IEEE Aerospace and Electronic Systems Magazine - December 2020 - 23

Duník et al.
compute position and timing with an accuracy that ranges
from a couple of meters to centimeters depending on the
type of signals, frequencies, and method (code/carrier) used
in such processing. Remarkably, a GNSS receiver leverages
state estimation in several of its building blocks, which are
briefly discussed hereafter.
Whereas acquisition of GNSS signals is typically considered as a detection (or classification) problem, the fine
estimation of the time-varying delay/Doppler parameters
of the signals is performed by the so-called tracking loops.
Those delay and phase lock loops (DLL and PLL, respectively), as well as its different variants, can be considered
instances of a larger state estimation framework where the
gain is fixed (selected through the choice of a loop bandwidth). For instance, Vila-Valls[64] provided a tutorial
review of KF-based carrier tracking techniques for GNSS
receivers, highlighting their relationship with legacy PLL
schemes. The use of state estimation to substitute standard
tracking loops was seen to be a promising tool in many
challenging scenarios such as in mitigating the effects of
ionospheric scintillation [65], [66], mitigating multipath
propagation [67], enabling resilient noncoherent tracking
of data-only channels [68], attenuating the effects of interference [70], coping with high, time-varying dynamics [71], or in designing robust real-time kinematic (RTK)
solutions in harsh propagation conditions [72], to name a
few examples.
In the context of position, velocity, and time (PVT)
estimation, whereas estimation of xk (i.e., containing the
PVT variables) can be carried out on an epoch-per-epoch
basis if signals from four or more GNSS satellites are
observed, the use of state estimation techniques (mostly
KFs) typically improves the overall performance due to
two facts [87]. First, the use of fk ðÁÞ from (1) to model the
receiver antenna motion constrains the degrees of freedom
of the unknown variable. In the case where an IMU is available, the filter state xk becomes the error of the inertial
strapdown computation and fk ðÁÞ becomes a system model
for those error states, thereby even further limiting the
degrees of freedom that need to be solved by the GNSS
observations (mainly IMU alignment and biases) [4]. Second, the state vector can be tailored to include GNSS-specific artefacts, like carrier phase ambiguities. The state
estimation technique is additionally used to fuse information from both code-phase (a.k.a. pseudorange) and carrierphase observables in a variety of ways. The resulting carrier-phase positioning techniques like carrier/Dopplersmoothing, RTK or precise-point-positioning are then typically implemented by means of (more or less sophisticated)
versions of KF-like algorithms [85], [86].
GNSS, like many radio-navigation systems, provides
measurements through a correlation process [88] and
hk ðÁÞ in (2) ideally captures all aspects of this. In open-sky
conditions, DLL or PLL discriminators (plus the loop filters) provide good approximations via linearization of the
DECEMBER 2020

Figure 5.
Categorization of typical signal processing problems in GNSS
receiver design.

correlation functions and a linear hk ðÁÞ well approximates
the real circumstances. However, in adverse signal conditions such as multipath, urban, or indoor scenarios, the
conventionally used discriminators do not provide accurate approximations, and as a consequence the resulting
state estimates including the covariance are far from
reflecting the real distribution of the user's position. To
circumvent these issues, Bayesian direct position estimation (BDPE) uses the correlation values at several timedelay/Doppler-shifts directly as measurements and hk ðÁÞ
is given by the signal's correlation function and thus
becomes nonlinear [79]. To solve the resulting nonlinear
state estimation both Gaussian derivative-free filtering [80]
and PF [83] methods were considered in the literature. The
latter showed, in real-world adverse signal conditions, that
non-Gaussian (even multimodal) PDFs for the user position may occur, thus the PF implementation provides
more realistic PDF estimates at the expenses of an
increased computational cost. BDPE (and DPE) was also
shown to provide higher sensitivity and resilience [81]
since it increases the effective signal-to-noise ratio by
combining the signals from different satellites as opposed
to legacy receivers [82]. However, BDPE is orders of
magnitude more computationally demanding than DLL/
PLL tracking plus KF-based PVT solvers. It is also more
difficult to tune and requires handling of satellite ephemeris or atmospheric errors as nuisance parameters [84].
Furthermore, modeling hk ðÁÞ via the correlation function
is still an approximation and a more complete formulation
requires stochastic modeling of propagation channel
parameters or inclusion of multipath reflection parameters
in the state vector xk .
A qualitative diagram of challenging GNSS areas can be
observed in Figure 5, similarly to that in Figure 4 for AHRS
and TAN systems. In this case, we highlight that jamming
interference may cause saturation of the analog-to-digital
(ADC) converters, bringing non-Gaussianity to the measurements. Implementing tracking using a discriminator-based

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IEEE Aerospace and Electronic Systems Magazine - December 2020

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