整數相位模稜參數為GPS載波相位測距和定位上舉足輕重的待求變數。理論上消去整數模稜或估計求定之，是等價的。利用餘弦函數來消去整數相位模稜於相對定位應用上，會產生空間模稜問題。此方法之關鍵點在於幾何位置的近似和與相位信號族波長之收斂空間。 使用二次差分電碼定位來建立並平滑一條初始時變趨勢軌跡，並且利用長波長寬巷線性組合聯解，由粗至細(由長至短)層次式逼近，來幫助幾何位置之收斂，在處理過程中並且考慮所有二次差分之電離層延遲量。最後以獨立不相關之載波觀測量L1、L2進行相位餘弦聯解之最小二乘估計，並且利用統計檢定來檢定其殘差二次型是否合理。本研究利用一個低動態實驗來探討此層次式位置收斂概念於相位餘弦模式之OTF相對定位的可行性。 Integer ambiguity parameters are very important, yet unknown variables when using GPS carrier phases for ranging and positioning. Theoretically, it is equivalent to either eliminate the integer ambiguities or to estimate them. The use of cosine functions to eliminate any integer ambiguities in relative positioning applications causes spatial ambiguity problems to arise, but both reasonably approximated positions and wavelength-dependent convergence ranges are of the utmost importance. Differential GPS-based position solutions are smoothed to create an initial time-varying trend trajectory. Long-wavelength wide-lane phase combinations are utilized to facilitate positional convergence, on a stage-by-stage basis. Although as by-products, all the double-difference ionospheric path delays will be obtained, when, finally, the respective cosines of the L1 and L2 carrier phases undergo a simultaneous least-squares estimation. In particular, the quadratic forms of the estimated phase residuals are linked with statistical testing to allow for a meaningful inference. Some low-dynamics experiments prove the feasibility of the hierarchical positioning concept.
