The carrier-phase multipath effect can seriously affect the accuracy of GPS-based positioning in static short baseline applications. Although several kinds of methods based on time domain and spatial domain techniques have been proposed to mitigate this error, they are still limited by the accuracy of the multipath model and the effectiveness of the correction strategy. After analyzing the existing methods, a new method based on adaptive thresholding wavelet packet transform (AW) and time domain bootstrap spatial domain search strategy (TB) is presented (AWTB). Taking advantage of adaptive thresholding wavelet packet transform, we enhance the precision of the correction model and the efficiency of the extraction method. In addition, by adopting the proposed time domain bootstrap spatial domain strategy, the accuracy and efficiency of subsequent multipath correction are improved significantly. Specifically, after applying the adaptive thresholding wavelet packet method, the mean improvement rate in the RMS values of the single-difference L1 residuals is about 27.93% compared with the original results. Furthermore, after applying the proposed AWTB method, experiments show that the 3D positioning precision is improved by about 38.51% compared with the original results. Even compared with the method based on stationary wavelet transform (SWT), and the method based on wavelet packets denoising (WPD), the 3D precision is improved by about 26.94% over the SWT method and about 22.96% over the WPD method, respectively. It is worth noting that, although the mean time consumption of the proposed algorithm is larger than the original method, the increased time consumption is not a serious burden for overall performance.

Embedded zero-tree image coding in wavelet domain has drawn a lot of attention. Among noteworthy algorithms is the set partitioning in hierarchical trees (SPIHT). Typically, most of images' energy is concentrated in low frequency subbands. For an image with textures, however many middle-high frequency wavelet coefficients are likely to become significant in the early passes of SPIHT; thus the coding results are often insufficient. Middle and high frequency subbands of images may demand further decompositions using adaptive basis functions. As wavelet packet transform offers a great diversity of basis functions, we propose a quad-tree based adaptive wavelet packet transform to construct adaptive wavelet packet trees for zero-tree image coding. Experimental results show that coding performances can be significantly improved especially for fingerprints images.