Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 40
A Tutorial on Kalman Filter-Based Techniques
= 10 ms, C/N0 = 35 dB-Hz, fd,0 = 2 Hz, and fd ,0 = 0.1 Hz/s. The
tested methods were second-order PLL (BPLL = 10 Hz), secondorder FLL-assisted third-order PLL (BFLL = 5 Hz, BPLL = 5 Hz), a
standard KF only tracking the dynamics (i.e., x*k [θ d , k f d , k fd , k ]
) and a KF, including the scintillation into the state-space formulation (termed KF-Aℜ).
The root mean square error (ℜMSE) obtained with the four methods is plotted in Fig. 7a, where it is easy to identify the two regions
in which the signal is corrupted by scintillation (indicated in the figure). ℜegarding the performance of the PLL-based techniques and
the standard KF, there are two key points that must be stated: i) the
standard techniques are unable to identify which phase variations are
due to dynamics (desired) and which ones come from the ionospheric
scintillation (undesired); ii) if these techniques are well tuned to track
fast phase variations (i.e., moderate to high dynamics) or time-varying scenarios, a desirable quality of a reliable and robust architecture,
they will also track the fast scintillation phase variations. The KF-Aℜ
provides an increased robustness and better performance. These two
statements are more evident in Figs. 7b, 7c, where the Doppler frequency and scintillation phase estimation are plotted for a single realization (only available for the KF-based techniques). In the Doppler
frequency estimation, one can see that the standard KF understands
the scintillation as frequency variations, while the KF-Aℜ correctly
decouples both contributions, giving always better performances and
being much more robust and powerful.
CASE 2: SIGNAL TRACKING IN DEEP SPACE
COMMUNICATIONS
Another example of challenging synchronization is found in deep
space communications for planetary exploration, an application
with extreme requirements in terms of received low signal power.
Synchronization in deep space involves an initial acquisition stage
in which the PLL is allowed to operate at a larger loop bandwidth
to acquire the carrier frequency in the presence of significant Doppler dynamics. Once the carrier frequency is acquired, the receiver
enters the tracking stage, where the loop bandwidth is typically
decreased to reduce the noise in the loop and cope with very low
received signal power [40]. Hence, the PLL must be configured to
different operating bandwidths that are adapted to the SNℜ and as
well as must cope with loop transitions. Under this scenario the inherent AKF bandwidth and filter flexibility may offer an advantage
on loop adaptation or configuration.
This study case considers the following telecommand transmitted (space-to-Earth) signal model known as remnant carrier modulation with sinusoidal subcarrier:
(
)
s (t ) = A sin 2π f ct + mc D (t )sin ( 2π f sct + φsc (t ) ) + φc (t ) ,
Figure 7.
(a) ℜMSE obtained from 200 Monte Carlo runs for different carrier
tracking techniques. Signal of interest corrupted by moderate and severe
scintillation. Doppler frequency (b) and scintillation phase (c) estimation for one single realization, using a standard KF and the improved
KF-Aℜ.
40
(42)
with fc, fsc being the carrier or subcarrier frequencies, ϕc(t), ϕsc(t) the
carrier or subcarrier phase, mc the modulation index (0 < mc < π),
D(t) the information data stream, and A the signal amplitude, with
D(t) = cn p (t − nTs ), cn ∈{+1,−1}, Ts symbol period and p(t) the
n
pulse shape. The communication channel is modeled as an AWGN
IEEE A&E SYSTEMS MAGAZINE
JULY 2017, Part II of II
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