Preface xv
Chapter 4 points out that least-squares code, carrier, and Doppler estimation
is optimal under white and colored noise for arbitrary sample rates including sub-
Nyquist sampling. The least-squares scheme is affected by the squaring loss, but a
numerical evaluation of the true Cramér-Rao lower bound demonstrates that the
least-squares scheme is an optimal estimator. In fact, a correct treatment of the car-
rier phase as a uniformly distributed nuisance parameter shows that the squaring
loss is part of the code phase and the Doppler Cramér-Rao lower bound. Linear-
ity conditions are discussed that the proposed least-squares multipath-estimating
discriminator has to fulfill to be optimal. Techniques like macroscopic long coher-
ent integration times and vector tracking are pointed out to fulfill the linearity re-
quirements, even for weak signals. Nonparametric (i.e., multipath-mitigating) and
parametric (i.e., multipath-estimating) least-squares discriminators are detailed in
Chapter 8, making use of the different classes of correlators presented in Chapter 7.
An efficient software receiver implementation relies on extra- or interpolation of
correlator values, a technique that is also investigated from the parameter-estima-
tion point of view in Chapter 4. Signal preprocessing, including quantization and
sampling, is detailed in Chapter 6, as well as the handling of colored noise. The
theoretical basis for signal detection or acquisition is laid out in Chapter 5. Signal
acquisition is a computational-extensive task that is most efficiently done via FFT
methods in a software receiver. Those methods are described in Chapter 9 and are
related to time-domain correlation.
Overall, this book covers signal processing, starting from the ADC up to the
estimation of the code phase, the carrier phase, and Doppler as depicted in Figure
P.1. Tracking loops are covered with respect to their influence on the discriminators.
For other navigation receiver aspects, like message decoding or positioning, the
reader is referred to other literature. Also, some specific high-precision techniques
like semi-codeless tracking and pulse blanking are covered.
The software receiver core algorithms consuming most of the processing time
are covered in Chapter 9. A run-time performance analysis is presented, making use
of x86 assembly language code snippets. The reader can find those snippets in the
exemplary source code on the homepage for this book, http://www.artechhouse.-
Figure P.1 Covered navigation receiver topics: black—fully covered; gray—partly covered; white—
not covered.