Abstract: Based on the ill-condition observation matrix and the principle of Tikhonov regularizer algorithm, an improved method of global positioning system (GPS) rapid ambiguity resolution using single frequency receivers is studied. Based on the wobble principle of singular values, an improved algorithm of UDVT decomposition is proposed. A new matrix is constructed by the observation matrix, and turned to upper Hessenberg 3-diagonal-matrix. Then accurate singular values are acquired using the shifting QR algorithm, and the non-stabilization of the regularizer matrix is avoided which is caused by small singular values. The improved regularizer matrix is deduced and the construction method is designed based on an analysis of the characteristics of the ill-condition matrix. Experiment results indicate that the improved method is more effective on improving ill-condition observation matrices as compared with the conventional least-squares ambiguity decorrelation adjustment (LAMBDA) algorithm and Tikhonov regularizer-LAMBDA algorithm, and more precise floating-point and fixing-point are acquired quickly and reliably by just 3-5 epochs.

Key words: global positioning system, integer ambiguity, floating-point, ill-condition matrix, UDVT decomposition, improved regularizer matrix