Global positioning systems is known to create bias effects such as multipath, ionospheric and tropospheric delays that behave like lowfrequency noise. Random measurement errors can also occur and these are typically characterized as high-frequency noise. The lowfrequency nature of a multipath is what causes the largest error, which in carrier phase measurements can reach up to 5 cm. For a static base station it is required that both error components (low and high-frequency) are removed and not included in the static baseline processing. This paper will introduce two different multi-resolution techniques that can be used separately or combined to remove the low to highfrequency GPS errors. The first technique is applied using the wavelets as a de-noising tool to tackle the high-frequency errors in the double difference domain. A detailed analysis is also made to choose the best wavelet base function and threshold technique estimator by comparing different wavelet parameters along with different thresholding techniques. The second technique discussed in this paper uses the wavelets technique as a de-trending tool to tackle the low-frequency portion of the double differenced measurements. The results of this research paper indicate that the de-trending technique can reduce the double difference errors dramatically for short baselines when compared to the de-noising technique. Conversely, the de-trending technique can cause a biased solution for long baselines, as it will enhance the RMS value and indicate good statistics for the solution. However, the will be shifted from it depending on the low frequency part of the error (ionosphere, low multipath). Therefore, it is important to isolate ionospheric error by modeling (and not spectrum filtering) before dealing with multipath, as it is hard to separate between both errors in the spectral domain.
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