Wavelet Spectral Techniques for GPS Errors Reduction

ABSTRACT
GPS measurements can be modeled as a true range plus
other errors such as orbital and clock biases, atmospheric
residual, multipath, and observation noise. Modeling is
one approach to deal with some of these errors, if their
characteristics are known (e.g. troposphere and
ionosphere errors). Another way to deal with these errors
is filtering in the frequency domain, where all these errors
have different frequency spectrum component. Each
errors is characterized by a specific frequency band, e.g.
the receiver noise can be characterized with high
frequency components, multipath errors, which have low
to medium frequency bands, while the ionospheric and
tropospheric errors are at a lower frequency band.
Wavelet spectral techniques can separate GPS signal into
sub-bands where different errors can be separated and
mitigated. This paper introduces two new wavelet spectral
analysis techniques to mitigate DGPS errors in the
frequency domain namely, cycle slip and multipath errors.
The first approach in this paper, Wavelet de-trending, is
introduced to remove the long wavelength carrier phase
multipath error in the measurement domain. The
presented wavelet-based trend extraction model is applied
to GPS static baseline solutions. The second approach in
this paper is introduced to detect and remove cycle slip
error which can be seen as a singularity in the GPS data.
The propagation of singularities between the wavelets
levels of decomposition is different from the propagation
of noise. This characteristic is used to identify the
singularities from noise.