Signal Processing - September 2017 - 73

of advanced receiver design aimed at improving position
gation channel is generically modeled by a linear time-varyaccuracy, reliability, and integrity [7]. Similarly, another chaling impulse response with N propagation paths [14], where
a i, n (t), z i, n (t), and x i, n (t) are the amplitude, phase, and delay
lenging scenario is that of dense urban environments or, to a
greater extent, indoor scenarios [8]. Some
of the nth propagation path for the ith satefforts have been devoted toward this area,
ellite, respectively. Notice that subindex
Time delays and Doppler
n = 0 denotes LOSS parameters. Typically,
which originated the concept of high-sensishifts
of
all
satellites
tivity (HS) GNSS receivers [9]-[12]. From
the assumptions are that amplitudes are Rice
a signal processing perspective, the design
(or Rayleigh, when shadowed) distributed
are intimately related to
of advanced GNSS receivers is a fertile and
[15], and time delays are assumed pieceone another through
appealing area of research, particularly when
wise constant in the observation interval.
the receiver motion
it comes to enhancing receivers in the most
In a first-order Taylor expansion, the timeparameters.
challenging scenarios.
varying phase has an independent term
This article presents an innovative conuniformly distributed [16] and a linear term
cept that helps overcome the aforementioned limitations. The
gathering the effect of the Doppler spread (i.e., a frequency
concept, known as DPE, was introduced in [13]. At a glance,
shift caused by the relative motion between the satellite and the
a receiver implementing DPE computes the position directly
receiver). In general, we consider that paths are independent,
from the sampled signal, as opposed to a conventional receiver
referred to as the wide sense stationary with uncorrelated
in which range estimates are required before solving for the
scattering (WSSUS) channel model. Thus, although subindex i
user's position. Therefore, conventional receivers are referred
was omitted for simplicity, N can be different between satellite
to as two-steps and DPE as one-step in what follows.
channels. Extensive measurement campaigns were performed
to characterize the GNSS propagation channel model, see, e.g.,
GNSS signal model
the results reported in [17]. As a consequence, a GNSS receiver
A general signal model for most navigation systems consists
senses measurements that are considered to be a superposition
of a direct-sequence spread-spectrum (DS-SS) signal, synof plane waves corrupted by noise and, possibly, interferences
chronously transmitted by all the satellites in the constellation.
and multipath. An antenna receives M scaled, time-delayed,
This type of signal enables code division multiple access
and Doppler-shifted signals with known signal structure. Each
transmissions, i.e., satellite signals are distinguished by orthogosignal corresponds to the LOSS of one of the M visible satelnal (or quasi-orthogonal) codes. These signals consist of two
lites, while traveling through the WSSUS channel model. The
main components: a ranging code [the pseudorandom noise
received complex baseband signal can be modeled as
(PRN)-spreading sequence] and a low-rate data-link (broadcasting necessary information for positioning such as satM
(1)
x (t) = / a i s i (t - x i) exp {j2rfd i t} + n (t),
ellites' orbital parameters and corrections). The complex
i=1
baseband model of the signal transmitted by the ith satellite is
s i (t) = s I, i (t) + js Q, i (t), where its phase and quadrature components may transmit independent signals. Each component
where s i (t) is the transmitted complex baseband low-rate navicould be either an unmodulated carrier (designed to assist in
gation signal spread by the pseudorandom code of the ith satelacquisition and tracking processes) or a modulated DS-SS siglite considered known, a i is its complex amplitude, x i is the
nal. In the latter case, the signal is composed of the sequence
time delay, fd i the Doppler deviation, and n (t) represents zerob
(
t
)
!
1
,
1
,
of low-rate data bits, I, i
mean additive noise with variance N 0 /2 and other unmodeled
"
, with Tb I being the bit
c
(
t
)
!
1
,
1
.
period, and the PRN spreading sequence, I, i
terms besides LOSS. Notice that subindex n is omitted since
"
,
The chip length of the code word and the chip period are
only LOSSs are explicitly modeled.
denoted by L c I and Tc I, respectively. Therefore, TPRN I = L c I Tc I
The primary goal of a GNSS receiver is to accurately estiis the code-word period. Several carrier frequencies can be
mate its position, velocity, and time (PVT), which is typically
used at one time, with the presented baseband structure being
accomplished by first estimating the parameters in the signal
thus replicated. GNSS systems typically transmit complemenmodel (1). These estimates are used to construct a set of observtary signals over several frequency bands, for which one of the
ables per satellite. Observables are a set of ranges computed
main reasons is combating the frequency-dependent perturbafrom time delay or phase-difference estimates, referred to as
tions suffered by the signal when traveling through the ionopseudoranges and carrier-phase measurements, respectively.
sphere and troposphere.
Once a set of valid observables is computed, a geometrical
When transmitted, satellites' signals travel through a propproblem is solved to compute the PVT solution for the receiver.
agation channel, which modifies their amplitude, phase, and
The propagation time that a signal takes between its transdelay. Many replicas of the same transmitted signal can evenmission from the ith satellite to the user is continuously estimattually reach the receiver's antenna due to multipath propagaed by tracking algorithms. This time delay estimate (denoted
tion. In general, these replicas are caused by reflections of the
by xt i ) provides an estimation of the distance between the
direct signal [or line-of-sight signal (LOSS)] in surrounding
ith satellite and the user. Under the maximum likelihood
obstacles (e.g., buildings, trees, the ground, etc). Such a propa(ML) principle, the unknown parameters in (1) are obtained
IEEE SIGNAL PROCESSING MAGAZINE

September 2017

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