Signal Processing - September 2017 - 107

Q
Q

(fD, τ)

Channel 1
F (S )

G (S )

.
.
.

Doppler
Code Phase
Estimation

.
Range and (ρ1, ρ1)
.
Range Rate
.
..
Measurement
(ρj, ρj)

EKF
Integrity
Check

PVT
Solutions

FIGURE 7. A block diagram for the VTL-A-STL. Range and range rate estimations from channels not affected by scintillation are processed through
an extended Kalman filter and selected through an integrity check routine
to provide receiver PVT solutions. The PVT solutions are combined with
satellite orbit information to derive Doppler and code phase estimation
as feedback for channels affected by scintillation. The VTL is used to
assist the STL instead of replacing STL in this scheme. (Figure used with
permission from [62].)

0.5

SI (dB)

Several algorithms based on vector processing concepts [58], [59]
have also been developed to improve carrier tracking performance in the presence of strong ionosphere scintillation by
exploiting GNSS signal spatial diversity and/or frequency diversity. These algorithms utilize an extended KF [60], [61] or adaptive Kalman filter (AKF) [62], in which the receiver-generated
PVT information is used as feedback to update and estimate the
parameters of all tracked channels. Henkel et al. [60] proposed
a multifrequency vector PLL that incorporated the ionosphere
delay error into the receiver state vector, where a multidimensional filter was used to filter the estimated receiver states to reduce
the noise. Yin et al. [63] presented an adaptive multifrequency
carrier tracking algorithm by utilizing the fact that deep amplitude fading tends to not occur simultaneously on all frequencies
transmitted from the same satellite [8]. Doppler frequency estimation from one or two healthy frequency channels can be used
to infer the Doppler frequency of the fading channel from the
same satellite.
A major drawback of a vector processing algorithm is that
the vector PVT solutions may not be optimal when multiple satellite signals are seriously affected by scintillation. Peng et al.
[62] developed a vector tracking loop-assisted-scalar tracking
loop (VTL-A-STL) method in which receiver-generated PVT
solutions were used to only estimate and update the parameters of affected satellite signals. VTL is used to assist STL but
not replace STL. This approach prevents errors experienced in
a compromised channel from affecting tracking accuracy in
other healthy channels. This algorithm has enabled the tracking of extremely violent scintillations lasting over a period of
hours on Ascension Island during the last two solar maxima.
Figure 7 shows the high-level block diagram of this algorithm.
Another deviation from the conventional vector processing is
the incorporation of known receiver position and satellite orbit
information. For scintillation-monitoring purposes, antenna
position can be surveyed precisely beforehand, and precise orbit
information is also available. Together, they can be used to compute the range and range Doppler to aid carrier tracking of a
scintillating channel. This is the rationale behind the open and
semiopen loop-tracking algorithm presented in [41] and [43].
This algorithm can be viewed as the ideal solution of a vector
processor in which the nearly perfect PV solutions are used for
feedback. Time is the only quantity that needs to be solved for

Incoming Signal

Vector processing

when combining the healthy channel's range and range Doppler
estimations. With a high-quality, stable oscillator, even this time
quantity is not necessary if the scintillation period does not last too
long. The semiopen loop algorithm was applied to some extremely
violent scintillations recorded in equatorial areas and revealed
interesting carrier-phase behaviors during deep amplitude fading
[64]. Figure 8 shows detrended triple-frequency carrier-phase and
signal intensity on GPS PRN 25 collected in Brazil, on 27 November 2013 starting at 05:43:25 UTC. Note that deep fades of over
40 dB were tracked on all three frequencies. These deep fades
were accompanied by half-cycle sudden-phase changes. Statistical analysis of these deep fades and sudden phase changes based
on data collected from Ascension Island, Hong Kong, and Brazil
indicates that nearly all deep fades with C/N 0 below 5 dB-Hz
are accompanied by sudden phase changes. The average amount
of time it takes for these phase changes to occur is ~40 ms.

Detrend π
(Cycle)

For C/N 0 outside this range, the loop bandwidth assumes
constant values.
The gain matrix is computed based on its corresponding filter bandwidth and its computation expense is rather high. To
reduce the cost, L can be computed beforehand for a series of
loop bandwidth values. During tracking, the prestored L matrix
can be used to map the relationship between the measured C/N 0
and the desired loop bandwidth. This simple approach allows
the variable gain KFP to work in real time on current available
hardware platforms. Zhang and Morton [57] demonstrated that
this adaptive gain KFP can successfully track extremely challenging strong equatorial scintillation signals.

0
-0.5
10
0
-10
-20
-30
-40
-50
0

0.2

0.4

0.6 0.8
1
Time (s)

1.2

1.4 1.6

FIGURE 8. Detrended triple frequency carrier phase and signal intensity
on GPS PRN 25 collected in Brazil, on 27 November 2013 starting at
05:43:25 UTC. Deep fades of over 40 dB were accompanied by half-cycle
sudden phase changes over a few tens of milliseconds on all three
frequencies. The deep fades do not occur at the same time on different
frequencies. (Figure used with permission from [52].)

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

107

Table of Contents for the Digital Edition of Signal Processing - September 2017