Signal Processing - September 2017 - 79

it should be included in c and estimated alongside the other
PVT parameters. Similarly, in two-steps receivers, the TOW
is estimated by augmenting the unknowns in the LS solution.

HS DPE receivers
One of the basic approaches to detect or acquire weak signals
is to accumulate signal energy over longer time intervals [12].
When the coherent integration time limit is reached, postdetection integration techniques can be performed. The most
common technique is the noncoherent integration of a number
of coherent correlations. Another interesting technique is the
differential correlation [46]. Integration within a DPE framework was previously seen in the section "DPE," where it was
already pointed out in (5) that extended integration times can
be considered. This process increases the receiver sensitivity
by a combination of coherent/noncoherent integration. When
this feature is not considered, the standard DPE solution [13]
arises where N nc = 1 noncoherent and N c = 1 coherent integrations are configured:
ct = arg max )
c

/ #0 T

PRN

x (t) s i (t - x i (c)) exp {- j2rfd i (c) t} dt 3 .

i=1

(7)
In some situations, HS is extremely important. The sensitivity
of a DPE-enabled receiver is generally larger than that of conventional two-steps receivers, mainly thanks to the 10 log10(M)-dB
gain with the number of used satellites. However, this improvement can be further improved if coherent/noncoherent integration is incorporated in DPE's solution.

Multiconstellation, multifrequency receivers
Today, GNSS receivers are enabled with multiconstellation
capabilities, i.e., the ability to receive and process signals from
different navigation systems (e.g., GPS and Galileo). The processing of multiconstellation signals can increase the sensitivity and availability of the GNSS receiver in harsh environments.
This involves, however, an increased computational burden
with the estimation or acquisition of the time offset between
different constellations. For instance, the GPS-Galileo time
offset (GGTO) [47] is necessary for their joint usage in a GNSS
receiver. In general, each system has its own internal clock
reference used to synchronize all system clocks and signals.
These time systems are different among GNSS systems.
If a navigation message can be recovered without error,
the GGTO is readily available and multiconstellation operation is feasible. The receiver needs to add the GGTO to one
set of pseudorange observables (from one of the two systems)
when solving the geometrical problem (through LS) in the conventional two-steps receiver. In a DPE receiver, the GGTO is
similarly used in the generation of the subset of x (c) related to
one of the systems. Otherwise, if GGTO is not available at the
receiver, it needs to be estimated. In two-steps receivers this
involves augmenting the parameter vector in the LS process. In
DPE, this estimation involves including the GGTO in vector c
and maximizing the cost function over this parameter as well.

Augmentation of DPE's equations to account for such possibility, involving estimation of intersystem clock offsets, would
improve PVT availability when GGTO cannot be obtained
through regular means.
In case of a receiver capable of hearing from dual- (or triple-) band frequencies, a conventional receiver would estimate
the various sets of observables corresponding to each frequency. In case of DPE, the received signals can be stacked together
into a new vector x (t) = (x 1 (t), x 2 (t)) <, where x 1 (t) and x 2 (t)
are the data streams from two different frequencies of the same
system as described by (1). The main differences between x 1 (t)
and x 2 (t) are due to the frequency-dependent parameters in (3)
and (4). The resulting cost function adds a summation over the
available frequency bands, thus providing enhanced performance to DPE at the cost of a larger computational complexity
due to the baseband processing of more signals.

Sensor hybridization and side information
DPE framework parameterizes the signal model with motion
parameters (c) instead of being synchronization dependent
(x, fd). This fact is not only seen to provide performance
improvements when implementing the corresponding PVT
estimators, but it brings an important feature: DPE allows the
use of prior information in a more natural way. Whereas under
the conventional approach it is difficult to propose an evolution
model or an a priori distribution for x and fd, incorporating
models for the parameters in c is more intuitive. DPE arises as
an appealing framework for the inclusion of prior information
since the modeling of motion parameters gathered in c has
been vastly addressed in the literature; for instance, [48] and
the references therein. The aprioristic information regarding
user's coordinates can either be obtained from existing motion
models, delivered by an inertial measurement unit (IMU) in
an ultratight integration configuration or by any other available source of information concerning a user's motion such as
altimeters/barometers (providing vertical information) or dead
reckoning methods. Therefore, we can claim that the use of
prior information when the target parameter is c is conceptually easier than in the legacy approach, where the use of prior
information is somehow less apparent since the evolution of
synchronization parameters cannot be modeled easily.
As an example of this versatility, consider map-matching
techniques, in which one has a map of the area in which the
receiver is navigating. Typically, there are forbidden areas
(which the receiver cannot reach, for instance, because it
involves crossing walls) that we would like to avoid. Including
this information in DPE is as simple as constraining the optimization in (5) to sets of valid c values. If the process of map
matching is represented by the functional M : R n 7 C, where
C is the subset in R n that contains c, then M (c) is a function
that maps c into valid locations (e.g., force the trajectory of a
car to be inside highway lanes).
c

Receiver autonomous integrity monitoring capabilities
Receiver autonomous integrity monitoring (RAIM) techniques
aim at computing protection levels based on the standard

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

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