5

10

(d)

Detr

ended S

I

5 10 15 20 250

0.5

1

Time (min)(e)

S4

5 10 15 20 25-2

-1

0x 10

6

(f)

Carrier Phase (CP)

Raw

CP

5 10 15 20 25-0.5

0

0.5

(g)

Detr

ended

CP

(ra

d)

5 10 15 20 25-0.5

0

0.5

(h)

Detr

ended

CP

(ra

d)

5 10 15 20 25-0.5

0

0.5

(i)

Detr

ended

CP

(ra

d)

5 10 15 20 25-0.5

0

0.5

(j)

Detr

ended

CP

(ra

d)

5 10 15 20 250

0.5

1

Time (min)(k)

σφ



Wavelet

Cascade Butterworth


Figure 7. Equatorial data: (a) L2C raw signal intensity; (b) standard Butterworth detrended signal intensity with @A = p.qrs; (c)


(f) L2C raw carrier phase; (g) standard Butterworth detrended carrier phase with @A = p. qrs; (h) cascaded Butterworth

detrended carrier phase; (i) adaptive Butterworth detrended carrier phase, @A = p. qqrs; (j) wavelet filtering detrended carrier

phase; (k) derived uv values

It has been shown in Bhattacharyya et al., [2000] that for

weak and moderate scintillation cases, phase scintillation

should follow the same trends as amplitude scintillation.

In order to determine which detrending method results in

more reliable scintillation parameters, we have

investigated the correlation between S4 and �� values.

Figures 8 and 9 show relationship between S4 and ��

indices for high latitude L1 and L2C signals, respectively.

Correlations between these values are summarized in

Table I. For this moderate scintillation scenario, all

methods result in good correlation between amplitude and

5 10 15 20 25-1

0

1x 10

11

(a)

Signal Intensity (SI)

Raw

SI

5 10 15 20 25-5

0

5

10

(b)

Detr

ended S

I

5 10 15 20 25-5

0

5

10

(c)

Detr

ended S

I

5 10 15 20 25-5

0

5

10

(d)

Detr

ended S

I

5 10 15 20 250

0.5

1

1.5

Time (min)(e)

S4

5 10 15 20 25-10

-5

0x 10

5

(f)

Carrier Phase (CP)

raw

CP

5 10 15 20 25-0.5

0

0.5

(g)

Detr

ended

CP

(ra

d)

5 10 15 20 25-0.5

0

0.5

(h)D

etr

ended

CP

(ra

d)

5 10 15 20 25-0.5

0

0.5

(i)

Detr

ended

CP

(ra

d)

5 10 15 20 25-0.5

0

0.5

(j)

Detr

ended

CP

(ra

d)

5 10 15 20 250

0.5

1

Time (min)(k)

σφ



Wavelet

Cascade Butterworth


phase scintillation parameters with wavelet performing

slightly better in this sense.

Correlation analysis of S4 and �� values for equatorial

data is presented in Figures 10 and 11 and summarized in

Table II. Here we have excluded pairs with unrealistically

large S4 values. For this severe scintillation scenario the

correlation between scintillation parameters decreases.

However, wavelet filtering results in a much better

correlation trend compared to other methods for both L1

and L2C signals.

Figure 8. S4 and uv values for L1 signal, Alaska data

Figure 9. S4 and uv values for L2C signal, Alaska data

Table I. Correlation between S4 and uv indices using

different detrending methods for L1 and L2C signals

(Alaska data)

Method Correlation

L1 L2C

BW fc = 0.1 Hz 0.86 0.90

Adaptive BW 0.90 0.93

Wavelet 0.92 0.93

Cascade 0.89 0.92

Figure 10. S4 and uv indices for L1 signal for equatorial

data.

Figure 11. S4 and uv indices for L2C signal for equatorial

data.

Table II. Correlation between S4 and uv indices using

different detrending methods for L1 and L2C signals

(equatorial data)

Method Correlation

L1 L2C

BW fc = 0.1 Hz 0.35 0.38

Adaptive BW 0.33 0.28

Wavelet 0.69 0.76

Cascade 0.34 0.34

CORRELATION BETWEEN GPS SIGNALS

In this section, we investigate exploiting multi-frequency

observations to determine characteristics of ionospheric

scintillations. For this purpose, correlation between L1

and L2C GPS signals as a function of scintillation has

been evaluated. Figures 12(a) and 12(b) respectively show

correlation coefficients for L1 and L2C detrended carrier

phase and carrier to noise ratio (e/a=) as a function of L1

S4 index. Four hours of equatorial data are used for this

investigation. As observed in Figure 12(a), during weak

scintillation periods (S4 < 0.2) the correlation between L1

0 0.05 0.1 0.15 0.2 0.25 0.30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

S4 (L1)

σφ

(L

1)



Wavelet

Cascade Butterworth

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.1

0.2

0.3

0.4

0.5

0.6

S4 (L2)

σφ

(L

2)



Wavelet

Cascade Butterworth

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

S4 (L1)

σφ

(L1)



Wavelet

Cascade Butterworth

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

S4 (L2)

σφ

(L2)



Wavelet

Cascade Butterworth

Co

rre

lati

on

co

eff

icie

nts


and L2C carrier phase signals is high (correlation

coefficients are close to one). As scintillation increases

(S4 > 0.2) L1 and L2C carrier phases tend to de-correlate.

In Figure 12(b), correlation coefficients are dominated by

noise for very weak scintillation (S4 < 0.1) [Carrano, et

al., (2012)]. When GPS signals are moderately

scintillated (0.2 < S4 < 0.4) correlations between L1 and

L2C e/a= are typically larger and decrease for higher

values of S4.

Ionospheric irregularities are dispersive in nature;

therefore, they cause different refraction effects on

different frequencies. This can lead to GPS signal

decorrelation as observed in Figure 12. By studying such

correlations between GPS signals, information about

characteristics, scale sizes of irregularities, and

distributions can be inferred. Potentially this type of

analysis can be used to select best receiver tracking

schemes. In previous work, we demonstrated L1 signal

information is beneficial in aiding acquisition and

tracking of L2C with improved receiver performance

during moderate scintillation [Najmafshar et al., 2013].

However, this receiver scheme may be detrimental for

severe scintillation in cases of significant signal

decorrelations.

Figure 12. Correlation coefficients of (a) L1 and L2C

detrended carrier phases, and (b) L1 and L2C w/xp.

CONCLUSIONS

One option to mitigate scintillation effects is to

underweight poor observations from severely scintillated

satellites in positioning and navigation applications. This

requires precise characterization of ionospheric

scintillations. Scintillations are commonly measured by

intensity and phase scintillation parameters. However

these parameters are highly dependent on the method that

is employed to remove non-scintillation fluctuations from

raw data which we refer to as detrending. Performance

analysis of four detrending methods is investigated in this

work. Conventionally, a 6th

order Butterworth filter with

0.1 Hz cutoff frequency is used in scintillation receivers.

Cascaded Butterworth and adaptive Butterworth filtering

are two other Butterworth based methods to detrend raw

signals. Wavelet filtering is another method that can be

employed to detrend data.

Moderate high latitude and severe equatorial scintillation

events were investigated in this work. It is observed that

adaptive Butterworth method chooses higher cutoff

frequencies than the standard 0.1 Hz typically used in

detrending high latitude carrier phase data. This suggests

that the shift in Fresnel frequency should be taken into

account when using Butterworth filters. Also, this

frequency depends on the frequency of the transmitted

signal. Detrending by wavelet algorithm results in less

noisy output signals for both cases.

It is observed that derived scintillation parameters are

dependent on the method used for data detrending.

Amongst the various methods, scintillation parameters

derived from wavelet approach showed higher correlation

of phase/amplitude scintillation for both moderate and

severe scintillation scenarios. Mitigation of scintillation

effects using such scintillation characteristics is of interest

for future positioning applications. Both high latitude and

equatorial real data sets will be examined and

improvement of positioning results will be investigated.

Multi-frequency GPS signal correlations decrease for

higher scintillation levels. This property may be exploited

for new scintillation analysis or incorporated as a decision

factor in scintillation mitigation using adaptive receiver

tracking schemes. The possibility of using this

information in scintillation mitigation and

characterization will be studied in our future work.

ACKNOWLEDGMENTS

The authors appreciate the support of Dr. Jade Morton

and her group at Miami University, Ohio, USA, and also

University of New Brunswick for providing high latitude

data sets which were collected as part of their projects in

Alaska and CHAIN network respectively.

Equatorial IF Data used in this research has been

collected under a cooperation project between the

0 0.1 0.2 0.3 0.4 0.5 0.60

0.2

0.4

0.6

0.8

1

S4 (L1)

(a)

0 0.1 0.2 0.3 0.4 0.5 0.60

0.2

0.4

0.6

0.8

1

S4 (L1)

(b)


Brazilian Institute of Geography and Statistics (IBGE),

the University of the State of Rio de Janeiro (UERJ),

Brazil, and the Position, Location and Navigation (PLAN)

Group of the Department of Geomatics Engineering,

University of Calgary, Canada, with Prof. Luiz Paulo

Souto Fortes, PhD (IBGE, UERJ) and Prof. Dr. Gérard

Lachapelle (PLAN Group) as principal investigators.

REFERENCES

Aquino, M., M. Andreotti, A. Dodson, and H. J.

Strangeways (2007), On the Use of Ionospheric

Scintillation Indices in Conjunction with Receiver

Tracking Models, Adv. Space Res., 40(3), 426–435,

doi:10.1016/j. asr.2007.05.035.

Aquino, M., J. F. G. Monico, A. Dodson, H. Marques, G.

De Franceschi, L. Alfonsi, V. Romano, and M. Andreotti

(2009), “Improving the GNSS Positioning Stochastic

Model in the Presence of Ionospheric Scintillation”, J.

Geod., doi:10.1007/s00190-009-0313-6.

Bhattacharyya, A., T. L. Beach, S. Basu (2000),

“Nighttime Equatorial Ionosphere: GPS Scintillations and

Differential Carrier Phase Fluctuations” Radio Sci., Vol.

23, No. 1, Pages 209-224, doi: 1999RS002213.

Carrano, C. S., K. M. Groves, W. J. McNeil, P. Doherty

(2012), “Scintillation Characteristics across the GPS

Frequency Band”, Proceedings of the 25th International

Technical Meeting of the Satellite Division of the Institute

of Navigation, ION GNSS, Nashville TN, Sep 17-21,

2012.

Conker, R. S., M. B. El‐Arini, C. J. Hegarty, and T. Hsiao

(2003), “Modeling the Effects of Ionospheric Scintillation

on GPS/Satellite‐Based Augmentation System

Availability”, Radio Sci., 38(1), 1001, doi:10.1029/

2000RS002604.

Forte, B., S. M. Radicella (2002), “Problems in Data

Treatment for Ionospheric Scintillation Measurements”,

Radio Sci., Vol. 37, No. 6, 1096, doi:

10.1029/2001RS002508.

Fremouw, E.J., R.L. Leadabrand, R.C. Livingston, M.D.

Cousins, C.L. Rino, B.C. Fair, R.A. Long (1978), “Early

Results from the DNA Wideband Satellite Experiment-

Complex Signal Scintillation”, Radio Sci. 13(1):167-187.

Doi: 10.1029/RS013i001p0016.

Ghafoori, F., S. Skone (2014), “Impact of Equatorial

Ionospheric Irregularities on GNSS Receivers Using Real

and Synthetic Scintillation Signals”, submitted to Radio

Sci., Sep 9, 2014.

“GSNRx™ User Manual” (2012), Position, Location and

Navigation (PLAN) Group, Department of Geomatics

Engineering, University of Calgary, Aug 3, 2012.

Materassi, M., C.N. Mitchell (2007), “Wavelet Analysis

of GPS Amplitude Scintillation: A case Study”, Radio

Sci, Vol. 42, RS1004, doi: 10.1029/2005RS003415, 2007.

Mushini, S.C., P.T. Jayachandran, R.B. Langley, J. W.

MacDougall, D. Pokhotelov (2011), “Improved

Amplitude and Phase Scintillation Indices Derived from

Wavelet Detrended High-Latitude GPS Data”, GPS Solut,

16:363-373, doi: 10.1007/s10291-011-0238-4, 2011.

Najmafshar, M., F. Ghafoori, S. Skone (2013), “Robust

Receiver Design for Equatorial Regions during Solar

Maximum”, Proceedings of ION GNSS, Nashville TN,

Sep 16-20, 2013.

Rino, C.L. (1979), “A Power Law Phase Screen Model

for Ionospheric Scintillation”, Radio Sci., 14 (6), 1135-

1145. 1979.

Strangeways, H. J., Y.-H. Ho, M. H. O. Aquino, Z. G.

Elmas, H. A. Marques, J. F. G. Monico, and H. A. Silva

(2011), “On Determining Spectral Parameters, Tracking

Jitter, and GPS Positioning Improvement by Scintillation

Mitigation”, Radio Sci., 46, RS0D15,

doi:10.1029/2010RS004575.

Torrence, C., G. Compo (1998), “A practical Guide to

Wavelet Analysis” Bulletin of the American

Meteorological Society 79(1):61-78. Doi; 10.1175/1520-

0477 (2002)083<1019:NDSFS>2.3.CO;2

Van Dierendonck, A.J., J. Klobuchar, Q. Hua (1993),

“Ionospheric Scintillation Monitoring Using Commercial

Single Frequency C/A Code Receivers”, Proceedings of

the 6th

International Technical Meeting of the Satellite

Division of the Institute of Navigation (ION GPS), Salt

Lake City UT, Sep 22-24, 1993.

gnss data processing investigations for characterizing … › position-location-and... ·...

Documents