Searching the Ambiguity of Navigation Satellite Carrier-phase Using the LLL Algorithm and the Whitening Filter

• Main Authors: Yang-Zen Chen, 陳揚仁
• Other Authors: Joz Wu
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/x75g3q

碩士 === 國立中央大學 === 土木工程研究所 === 97 === Generally, the GNSS carrier-phase is more accurate then the pseudorange. While using carrier-phase for positioning, the key point is how to obtain the correct integer ambiguity quickly and efficiently. However the high correlation between parameters makes it to be difficult. The problem can be improved by the changing of the geometric of satellites. But it needs longer observation time to reach. Therefore the LLL algorithm and the whitening filter are techniques mapping the parameters from a higher correlation space to a lower correlation space. And the effects of mathematics changing and the geometric changing can be the same. Then the result can be gotten within a short observation period. The LLL algorithm decomposes a positive-definite symmetrical matrix into the upper/lower triangular matrix. Then uses the Gram–Schmidt orthogonalization to transform vectors of the matrix into orthogonal each other. Then the diagonal covariance matrix can be gotten by the transpose of the orthogonal matrix multiplying to the orthogonal matrix. Whitening filter uses crout factorization to decompose a positive-definite symmetrical matrix into the continue multiplication of diagonal matrix and unit upper/lower triangular matrix. Applying the specifics of its diagonal matrix condition to covariance matrix can get the diagonal covariance matrix. Using the diagonal covariance matrix can reduce the number of candidates for integral ambiguity. Final, the candidates are inserted into the observation equations to determine the solution again. It is believed that the integer candidate which produces the smallest sum of squares of the residual is the most likely solution we want.