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 way to deal with some of these errors, if their characteristics are known (e.g. troposphere and ionosphere errors). Another way is to filter in the frequency domain, where all these errors have a different frequency spectrum component. Each error is characterized by a specific frequency band. For example, 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 signals into sub-bands where different errors can be separated and mitigated. Using wavelets to transform the GPS measurements into frequency domain helps localize both location and frequency of GPS errors, which allows for easy error separation in frequency domain. This thesis introduces new wavelet spectral analysis techniques to mitigate DGPS errors in the frequency domain, namely cycle slip, code and phase multipath errors. The wavelet-based trend
extraction model is applied to DGPS static baseline solutions and compared with the
traditional de-noising technique. The de-trending methodology performed impressively for short baselines in RMS and bias reduction as the average RMS and bias reductions were around 80%. However, for longer baselines the bias reduction is minimal although the RMS reduction is still in the 70-80% reduction.
A second approach is introduced to detect and remove cycle slip errors, which can be
seen as a singularity in the GPS data. The propagation of singularities between the levels of wavelet decomposition is different from the propagation of noise. This characteristic is used to identify the singularities from noise. The performance of the multi-scale singularity detection technique is evaluated and tested over GPS Code minus Carrier (CmC) and Phase1 minus Phase2 measurements where different cycle slips are added to the measurements. All the simulated cycle slips in CmC test quantities with SNR larger than 30 are effectively detected by the proposed technique. The error in the estimation process is, in most instances, less than 0.1 cycles.
Finally, the Multi-resolution Real-time (MRRT) Code-smoothing technique is introduced
to real-time scenarios to mitigate code multipath error (medium to high-frequency) and noise (high-frequency) and retain the ionospheric error (low-frequency) untouched in the mitigation.