Tikhonov-based ARCE algorithm and its applications in rapid positioning using single frequency GPS receivers

摘要

ARCE (Ambiguity Resolution Using Constraint Equation) is a new fast method to resolve the integer ambiguities based on LSE (Least-Squares Estimate) and null space, which is suitable for single frequency GPS receivers and whose necessary observation time span of fixing the integer ambiguities correctly is relatively long (say, at least one minute). In this paper, ARCE is improved for deformation monitoring when there is only one epoch phase observation. In this instance, the normal matrix is rank-deficient and it is impossible to fix the integer ambiguities correctly using ARCE if LSE is employed. In allusion to the above case, based on Tikhonov regularization theorem, a new regularizer is designed to transform the rank-deficient normal matrix to a full rank one. The accurate float ambiguity solutions are obtained and the corresponding search range of the integer ambiguities diminishes. So, the integer ambiguities can be fixed using ARCE. The effect of the single epoch algorithm is tested utilizing a baseline whose length over 3KM and the results show that the success rate of fixing the integer ambiguities using the new algorithm can achieve to over 90 percent.