Abstract
Navigation receivers in systems like GNSS (global navigation satellite system) estimate their positionand their velocity from the time of arrival (TOA) of several incoming signals. In this estimation,
the multipath phenomenon is one of the main error sources. This phenomenon consists in
the propagation along different paths of a transmitted wave, and produces a superposition of signal
replicas at the receiver input. The main effect of multipath is a bias in the delay, phase, amplitude
and Doppler shift estimates that translate into biases in the position and velocity estimates.
To mitigate multipath, navigation receivers resort to closed-loop or to open-loop approaches. The
closed-loop approach is an attempt to keep the conventional operation of a navigation receiver,
which is based on the delay-locked loop (DLL), but giving a multipath mitigation capability. And
the open-loop approach is a direct approach in which the multipath parameters are directly estimated.
Among the closed-loop approaches there are fundamentally two kinds. The first mitigates
biased delay estimates by a simple modification of the loop discriminator to enhance its mitigation
capability, like in the narrow correlator. And the second assumes that there is some delay and
complex amplitude estimates available and performs an interference cancelation, where the loop
discriminator remains unchanged. On the contrary, all open-loop multipath mitigation approaches
dispense with any loop estimates for the channel delays and the channel phasors. Thus, open-loop
multipath mitigation approaches must resort to multidimensional high resolution estimators of the
channel parameters.
Maximum likelihood (ML) estimators, or Bayesian estimators, such as the extended Kalman
filter (EKF) or the particle filter (PF), are candidates for the multidimensional high resolution estimators.
However, the main drawback of ML and Bayesian estimators is their high computational
complexity. The high computational complexity precludes a simple hardware implementation in
mass-market receivers such as mobile handsets; for applications such as multipath mitigation,
low-complexity algorithms are required. The closed-loop and the open-loop multipath mitigation
algorithms have to cope with the complexity of the estimation and with the time-variant nature of
the multipath channel. The closed-loop approach accounts for the variations fundamentally. And
the open-loop approach handles the complex estimation of several signal replicas. Obviously, a
combination of closed-loop and open-loop approaches needs to account for the complexity constraint
and the time-variant channel properties at the same time. Thus, especially for time-variant
channels, ML estimators are prohibitive, since the high complexity is even required for each time
instant. Additionally, the independent ML multipath channel delay and channel phasor estimators
in each time slot prevent an additional noise averaging over several time instants.
A suitable combination of open-loop and closed-loop approaches works as follows. Within one
time slot, where the channel delays are approximately constant and where only the channel phasors
alternate significantly, we use the open-loop approach to get low complexity high resolution multipath
delay estimators. These low complexity high resolution multipath delay estimators enable
the two closed-loop approaches that keep the conventional operation of a navigation receiver. In
the successive time slot, the open-loop approach computes again a low complexity high resolution
multipath delay estimator as input for the closed-loop approach. To minimize the complexity of
multidimensional high resolution time-variant estimators, we present as an open-loop approach
novel low complexity high resolution channel estimators. We modify two subspace based algorithms,
the multiple signal classification (MUSIC) and the estimation of signal parameters via
rotational invariant techniques (ESPRIT) for application to the task of TOA estimation. Both of
our novel methods reuse existing receiver sub-systems, such as sliding correlator outputs corresponding
to several chip-delayed matched filters (MFs) that have already been computed at the
acquisition stage. We focus on the unitary ESPRIT method since it achieves a decomposed estimation
in the delay, Doppler, and angle of arrival (AOA) domains and yields automatically paired
delay, Doppler, and AOA estimates. Our simulation results show that unitary ESPRIT approximates
the Cramer-Rao bound (CRB) quite closely, even though the computational complexity is
far smaller in comparison to ML estimators. The decomposed estimation directions enable a much
faster multidimensional acquisition compared to the two- or three-dimensional maximization of
MUSIC spectra. Because of the time-variant channel delays that are typical for real environments
for positioning applications, however, repeated computation of the corresponding signal subspaces
is required. Thus, we provide both algorithms for the open-loop approach with a suitable projector
tracking algorithm to account for the variation of the mobile channel over time and space.
The projector tracking algorithm allows the already small computational complexity of the two
subspace methods to be reduced even further. The ESPRIT projector tracking variant performs
an additional noise averaging in the time direction. We thereby obtain a considerably enhanced
estimation accuracy at low signal to noise ratios (SNRs) with a reduced computational complexity.
Our combination of high resolution channel estimators, such as MUSIC and ESPRIT, and
projector tracking yields besides the open-loop multipath mitigation approach also a closed-loop
multipath mitigation approach. The high resolution time-variant multipath channel estimators enable
the application of interference minimization or interference cancelation to eliminate the timevariant
loop delay bias and the time-variant phasor bias. For the closed-loop multipath mitigation
approach, our novel time-variant multipath mitigation techniques are based on the acquisition stage
and hence permit the tracking complexity to be reduced. Our novel approach based on high resolution
time-variant projector tracking needs one DLL only contrary to conventional closed-loop
multipath mitigation approaches, where each time-variant channel path is tracked with a separate
DLL. To evaluate the performance of the closed-loop multipath mitigation approach, we need to
compute the jitter and the mean time to lose lock (MTLL) of the closed-loop multipath mitigation
approaches. Standard methods for DLLs fail to provide analytical jitter and MTLL results; these
figures are usually obtained from simulations. At high SNRs, however, the simulation time grows
extremely rapidly. To address this high simulation complexity, we design a novel algorithm based
on the Ornstein-Uhlenbeck (OU) stochastic differential equation (SDE) and the corresponding OU
random processes. The main merit of our algorithm, besides its simplicity, is the joint analytical
jitter and MTLL computation. We investigate the jitter and MTLL of closed-loop multipath mitigation
approaches. Also, we demonstrate the relation between closed-loop multipath mitigation
approaches with jitter and MTLL figures and show the influence of the multipath propagation on
the jitter and MTLL figures. We reveal how the closed-loop multipath mitigation approaches that
involve interference minimization or interference cancelation remove the multipath bias component
of the jitter and increase or decrease theMTLL. Furthermore, our novel closed-loop multipath
mitigation algorithms also yield valuable approaches for the jitter and MTLL of related multipath
mitigation algorithms, such as the EKF or the PF.
| Date of Award | 29 Sept 2011 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Gonzalo Seco Granados (Director) & Jesús Selva Vera (Director) |