Reduction as an improvement of a precise satellite positioning based on an ambiguity function

Abstract

Abstract It is well-known that the solution domain has a discrete character in precise satellite positioning because of the integer nature of ambiguities. Therefore, in addition to the classic least squares estimation, the search procedure has to be employed in the computation process to obtain the so-called ‘fixed solution.’ The article’s subject is to improve the search procedure conducted in the coordinate domain. The reduction process is to transform the original math model into an equivalent one in the sense of obtaining the same solution. The reduction aims to increase the efficiency of searching for some parameters, i. e., integer ambiguities. The article presents the concept of employing the reduction procedure to the computation process of precise positioning based on the ambiguity function. The transformation matrix for the reduction is based on the well-known integer decorrelation procedure. Numerical experiment results display a positive impact of the reduction process on the search procedure efficiency. This positive impact is manifested by a dramatic decrease in the number of candidates needed to test all admissible solutions inside the search region. The percentage decrease in that magnitude is at least 50 % for all session lengths and achieves a maximum value of over 75 % for the 10-minute session. Computational time decreases by over 40 % while short sessions are processed. There is no improvement for sessions longer than 15 minutes, but, as explained in the paper, there is no need to improve that magnitude in such cases.